Keywords: Anisotropic colloids, colloidal diblocks, filamentous bacteriophage, helical superstructures, self-assembly and self-organization. vii

between gold nanobeads incorporated into hybrid colloids favor formation of Smectic-B like fibrils in which virus particles are organized in periodic layers separated by layers of gold nanobeads. Finally, we have studied the effect of introducing a weak asymmetry into hybrid virus-based colloids and investigated the possible segregation of their respective blocks through the formation of the lamellar Smectic-A phase.

Overall, we have demonstrated an efficient way to control self-organization of virusbased colloids by varying interactions between them, which results in formation of various original self-assembled morphologies.

i

Résumé

Les bactériophages en forme de filament, en raison de leurs propriétés physiques uniques, telles que leur monodispersité en taille et leur haute stabilité colloïdale, sont largement utilisés en matière molle en tant que système modèle de bâtonnets colloïdaux. En dispersions aqueuses, l'auto-organisation de ces virus s'est révélée être essentiellement conduite par l'entropie, ce qui implique des interactions purement répulsives entre les particules virales.

Dans cette thèse, en modifiant la nature des interactions entre les bâtonnets viraux, nous avons étudié leur auto-organisation en phase cristal-liquides. Dans ce but, nous avons d'abord étudié un système de bâtonnets purement répulsifs à très basse force ionique, et longue répulsion électrostatique. Le comportement de phase de ces suspensions a été déterminé par l'utilisation de la diffusion des rayons X aux petits angles et de la microscopie optique. Nous avons montré que la phase Smectique-A n'est pas stable dans les cas de forte répulsion électrostatique entre particules virales et que le système présente une transition directe de la phase de Cholestérique à la phase Smectique-B en augmentant la fraction volumique. De plus, nos résultats mettent en évidence que les virus dans ces conditions ne forment pas de verres colloïdaux à forte concentration, ce qui contredit de récents travaux réalisés sur le même système.

Dans une deuxième partie, nous avons modifié les interactions entre particules virales passant de purement répulsives à attractives en ajoutant des polymères libres aux suspensions, ce qui conduit à un effet de déplétion. En utilisant des polymères dont la taille est similaire au diamètre des bâtonnets, l'auto-organisation des virus, initiée dans la phase cristal-liquide cholestérique, conduit à une croissance de superstructures hélicoïdales. Dans ces structures, les bâtonnets sont principalement orientés le long de l'axe principal et présentent un ordre positionnel à longue portée, démontré par la diffusion des rayons X aux petits angles et le suivi de particules individuelles en microscopie optique. Les diagrammes de phase dse mélanges virus/polymères ainsi que la stabilité dans le temps des superstructures hélicoïdales ont été déterminés et comparés pour deux tailles différentes de polymères.

Dans la dernière partie, nous avons favorisé les interactions attractives de Van der Waals dans notre système en introduisant des nanoparticules d'or dans des colloïdes hybrides autoassemblés à base de virus. Ainsi, différents colloïdes hybrides consistant en un (en forme de sceptre) ou deux (dibloc) virus attachés à la même nanoparticule d'or ont été produits. Cette approche utilisant les nanoparticules d'or a été étendue afin de lier ensemble deux virus de différentes longueurs pour obtenir des diblocs colloïdaux asymétriques. L'auto-organisation des particules en forme de sceptre et des diblocs symétriques induite par déplétion a été explorée et ii les diagrammes de phases correspondants ont été établis. Nous avons ainsi montré que les interactions de Van der Waals entre nanoparticules d'or favorise la formation de fibrilles de type Smectique-B dans lesquelles les particules de virus sont organisées en une succession de couches séparées par des couches de nanoparticules d'or. Finalement, nous avons étudié l'effet de l'introduction d'une faible asymétrie dans de ces colloïdes hybrides et l'effet sur la ségrégation potentielle de leurs blocs respectifs au travers de la formation de phase lamellaire de type Smectique-A.

Dans cette thèse, nous avons ainsi démontré une manière efficace de contrôler l'autoorganisation de colloïdes en forme de filament en modifiant leurs interactions, ce qui conduit à la formation de diverses morphologies auto-assemblées originales.

Mots clés : Auto-organisation et auto-assemblage, bactériophage filamenteux, colloïdes anisotropes, diblocs colloïdaux, superstructures hélicoïdales.

iii Summary Filamentous bacteriophages, due to their unique physical properties, such as size monodispersity and high colloidal stability, are widely used in soft condensed matter as a system of rod-shaped colloids. In aqueous dispersions, self-organization of these viruses has been shown to be essentially driven by entropy, which means purely repulsive (hard core) interactions between viral particles. In this thesis, by varying the nature of the interactions between viral rods, we have studied their resulting self-organization into liquid crystalline phases. For this purpose, we have first investigated the system of purely repulsive rods at very low ionic strength, where thick electric double layers are present. The phase behavior of virus suspensions at very low ionic strength has been determined using small angle X-ray scattering (SAXS) and optical microscopy techniques. We have found that the Smectic-A phase is not stable in case of high electrostatic repulsion between viral particles and that the system undergoes a direct Cholesteric to Smectic-B phase transition by increasing rod concentration. Moreover, our results evidence that viruses with thick double layers do not form colloidal glasses at high concentrations, which contradicts recently reported findings for the same system.

In a second part, we have tuned viral particle interactions from purely repulsive to attractive ones by adding non-adsorbing polymers in their suspensions, which act as depletant agent. By using polymers with coil size comparable to the rod diameter, virus self-organization initiated from the Cholesteric liquid crystalline phase results in a growth of original chiral superstructures, called helical bundles. Viruses are mostly oriented along the main bundle axis and exhibit long-range positional order, as proved by SAXS and by single particle tracking using optical microscopy. Phase diagrams of virus/polymer two-component mixtures as well as the stability with time of the resultant helical superstructures have been determined and compared for two different polymer sizes.

In the last part, we have increased Van der Waals attractive interactions in our viral system by introducing gold nanoparticles into self-assembled hybrid virus-based colloids. Thus, different hybrid virus-based colloids consisting of one (scepter-like) or two (diblocks) viral filaments attached to the same gold nanoparticle have been produced. This approach using gold nanobead has been extended to link together two bacteriophages of different lengths to achieve asymmetric colloidal diblocks. Self-organization of scepter-like particles and symmetrical diblocks driven by soft effective attraction has been explored and the corresponding phase diagrams have been established. We have found that Van der Waals attractive interactions

Colloids

Colloidal particles, or colloids, in the classical way of understanding usually refer to dispersions of microscopically insoluble particles with at least one of their dimensions within a certain range (typically 10 nm -1 μm) suspended through another substance [1]. They may be considered as an intermediate state between molecules and bulk matter. Investigations on colloidal science started at the beginning of the 20 th century when the existence of microscopic particles was proven [2]- [4].

When dispersed in a liquid, colloids exhibit thermal fluctuations and are moving spontaneously and randomly in the dispersing medium (so-called Brownian motion). A. Einstein and J. Perrin were the pioneers who showed that colloidal particles could behave similarly as their "neighbors"small molecules or atoms. Thus, colloidal particles are often considered as giant atoms and their behavior can be described using the same thermodynamic statements [1], [5]. Nevertheless, compared to atoms and molecules colloidal particles are from 10 to 10.000 times larger, which allows direct observation via optical microscopy techniques for a majority of colloidal particles (in the case when one of their dimensions is higher than 0.1 μm). The possibility to directly visualize colloidal particles generates great interest in studying the main behaviors and principles of condensed matter within colloidal systems [2], [3], [6]. Thus, a model system of colloidal particles has often been used for investigations of the crystal growth and melting [7], formation and properties of liquid crystalline phases [8]- [14] as well as glass transitions in fluids [15], [16]. Another feature of colloids is that their interaction potential can be tuned by varying properties of the dispersion media or particle surface. Due to the points described above, colloidal particles were widely used as building blocks to create the assemblies with target larger structures. By varying their shape, size, chemical or physical properties as well as inter-particle interactions, it is possible to produce an abundance of materials and macroscopic objects [17], [18]. It was shown that for simplest systems of purely repulsive colloids introducing shape anisotropy is enough to extend their phase behavior compared to isotopically shaped particles (spheres). Similar to anisotropically shaped molecules (discotic, conic (bowl-like), and rod-shaped molecules), these particles do not show a single transition from solid crystal to isotropic liquid. Instead, they tend to form states of mater, which are intermediate between these two phases and are usually called liquid crystalline or mesomorphic phases (mesophases or intermediate phases) [19]. As far as mesophases are intermediate states between fully disordered liquid and crystal exhibiting long-range positional order in all of its dimensions, they can be obtained by introducing orientational order or by imposing positional order in one or two dimensions of an isotropic system consisting of anisotropic species (including molecules and colloids). Since in this thesis, we have dealt only with colloidal particles, we will consider the general determinations of liquid crystalline phases within colloidal systems.

Liquid crystalline phases can be characterized by the order of their constituent particles. Systems in which anisotropic colloids have no positional order in all three directions but particles are aligned preferentially along one direction (orientationally ordered) are referred to a Nematic mesophase. In other words, within a Nematic phase, colloids have no long-range positional order, meaning that the correlations between positions of neighboring particles over distances higher than interparticle ones (long distances) are very weak and are similar to those in the Isotropic liquids (i.e. exhibiting short-range positional order for which a local environment of particles is similar to each other but this regularity does not persist over long distances) [19]. At the same, particles exhibit orientational correlations over long distances (long-range orientational order). When long-range positional order is introduced in one dimension (1D), the system can be described as a set of twodimensional liquid layers (i.e. with short-range positional order of constituent particles) stacked on top of each other with well-defined interlayer spacing and called Smectic mesophases. In the case of systems with two-dimensional (2D) long-range positional ordered of particles, colloids can organize in 2D arrays of liquid tubes and are called a Columnar phase [19]. Consequently, depending on the order of anisotropically shaped particles, the formation of various liquid crystalline phases, such as Nematic, Smectic, or Columnar phases were detected in the suspensions of repulsive rods or disks [10], [11], [20]- [24].

In this thesis, by tuning interactions between colloidal particles from highly repulsive to complex attractive, the self-organization of rod-shaped anisotropic particles will be investigated. Thus, at the beginning of the introduction chapter, we will explain the nature of colloidal interactions.

Then we will describe the concept of purely repulsive interactions, which was successfully used for theoretical predictions of liquid crystalline phase transitions. In the end, we will show how attraction can be introduced into colloidal systems.

Colloidal interactions

Colloidal particles in suspensions are affected by forces arising from dipole-dipole interactions, also known as van der Waals interaction, repulsion arising from the overlapping of their electrical double layers, known as electrostatic repulsion, and in the case when the colloidal particles are covered by a polymer layerthe repulsive forces which are known as steric repulsion. These interactions between colloids can be controlled using different dispersion mediums (such as Chapter 0 polymer/water two-component mixtures), adjusting the pH and ionic strength of the solution, or attaching polymers via adsorption or chemical reaction to the surfaces of the particles for inducing steric repulsion. Understanding the origin of these interactions makes it possible to control the behavior of colloidal particles in their suspensions. In this section, we will consider interactions between colloids in aqueous suspensions as well as the main theories based on these interactions and describe the behavior of colloidal systems [25].

0.2.1.

Hard-core interactions

The simplest interaction model was proposed for systems of purely repulsive particles (socalled hard-core particles) which are not interacting when they are not in direct contact, and which are exhibiting infinitely large repulsion when they start to overlay (fig. 1). The system of nearly hard spheres was achieved experimentally by the covering of spherical colloids by a very thin polymer brush (i.e. by introducing steric repulsion at short interparticle distances) and their following dispersions in the solvent with the same refractive index as for colloidal particles [16]. Since the free energy of hard-core systems is independent of their internal energy, the self-organization of particles with hard-core interactions is driven by entropy alone. In such kinds of systems, phase transitions are caused by changes in the volume fraction of colloidal particles and are independent of temperature.

In the case of hard spheres, the phase diagram was established as a function of their volume fraction by P.N. Pusey and W. van Megen [15], [16], who with increasing particle volume fraction (concentration) have detected, firstly hard sphere crystallization and then the glass formation (fig. 2).

Moreover, hard-core interaction model was successfully used in first computer simulations of the phase behavior of colloidal spheres [26]- [28].

Figure 1. Schematic interaction energy versus interparticle distance profiles of hard-core (solid line) interaction between colloidal spheres covered with a thin polymer layer.

As already mentioned above, introducing shape anisotropy into hard colloidal systems leads to rich phase behavior with the formation of many liquid crystalline phases. First observations of Isotropic/Nematic phase transition in suspensions of rod-shaped particles were done by H. Zocher in 1925 [29] for V2O5 inorganic colloids and F. C. Bawden together with N. W. Pirie in 1935 [12], [30] for Tobacco Mosaic Viruses (TMV). Inspired by their works, L. Onsager proposed the theory, which describes this transition for infinitely long hard rods [31]. This theory was the first which successfully predict the entropically driven phase transition in colloidal suspensions and it is widely used nowadays. Much later, a lot of investigations were done for very long hard rods. Thus, it was found that with increasing their volume fraction colloidal rods exhibit liquid Isotropic, Nematic, Smectic, and Columnar mesophases [32]- [35]. Onsager theory, as well as rod phase behavior, will be discussed in paragraph 0.2.4. defined as ф 𝐸 = (0.494/0.407)ф 𝑐 [16],

where 0.407 is the core volume fraction фс at which freezing starts and 0.494 is an effective volume fraction ф E of hardspheres freezing predicted by computer simulations [36].

Van der Waals interactions

Van der Waals interactions are distance dependent forces between particles separated by any medium including air or vacuum [25]. Van der Waals forces include three different types of dipoledipole interactions: (i) Keesom interactions which arises between two permanent dipoles and induces attraction between polar particles; (ii) Debye interactions defined as the attractive energy between polar and nonpolar particles; and (iii) London dispersion forces created by the induced dipoles arising from electronic polarization of interacting particles. Van der Waals forces act over relatively short interparticle spacings and quickly vanish at long distances between interacting particles (fig. 3). For two spheres of the same radius R, the van der Waals interaction energy can be defined as a function of the particle separation r [25] 𝑊(𝑟) = -𝐴 131 𝑅 12𝑟

(0.1)
where A131 is the Hamaker constant, which depends on the relative dielectric constants (i.e. on the refractive indexes) of the colloidal particle (1) and medium (3).

0.2.3.

Electrostatic interactions

Electrostatic interactions are present in systems of charged particles interacting through a polar medium and usually are dominating in the colloidal suspensions. Since at the equilibrium all systems tend to be electroneutral, charged colloids in their suspensions compensate a surface charge by ions chemically bonded to their surface in the region immediately next to the surface (Stern layer)

and by electrostatically accumulated oppositely charged ions (counterions) from the bulk solution located at the outer side of the Stern layer ( so-called Gouy-Chapman layer) [25] (fig. 4a). The Stern potential dictates the magnitude of charge in the counterion layer while the Gouy-Chapman layer controls the electrostatic repulsion that arises from overlapping counterion layers (fig. 4b).

The simplest example of the electric potential dependence from the distance was shown for a flat surface with homogeneously distributed charges. For small surface potentials the electrical potential, Ψ(x), in solution decreases exponentially with distance h from the surface [25] Ψ(𝑥) = Ψ 𝑠 𝑒 -кℎ (0.2)

where Ψ 𝑠 is the Stern potential, κ -1 is the Debye screening length.

The potential decreases by a factor, 1/e, for the distance κ -1 defined as

к -1 = √ 𝜀 𝑟 𝜀 0 𝑘 𝐵 𝑇 2𝑒 2 ∑ 𝐶 𝑖 𝑧 𝑖 𝑖 (0.3)
where 𝑒 is an elementary charge, 𝜀 𝑟 is the relative dielectric constant of the medium, 𝜀 0 is the vacuum permittivity, 𝑘 𝐵 is the Boltzmann constant, 𝑇 is the absolute temperature, C is the molar concentration of i th ion with valence z.

Debye screening length varies with the inverse square root of suspension ionic strength defined by

I= ∑ 𝐶 𝑖 𝑧 𝑖 2 𝑖 2
. Consequently, ionic conditions of the suspension play a major role in controlling the range of the electrostatic repulsion, and by tuning ionic strength repulsion between charged colloids can be changed.

Figure 4. The electrical double layer at a charged surface with a Stern layer of positive ions adsorbed

to the surface (a). Ψ0 and Ψs are the potential at the surface and the Stern potential, respectively [25].

Schematic interaction energy versus interparticle distance profiles of electrostatic repulsion between colloidal spheres arising from the overlay of their electrical double layers (b)

, where к -1 is Debye screening length.

0.2.4.

Onsager theory for an entropy driven

Isotropic/Nematic phase transition

In 1949 Onsager has developed the first theory, which describes an Isotropic/Nematic phase transition in suspensions of purely repulsive stiff colloids [31]. His work has considered hard monodisperse rods with infinite length and it is based on the maximization of entropy. Onsager theory describes the transition from a fully disordered (isotropic liquid) phase to a Nematic phase, in which rods are orientationally ordered (fig. 5). As already described above, in an Isotropic phase, particles exhibit short-range positional and orientational orders, while after phase transition into Nematic phase, hard rods keep short-range positional order with achieving long-range orientational order.

Onsager has showed that the self-organization of hard long rods can be explained as a result of the competition between the loss of orientational entropy and the gain in the free volume, i.e. translational entropy.

Onsager theory treats an Isotropic/Nematic phase transition within a second virial expansion of the free energy, which fails for highly aligned and concentrated rods and cannot be used to describe transition into phases with higher particle order. The free energy can be found as a sum of three terms: the free energy of an ideal solution, the contribution of the orientational entropy, and the interactions between the particles, related to the second viral coefficient (eq.0.4). 𝐹 = 𝐹 𝑖𝑑 + 𝐹 𝑜𝑟 + 𝐹 𝑖𝑛𝑡 (0.4) Since the system is assumed to be homogeneous in all directions and the particle density can be determined as 𝜌(𝑟, 𝛺) = ( 𝑁 𝑉 ) 𝑓(𝛺), where V is the volume of the system, N is the number of rods, r is the vector describing the position of hard rod and Ω is the solid angle describing its orientation.

The function f(Ω) shows the probability that a particle is oriented with the solid angle Ω and this probability can be normalized as ∫ 𝑓(𝛺)𝑑𝛺 = 1. Using the particle density with the function showing the probability that a particle exhibits solid angle Ω, equation 0.4 can be re-written as

𝐹 𝑘 𝐵 𝑇 = 𝑙𝑜𝑔 𝑁 𝑉 + ∫ 𝑓(𝛺) log[4𝜋𝑓(𝛺)] 𝑑𝛺 - 1 2 𝑁 𝑉 ∬ 𝛽(𝛺, 𝛺 ′ )𝑓(𝛺)𝑓(𝛺 ′ )𝑑𝛺𝑑𝛺 ′ (0.5)
where 𝛽(𝛺, 𝛺 ′ ) is the Mayer overlap function, which for hard rods is equal to the overlap volume of two particles with orientations 𝛺 and 𝛺 ′ . Thus, the angle between these rods γ can be introduced

𝛽(𝛺, 𝛺 ′ ) = -𝑉 𝑒𝑥𝑐𝑙 (𝛺, 𝛺 ′ )~-2𝐿 2 𝐷 × sin (𝛾) (0.6)
where 𝑉 𝑒𝑥𝑐𝑙 is the volume, which is occupied by a given rod and as result is excluded to another particle, called excluded volume. The schematic illustrations of the excluded volumes of two identical rods are illustrated in figure 5 (b-c). The second and third terms in equation 0.5 are related to the orientation and packing entropies, correspondingly.

Similar to suspensions of hard spheres, the formation of liquid crystalline phases in suspensions of hard rods is athermal and depends on rod volume fraction (concentration). The volume fraction of hard rods at the Isotropic/Nematic phase transition was obtained by stability analysis of the Onsager equation (eq.0.5) and is 𝜑 ≅ 4

𝐷

𝐿

, where L and D are the length and diameter of hard rods, correspondingly. Within his theory, Onsager determined that for thin and long hard rods with an aspect ratio (L/D) higher than 100, driven by entropy an Isotropic/Nematic phase transition is first order. For lower aspect ratios the free energy expansion has to consider third or higher virial terms for defining interactions between shorter particles.

Since used in theoretical predictions identical (with the same length and diameter) rigid hard rods do not exist in nature, different considerations were taken into account to study real experimental systems. Extensions of Onsager theory were done for semi-flexible particles with persistence length P [37]- [39]. The rod flexibility destabilizes the Nematic phase, which results in the shift of the Isotropic/Nematic phase transition to higher rod volume fractions. Another extension was done for taking to account the size polydispersity of hard rod systems [40]. For colloidal systems, an increase of the polydispersity leads to the increasing coexisting region with a shift the position of the Isotropic/Nematic phase transition to lower rod volume fractions. Considering that many colloidal particles, including filamentous phages in their dispersions, are stabilized thanks to electrostatic repulsions, one more important extension was made for charged colloids. Since identically charged particles at small interparticle distances exhibit an electrostatic repulsion (fig. 3b), the assumption that they behave as a hard-core system can be done. For this purpose, a concept of the effective diameter [41] has to be introduced. Within this concept, the bare rod diameter D has to be replaced by effective diameter Deff. The effective diameter of the charged rod is related to the Debye screening length (eq. 0.

3) which depends on the ionic strength of the suspension, and Deff can be described using the following equation

𝐷 𝑒𝑓𝑓 = 𝐷 + 𝛼к -1 (0.7)
where α is a free parameter.

Thus, for charged colloids, in Onsager equation (eq. 0.5) the bare rod diameter has to be replaced by effective diameter Deff and the predicted volume fraction at which rods will undergo the Isotropic/Nematic phase transition will depend on the Debye screening length, i.e. on the ionic strength of the suspension.

Based on these extensions of the Onsager theory, many theoretical and experimental research focused on liquid crystal phase behavior were done. Thus, the phase behavior of inorganic colloidal particles, including vanadium pentoxide, boehmite [14], silica rods [21] or biological systems, such as TMV [34], fd or M13 viruses [9], [20], [32], [33] was investigated. Viral rods, especially fd and M13 bacteriophages, were the most studied since these particles have a high aspect ratio (L/D>100), high size monodispersity, and can be easily produced in a big amount. Their properties make an advantage to use viral colloids as a model system of hard rods for experimental studies, which can be described using simple Onsager theory with extensions done for their flexibility and charge. A detailed description of these bacteriophages, as well as their phase behavior, will be discussed in section 0.3.

0.2.5.

Polymer induced effective attraction between colloidal particles

In the previous paragraph, we have discussed purely repulsive interactions between colloidal particles. The interactions between particles can be tuned from repulsive to attractive ones by adding to their suspensions neutral polymer, small (compared to these particles) colloids, or micelles. In the second half of the 20 th century Sh. Asakura and F. Oosava [42], [43] have developed the theory that describes the effective attraction, called depletion, arising between colloidal particles that emerged in a solution of the non-interacting polymer. Depletion is driven by entropy associated with the added polymer, considered as a small hard sphere, to a colloidal suspension. In colloid/polymer twocomponent mixture each big colloidal particle is surrounded by the excluded layer with the thickness equal to the radius of polymer sphere δ. The depletant cannot penetrate this excluded layer which leads to the difference in polymer concentrations inside the excluded volume (near the surface of a colloidal particle) and the suspension bulk. It drives to the difference in osmotic pressures, and as a result to the attraction between colloids. When the excluded layers of colloid pair overlay, it increases the volume accessible for polymer and results in the increase of their translational entropy. The schematic illustration of depletion potential for two spherical colloids is presented in figure 6 and depletion between rod-shaped particles will be discussed in Chapter 3 of this thesis. In our study, as model systems of monodisperse, colloidal rods were used rod-shaped fd and M13 viruses. They are bacteriophages that specifically infect and replicate within the bacterium Escherichia Coli (E. Coli) and can be described as biological semiflexible polyelectrolytes composed of a single-strained circular DNA molecule (ssDNA) encapsulated in a long cylindrical protein coat [44]- [46]. This coat, so-called virus capsid, consists of about 2800 copies of the major coat protein P8 and five copies of each minor coat proteins at both capsid tips: P7 with P9 at the distal end and P3 with P6 at the proximal end as illustrated in figure 7. The main P8 proteins of the viral capsid have α-helix structure and they are composed of 50 amino acid units [44]. P8 proteins are helically wrapped around ssDNA, which makes the virus capsid a chiral object. The virus chirality will be discussed in Chapter 3. The virus surface charge is mainly dictated by the water exposed part of the P8 protein [47] and will be introduced below.

Filamentous bacteriophages as a model system of colloidal rods

Bacteriophages fd and M13 are two closely related strains with a length of about 1 μm, a diameter of 7 nm, and almost identical genome with P8 coat proteins differing by only one single amino acid: negatively charged aspartate in fd (Asp12) corresponding to uncharged asparagine in M13 (Asn12) [48]. As a result of this difference, M13 has one charge less per P8 subunit compared to fd strain, which leads to a total charge reduction of about 30%. The charge of the viruses (dictated by water exposed amino and carboxyl groups of the viral capsid) is pH dependent. It is explained by the fact that similar to any other weak bases or acids, a protein dissociation is affected by pH. The isoelectric point of fd viruses is located at pH 4.2 [47] and their linear charge density is equal to 10e -/nm [33] at pH 8.2. For M13 viruses the charge is reduced to 7e -/nm at the same pH [49]. Using genetic engineering both of these bacteriophages were modified for obtaining target properties. Consequently, the library of viruses with various contour lengths and flexibilities was obtained. The virus length is controlled by the length of ssDNA, which is encapsulated in a viral capsid and usually carries out the genetic information of a given strain [START_REF] Brown | An easy-to-prepare mini-scaffold for DNA origami[END_REF], [START_REF] Marchi | Toward larger DNA origami[END_REF]. To produce a stable M13 virus with a length higher than 1 μm, additional DNA has to be introduced into wild-type M13

ssDNA [START_REF] Hines | Construction and Characterization of New Coliphage M 13 Cloning Vectors[END_REF]. In contrast, to create short M13 viruses (L<1 μm) more complicated procedure is required. Thus, the genetic information of short viruses should be carried out by the long helper phage (with similar sequencing to wild-type M13 virus), while the virus length is controlled by shorter DNA surrounded by M13 capsid [START_REF] Brown | An easy-to-prepare mini-scaffold for DNA origami[END_REF]. The virus flexibility can be decreased through the single mutation in P8 coat proteins of fd or M13 bacteriophages: for viruses with persistence length P of 2.8±0.7 μm tyrosine (Tyr21) was replaced by methionine (Met21), which raises M13 or fd persistence length (i.e. stiffness) to the value of 9.9±1.6 μm [11]. Moreover, a mutant of M13 virus, called M13C7C, fused with disulfide contained peptide at the end of P3 protein, which introduces additional water exposed cysteines in the proximal virus end [START_REF] Wu | Hybrid colloidal molecules from self-assembly of viral rod-like particles[END_REF]. Properties of the different virus mutants are summarized in table 0.1.

Similar to TMV, fd and M13 filamentous bacteriophages were widely used as model systems of colloidal rods starting from the second half of the 20 th century [20], [33], [34], [START_REF] Dogic | Filamentous phages as a model system in soft matter physics[END_REF]- [START_REF] Marvin | Filamentous Bacterial viruses[END_REF]. Such interest in these experimental systems rises from the facts that filamentous bacteriophages: (I) can be easily produced in a big amount, (II) they have high size and shape monodispersity, (III) high aspect ratio (more than 100 for all strain except miniM13 virus) and (III) can be observed at the singleparticle level using optical microscopy [33]. As already mentioned in paragraph 0.2.1, after the introduction of the effective diameter concept, these charged viral filaments can be approximated as hard rods, which can be described using a simple Onsager theory [9], [33], [41].

In this section, we will focus on the phase behavior of filamentous viruses. The structures formed under depletion attraction for these viruses will not be introduced in this Chapter, since they will be described in Chapter 3 of this thesis.

0.3.1.

Phase behavior of filamentous bacteriophages

The self-organization of filamentous viruses in aqueous dispersions was widely studied for the past few decades. For infinitely long rigid rods, the formation of not only a Nematic phase was theoretically described [31] but also the existence of more complex phases, such as Smectic or Crystalline phases, was shown using computer simulations based on Onsager theory [START_REF] Frenkel | Thermodynamic stability of a smectic phase in a system of hard rods[END_REF], [START_REF] Veerman | Relative stability of columnar and crystalline phases in a system of parallel hard spherocylinders[END_REF]. All these phases were obtained experimentally for fd and M13 viruses. Thus, with increasing their concentration the Isotropic liquid, (Chiral) Nematic (N (*) ), Smectic-A and -B (SmA, SmB) and not expected from simulation points of view [START_REF] Stroobants | Columnar versus Smectic Order in Binary Mixtures of Hard Parallel Spherocylinders[END_REF], [START_REF] Dussi | On the stability and finite-size effects of a columnar Chapter 0 phase in single-component systems of hard-rod-like particles[END_REF] Columnar (Col) mesophases were formed (fig. 8) [20], [32], [33], [START_REF] Dogic | Cholesteric Phase in Virus Suspensions[END_REF], [START_REF] Grelet | What Is the Origin of Chirality in the Cholesteric Phase of Virus Suspensions?[END_REF], [START_REF] Dogic | Isotropic-nematic phase transition in suspensions of filamentous virus and the neutral polymer Dextran[END_REF]. Filamentous bacteriophages are charged particles for which the effective diameter has to be introduced as described by equations 0.3 and 0.7. Consequently, the phase diagram of filamentous phages depends on the ionic strength of the suspensions, since it defines particle effective diameter (i.e. virus concentrations at which phase transitions occur). Since filamentous bacteriophages are chiral objects, instead of typical Nematic phase they form a Chiral Nematic or Cholesteric one. In this mesophase, the averaged particle orientation (director) follows a helical path, as viruses twist concerning each other [START_REF] Grelet | What Is the Origin of Chirality in the Cholesteric Phase of Virus Suspensions?[END_REF]. The nature of the twist in a Cholesteric phase will be discussed in Chapter 3. The full turn (2π) of the director, called cholesteric pitch (P0 in fig. 8 left), determines the periodicity of a Cholesteric phase, and achiral Nematic phase can be described as a Cholesteric one with infinitely long pitch. Consequently, both of these phases locally have the same structure. The location of Isotropic/Cholesteric phase transition was found experimentally [9] in a good agreement with Onsager theory extended for taking to account virus flexibility [START_REF] Dussi | On the stability and finite-size effects of a columnar Chapter 0 phase in single-component systems of hard-rod-like particles[END_REF] and charge (eq.0.3, 0.7) [33], meaning that the chirality contribution to the total free energy is negligibly low. Thus, the Isotropic/Cholesteric phase transition was found for the various ionic strengths as illustrated in figure 9 (a). Moreover, virus flexibility affects the location of the Isotropic/Cholesteric phase transition. As was experimentally shown by Barry et al. [11] the Isotropic/Cholesteric phase coexistence for filamentous bacteriophages at the fixed ionic strength of 110 mM is located at virus concentrations of 19.8-22.6 mg/ml for fd-wt (P=2.8 μm) and 13.9-18.9 mg/ml for fdY21M (P=9.9 μm). The Smectic-A and Smectic-B phases are typical for viral suspensions. Both of these phases form lamellar periodic texture with viruses normal to the smectic layers (fig. 8 middle), but these phases differ in the particle ordering. Thus, viruses exhibit liquid-like order within the layers for Smectic-A and long-range positional order with hexagonal particle organization for Smectic-B phase, which was proven by small angle X-ray scattering (SAXS) [33]. Moreover, these two Smectic phases differ in particle dynamics: using single-particle tracking of fluorescently labeled viruses via optical microscopy, hopping-like behavior of parties between the layers was observed for Smectic-A phase (fig. 10b) [8], [START_REF] Lettinga | Self-diffusion of rodlike viruses through smectic layers[END_REF]- [START_REF] Lettinga | Self-diffusion of rod-like viruses in the nematic phase[END_REF] while for Smectic-B phase viruses do not have any significant motion.

Hopping-like diffusion within the Smectic-A phase shows that the virus migration through smectic layers takes place in quasi-quantized steps of one-rod length.

Similar to the Isotropic/Cholesteric phase transition predicted by Onsager theory, in order to describe Choletsteric/Smectic-A phase transition via computer simulations [START_REF] Frenkel | Thermodynamic stability of a smectic phase in a system of hard rods[END_REF], [START_REF] Bolhuis | Numerical study of the phase behavior of rodlike colloids with attractive interactions[END_REF] the concept of Chapter 0

effective rod diameter has to be used. To determine the effective diameter of highly charged viral rods in their dense suspensions, the concentration of virus counterions has to be taken into account by using Manning theory or Poisson-Boltzmann cell model [START_REF] Manning | Counterion Condensation on Charged Spheres, Cylinders, and Planes[END_REF]- [START_REF] Trizac | Analytical estimation of effective charges at saturation in Poisson-Boltzmann cell models[END_REF]. Both of these models and the effect of the virus counterions on the suspension ionic strength (i.e. effective diameter) will be discussed in Chapter 2. Ttranslational order within the smectic layers shows the evolution from liquid-like (dotted black line, SmA phase) to hexagonal positional (solid red line, SmB phase) order by slightly increasing the rod concentration [33]. Bragg refractions (100) and ( 110) were indexed according to the ratios of the scattering vector q: 1: √3: √4: √7: √9… of a two-dimensional hexagonal lattice, corresponding to the Miller indices (hkl) with l defined as a direction along the viruses.

As mentioned above, the formation of the Columnar phase in suspensions of hard monodisperse rods has not been predicted theoretically by using computer simulations [START_REF] Dussi | On the stability and finite-size effects of a columnar Chapter 0 phase in single-component systems of hard-rod-like particles[END_REF]. The existence of the Columnar phase in suspensions of filamentous bacteriophages [20] may be explained by virus flexibility [START_REF] Hentschke | Isotropic, nematic, and columnar ordering in systems of persistent flexible hard rods[END_REF]. The studies of particle order within the viral Columnar phase [20] show that rods exhibit short-range positional order and have a hexagonal organization. Similar to a Smectic-A phase, in a Columnar phase hoping-type diffusion of particles along their main axis with their full-and half-jumps was detected, but the jump frequency in a Columnar phase is more than 2 orders of magnitudes lower compared to a Smectic-A phase [8].

0.3.2.

Chemical modification of the virus body using bioconjugation

Virus bioconjugation via specific chemical reactions is one of the frequently used technique to achieve the functionalization of its body or tips. For the bacteriophage body functionalization reactions with primary amine groups (the NH2 side of lysine and terminal NH2 of P8 proteins) are often used. For this propose N-hydroxysuccinimide (NHS) ester or tetrafluorophenyl (TFP) ester activated compounds can be used as a counterpart of the reaction (fig. 11a). As a result, filamentous phages were chemically altered with drugs [START_REF] Yacoby | Targeted drug-carrying bacteriophages as antibacterial nanomedicines[END_REF]- [START_REF] Yacoby | Targeting antibacterial agents by using drug-carrying filamentous bacteriophages[END_REF], RGD peptides (tripeptide consisting of arginine, glycine, and aspartate) [START_REF] Rong | Oriented cell growth on self-assembled bacteriophage M13 thin films[END_REF], fluorophores [START_REF] Lettinga | Self-diffusion of rod-like viruses in the nematic phase[END_REF], [START_REF] Li | Chemical modification of M13 bacteriophage and its application in cancer cell imaging[END_REF], and polymers [START_REF] Zhang | Reversible gelation of rodlike viruses grafted with thermoresponsive polymers[END_REF], [START_REF] Dogic | Development of model colloidal liquid crystals and the kinetics of the isotropic { smectic transition[END_REF]. Chemical modification of water exposed carboxyl groups of virus coat proteins through the reaction with organic amines results in virus charge reversal [START_REF] Zhang | Charge reversal of the rodlike colloidal fd virus through surface chemical modification[END_REF]. Within this thesis we will use full body virus bioconjugation with fluorescent dyes in order to visualize individual particles with fluorescence microscopy techniques.

The detailed protocol for this conjugation will be described in Chapter 1. and one M13 virus [START_REF] Wu | Hybrid colloidal molecules from self-assembly of viral rod-like particles[END_REF].

Chapter 0

To achieve the bioconjugation only on one virus tip, the exposed disulfide groups formed by cysteines of P3 coat proteins located at the virus proximal end are often used. Recently in our group has been found that these disulfides similar to thiol groups can efficiently react with nanoparticles of noble metals due to the sulfur-metal reaction (fig. 11b) [START_REF] Wu | Hybrid colloidal molecules from self-assembly of viral rod-like particles[END_REF]. Gold (Au), silver (Ag), and platinum (Pt) nanoparticles have been attached only to the proximal end of M13C7C viruses. Bioconjugation of virus tips with gold nanoparticles will be used in our research for increasing van der Waals attraction (eq.0.1) between viral rods. The protocol for this reaction has been established in our group [START_REF] Wu | Hybrid colloidal molecules from self-assembly of viral rod-like particles[END_REF] and will be described in the next Chapter. Hybrid colloidal particles obtained via tip bioconjugation between Au nanoparticles and filamentous viruses will be used to study their selforganization in Chapter 4.

Outline of the thesis

Due to rich properties of filamentous bacteriophages as a model system of colloidal rods, our group has used these viruses for investigation of liquid crystalline phases and hierarchical colloidal architectures for the nearly last two decades. In this thesis, filamentous bacteriophages are used as building blocks to study their self-organization into various morphologies, including liquid crystalline mesophases and macroscopic hierarchical architectures. For this purpose, the nature of particle interactions is tuned from highly repulsive to complex attractive ones by varying the properties of our colloidal systems. Thus, for obtaining highly repulsive rods, in the beginning, we will investigate very low ionic strength viral suspensions, then we will change interparticle interactions to attractive ones using depletion mechanism, and at the end, we will increase interparticle van der Waals attraction by using virus-based hybrid colloids composed of filamentous viruses and gold nanoparticles.

In Chapter 1, we describe experimental procedures followed in this thesis from general protocols used for material preparation to the data acquisition by optical microscopy or X-ray scattering techniques. We start by describing the standard protocol for virus production and purification, body-labeling of viruses via their bioconjugation with fluorescent dyes, and the production of hybrid colloids using the reaction of virus proximal ends with spherical gold nanoparticles. Then, the experimental setups used in our investigations are discussed and at the end, we present preparation protocols of the buffer solutions and polymer/virus two-component mixtures.

In Chapter 2, the phase behavior of viruses surrounded by very thick electrical double layers, which induce their long-range electrostatic repulsion is studied. Repulsion between viral rods is achieved by using the very low ionic strength (I=0.16mM) medium. In the beginning, we consider theoretical aspects of the used viral system at such low ionic conditions. Concentrations of counterions associated with highly charged viruses and their contribution to the suspension ionic strength are calculated using Manning theory and then, these concentrations are analytically estimated within the Poisson-Boltzmann cell model as proposed by E. Trizac et al for concentrated charged rods [START_REF] Trizac | Analytical estimation of effective charges at saturation in Poisson-Boltzmann cell models[END_REF]. The experimental phase diagram of equilibrated viral suspensions at the very low ionic strength is obtained as a function of virus concentration via optical microscopy and SAXS techniques.

Whereas in recent scientific papers have been reported about the glass formation in viral suspensions at the same ionic conditions, particular attention is devoted to the particle ordering in dense viral suspensions (at concentrations above the ones needed for the formation of the Cholesteric phase).

In Chapter

Introduction

Here, we describe experimental procedures followed in this thesis from general protocols used for material preparation to data acquisition by techniques such as optical microscopy and X-ray scattering. In the beginning, we present a standard protocol for virus production and purification, body-labeling of viruses with fluorescent dyes, and the production of hybrid colloids via bioconjugation with gold nanobeads (AuNBs). Then we discuss the experimental setups used in our investigations and at the end we describe buffer (including one at very low ionic strength I=0.16mM)

and polymer/virus two-component mixture preparation protocols.

Virus production and purification

Filamentous bacteriophages (fd, M13, and f1) are well known for their ability to infect Escherichia Coli bacteria via the complex formation between their minor coat protein P3 and the bacteria integral membrane protein TolA [1] [2]. As follows, the virus introduces its single-stranded DNA (ssDNA) into the bacteria cytoplasm with following DNA replication as a double-stranded intermediate from which the ssDNA containing phage particles are produced [3] [4].

Preparation of fd and M13 phages of different strains (except miniM13 virus, see Chapter 4) has been performed using the standard biological protocol [3]. E.Coli strain ER2837 has been used as host bacteria. Luria-Bertani (LB) media consisting of peptone 140 (10 g/l), yeast extract (5 g/l), and NaCl (5 g/l) has been used for bacteria growth. All materials and LB media have been autoclaved before virus production. The infection procedure has been done in extremely clean conditions under previously sterilized with UV light biological laminar-flow hood. To avoid the introduction of any biological contaminations hood walls, pipettes, packages of sterile instruments (outside walls of the boxes, which contain pipette tips, vials, etc.) as well as operator hands have been cleaned with ethanol before introducing them under the laminar-flow hood.

As a first step of the infection protocol, we have pre-amplified 3 ml of sterile LB media containing antibiotic Tetracycline (TET), CTET=1.5×10 -2 mM, with one isolated colony of the bacteria. Then, we have incubated LB media infected by E. Coli at 37ᴼC and 200 rpm stirring speed for around 5 hours. We have placed 1 ml of the obtained bacteria suspension in 500 ml Erlenmeyer flask, which contained 100 ml of LB media with CTET =1.5×10 -2 mM and let E. Coli grow overnight at 37ᴼC and 200 rpm.

For the infection of bacteria with bacteriophages, 6 liters of LB media has been used in one production run. LB has been divided into 3 parts (2 liters each), placed into 5 liters Erlenmeyer flasks, and sterilized. Then, 20 ml of pre-amplified bacteria and 1 ml of the virus infecting solution, which contains around 10 9 infecting phages per ml, have been added into each flask. To speed up the virus growth, LB media in the flasks had a temperature of 30-37 ᴼ C. Dispersion of infected with viruses bacteria in LB media has been stirred at 37 ᴼ C and 200 rpm for at least 5 hours. The virus growth has been tracked with spectrophotometry using bacteria adsorption at λ=600 nm. The virus production has been stopped at the end of bacteria exponential growth (fig. 1). At the end of the virus production, we have obtained 6 liters of bacteria/virus mixture. To remove the bacteria, which are much bigger than fd or M13 viruses (E. Coli is approximately 2μm long with a diameter of about 1μm) centrifugation has been performed. Thus, using F10-4x1000LEX rotor in a Solrvall RC6+ centrifuge, bacteria have been sedimented by 6,000g run at 4ᴼC for 20 min.

The supernatant containing viruses in LB media has been separated from bacteria pellets by its exchange into sterile Erlenmeyer flasks. By adding 15 g/l of NaCl and 20 g/l of neutral polymer (polyethylene glycol with an average molecular weight of 8 kDa) we depleted produced viruses for at least 1 hour in order to be able to collect them at low centrifugal force from high volumes used during their growth. In the next step, aggregated viruses have been collected using the same rotor by 6,000 g centrifugation run for 30 min at 4ᴼC. Obtained virus pellets have been re-dispersed in around 20 ml of distilled water and transferred in an ultracentrifuge tube. Few 45min long centrifugation runs at 4ᴼC and 24,000 g have been used to sediment the remaining bacteria. To completely remove any free polymer after depletion, bacteria-free supernatant has been centrifuged for 3 hours at 215,000 g Chapter 1 and 4ᴼC. After the last centrifugation step, viruses have been sedimented, and the supernatant has been discarded. For high centrifugation forces (higher than 15,000 g) Sorval WX Ultra 80 centrifuge with F50L-8x39 or Ti50.2 rotor has been used.

As the last step of the virus purification, pellet which contains produced viruses has been redispersed in 20 ml of the desired buffer and dialyzed against the same buffer for at least 8 hours at 4ᴼC. After one production run, the typical amount of collected and purified viruses is around 100 mg.

To exclude any cross-contaminations, the DNA extraction has been done after each production, and DNA sequence has been checked.

Pure viruses have been concentrated by ultracentrifugation run at 215,000 g for 3 hours (T=4 ᴼ C) and stored at 4 ᴼ C. These purified viral suspensions have been used for our experiments. The virus concentration in their aqueous dispersions can be determined by measuring the light adsorption at 269 nm for fd-wt or M13 viruses with an extinction coefficient of 3.84 cm 2 /mg [5], and at 266 nm for fdY21M or M13K07Y21M with an extinction coefficient of 3.63 cm 2 /mg [6], [7]. For this purpose, a spectrophotometer, Genesys 10 UV scanning (Thermo) equipped with 1 cm quartz cuvette or Nanodrop one (Thermo) have been used. To verify the suspension purity, the ratio between the absorbance at 269 nm and 244 nm has been checked and for clean suspensions (less than 1% of impurities) this ratio should stay below 1.41 [8]. [Dylight550-NSH] according to previously established protocol [9] with some minor changes in the dye excess and the duration of the reaction. The absorption (excitation) and emission spectra of these dyes are shown in figure 2.

Preparation of chemically modified fluorescent viruses

Green and red body labeled bacteriophages with a maximum of emission at 525 and 576 nm, respectively, have been prepared as a product of the reaction between amino groups of virus coat proteins and fluorescent dyes functionalized with NHS or TFP groups. These dyes have been bound

to the virus body in phosphate buffer with pH 7.8 and at the ionic strength of 350 mM (Dylight550-NSH) or in sodium carbonate buffer with pH 9 and at the ionic strength of 150 mM (Alexa 488-TFP).

Since the reaction occurs between dyes and amino groups of virus coat proteins, using any materials with amino groups (such as Tris buffer) should be excluded. For the reaction have been used dilute virus suspensions with a concentration of 0.2 mg/ml. Dyes have been dissolved in N,Ndimethylformamide (DMF) and added to viruses with the experimental excess of about 3 dyes per major P8 coat protein (about 3,000 dyes per virus) [10]. To avoid any denaturation of the phages by the organic solvent, particular care has been taken, and the amount of DMF did not exceed 20% of the total volume. Once the dyes and the viruses have been mixed, the reaction has been carried out under stirring for 1 hour at room temperature and overnight at 4°C. The scheme of the body labeling reaction is illustrated in figure 3. Modified viruses have been purified by proceeding extensive dialysis against the desired buffer (typically Tris buffer with pH 8.2) with followed concentrating by 215,000 g

Chapter 1 ultracentrifugation run for 3 hours at 4ᴼC. Purified suspensions have been diluted with the same buffer solution to the final virus concentration of around 1 mg/ml and stored at 4ᴼC inside protected from the light vials. These viruses have been added in tracer amount into raw virus suspensions in ordered to visualize their behavior at the single-particle level. Since labeled and raw viruses should have the same length and diameter, in all our studies we assume that they behave as the unlabeled viruses.

The most important practical point, which should be taken to account during and after the labeling process, is that used fluorescent dyes in their solutions or immobilized on virus bodies can lose their fluorescent properties after illumination with UV light (photo-bleaching). Consequently, all the materials containing fluorescent dyes (free or immobile) should be protected from the light during all manipulations.

Preparation of hybrid virus-based colloids

Recently in our group has been developed the effective production protocol of virus-based hybrid particles via bioconjugation between the proximal end of M13KE or M13C7C viruses and noble metallic (Au, Ag, or Pt) nanoparticles [11]. Thus, as a result of the metal-sulfur bond formation between cysteine groups of the virus P3 protein and spherical nanoparticles, hybrid colloids consisting of several (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) viruses attached to the one metallic nanoparticle could be obtained. The amount of attached viruses to the same nanoparticle (n) depends on the size of this nanoparticle (when the reaction is carried out with virus excess) and the ionic strength of the reaction mixture. Thus, it can be controlled experimentally [12]. In this thesis, we will use bioconjugation of fd and M13 viruses with 11.1 nm gold nanobeads (AuNBs) to produce hybrid colloids with one (scepter-like particles, AB type) or two (diblock, AB2 type) viruses attached to the same AuNB. For the reaction, tannic acid stabilized AuNBs have been purchased from NanoComposix. Before the reaction, concentrations of AuNB solutions have been determined based on the light absorption (fig. 4, measured by Nanodrop one, Thermo) due to the surface plasmon resonance effect. Thus, AuNB concentration can be determined from the light absorption at 400 or 520 nm [12], [13].

(I) Based on the absorption at 400 nm the molar gold concentration can be calculated as C Au(0) =OD 400 /ε 400 , where OD 400 is the optical density measured at 400nm with the molar extinction coefficient ε400=2400M -1 cm -1 [14]. By taking to account AuNB diameter of 11.1 nm and knowing that one bead has a mass of m=ρAu×VAuNB (where ρAu=19.3 g/cm 3 (II) Based on the absorption at 520 nm the particle concentration can be calculated using the same equations as in the case of absorption at 400 nm but with taking to account the optical density measured at 520nm CAu(0)=OD520/ε500 with the molar extinction coefficient ε520=3700 M -1 cm -1 obtained by AuNB supplier. Consequently at OD520=0.89 (fig. 4) CAuNB=3.47×10 12 particles/ml.

The values of the AuNB concentrations obtained for both methods are consistent within a small error (CAuNBs=3.43±0.04×10 12 particles/ml) and this average concentration will be used for the following calculations.

1.4.1.

Production of the AB type hybrid colloids

For the production of hybrid colloids consisting of one AuNB and one attached filamentous virus (AB type hybrid colloids) 30ml of AuNBs with a concentration of 3.43±0.04×10 12 particles/ml has been mixed with filamentous viruses to obtain AuNB molar excess α=NAuNBs/Nvirus=3. The virus mass needed for the reaction (mv) has been calculated as

𝑚 𝑣 = 𝐶 𝐴𝑢𝑁𝐵𝑠 × 𝑉 𝐴𝑢𝑁𝐵𝑠 𝛼 × 𝑀 𝑣 𝑁 𝐴 (1.1)
where 𝑉 𝐴𝑢𝑁𝐵𝑠 is the volume of the AuNB suspension with the concentration 𝐶 𝐴𝑢𝑁𝐵𝑠 in [particles/ml],

α is the AuNB excess, 𝑀 𝑣 is a molecular weight of the filamentous virus used in the reaction and, 𝑁 𝐴 is the Avogadro's number.

Thus, the final concentration of the viruses in the reaction mixture is Cv<0.035 mg/ml (Cv~0.035 mg/ml for the M13C7C with contour length of 1 μm and Mv=1.85×10 10 mg/mol). Besides, the virus concentration during this reaction should be lower than the overlapping concentration Cv * [12], which is the concentration when two viruses start to overlap with each other. The Cv * for viruses calculated with assuming of the close packed spheres (with the volume fraction of 0.74) of a diameter corresponding to one virus length (L), given by Cv * = 0.74×𝑀 𝑣 3 4 ⁄ ×𝐿 3 ×𝑁 𝐴 are presented in table 1.1.

After mixing viruses with AuNBs, the ionic strength of the reaction mixture has been increased by dialysis against Tris/HCl/(NaCl) buffer with pH 8.2. To avoid aggregation of AuNBs, it has been done gradually (I=10, 20, 40…mM) with overnight reactions done at room temperature and 300 rpm stirring at each ionic strength conditions. The reaction efficiency has been checked after each reaction by transmission electron microscopy (TEM) and the increase of the ionic strength has been stopped when >90% of viruses have been reacted with AuNBs (usually it occurs at I~10 mM for raw and at I~40 mM for body labeled M13C7C viruses). To avoid AuNBs aggregation, the ionic strength of the reaction mixture should not be higher than 80 mM [12]. To stop the reaction, the ionic strength of the virus/AuNB mixture has been decreased via dialysis against deionized water or low ionic strength (I<2mM) buffer. The virus/AuNB conjugation results in around 1 mg of AB type colloids (in case of using ~1μm long viruses and 30ml of AuNB suspension). Free beads, which are present in suspension after the conjugation, have been removed by 5 centrifugation runs at 12,000 g for 45 min [12]. These multiple purification steps help to remove around 95% of free beads without their aggregation. Thus, the sedimented beads may be re-used for the reaction with the same virus strain to produce a second batch of hybrid particles. ) determined by TEM after their purification. Spectrophotometry can not be used for direct determination of the virus concentration due to the overlay of virus absorption with AuNBs absorption at λ<300 nm (fig. 4).

Production of the AB2 type hybrid colloids

The production of hybrid colloids consisting of one AuNB and two attached filamentous viruses (AB2 type hybrid colloids) has been performed by one step reaction with 11.1 nm AuNBs.

For this 30ml of AuNBs with the concentration of 3.43±0.04×10 12 particles/ml have been mixed with filamentous viruses to obtain virus excess 1/α=Nvirus/NAuNBs=2. For the reasons described above, the ionic strength of the reaction mixture has been increased gradually. To improve the reaction efficiency, 2 mM of tris(2-carboxyethyl)phosphine (TCEP) has been added by dialysis as the last reaction step at I=40mM [12]. TCEP reduces disulfide bridges located at the virus proximal ends to the thiols, which makes sulfurs more exposed to the AnNBs. 14 h reactions have been proceeded at room temperature and 300 rpm stirring for each ionic strength condition. The reaction efficiency has been checked after each reaction by TEM (fig. 5). Then, the obtained structures have been dialyzed

against low ionic strength buffer (I≤2 mM) for storage and concentrating procedure. To concentrate AB2 type hybrid colloids, 1 hour centrifugation run has been performed with the acceleration of 250,000g. Similar to AB type colloids, the final concentration of hybrid particles has been calculated from the AuNB light absorption. As a result of the reaction (V=30 ml), up to 6 mg of AB2 type colloids (in case of using ~1μm long viruses) can be produced.

Optical microscopy techniques: sample preparation and observation

Optical microscopy sample preparation. Glass cells or cylindrical capillaries, have been prepared using previously cleaned with sulfochromic acid glasses and capillaries. Sulfochromic acid for glassware cleaning has been purchased from Sigma-Aldrich. For cleaning, cylindrical capillaries

0,0 0,1 0,2 0,3 0,4 0,5 Au-M13C7C f(M13C7C) N Tot =234, I=10 mM N Tot =251, I=40 mM, C TCEP =2mM

M13C7C

Au-M13C7C 3 Au-M13C7C 2 have been firstly broken from the one side and then all glassware (coverslips, glass slides, and cylindrical capillaries) has been washed with water, dried with azote flow, and after covered with the acid for 15-20 minutes. Cleaned with a sulfochromic acid glassware has been rinsed with a big amount of fresh distilled water (DW) and stored in a clean beaker covered with DW for a maximum of 12-14 hours. After this time glassware has been cleaned again with the sulfochromic acid as described above.

Before sample preparation clean glasses have been washed with 90% ethanol, a big amount of DW, and dried using azote flow. Glass cells have been composed of coverslip and glass slide with Optical microscopy observations. Differential interference contrast (DIC), fluorescence, polarizing and bright field (BF) microscopy images have been obtained using three different microscopes.

1. An inverted microscope Olympus IX71 equipped with a 100X oil-immersion objective (NA 1.4, UPLSAPO), a piezo device for setting different z-positions (P-721 PIFOC Piezo Flexure Objective Scanner, PI), ), proprietary 120W mercury vapor short-arc excitation source (X-cite120Q, Excelitas), motorized fluorescent cube (IX2-RFACA), fluorescence imaging camera (NEO sCMOS, Andor Technology) and dual emission image splitter (Optosplit II Andor). The microscope with all devices is operated by computer interface software (Meta-Morph, Molecular Devices). Thanks to the presence of the dual emission image splitter, this microscope allows us to observe at the same time two fields of view, corresponding to two fluorescence emission wavelengths, on to two halves of a sensor of an ultra-fast electron-multiplying camera (fig. 7). Piezo device for setting different z-positions helps to precisely measure sample thickness and record acquisitions through the sample with a defined step between the frames.

2. An upright microscope Olympus BX53 is equipped with a 100X oil-immersion objective (NA 1.3, UPlanFLN), proprietary 120W mercury vapor short-arc excitation source (X-cite120Q, Excelitas), and a fluorescence imaging camera (sCMOS, pco.edge 4.2 LT).

The microscope with all devices is operated by computer interface software (Micro Manager, MMStudio). Compared to the Olympus IX71, the camera sensor of this microscope is not divided into two parts, which allows us to record a twice bigger sample area in the same image.

3. An upright microscope Olympus BH-2 is equipped with 5x objective (NA=0.13, Neo SPlan 5 NIC) and color imaging camera (CVM-7 + , Clara Vision). This microscope has been used for taking low resolution polarizing microscopy images.

Small-angle X-ray scattering

Particle order within low ionic strength virus suspensions (Chapter 2) or formed mesoscopic structures under depletion attraction (Chapter 3 and 4) has been probed by small-angle X-ray scattering (SAXS). For this purpose, synchrotron irradiation has been used in order to obtain high enough resolution for low virus concentrations and high inter-rod distances at I=0.16mM [17], [18]. SAXS experiments for low ionic strength viral suspensions have been carried out at the ESRF-ID02 beamline (Grenoble, France) working at λ = 0.775 Å and with a sample to detector distance 5 m. For self-assembled structures formed from viral suspensions under effective attraction, the SOLEIL-SWING beamline (Saint-Aubin, France) working at a wavelength of λ = 0.826 Å and with a sample to detector distance of 2 m has been used. From SAXS patterns, azimuthal integration has been performed using SAXS Utilities (for patterns obtained with ESRF-ID02 beamline) or Foxtrot (SOLEIL-SWING beamline) software to provide the scattered intensity as a function of the scattering vector modulus, q. The patterns of the direct beams, which define the SAXS resolution can be found in Appendix I.

Preparation of Tris buffer solutions with millimolar ionic strength range

I=1/2([T + ]+[Cl -])=C s
HCl results in I=10 mM.

For experimental checking of ionic strength calculations, conductometry has been used as an independent method. Because the ionic conductivity and ionic strength are determined by the concentrations of ionic species present in the solution, these two characteristics are directly related.

Thus, by comparison of experimental (measured) and theoretical (calculated) ionic conductivity of the Tris/HCl buffers, we can conclude about the validity of the ionic strength calculations. The ionic conductivity (Ke) in general case determines as

𝐾 𝑒 = ∑ 𝑎 𝑁 𝐶 𝑁 𝜆 𝑁 0 𝑑 (1.2)
where 𝜆 𝑁 0 is the molar conductivity at infinite dilution regime for ionic specie N with concentration

[𝑁] and activity coefficient 𝑎 𝑁 , d is the cell constant of the conductometer.

The molar conductivity of the ionic specie N out of infinite dilution regime is defined as

𝛬 𝑁 = 𝑎 𝑁 𝜆 𝑁 0 (1.3) 𝛬 𝐴𝐵 = 𝛬 𝐴 + 𝛬 𝐵 (1.4)
Thus, using eq.1.2 with taking to account eq. 1.3 and 1.4, the conductivity of 10mM Tris/HCl buffer can be calculated as T + Cl -molar conductivity as a function of Tris/HCl buffer Ionic strength at pH=pKa [2].

𝐾 𝑒 (𝑇𝑟𝑖𝑠 10𝑚𝑀) = 𝐼 × 𝛬 𝑇 + 𝐶𝑙 - 𝑑 (1.
S.D. Klein and R.G. Bates in their work [19] experimentally determined molar conductivity of T + Cl -at 25 ᴼ С (fig. 3) as a function of its concentration (ionic strength). Thus, for 10mM buffer stock theoretical conductivity calculated with eq.1.5 is Ke theor (10mM)=0.97mS/cm which is equal to the experimentally measured conductivity of our 10 mM buffer stock and confirms that its ionic strength is the same as theoretically calculated one. This buffer stock has been used for the preparation of other Tris buffers by its dilution (for buffers with I<10mM) or by introducing NaCl (for buffer with I>10mM).

Preparation of the 0.16mM Tris/HCl buffer

As a first step, Tris/HCl buffer stock has been prepared as described above. Then, this buffer stock has been diluted using de-ionized water with dilution factor F=125 as described in previously reported protocol [20]. As a result, low ionic strength Tris/HCl buffer with analytical concentrations CTris=0.16 mM and CHCl=0.08mM has been obtained. It is known that for the Tris/HCl buffers with I<1mM CO2, which is present in the air in a big amount, can change bothits ionic strength and pH.

Thus, to stabilize the ionic strength and pH these buffers should be saturated with CO2 [20]. We have Chapter 1

saturated our low ionic strength Tris/HCl buffer with CO2 by its stirring in a glass flask covered by holed Parafilm at 4 ᴼ C during at least few days.

To calculate the ionic strength of the Tris/HCl buffer, the amount of dissolved CO2 should be taken to account as described [20]. For this propose, we assume that all processes are in equilibrium and during measurements, buffer does not change its composition. All measurements and calculations for low ionic strength buffer have been done at 25°C.

The concentration of dissolved and hydrated carbon dioxide (next H2CO3) is directly proportional to the gaseous CO2 partial pressure p CO 2 in the air,

[𝐻 2 𝐶𝑂 3 ] = K CO 2 p CO 2 (1.6)
where [N] is the concentration of a substance N in M=moles/L.

In the aqueous solution, H2CO3 dissociates on H + , HCO3 -and CO3 2-. Constants (eq. 1.7 and 1.8)

describe the dissociation processes.

𝐾 𝑐1 = [𝐻 + ]×[𝐻𝐶𝑂 3 -] [𝐻 2 𝐶𝑂 3 ] = 4.3 × 10 -7 [𝑀] pKa1 =6.37 (1.7
)

𝐾 𝑐2 = [𝐻 + ]×[𝐶𝑂 3 2-] [𝐻𝐶𝑂 3 -] = 5.6 × 10 -11 [𝑀] pKa2 =10.25 (1.8)
Denote unprotonated and protonated Tris as T and T + respectively. The dissociation constant for Tris is

𝐾 𝑇 = [𝐻 + ]×[𝑇] [𝑇 + ] = 7.9 × 10 -9 [𝑀] pKa =8.1 (1.9)
Note, that KT is strongly dependent on temperature.

Neglecting any un-dissociated HCl gives

[Cl -]=CHCl (1.10)
The dissociation constant for water is

𝐾 𝑤 = [𝐻 + ][𝑂𝐻 -] = 1 × 10 -14 [𝑀 2 ] (1.11)
Tris analytical concentration can be expressed as

[𝑇] + [𝑇 + ] = 𝐶 𝑇 (1.12)
Concentration of protons can be found from experimentally measured pH value as

[H + ] = 10 -𝑝𝐻 (1.13)
Concentrations of various ions can be rewritten in terms of [H + ]. In this case for calculations can be used the following equations

[OH -] = 𝐾 𝑤 [𝐻 + ] (1.14) [𝐻𝐶𝑂 3 -]= 𝐾 𝑐1 ×K CO 2 p CO 2 [𝐻 + ]
(1.15)

[𝐶𝑂 3 2-] = 𝐾 𝑐2 × [𝐻𝐶𝑂 3 -] [𝐻 + ] (1.16) [𝑇 + ] = 𝐶 𝑇 [𝐻 + ] [𝐻 + ] + 𝐾 𝑇
(1.17)

6.3 6.4 6.5 6.6 6.7 6.8 6.9 From the neutrality condition of the total ionic species in the solution

[𝐻𝐶𝑂 3 -] + 2[𝐶𝑂 3 2-] + [𝑂𝐻 -] + [Cl -]=[𝑇 + ]+ [𝐻 + ] (1.18)
After taking to account eq.1.6-1.18 the amount of [H + ] can be found by solving the following equation [20] [

𝐻 + ] 4 + [𝐻 + ] 3 (𝐶 𝑇 + 𝐶 𝐻𝐶𝑙 + 𝐾 𝑇 ) -[𝐻 + ] 2 (𝐾 𝑤 + 𝐶 𝐻𝐶𝑙 𝐾 𝑇 ) -[𝐻 + ]𝐾 𝑤 𝐾 𝑇 = 𝐾 𝐶1 𝐾 𝐶𝑂 2 𝑝 𝐶𝑂 2 {[𝐻 + ] 2 + [𝐻 + ](2𝐾 𝐶2 + 𝐾 𝑇 ) + 2𝐾 𝐶2 𝐾 𝑇 } (1.19)
Then, ionic strength is equal to

𝐼 = 1 2 ∑ 𝐶 𝑖 𝑧 𝑖 = 1 2 ([𝐻 + ] + [𝑂𝐻 -] + [𝐶𝑙 -] + [𝑇 + ] + [𝐻𝐶𝑂 3 -] + 4[𝐶𝑂 3 2-]) 𝑛 𝑖 (1.20)
The concentration of dissolved and hydrated carbon dioxide (eq.1.6) in the low ionic strength buffer has been calculated for wide range of pH using eq.1.19 and the results are presented in the figure 9.

For experimentally obtained pH at 6.5 [𝐇𝐂𝐎 𝟑 ] = 𝐊 𝐂𝐎 𝟐 𝐩 𝐂𝐎 𝟐 = 𝟓. 𝟔 × 𝟏𝟎 -𝟓 [𝐌] and this value will be used in following calculations of the ionic strength. So, taking to account concentrations of each ionic species in the low ionic strength buffer (table 1.2), we can calculate the ionic strength with eq.1.20. For prepared buffer with pH 6.5 I= 𝟎. 𝟏𝟔[𝐦𝐌]. Similar to the Tris/HCl stock buffer solution, the calculations done for determining the ionic strength of the low ionic strength buffer can be checked experimentally by measuring conductivity of this buffer. Thus, theoretically expected conductivity of buffer solution can be calculated using equation 1.2. With assumption that for ions in low ionic strength buffer 𝑎 𝑁 = 1, meaning that we are near to the infinite dilution regime, conductivity can be rewritten as

𝐾 𝑒 = ∑ 𝐶 𝑁 𝜆 𝑁 0 𝑑 (1.21)
Thus, for our low ionic strength buffer conductivity can be calculated as

𝐾 𝑒 = [𝐻 + ] × 𝜆 𝐻 + 0 + [𝑂𝐻 -] × 𝜆 𝑂𝐻 - 0 + [𝐶𝑙 -] × 𝜆 𝐶𝑙 - 0 + [𝑇 + ] × 𝜆 𝑇 + 0 + [𝐻𝐶𝑂 3 -] × 𝜆 𝐻𝐶𝑂 3 - 0 + [𝐶𝑂 3 2-] × 𝜆 𝐶𝑂 3 2- 0 𝑑 (1.22)
Using ion concentrations and their molar conductivities from table 1 . The difference between measured and calculated conductivities is within an error for the used method which proves the validity of ionic strength calculations.

Preparation of samples with depletion interactions between particles

Preparation of polymer stock solutions. To induce attraction between the particles, nonadsorbing polymer should be added to colloidal suspensions. For this purpose, a stock solution of the polymer with a target average molecular weight has been prepared. Thus, polymer has been dissolved in the same buffer solution, used for colloidal suspensions to obtain polymer concentration from 80 to 200mg/ml, depending on the experiment. To prepare solutions with lower polymer concentrations compared to the polymer stock solution, this stock solution has been diluted with the same buffer.

Preparation of virus/polymer mixtures. For the preparation of virus/polymer aqueous mixtures, viruses and polymer dissolved in the same buffer solution have been used (called virus (hybrid virus-based colloid) stock suspension and polymer stock solution). Aliquots of the stock solutions with concentrations Cstock(virus) and Cstock(polymer) have been placed in Eppendorf tube.

The volumes of the aliquots have been measured by mass (ma) with the assumption that the densities of our stocks are equal to the water density. Thus, the concentrations of viruses and polymer in prepared samples have been calculated as

𝐶(𝑣𝑖𝑟𝑢𝑠) = 𝐶 𝑠𝑡𝑜𝑐𝑘 (𝑣𝑖𝑟𝑢𝑠) × 𝑚 𝑎 (𝑣𝑖𝑟𝑢𝑠) 𝑚 𝑡𝑜𝑡𝑎𝑙 (1.23) 𝐶(𝑝𝑜𝑙𝑦𝑚𝑒𝑟) = 𝐶 𝑠𝑡𝑜𝑐𝑘 (𝑝𝑜𝑙𝑦𝑚𝑒𝑟) × 𝑚 𝑎 (𝑝𝑜𝑙𝑦𝑚𝑒𝑟) 𝑚 𝑡𝑜𝑡𝑎𝑙
During aliquot mass measurements, it is important to avoid contact between the polymer and virus stocks inside the Eppendorf tube, which can induce the gradient of depletion forces. The homogenization of the polymer and virus concentrations inside prepared samples has been performed using a vortex mixer. After the mixture preparation, they have been immediately injected into homemade optical microscopy cells and cylindrical capillaries for their followed investigations.

1.10.

Introduction

The self-organization of colloidal particles is a subject of intensive debates for the past few decades [1]- [5]. Forces, which drive a colloidal organization, could have different origins, such as the formation of hydrogen bonds, hydrophobic-hydrophilic or electrostatic interactions. In the case of colloidal particles, when interactions between colloids are near to the purely repulsive (hard-core), particle self-organization can be driven by entropy alone. Thus, monodisperse spheres crystallize into colloidal lattices from their liquid suspensions, if the particle concentration is above a given threshold [1], [4]. Introducing a shape anisotropy into hard-core systems results in more complex phase behavior, compared to suspensions of isotopically shaped colloids. For this reason, colloidal rods, as one of the simplest examples of anisotropic particles, have drawn a lot of attention. Experimentally, the phase behavior was extensively investigated for various rod-like colloidal suspensions, such as inorganic rod-shaped crystals (vanadium pentoxide, iron oxyhydroxide, tungstic acid) [6], silica rods [7], and cellulose nanocrystals [8]. All these stiff colloids are intrinsically highly polydisperse in size and their monodisperse fractions can be obtained after long synthesis and/or purification procedures [6]- [9].

In contrast to inorganic anisotropic colloids, biological rod-shaped particles have many advantages. Thus, different strains of filamentous viruses, such as tobacco mosaic virus (TMV), fd or M13 viruses, were widely used as a model system of stiff or semiflexible rod-shaped colloids for investigations on liquid crystals. Main features of these biological systems lie in the fact that viruses are highly monodisperse charged filaments with a high aspect ratio (from ~17 for TMV to ~140 for M13 virus). As described in Chapter 1, fd and M13 bacteriophages can be easily produced in a big amount by replication within bacteria Escherichia coli. Due to their micrometer length, viruses can be detected at the single-particle level using optical microscopy methods [10]. These charged rodlike colloids, whose interactions are predominantly repulsive [11], were shown to behave nearly as hard rods, by defining an effective diameter, which accounts for their electrostatic repulsion at different ionic strengths [12]. The effective diameter (eq.0.7) which extends the concept of hard to charged particles will be discussed in more details below. The biological origin of these particles limits their stability in organic solvents [13], but in aqueous media they show to be highly stable.

Thereby, phase behavior of aqueous viral suspensions was studied both, theoretically via computer simulations and experimentally, as a function of the virus volume fraction at a given ionic strength. Driven by a gain in excluded volume (i.e., by a gain in entropy), filamentous viruses, considered as hard impenetrable rods, self-organize into plethora mesophases with increasing rod concentration. As described in Chapter 0, suspensions of filamentous bacteriophages at ionic strengths higher than 5 mM have rich phase behavior. Were shown that from the isotropic liquid, with increasing virus concentration they self-assemble into (Chiral) Nematic (N (*) ), Smectic (Sm), and not expected from simulation points of view [14], [15] Columnar (Col) mesophases [5], [11], [12], [16]- [18]. In the N mesophase viruses exhibit liquid-like organization with the same average orientation (also called director) of rods, while for the N* phase the director exhibits helical rotation along a

given axis [16]. As mentioned in paragraph 0.3.1, in Sm phases the particle density is periodic in one dimension parallel to the long rod axis (fig. 1 b), while interparticle correlations perpendicular to this axis are short-ranged for the Smectic-A (SmA) or long-ranged for the Smectic-B (SmB) phases, corresponding to 1D or 2D positional order [11], [19]. In the Col mesophase rod-like viruses are confined to liquid-like columns which, in turn, are organized in a 2D hexagonal arrays [11]. The change of the positional order dimensionality strongly affects the particle dynamics within the different mesophases. Thus, for self-diffusion along the main virus axis (parallel diffusion) to take place within a Sm phase, the rods jump between adjacent smectic layers, overcoming an energy barrier related to the lamellar organization, called smectic ordering potential (fig. 1 c). This hoppingtype diffusion was detected for the SmA phase [20] with full-jumps of the particles. Similar dynamic behavior with full-and half-jumps of the viruses was detected in the Col phase, but the jump frequency was more than 2 orders of magnitudes lower compared to the particle motion within SmA phase [21]. For the SmB phase with its 2D positional order, a lack of significant dynamics (i.e. frozen or arrested dynamics) in all directions was observed. As predicted by Onsager, the I/N phase transition of infinitely long hard rods is expected at ф 𝐼/𝑁 ≈ 4 𝐷 𝐿 [22]. For charged viral particles the effective diameter (eq. 0.7) has to be introduced to extend the concept of hard to charged particles [12]. D eff is related to the Debye screening distance к -1 (eq. 0.3) and, as a result, is dependent on the ionic strength I, defined as follows

𝐼 = 1 2 ∑ 𝑛 𝑖 𝑍 𝑖 2 𝑖 (2.1)
with 𝑛 𝑖 the molar concentration of the i th mobile microion inside the suspension and 𝑍 𝑖 the charge number of this ion.

Consequently, the virus volume fraction at which transitions between different mesophases can be

observed ф = 𝐶 * 𝑣 𝑁 𝐴 𝜋𝐿𝐷 2 4
(where 𝐶 * 𝑣 is the molar concentration of viruses with the length L and bare diameter D) is highly dependent on the ionic composition of suspensions, which was evidenced experimentally [12].

Since the ionic strength of virus suspensions has a crucial influence on the effective particle diameter as well as on its effective aspect ratio ( 𝐿 𝐷 𝑒𝑓𝑓 ⁄ ) [12], [23], a strong decrease of the ionic strength could lead to deviations from theoretical predictions made for rods with high aspect ratios.

K. Kang and J. K. G. Dhont in their recent work have reported that at very low ionic strength (I~0.16mM) with increasing their concentration fd viruses exhibit a second-order glass transition within the N suspensions (fig. 2 a) [24]- [26]. In obtained glasses, the virus organization remains unchanged keeping the same order as in the N liquid crystalline phase, but virus dynamics differ from the one detected within N mesophase. Precisely, the dynamic particle arrest on the experimental timescale is expected for colloidal particles in their glassy state, which results in the absence of the significant self-diffusion [27]. Obtained viral glass is described as a Wigner glass (a phase with quasilong-range structural order whose formation is related to the existence of long-range electrostatic interactions [26], [28]) in which each rod is caged by the thick electrical double layers of its neighbors.

A glass state of colloidal rods is sketched in figure 2b, where the blue shells indicate the extent of the electric double layers around grey rod-shaped colloids. Experimentally, the particle dynamics within viral glasses have been probed by dynamic light scattering (DLS) [24], [25], and results show a lack of significant motion (over distances larger or comparable to the rod length) for the virus concentrations Cv>11.1 mg/ml (fig. 2 d). At the same time, frozen domain texture within the glass state of the viruses has been detected by low-resolution polarizing microscopy. microscopy images of the corresponding phase (state) textures [24], [25]. Ensemble averaged DLS correlation functions for various fd concentrations at 0.16mM ionic strength (d) [24]. Numerical values indicate the virus concentration in mg/ml.

Since the lack of significant self-diffusion and birefringent texture of the suspensions, observed with low-resolution microscopy (fig. 2), are similar for both -Glass state and Smectic phase, and with taking to account that particle order within viral glasses has not been probed, the probability of finding a N * /Sm phase transition instead of a glass transition can not be excluded. Consequently,

to give the answer on the question "Is it a Glass or a Phase transition that occurs in very low ionic strength viral suspensions?", deeper investigations, including probing particle order via SAXS analysis as well as detecting the existence of lamellar smectic structure via high-resolution optical microscopy should be performed.

Here we will present direct evidences of the N * /SmB phase transition obtained in suspensions of fd viruses at 0.16mM ionic strength. The characterization of virus dispersions shows the formation of the one-virus-length lamellar periodicity (smectic layers) for the range of particle concentrations between 6.4 and 15.1 mg/ml. In agreement with DLS results obtained for "glassy" viral suspensions [24], [25], rod dynamics probed by single-particle tracking using video fluorescence microscopy are nearly frozen for all smectic range. The formation of the SmB phase with its hexagonal long-range positional virus organization within the layers [12] has been directly proved via synchrotron SAXS experiments. The influence of the equilibration process on the virus phase behavior at low ionic strength will be finally discussed.

Theoretical considerations on counterion condensation

In order to revise the system investigated by K. Kang and J. K. G. Dhont [24]- [26], in our research the same fd virus strain, called fd-wt, has been used as a model system of monodisperse colloidal rods. It is a very long (L=880 nm) highly charged semiflexible filament with a bar diameter D=6.6 nm. Its capsid consists of 2700 identical major coat proteins, which form about 99% of total protein mass in the virus [29]. The fd virus charge density is pH-dependent, and in the case of a very low ionic strength medium with pH 6.5 it is 3e/protein (fig. 3) [29], which results in the total negative virus charge Zv (pH 6.5)=8100. Thus, fd-wt can be considered as a polyelectrolyte with the linear charge density of λ v = Z v L ⁄ = 9.2 eq/nm. It is well known that for reducing their charge, polyelectrolytes could condense their counterions on the polymer chain. This phenomenon has led to the concept of counterion condensation and was firstly introduced by Manning [30]. According to his theory, when an infinitely long linear polyelectrolyte has the spacing between two charges lower than the Bjerrum length, defined by eq. 2.2, i.e. for polyelectrolytes with a linear charge density λ > 1/𝑙 𝑏 (λ > 1.4 eq/nm for polyelectrolytes in their water solutions at room temperature), the counterion condensation occurs leading to a reduction of the particle charge, such as in suspensions of fd viruses.

𝑙 𝑏 = 𝑒 2 4𝜋𝜀 𝑟 𝜀 0 𝑘 𝐵 𝑇 (2.2)
where lb is the Bjerrum length with the elementary charge 𝑒, the relative dielectric constant of the medium 𝜀 𝑟 , the vacuum permittivity 𝜀 0 , the Boltzmann constant 𝑘 𝐵 and the absolute temperature 𝑇 (𝑙 𝑏 ~0.71 nm in water at room temperature).

In this section, we will quantitatively characterize the effect of the counterion condensation on the ionic composition of the virus suspensions using previously developed models. According to the Manning theory, inside polyelectrolyte suspensions, a part of counterions is condensed on a polymer chain (condensed counterions) while another part freely migrates to a surrounding solution (free counterions). Free ions (counterions and ions of added salt) contribute to the total ionic strength of the suspension, which in terms of molarity can be expressed for monovalent microions by

𝐼 = 1 2 𝐶 𝑐 + 𝐶 𝑠 (2.3)
where 𝐶 𝑠 is the concentration of added salt and 𝐶 𝑐 is the concentration of free counterions, which can be calculated as Since for fd viruses the coat protein dissociation, as well as the dissociation of any other weak acids or bases, is pH-dependent, the virus charge is varying with changing pH. Thus, with the pH increasing from 6.5 to 8.1, the total negative charge of viruses increases to Zv(pH 8.1)= 9180 and by decreasing pH to 4.2 it reaches the isoelectric point with Zv(pH 4.2)= 0 (fig. 3) [29]. These pH changes strongly affect the fraction of free counterions as well as the total ionic strength of the suspension (eq. 2.3-2.4). To fix the concentration of added salt and pH of our experimental system, the buffering solution with fixed pH should be used as a medium for fd-wt suspensions. This solution consists of a weak acid with its conjugate base and keeps pH nearly the same value after adding bases or acids in a small amount compared to active buffer component (conjugate acid/base pair) concentrations.

𝐶 𝑐 = 𝑄 × 𝐶 𝑣 𝑀 𝑣 × 𝑍 𝑣 (2.
Following previous investigations [24]- [26],in our experiments the low ionic strength buffer with pH 6.5 and the ionic strength Ibuffer=0.16mM has been used, which results in the Debye screening length of к -1 =27 nm. This buffer has been prepared using the dilution protocol [31] and for more information on its preparation see Chapter 1 of this thesis. Consequently, all our future calculations will be referred to fd-wt viruses at pH 6.5.

The fraction of free counterions depends on boththe concentration of added salt, since it affects the Debye screening length (i.e. the effective diameter of the particle [eq. 0.7]) and the virus concentration. In the infinite dilution limit, for charged long rods (𝐿 ≫ 𝑟) with a vanishingly small radius (κ0r ≪1, with κ0 -1 the Debye screening length associated with added salt Cs) the fraction of free ions can be calculated accordingly to the primitive Manning model [30] 𝑄 0 (𝑀𝑎𝑛𝑛𝑖𝑛𝑔) = 1 𝑙 𝑏 × λ v (2.5) which for fd-wt in water at pH 6.5 and room temperature (λ v =9.2 eq/nm, 𝑙 𝑏 =0.71 nm) results in Q0(Manning)=0. 15. The approximations used in the primitive model are valid only for the salt-free suspension of infinitely long needle-like objects at a concentration of C→0. Later Manning developed an analytical approach for different geometries of polyelectrolytes and charged colloids, where the fraction of free counterions is calculated from the balance between enthalpic electrostatic binding of counterions and their dissociation entropy [32]. Accordingly, for infinitely long and thin cylinders with к0r<<1, the fraction of free counterions is the same as in the case of Manning's primitive model.

When the relative thickness of cylinders increases due to the Debye screening length decreasing (к0r~1), the fraction of free counterions can be defined as follows [12], [32]

𝑄(𝑀𝑎𝑛𝑛𝑖𝑛𝑔) = - 1 𝑙 𝑏 λ v ln ( к 0 λ v ) × к 0 𝑟 × 𝐾 1 (к 0 𝑟) 𝐾 0 (к 0 𝑟) (2.6)
where 𝐾 0 (𝑥) and 𝐾 1 (𝑥) are modified Bessel functions of the second kind.

In our specific case (Ibuffer~Cs=0.16mM), the Debye screening length associated with added salt Cs is к 0 -1 =27nm [24], which leads to к 0 𝑟 = 0.12. Thus, deviations from both cases -Manning theories for thick (к 0 𝑟~1) and thin (к 0 𝑟 ≪ 1) cylinders are expected. At the thick cylinder limit, calculated with eq. 2.6 the fraction of free counterions is around twice higher (Q(Manning)=0.38) compared to the thin cylinder limit (Q0(Manning)=0.15). Moreover, this new model allows us to take into account the amount of added salt in the polyelectrolyte suspension, but still, it keeps the main restriction of the Manning theoryit is applicable only for infinitely diluted suspensions.

To take into consideration both particle and added salt concentrations, a mean-field Poisson-Boltzmann theory within a cell model [33], [34] should be used. In this model, a charged rod is enclosed in a cylindrical cell together with its counterions and it replaces the colloidal suspension containing many charged particles with a simpler one-particle system. A solution of the nonlinear Poisson-Boltzmann equation [35] provides the number of free counterions (Cc), which can be taken to account for the precise renormalization of the total ionic strength using eq.2.3. For simplifying this theory, the analytical expressions for the Poisson-Boltzmann cell model were derived from calculations of the effective polyion charge by Trizac et al. [36]. Thus, for infinitely long rods, assuming that the amount of added salt in 0.16mM Tris buffer is negligible compared to the amount of fd-wt counterions (no added salt limit), the effective virus charge (Zeff), as well as the fraction of free counterions in viral suspensions with various rod concentrations, can be calculated using eq. 2.7 and 2.8

𝜆 𝑒𝑓𝑓 = 3 2 ⁄ + 8ф + 2√6ф + 16ф 2 𝑙 𝑏 (2.7) 𝑄 = 𝜆 𝑒𝑓𝑓 𝜆 (2.8)
where ф =

С 𝑣 ×𝑁 𝐴 𝑀 𝑣 × 𝜋×𝐿×𝐷 2 4
is the virus volume fraction.

Trizac's asymptotic solution of the Poisson-Boltzmann equation becomes inaccurate for κeffr<1(κeff is the effective Debye screening length associated with the total amount of microions Cs+ Cc), which implies that the calculated Q(Trizac) becomes less reliable in the salt-free case for very small virus concentrations [36].

 C c (mM)  Q Figure 4
illustrates the comparison of the calculated free counterion fractions and corresponding free counterion concentrations using Trizac's and both Manning's models for fd-wt dispersed in 0.16mM Tris buffer at pH 6.5. Our calculations show that with increasing virus concentration, concentrations of uncondensed counterions (C c ) rise, and at C virus ~1-2 mg/ml, C c becomes comparable with the concentration of added salt (Ibuffer). Firstly, it affects the effective ionic strength of the suspension defined by eq. 2.3 (a strong increase of the ionic strength when the virus concentration increasing), and, secondly, the buffer ability to fix pH of the suspension (a buffer solution can fix pH only if it (i.e. added salt) is in excess compared to other components of the system). Since the virus charge, i.e. counterion condensation and related with it total ionic strength (eq.2.3-2.4), are pH-dependent [29], in order to fix boththe suspension ionic strength and virus charge (pH), dialysis of dispersions should be done for each virus concentration at which Cc≥Ibuffer.

Preparation of virus suspension with 0.16mM ionic strength

As mentioned in the previous paragraph, suspensions of the semiflexible fd-wt viruses have been selected as an experimental system in this chapter. To visualize virus behavior at the singleparticle level, body-labeled fd-wt-Alexa448 have been added to the suspensions in the amount of 1 labeled particle per 10 5 raw ones. Here we have used the same ionic conditions as K. Kang and J.K.G.

Dhont in their experiments on the viral "glass" transition (Tris/HCl buffer with I=0.16mM and pH 6.5 as a dispersion medium) [24], [25]. Since at the range of virus concentrations investigated in this research (Cfd-wt>2 mg/ml) used as a medium buffer is not in excess compared to the concentration of counterions associated with dispersed viruses (Ibuffer <Сс, fig. 4), even at small variations of the dispersion ionic composition, this buffer is not able to stabilize the pH of fd-wt suspensions. That is, the Tris/HCl mixture loses its buffering properties in the presence of viruses. To control the pH and ionic strength of our viral dispersions in such low ionic strength "buffer", suspensions at each virus concentration have to be dialyzed against a big reservoir (Vreservoir>>Vsuspension, where V is the volume of the reservoir and virus suspension, respectively) of this "buffer". The classical ways of the suspensions preparations, either dilution with buffer or concentration by centrifugation may affect the ionic conditions of the 0.16mM Tris/HCl "buffer" (i.e. virus phase behavior).

The "buffer" solution has been prepared using the dilution protocol [31] with additional experimental checking of the ionic strength using conductometry, as described in Chapter 1. For the virus dialysis Float-A-Lyzer G2 dialysis devices or Spectra/Por ® 7 pre-treated regenerated cellulose dialysis tubes with the pore size of 8-10 kDa, purchased from the Spectrum Lab, have been used. At least 0.3 ml of the suspension have been dialyzed in one device or 1.0 ml in one dialysis tube. At the end of the dialysis, we expect to equilibrate our viral suspensions with the dialysis bath and to establish the equilibrium, also called Donnan equilibrium. It can be achieved when electrochemical potentials, as well as osmotic pressures from both sides of a semipermeable membrane (i.e. for virus suspension and dialysis bath), become equal tanks to migration of microions and water molecules [37], [38]. In our case, suspension volumes have not been fixed and their dialysis against the reservoir with lower osmotic pressure (Пbuffer<Пsuspension) results in suspension volume increasing (i.e.

decreasing virus concentration and proportional to it via П=𝑅𝑇𝑐 𝑖 suspension osmotic pressure, where ci is a molar concentration of each component of the system [38]). This effect is often called osmosis.

Since the osmotic pressure of the dialysis baths has been fixed by using 0.16mM "buffer" (Пbuffer=const), the osmotic pressures of the equilibrated suspension (i.e. the related to them virus concentrations or volumes) should reach a constant value at the equilibrium. Thus, to experimentally identify the equilibrium point, the virus concentration has been tracked with time by measuring the phage absorption at λmax=269 nm [16] (direct tracking) or by measuring the suspension height (related to the concentration) inside cylindrical-shaped devices (indirect tracking). Note that height measurements were possible only for suspensions dialyzed inside dialysis devices and they have been done with a ruler. Indirect tracking helps to avoid undesired contaminations of the samples with any impurities, as well as their accident dilution by introducing the buffer from the dialysis bath.

Therefore, it minimizes any external effects on the process of the suspension equilibration during its dialysis. Suspension height inside the dialysis device can be easily renormalized to the virus concentration using the simple linear equation, which has been obtained as follows.

The suspension height inside the dialysis device has been measured as a distance between the device bottom and the suspension meniscus (fig. 5). To find the correspondence between the

Results and discussions

For the investigation of fd-wt suspensions at very low ionic strength, we have performed experiments, which allow us to follow virus self-organization into various mesophases. Thus, the suspension structure (lamellar or not), single-particle dynamics, as well as particle order within viral suspensions have been studied after their short-term dialysis (which was done for reproducing K.

Kang's and J.K.G. Dhont's experimental system [24]) and after their complete equilibration by longterm dialysis. Here we will discuss the results of our studies as well as the effect of the equilibration process on the fd-wt behavior.

2.4.1.

Phase diagram after short-term dialysis

To revise K. Kang's and J.K.G. Dhont's experimental system [24], viral suspensions have been dialyzed against 0.16mM Tris/HCl "buffer". Since the amount of counterions associated with viruses is in excess compared to the "buffer" ionic strength (see section 2.2. of this chapter), dialysis with a duration of 3-7 days has been caried out for each virus concentration. Thus, suspensions have been dialyzed against the dialysis bath (i.e. reservoir) of 0.16mM "buffer" with Vreservoir/Vsuspension>200. Considering that the buffering capacity of 0.16 mM "buffer" is very low, to minimize any deviations in the ionic composition of the dialysis bath it has been replaced by the fresh one once per 1-2 days. Thus, the virus dispersion with the initial concentration C in (fd-wt)=32.8 mg/ml has been dialyzed during 7 days against 0.16mM Tris/HCl "buffer". This suspension has been inspected via Differential Interference Contrast (DIC) microscopy before the beginning of its dialysis and after its end (fig. 6 a-b). After one week of the dialysis, a strong decrease of the virus concentration takes place due to the osmosis effect (see paragraph 2.3) and the highest reached concentration is C(fd-wt)=15.8 mg/ml. Suspensions with lower concentrations have been obtained by dilution of already dialyzed suspensions (by adding a small amount of 0.16mM "buffer") with their following re-dialysis for at least 3 days. In this way, suspensions with the virus concentration range from 15.8 to 2.2 mg/ml have been prepared and studied.

For this purpose high-resolution DIC microscopy and low-resolution polarizing microscopy have been used. The formation of the Sm phase lamellar structure has been detected via DIC microscopy (fig. 6 b) for the suspensions with C(fd-wt)≥6.1 mg/ml, which contradicts resent K. Kang's and J.K.G. Dhont's research focused on the viral glasses [24], [25], [39]. At 0.16mM ionic strength, smectic layers appear with lower contrast between the virus-rich (smectic layer) and virus-poor (interlayer spacing) regions compared to layers observed at I>5mM, which raises difficulties in their detection via optical microscopy. This decrease of the contrast can be explained by the difference in virus concentrations typical for the Sm phase formed at millimolar (I>5 mM) and sub-millimolar (such as 0.16mM ) ionic strengths. For example, at I=110mM the Sm phase was observed for suspensions with C(fd-wt)>175 mg/ml [12], which is more than 10 times higher compared to the virus concentration in our system. Thus, the difference between the refractive indexes of viral layers and interlayer spacing becomes lower with decreasing virus concentration, and it reduces the contrast. In spite of this, the smectic texture for low ionic strength suspensions has been detected for the virus concentrations between 6.1 and 15.8 mg/ml. Its periodicity, called layer spacing (LLayer), has been measured as an average value over at least 10 Fast Fourier Transformation (FFT) of the DIC microscopy images taken at different regions of the optical microscopy cells.

For suspensions with C(fd-wt)<6.1 mg/ml typical for the N * phase fingerprint texture has been observed via polarizing microscopy. Corresponding full turn of the virus director named Cholesteric pitch (P) has been determined as a distance, which consists of two bright and two black lines of the fingerprint texture (light green arrow in fig. 6 f). The pitch has been derived as an average of 10 or more measurements done along the full length of the same cylindrical capillary filled with virus suspension. Obtained results confirmed earlier findings that both, the smectic layer spacing (LLayer) [12] and Cholesteric pitch (P) [16] of fd-wt increase with decreasing virus concertation at fixed ionic strength (fig. 7). Besides, bulk suspensions with virus concentrations C(fd-wt) ≥6.1 mg/ml, as well as glass cells and cylindrical capillaries filled with these suspensions are iridescent after their illumination with visible light (fig. 6 c), which again can sing about the formation of periodic smectic layers. The time evolution of the sample textures has been followed via polarizing and DIC microscopy. For this purpose samples have been observed 15 minutes, 1, 7, 14, and 21 days after their preparation. Similar to the "glassy" virus suspensions which relax to the N * phase [24], [25] with time, the periodic smectic structure of our fd-wt suspensions with C(fd-wt)<15.8 mg/ml are also metastable. Thus, over time, iridescent suspensions with the lamellar texture evolve into the N * phase with its typical fingerprint texture (fig. 6 e,f). Phase diagrams as functions of the virus concentration have been obtained at different elapsed times after optical microscopy samples preparation. One day after preparation (t=1, fig. 7 a), the formation of the N * phase has been observed for both, glass cells and cylindrical capillaries filled with suspensions with C(fd-wt)< 6.1 mg/ml. At C(fd-wt)= 2.0 mg/ml, the I/N * phase coexistence has been detected. All suspensions with C(fd-wt)≥ 6.1 mg/ml form the lamellar Sm phase.

The experimental results obtained at 7, 14, and 21 days after sample preparation are show in figure 7 (b-c). Thus, at t=7 days for the virus concentrations of 6.5 mg/ml≤C(fd-wt)≤7.5 mg/ml inconsistency in the phase behavior for different samples takes place (fig. 7 b). Within this concentration range, the Sm phase has been observed for 100 μm thick glass cells, while birefringent cylindrical capillaries, which were iridescent at t=0-1 day (fig. 6 c-d), have evolved to the N * phase with its typical fingerprint texture (fig. 6 f). A gain of the elapsed time after sample preparation increases this inconsistency region (fig. 7) with an evolution of the suspension at I/N * phase coexistence to the Isotropic liquid at C(fd-wt)=2.0 mg/ml.

Assuming that with time the virus concentration stays constant for all prepared samples, their evolution may be related to the relaxation of the virus suspensions, which may be not at the equilibrium after short-term dialysis. Donnan equilibrium can be reached by proceeding the longterm, extensive dialysis of viral colloids with experimental determination of the equilibrium (see paragraph 2.3). The long-term dialysis will be discussed in more detail in the following section.

2.4.2.

Phase diagram for equilibrated suspension by long-term dialysis

The long-term dialysis of viral suspensions against a big reservoir of 0.16mM Tris/HCl "buffer" (Vreservoir/Vsuspension>200) has been done using dialysis devices with indirect tracking of the particle concentrations. Accordingly, fd-wt suspensions with various initial virus concentrations (Cin)

have been dialyzed with the periodic checking of their heights inside dialysis devices, and therefore rod concentrations (eq. 2.10). When suspension heights have reached a plateau, meaning that the particle concentrations stay constants during dialysis and the osmotic pressures outside and inside of the dialysis devices are equal, virus suspensions become fully equilibrated [38]. Since the osmotic pressure of dialysis baths has been fixed by using 0.16mM "buffer" (Пbuffer=const), in agreement with theoretical predictions, the particle concentrations for equilibrated suspensions (Ceq) do not depend on their initial concentrations Cin and at the end of the dialysis Ceq(fd-wt)=6.8±0.6 mg/ml (error bar indicates data dispersion from the averaged value for all virus suspensions dialyzed against 0.16mM Tris/HCl "buffer" in different devices). Our experiments show that it takes more time to equilibrate viruses with higher Cin. Thus, for devices containing suspensions with Cin(fd-wt)=15.4 mg/ml equilibration takes around 40 days, while for the Cin(fd-wt)=40.3 mg/ml this process is more than 3 times longer (fig. 8). To obtain suspensions with virus concentrations higher than C eq (fd-wt), particles have been concentrated using 15ml Amicon ® Ultra centrifugal regenerated cellulose filters with an average pore size of 30kDa (fig. 9). For this purpose, the equilibrated virus suspension has been placed into a prewashed with 0.16mM Tris/HCl "buffer" centrifugal filter and concentrated by several centrifugations of 2000g for 2 minutes. The suspension has been homogenized using a vortex mixer after each run.

The conductivity of the collected filtrate (Ke(filtrate)), which was separated from the equilibrated fd-wt suspension and only contains the "buffer" without viral colloids, has been measured at 25 ᴼ C.

The obtained results shows that Ke(filtrate) is 15% higher, compared to Ke(buffer) measured at the same conditions (Ke(filtrate)=16.8 μS/cm and Ke(buffer)=14.6 μS/cm). It evidences that the effective ionic strength for equilibrated suspensions has been within 15% deviation from 0.16mM. Brownian motion within smectic layers can be proved by the comparison of its dynamics with the dynamics of the fully immobile particle (fig. 12 a). These dynamic properties argue the formation of the SmB phase in low ionic strength viral suspensions [12]. In the N * phase viruses are highly diffusive, compared to the SmB phase (fig. 10 d). These changes of fd-wt dynamics from nearly frozen to diffusive ones together with the changes of the lamellar structure on the fingerprint texture are first signs of the N * /SmB phase transition at I=0.16mM, which contradicts the claim of the glass transition in the N phase of the same system recently reported by J.K.G Dhont and K. Kang [24], [25]. To prove the existence of the SmB phase with long-range positional order and hexagonal virus organization within the layers in the 0.16mM fd-wt suspensions, particle order has been directly probed via SAXS and the results of this experiment will be discussed below.

2.4.3.

Small angle X-ray scattering experiment on fd-wt suspension at I=0.16 mM

Optical iridescence, lamellar periodic structure, and nearly frozen particle dynamics evidence the SmB phase formation in fd-wt suspensions but do not provide direct proofs of expected long-range positional order of viruses within smectic layers. Since virus suspensions at very low ionic strengths correspond to relatively low particle concentrations and high inter-rod distances (for I=0.16mM the Debye screening length related with added salt is к0 -1 =27nm), using synchrotron radiation at small angles with high resolution is requested to probe fd virus order. Thus, SAXS experiments have been carried out at the ESRF-ID02 beamline (λ = 0.775 Å, with a sample to detector distance 5 m). The range of investigated scattering vectors q corresponds to interaxial distances between two viruses up to a few hundred nm. The patterns for suspensions with C(fd-wt)≥6.4±0.1 mg/ml display several Bragg peaks, whose positions in reciprocal space relative to the position of the first peak are 1: √3: √4: √7 (fig. 11 c), which is the typical signature of hexagonal order in the plane normal to the rod long axis [11].

Moreover, the pattern obtained for the suspension with C(fd-wt)=8.2 mg/ml (fig. 11 a) shows nearly the existence of the six-fold symmetry. For suspensions with C(fd-wt)<6.4±0.1 mg/ml only one peak has been detected, which signs the lack of long-range positional order at these concentrations.

X-ray scattering patterns with their azimuthally integrated radial profiles have been obtained

for the range of virus concentrations between 2.8 and 8.5 mg/ml. The analysis of q100 peaks, Assuming local hexagonal order around the viruses, these data have been numerically fitted using a power law 𝑞 100 = 𝜂 × 𝐶 1/2 with the pre-factor of the swelling law 𝜂 (for infinitely long hexagonally packed rods calculated pre-factor is 𝜂 = 3.84 × 10 -2 with q in nm -1 and C in mg/ml) and the exponent 1/2 as a signature of a 2D swelling, which is expected in our system because of the virus high aspect ratio (L/D > 1) [41]. Using the position of q100 Bragg peak, the distance between centers of two neighbor particles calculated because of hexagonal order as 𝑠 = 4𝜋 √3×𝑞 100 -1 is shown as the right ordinate in fig. 11 (d), and for viruses within the SmB phase this distance is higher than the distance of close-packed rods, in the first approximation calculated as 𝑠 ′ = 𝐷 𝑒𝑓𝑓 = 2 × к -1 + 𝐷 (for fd viruses with a bare diameter of D=6.6 nm and the Debye screening length at I=0.16mM of к -1 =27 nm, 𝑠 ′ = 60.6 𝑛𝑚). Consequently, the overlay of Debye screening lengths has not been evidenced.

The presence of wide Bragg diffraction peaks for suspensions with the lamellar virus organization has not been detected, what one more time argues for the absence of the stable SmA phase at very low ionic strength. Consequently, the SmA phase is not typical for the equilibrated low ionic strength suspensions of fd viruses or it exists in a very small range of virus concentrations that could be probed by SAXS.

2.4.4.

Calculation of the Smectic ordering potential

Dynamic studies at the single-particle level are fundamental for understanding the physics of mesophases, where an order is dependent on the considered plane orientation compared to the rod main axis (spatial order). As mentioned in the introduction section, a hopping-type diffusion typical for the SmA phase can be explained by overcoming an energy barrier associated with layered periodicityunidimensional smectic ordering potential 𝑈 𝐿𝑎𝑦𝑒𝑟 (fig. 1). It can be experimentally obtained from particle fluctuations concerning the middle of the smectic layer. The distribution of particle fluctuations is proportional to the probability P(z) of finding the center of mass of rods at position z along their director with respect to the middle of the layer, via the Boltzmann factor

𝑃(𝑧)~𝑒 -𝑈 𝐿𝑎𝑦𝑒𝑟 (𝑧) 𝑘 𝐵 𝑇 ⁄

. The potential 𝑈 𝐿𝑎𝑦𝑒𝑟 has been experimentally obtained for various virus systems at the relatively high ionic strength (I=20mM) and at a given ionic strength it increases with increasing virus concentration [20], [40], [42], [43]. Thus, for fd viruses at I=20mM, the smectic potential depth 𝑈 𝐿𝑎𝑦𝑒𝑟 𝑀𝑎𝑥 is ~4 kbT for the SmA phase [20], [40] and it increases for the SmB phase [42].

Here we will investigate the properties of the SmB phase potential in fd-wt suspensions at I=0.16mM To mathematically describe deconvolution, let's firstly consider the convolution of two

Gaussian functions centered at xc=0 (eq.2.11)

𝑓(𝑥) = 1 𝜎 𝑓 √2𝜋 𝑒 - 𝑥 2 2𝜎 𝑓 2 (2.11) 𝑔(𝑥) = 1 𝜎 𝑔 √2𝜋 𝑒 - 𝑥 2 2𝜎 𝑔 2
where 𝜎 is a standard deviation of the Gauss distribution

Convolution of two functions is an integral that expresses the amount of overlap of one function g(t)

as it is shifted over another function f(t). Convolution of two Gaussian functions (eq. 2.11) results in a Gaussian function with the standard deviation 𝜎 𝑐𝑜𝑛𝑣 (eq.2.12) and it is the main advantage to use Gaussian functions for deconvolution of the experimentally obtained particle probability distributions P(z). Details on the convolution of two Gaussian functions are described in Appendix II.

(𝑓 ⊗ 𝑔)(𝑥) = 1 𝜎 𝑐𝑜𝑛𝑣 √2𝜋 𝑒 - 𝑥 2 2𝜎 𝑐𝑜𝑛𝑣 2 (2.12) 𝜎 𝑐𝑜𝑛𝑣 2 = 𝜎 𝑓 2 + 𝜎 𝑔 2
In analogy with the convolution operation, one Gaussian deconvoluted from another results in a Gaussian function

𝑓(𝑥) = 1 √2𝜋𝜎 𝑑𝑒𝑐𝑜𝑛𝑣 2 𝑒 - 𝑥 2 2𝜎 𝑑𝑒𝑐𝑜𝑛𝑣 2 (2.13)
with the standard deviation of the deconvoluted Gaussian function

𝜎 𝑑𝑒𝑐𝑜𝑛𝑣 2 = 𝜎 𝑐𝑜𝑛𝑣 2 -𝜎 𝑔 2 (2.14)
Knowing the relationship between the widths of the Gaussians before and after convolution (eq.2.11-2.14), we can calculate when the PSF, described as a Gaussian function starts to contribute to the real particle fluctuation distributions as well as to real smectic potentials. Thereby, the absolute deviation of 𝜎 𝑟𝑒𝑎𝑙 for the real probability distribution 𝑃(𝑧) 𝑟𝑒𝑎𝑙 from 𝜎 𝑒𝑥𝑝 of the experimentally obtained distribution 𝑃(𝑧) 𝑒𝑥𝑝 has been calculated for various 𝜎 𝑒𝑥𝑝 /𝜎 𝑃𝑆𝐹 ratios. The results of these calculations show that when the 𝜎 𝑒𝑥𝑝 = 3𝜎 𝑃𝑆𝐹 the deviation of 𝜎 𝑟𝑒𝑎𝑙 obtained after deconvolution from 𝜎 𝑒𝑥𝑝 is around 3% and when 𝜎 𝑒𝑥𝑝 ≫ 𝜎 𝑃𝑆𝐹 this deviation goes to zero (fig. 13). Consequently, when 𝑃(𝑧) 𝑒𝑥𝑝 is 3 or more times wider than 𝑃(𝑧) 𝑃𝑆𝐹 , the deconvolution of the experimental data is not necessary for obtaining the real smectic potential and 𝑃(𝑧) 𝑒𝑥𝑝 ≈ 𝑃(𝑧) 𝑟𝑒𝑎𝑙 . In the case of our experimental results obtained for fd-wt viruses at 0.16mM ionic strength, particle probability distributions 𝑃(𝑧) 𝑒𝑥𝑝 and 𝑃(𝑧) 𝑃𝑆𝐹 , previously assumed as normal distributions in theoretical considerations of the convolution operation, are in good agreement with their Gaussian fits (fig. 14 a). Corresponding 𝜎 𝑒𝑥𝑝 extracted from Gaussian fits of our experimental data (𝜎 𝑒𝑥𝑝 < 0.062 in units of [z/LLayer]) are not 3 times higher than 𝜎 𝑃𝑆𝐹 = 0.025 ( 𝜎 𝑒𝑥𝑝 𝜎 𝑃𝑆𝐹 < 2.5 ). Thus, in order to get real smectic potentials, deconvolution of the experimental data should be done. For this purpose, we can use the analytical expression for deconvolution of Gaussian distributions (eq. 2.13-

2.14).

Standard deviations 𝜎 𝑒𝑥𝑝 and 𝜎 𝑃𝑆𝐹 for corresponding probability distributions 𝑃(𝑧) 𝑒𝑥𝑝 and 𝑃(𝑧) 𝑃𝑆𝐹 have been extracted from their Gaussian fits of the experimental data done using Origin.

Deconvoluted probability distributions 𝑃(𝑧) 𝑟𝑒𝑎𝑙 have been obtained for various virus concentrations using eq.2.13. Corresponding smectic potentials have been calculated as 𝑈 𝐿𝑎𝑦𝑒𝑟 (𝑧)𝑘 𝐵 𝑇~-ln [𝑃(𝑧)] and they are shown in figure 14. Experimental measurements of the smectic potential depth 𝑈 𝐿𝑎𝑦𝑒𝑟 𝑚𝑎𝑥 > 𝑈 𝑃𝑆𝐹 𝑚𝑎𝑥 (𝑈 𝑃𝑆𝐹 𝑚𝑎𝑥 ~10 kBT is the depth of PSF function potential) are not possible due to resolution limitations of the used method, but from the decrease of the 𝜎 𝑒𝑥𝑝 as well as the 𝜎 𝑟𝑒𝑎𝑙 with C(fd-wt) increasing we can conclude that similar to millimolar ionic strength (I=20mM) viral suspensions [42], [43], the 𝑈 𝐿𝑎𝑦𝑒𝑟 𝑚𝑎𝑥 at I=0.16 mM (which is inversely proportional to the standard which can decrease the virus concentration has been proved by the revision of the low ionic strength suspensions using transmission electron microscopy (TEM). Thus, for suspensions stored for more than one year at room temperature, the destruction of virus capsid with releasing its DNA has not been evidenced. Consequently, the evolution of viral suspensions is induced by increase of suspension ionic strength and the factors which could explain these changes will be discussed in the next paragraph.

2.4.5.

Increase of the ionic strength as the main reason of time evolution in equilibrated fd-wt suspensions at very low ionic strength

As described above, an equilibrated by long-term dialysis fd-wt suspensions at I=0.16 mM exhibit from the SmB to N * , passing the metastable SmA, time induced transition. These changes may be caused by increasing the suspension ionic strength. Since the used "buffer" solution cannot fix medium properties (such as pH) for our dispersions (see paragraph 2.3), even a small introduction of additional electrolytes (including H + and OH -ions) can dramatically change boththe pH and ionic strength of the suspension. For this reason, here we will discuss possible sources of electrolytes in our systems, consisting of the virus suspension and surface of the glass cells or cylindrical capillaries used for the optical microscopy samples preparation (see Chapter 1).

We selected the three most probable sources of additional electrolytes in our system. The first of them is related to the glass cleaning method. Thus, charged ions could be introduced from the cleaned with the sulfochromic acid glass surfaces used for preparing the optical microscopy samples (see chapter 0). It could happen if the remains of the sulfochromic acid have not been removed completely from the glass surface. Multivalent ions typical for this acid (such as SO4 2-, Cr2O7 2-, Cr 3+ ) can dramatically increase the ionic strength of our suspension (see eq.2.1). To avoid using ionogenic materials during the glass purifying, as an alternative, glassware have been treated with HellmanexTMIII (Hellma Analytics) cleaning solution based on surface-active substances. The time evolution of the same viral suspensions placed into optical microscopy samples prepared using Hellmanex and sulfochromic acid cleaned glassware has not shown any significant difference.

Consequently, the glass cleaning method does not induce an increase of the suspension ionic strength with time (i.e. its time evolution).

Another reason for the ionic strength growth could be related to the glass dissolution and dissociation of its silanol groups. These processes have been detected in many aqueous systems and may be attributed to the following reactions (eq.2.17-2.19) [44], [45]. If the ratio of the glass surface area to solution volume is big enough, both -glass dissolution and dissociation can contribute to the overall mobile ion concentration and, as a result, increase the ionic strength of the suspension. At the fixed surface area of the glass-water interface, the number of mobile ions released into the water, as well as glass dissociation constant, depends on several factors, such as the glass nature, temperature, water salinity, and its pH [44]- [46]. Consequently, precise numerical calculations of the glass surface contribution to the overall ionic strength raise a challenge, but we expect to observe a faster evolution of samples with a higher ratio between the glass surface area and suspension volume. Instead, experimentally we have found that samples with lower glass surface area to suspension volume ratio (glass capillaries) have evolved faster. It shows that the glass surface of our optical cells (capillaries)

does not affect the suspension ionic strength.

𝑆𝑖𝑂𝐻 ↔ 𝑆𝑖𝑂 -+ 𝐻 + 2.17 The last factor, which can induce ionic strength increase is related to the biological origin of our system. Since after the virus production we are not able to remove 100% of used host bacteria by centrifugation (see Chapter 1), some small amount of E.Coli is always present in our suspensions. To experimentally estimate the purity of viral suspensions (the amount of bacteria) spectrophotometric measurements of an absorption ratio at 269 and 244 nm (A269/A244) can be used. Thus, the ratio of A269/A244≤1.41 indicates impurities below 1% [47], which is the case for our experimental systems.

Consequently, lower than 1% of E.Coli are present in our viral suspensions after their purification.

These bacteria can live and multiply at temperatures, which are lower than ones used for the dialysis and storing of our viruses [48]. Throughout suspension equilibration, sample observations, and storage, present E.Coli release various by-products as a result of their life cycle. These bacteria byproducts could be ionogenic compounds and contribute to the ionic composition of the suspension [49]. In the case of sealed with UV glue optical microscopy samples, by-products of E.Coli could increase the ionic strength of suspensions locally, close to regions with a big amount of bacteria.

Considering that E.Coli are facultative anaerobic organisms, meaning that they can metabolize energy aerobically or anaerobically (fig. 16 [III]), and that aerobic respiration generates more ATP than fermentation, they gather mostly at the air/liquid interface. It has been detected experimentally for our cylindrical capillaries, in which many bacteria have been observed close to the suspension meniscus (fig. 17 a) after the storing. For the same reasons, the N * phase formation inside capillaries

In this paragraph, we have shown the effect of different factors, such as glass surface cleaning methods, glass dissolution and dissociation, as well as the bacteria growth, which can increase the ionic strength of our experimental systems consisting of fd virus suspensions (I=0.16mM) placed in glass cells or cylindrical capillaries. We have experimentally found that the glass surface has negligible contributions to changes of the ionic strength, and it cannot induce the suspension time evolution from SmB to the N * phase. While ionic strength increasing induced by by-products of E.Coli, which are always percent inside viral suspensions in small amounts, shows to have a significant contribution to the evolution of equilibrated suspensions. Thus, all samples after their preparation have to be stored at 4°С in order to minimize the bacteria growth, and, as a result, suspension time evolution.

Conclusions

Here, we have proved the formation of the Smectic liquid crystalline phase in suspensions of fd-wt viruses at 0.16mM ionic strength. The periodic lamellar structure of the crystalline mesophase has been detected at virus concentrations C(fd-wt)>6.4 mg/ml. Single-particle tracking of viruses within the all Smectic phase range shows that they exhibit only Brownian motion within the layers without any hoping-type diffusion, while SAXS experimental results evidence their hexagonal longrange positional order. All these findings prove the formation of the SmB liquid crystalline mesophase in very low ionic strength viral suspensions. Liquid-like order of particles within smectic layers has not been detected. It argues the absence of the SmA phase for all probed virus concentrations and it is the distinctive feature of the virus phase behavior at very low ionic strength (SmA phase is characteristic of viral suspensions at the millimolar (I>5mM) ionic strength range [12]).

We have shown that the equilibration of dense viral dispersions is a long and complex process that requires long-term dialysis (fig. 8). However, even after short-term dialysis (at least 3 days for each virus concertation), the virus phase behavior at very low ionic strength is the same as for fully equilibrated suspensions, and the N*/SmB phase transition occurs at C(fd-wt)~6.1 mg/ml. Still, the fd-wt equilibration helps to stabilize viral suspensions in time and to control their ionic conditions (pH and ionic strength). Nonetheless, an increase of the ionic strength during storage of equilibrated viral suspensions leads to their time evolution. During this evolution, the formation of the metastable SmA (could originate from the increase of the ionic strength occurring in the sample) has been detected between the SmB and N * mesophases. After experimental studies of various factor influences on the suspension evolution, we believe that the detected time evolution of equilibrated suspensions is related to the biological origin of our system and from the SmB to N * evolution is induced by the bacteria growth inside fd-wt suspensions. The sample storage at low temperature (4°C) after their preparation helps to minimize the effect of bacterial growth on the ionic strength of the suspension (i.e. on the time evolution).

Accordingly, in this Chapter, we have proved that the existence of the glass transition is not typical for very low ionic strength suspensions of fd viruses, and they exhibit from the N * to SmB phase transition with increasing rod concentration in either fully equilibrated or not (after short-term dialysis) suspensions.

Introduction

Chirality, which is derived from the Greek word χείρ (cheir, hand), was introduced in 1884 by Lord Kelvin in his Baltimore Lectures [1] and defines as a lack of mirror symmetry. Geometrically or mathematically speaking, an object is chiral if it cannot be precisely mapped onto its mirror image by any kind of rotation or translation. Chirality plays a huge role in science since it was observed at virtually all length scales in nature. For example, in massless subatomic particles, chirality is determined by the coupling of spin and motion [2]. On the other side of the scale, we can find fascinating examples of macroscopic chiral objects, including right-and left-handed snail shells [3],

up to two meters narwhal tusks [4], or impressively huge spiral galaxies [5]. Due to its importance, great efforts were made to investigate the origin of chirality as well as its amplification on different length scales. Thus, it was established that interactions between chiral molecules change dramatically when one of them is replaced by its mirror image (enantiomer). This specificity of chirality is the basis of most industries producing chiral drugs [6]. In the area of molecular liquid crystals, chirality leads to the formation of phases with a twist of the molecular orientation, such as the Chiral Nematic (also called Cholesteric) or Blue Phases [7]. Amphiphilic molecules in their aqueous solutions selfassemble into aggregates, which are often spherical or bilayered. Experiments have shown that bilayers of many chiral molecules form long, narrow cylinders, known as tubules [8]. Thus, chirality affects not only the interactions between objects but also their assembly.

Self-assembly of chiral objects is widely used for investigations of a chirality transfer. It is based on the process in which a collection of particles or molecules organizes into well-defined larger structures and materials, held together only by non-covalent interactions. A morphology of selfassembled systems is expected to depend on the shape of individual building blocks as well as specific interactions between them. Colloidal building blocks are favored for these studies because they can be considered as giant atoms [9], which enables their direct observation via optical microscopy.

Anisotropic colloids with purely repulsive or hard-core interactions (driven only by entropy) selforganize into different liquid crystal mesophases with changing their concentration, including liquid Isotropic, Nematic, Smectic, and Columnar phases [7]. Similar to molecular liquid crystals, introducing chirality into anisotropic colloids could induce the formation of the Chiral Nematic or Cholesteric (N * ) liquid crystalline phase, such as in suspensions of fd virusesthe widely used model system of chiral rods. As mentioned in the introduction chapter in a N * phase the averaged particle orientation exhibits helical rotation along a given axis [10]. As a consequence of the twisted rod orientations, well-defined optical "fingerprint" textures (fig. 1 e) related to the cholesteric periodicity or pitch (P0) were observed via polarizing optical microscopy for various viral systems [10]- [12]. In order to understand the origin of this twisted mesophase in viral suspensions, let's consider constituent particles (viruses) as chiral semiflexible thin filaments with a high aspect ratio. The reasons for their intrinsic chirality lie in a helicoidal wrapping of the α-helical coat proteins (fig. 1 bc) around the single strained DNA and a possibility of some helical conformation of the virus body by itself (fig. 1 d) [11]. Over the past decades, many efforts were done to understand the origin of chirality in viral systems, its amplification [10]- [18], as well as its implications for self-assembling processes [16]- [19]. Here we will extend these investigations using chiral self-assembly of fd viruses induced by effective attraction.

3.1.1.

Depletion interactions

Depletion interactions, which were introduced more than 50 years ago by Japanize physicists [20], [21], are used nowadays as one of the self-assembly strategies [22], [23]. Depletion was defined as forces arising between two bodies immersed in a depletant solution. Small colloidal particles, nonadsorbing polymers, or micelles can be used as depletant agents. The physical origin of depletion forces lies in the increase of the volume accessible to a small depletant (free volume) after the overlap of big object excluded volumes. An increase in the system entropy (S) results in its free energy (𝐹 𝐻 = -𝑇𝑆) decreasing. Consequently, depletion forces are purely entropic, which means that their properties are determined by a tendency of a whole system to increase entropy, as stated by the second law of thermodynamics. Since the effective attraction, which favors the self-assembly of colloidal objects immersed into a fluid of depletants, is caused by a difference in osmotic pressures near the surface of colloidal particles and the suspension bulk (see paragraph 0.2.5), the strength and range of the depletion potential between two particles depend on the depletant concentration and size, respectively [20].

In the case of rod-shaped colloids suspended in a liquid of rigid spherical macromolecules (nonadsorbing polymer) with radius R=Rg (Rg is the radius of gyration), depletion forces cause the overlay of the rod excluded volumes, as schematically shown in figure 2. An excluded volume (dashed cylindrical shell) surrounds each particle with length L and radius r. When the excluded volume shells of a rod pair overlap (red zones), a free volume accessible to polymer molecules increases (white region inside black rectangles). The depletion interactions result from the overlapped volume between crossed cylinders (fig. 2 c-d) and that of the rod ends (fig. 2 b). When the rod length is sufficiently large (L →∞, L>>2r), the main contribution to a free volume gives the overlap of crossed cylinders [25]. In this case, a side-by-side condensation of long rods (fig. 2 d) is entropically favored.

Figure 2. Schematic illustration of the excluded volume of a rod-shaped particle (a) and free volume (white regions inside the black rectangles) (b-d). Each rod (length L and radius r) is surrounded by a cylindrical shell with radius R=Rg+r, defining its excluded volume. When excluded volumes of a rod pair overlap, the free volume accessible to the depletant increases. An increase of the excluded volume overlap (red zones) increases a free volume (and decreases the total energy of the system), which favors side-by-side rod aggregation. Cylindrical (spherical) dashed regions around the rods (polymer chains) indicate their excluded volumes.

Consequently, depletion interactions induced for very long and thin bacteriophages usually result in their side-by-side condensation. Experimentally, a depletion principle was tested for rod-like virus suspensions at relatively high ionic strengths (I) where the Debye screening length (eq. 0.

3) is smaller than the radius of gyration Rg of a used polymer. In these virus/polymer mixtures, depletion attraction is dominating and induces the formation of various self-assemblies [14], [16]- [18], [26]- [29]. All these structures will be described in more detail in section 3.1.3 of this chapter. To better understand the inter-particle twist in viral self-assemblies, let's firstly discuss its origin in the chiral nematic phase.

Twist between filamentous bacteriophages in their Cholesteric liquid crystalline phase

Here we will pay an attention to the (Chiral) Nematic phase formed in suspensions of filamentous semiflexible rods, such as Tobacco Mosaic Virus (TMV), fd, M13, or Pf1 viruses. The origin of the twist between particles in the cholesteric (N * ) phase as well as in other dense-packed states is very complex, and molecular chirality does not guarantee the existence of a macroscopic chiral structure, such as a N * phase. For instance, TMV [30] or Pf1 [10] chiral viruses with an extremely similar to fd or M13 helical capsid structure exhibit only an achiral N phase, that can be considered as a N * phase with an infinite pitch. It shows how tiny differences in microscopic surface properties of viruses can influence the amplification of their chirality at the mesoscopic scale. Several theories were proposed to explain the origin of the twist between viruses in the N * phase. The independence of the N * phase formation from the chiral wrapping of coat proteins (fig. 3 a-c) was proved by the formation of the N * phase for PEGylated viruses, whose bodies were covered by a neutral and achiral polymerpolyethylene glycol (PEG). It was expected that a polymeric layer fully screens the intrinsic chiral nature of the virus capsid, but the N * phase was observed for PEGylated viruses [11]. Only systems of viruses with very thick polymeric shells (PEG20k, Mw=20 kDa) at high ionic strength (i.e. к -1 <<Rg) can form an achiral N phase. Then it was shown that similar to the PEGylated with PEG20k viruses, fd-wt covered by a thermosensitive polymer, poly(N-isopropyl acrylamide) (PNIPAM), tends to form only a N phase, especially at high ionic strength and virus concentrations, where inter-particle interactions are dominated by the polymer layer [12], [13]. Since even after polymer grafting to the virus capsid, each protein bears some ionic charges, the chiral arrangement of the coat proteins implies a helical charge distribution, similar to the raw (uncoated) viruses (fig. 3 c) [31]. Thus, not only shape chirality could induce the twist between viral particles, but it also may be related to the chiral charge distribution along the virus [31]. It has brined authors to conclusions that the origin of chirality in the N * phase could be induced by the chiral charge distribution along the virus or (and) its corkscrew shape [11], which is assumed to stem from interactions between the viral DNA and the coat proteins (this relation was not experimentally evidenced) [32]. Later, the charge reversal of the fd-wt was done by the chemical modification of its capsid water exposed carboxyl groups with amines [12], [15]. Increasing the rod concentration in suspensions of the positively charged fd-wt shows an achiral N phase formation.

Unfortunately, many parameters of the system could change compared to the raw virus during its charge reversal, such as the virus flexibility, strength of protein-DNA interactions as well as helical symmetry of the virus surface. Besides, hydrophobic interactions between modified viruses cannot be excluded, as well as virus cross-linking during reaction with ethylenediamine dihydrochloride.

Thus, the surface modification changes the helical symmetry of the positively charged viruses that could vanish the steric and electrostatic contributions of their chirality amplification.

Another piece of work dealing with virus chirality was done using fd virus mutant, called fdY21M. In this study was found that the single mutation in each main coat protein (tyrosine (Y) at the position 21 in the wild-type fd (fd-wt) is replaced by methionine (M) in fdY21M mutant) results

in the opposite (right-handed) handedness of the formed by fdY21M N * phase, compared to the lefthanded one detected for fd-wt. Moreover, the cholesteric pitch in fdY21M suspensions is larger than in fd-wt ones in the same conditions [14]. These results could be interpreted in the framework of the corkscrew-shaped virus conformation [11], [12], where the virus mesoscopic length-scale chirality would be responsible for the macroscopic twist of the cholesteric phase.

All these findings highlight the role of different factors in the existence of a macroscopic chirality. As was shown [11]- [13], the virus capsid with helicoidally wrapped coat proteins is not the only contribution for the twist between filamentous viruses, while the related with protein arrangement charge distribution could induce chirality amplification [31]. Another factor, which cannot be excluded from considerations, is interactions between virus DNA and its coat proteins,

which affect the phage flexibility. It may cause a virus corkscrew shape and leads to chiral selfassembly. Consequently, the origin of chirality in viral dense-packed states remains an open question.

3.1.3.

Virus self-assemblies formed under depletion interactions

In paragraphs 0.2.5 and 3.1.1. we have described the main principles of depletion interactions and showed that in the case of infinitely long rods, depletion forces depend on the anisotropic colloid mutual orientation. Expected side-by-side condensation of colloidal rods was experimentally observed for stiff inorganic nanoparticles (fig. 4) [33] as well as for semiflexible rod-like viruses (fig. 56) [14], [17]- [19], [26]- [29] under depletion attraction. In the case of chiral bacteriophages, various self-assemblies were obtained by changing attraction range and strength between rods in their two-component mixtures with neutral hydrophilic polymer (Dextran or PEG) [26]. Z. Dogic and coworkers have investigated depletion induced selfassembly from highly monodisperse isotropic viral suspensions using relatively big polymer (Rg>>r) as a depletant. In such a way, 2D colloidal membranes (fig. 5 a), which are one-rod-length-thick liquid-like monolayers of aligned rods, were obtained after adding Dextran of MW 500kDa (Rg=18 nm) into Isotropic suspensions of fd or M13 viruses [17], [27]- [29]. These membranes were observed as freely suspended disks with exposed edges. The membrane bulk is reminiscent of the Smectic-A (SmA) phase organization with its quasi-1D positional order, while membrane edges have a local twist induced by the intrinsic chiral nature of the virus [16]. In contrast to membranes made of achiral rods, for which the twist at the edges is equally likely to be left-or right-handed, the twist in membranes made of chiral viruses is dictated by the microscopic chirality of constituent particles.

The membrane bulk stays achiral, due to the incompatibility of the particle twist with the membrane layered structure [16], [34]. Increasing attraction strength results in condensation of individual colloidal membranes into their stacks (fig. 5 c). These mesoscopic disks stacked up on top of each other produce filaments of the SmA phase in an isotropic matrix [27]. With decreasing attraction between viral particles, colloidal membranes undergo a structural transition into 1D twisted ribbons.

Particles are oriented perpendicular to the long ribbon axis, and figure 5 Recently, our group has studied the crystallization of fd viruses from an Isotropic phase under depletion interactions [18]. In this research, the attraction has been induced by a relatively small molecular weight polymer PEG8k (PEG, MW 8000, Rg=4 nm), resulting in the formation of crystalline hexagonal platelets (fig. 6) [18], [26]. These platelets are monolayers of aligned viral rods with hexagonal packing and long-range positional order of the particles. Platelet growth studies show that firstly the formation of few micrometers long bundles with the Columnar phase organization Chapter 3

(columnar bundles) and a diameter of about 0.3 µm takes place. Then, these filaments act as nucleation sites for virus crystallization. In contrast to previously discussed liquid-like colloidal membranes or twisted ribbons, in self-assembles with positional order of building blocks, a twist in the direction perpendicular to the long rod axis is not possible due to geometrical frustrations [35]. A geometrical incompatibility of particle positional order with their twist, generated by virus chirality, induces a single defect, called a screw dislocation in the center of each platelet. The screw dislocation of the platelet uses a thin bundle as a central core, and the defect is either left-or right-handed for the viruses with the same microscopic chirality. As a result, chiral platelets with opposite handednesses have been obtained (fig. 6 b). At a fast structure formation, the handedness of screw dislocations in a majority of the platelets is dictated by the microscopic chirality of constituent rods. Thus, for the suspensions in which virus chirality is vanished (racemic mixture of the viruses with opposite handednesses), the number of the structures with right-handed and left-handed screw dislocations are equal [18]. A decrease of the growth speed results in the formation of intrinsically frustrated flat (achiral) 2D platelets without any twist of the constituent particles, including those lying at the edges. which each layer represents a small hexagonal platelet with a width of about one-rod length. In contrast to smectic fibrils, columnar fibers do not have any layered organization along their main axis, but they have the hexagonal crystalline structure in a perpendicular direction compared to their long axis [36].

In this chapter, we further investigate the chirality amplification into structures with positional particle order, where the twist propagated in a perpendicular direction compared to the long rod axis is forbidden. In contrast to previously discussed studies, where various structures have been formed from dilute Isotropic suspensions, we will focus on viral self-assembly initiated from the N * liquid crystalline phase via depletion interactions. Effective attraction, created by adding nonadsorbing polymer with Rg smaller than virus radius, results in 1D growth of new helical superstructures, called helical bundles. Features of their growth, stability, periodicity, handedness, as well as their structure, studied by optical microscopy methods and Small Angle X-ray Scattering (SAXS), will be discussed.

Results and discussions

In our experiments on chiral self-assembly, we have used two-component mixtures consisting of stiff fd virus mutant -fdY21M and nonadsorbing polymer PEG as a depletant. Adding polymer to a dilute isotropic suspension of viral rods induces their self-assembly into a myriad of morphologies with liquid-like or positional order of particles, as described above [16]- [19], [27], [28], [36], [37].

The size of a polymer coil has a crucial role in virus condensation, and by tuning this parameter, we can vary the organization of particles within the resultant self-assemblies. Thus, short-range depletion attraction (induced by polymers with Rg~dvirus) favors small inter-rod distances and results in the growth of crystalline structures [18], [36], while long-range depletion (Rg>>dvirus) leads to particle self-assembly into liquid-like architectures with relatively large inter-rod distances [16], [27]. In our research, we have tested two polymer sizes that are compatible with fd virus diameter. Thus, PEG2k

and PEG8k with corresponding radiuses of gyration Rg=1.8 nm and Rg=4.1 nm [38] have been used

Chapter 3

to induce virus condensation from the N * liquid crystalline phase. As a result of virus self-assembly, helical bundles (fig. 7) have been produced. Here we will study these self-assemblies, as well as the phase behavior of virus/polymer two-component mixtures.

3.2.1.

Influence of the PEG size on the helical bundles growth and stability

To promote dense self-assemblies, we have started our investigations by using the same depletant as the one that induces the formation of crystalline structures from the isotropic viral suspension (PEG8k) [18], [36]. As a matrix for virus condensation, we have used suspensions in which the N * phase is present. For this purpose, we have dispersed fdY21M viruses in Tris/HCl/NaCl buffer with CTris=20 mM, pH 8.2, and ionic strength I=110 mM. The first-order I/N * (from the liquid Isotropic to the Chiral Nematic) phase transition for fdY21M polymer-free suspensions at room temperature is located between virus concentrations of 13.9 mg/ml and 18.9 mg/ml [14]. The selfassembly of viruses has been initiated from suspensions at I/N * phase coexistence as well as from a pure N * phase (i.e. more concentrated). The growth of structures made of viral rods has been followed using Differential Interference Contrast (DIC) microscopy. Similar to crystalline platelets [18],

helical bundles begin their growth with the formation of nucleation sitesthin, few micrometers long bundles, next nuclei (fig. 7, 0-800 min). These nuclei have grown only within N* droplets (also called tactoids) and become thicker and longer as well as exhibit some curved shape with time (fig. 7, 1000 min). Their subsequent growth leads to the formation of one-dimensional chiral self-assemblieshelical bundles. These new superstructures have never been detected within the isotropic phase, and they remain inside tactoids during the evolution from nuclei to a helical bundle.

Since virus condensation decreases the average concentration of free viruses (not incorporated into self-assemblies) inside a surrounding matrix, in the case of I/N * phase coexistence, it does not change rod concentrations within isotropic or nematic domains but decreases the size of nematic droplets or increases the size of isotropic ones (A-tactoids). A gain of the isotropic phase fraction inside a sample matrix with time results in a confinement of helical bundles (which remain only within the N * phase) by the I/N * interface. This confinement, in turn, results in a helical bundle compression followed by their aggregation. To avoid the growth of structures with liquid-like order of particles and to stabilize selfassemblies with positionally ordered viruses, we have decreased the range of attraction forces by decreasing the polymer size twice thanks to the use of PEG2k. The repulsion between viruses has been screened by increasing the suspension ionic strength (Tris/HCl/NaCl, I=260mM, CTris=20mM, and pH 8.2). The binodal for the I/N * phase transition of polymer-free fdY21M suspension at I=260mM have been determined experimentally, and they are located at virus concentrations of 17.0±0.3 mg/ml and 20.7±0.6 mg/ml. As expected from our previous results, after

Chapter 3

adding PEG2k to viral suspensions, rods have condensed into helical bundles within the N * matrix.

Helical bundle growth has the same mechanism as in the case of fdY21M/PEG8k mixtures. It is independent of the polymer size and follows the previously described scenario. Decreasing the depletant size does not stabilize helical superstructures out of the N * matrix, but prevents a twisted ribbon or liquid-like colloidal membrane formation from the liquid isotropic phase (fig. 8 c-d).

Thereby, only hexagonal platelets (with long-range positional order) have been obtained from a fully isotropic matrix after helical bundle aggregation. Moreover, platelets start their growth only after long storage of aggregated samples (up to a few weeks), which allows us to study helical bundles separately from any other structures. Helical bundles and hexagonal platelets have never been storage of aggregated samples (up to a few weeks), which allows us to study helical bundles separately from any other structures. Helical bundles and hexagonal platelets have never been observed at the same time. Thus, using PEG2k as a depletant allows us to obtain the systems consisting of the defined selfassembly type and not of their mixture, which is an advantage for future investigations of helical bundles.

3.2.2.

Phase diagrams of fdY21M/PEG mixtures

Phase diagrams of formed self-assemblies under depletion attraction in fdY21M/PEG2k and fdY21M/PEG8k two-component mixtures have been studied as functions of initial virus concentrations. As expected from previous investigations done in our group [18], [36], with increasing PEG2k concentration, hexagonal platelets (CPEG2k<50 mg/ml), smectic fibrils (50 mg/ml<CPEG2k<170 mg/ml) and columnar fibers (CPEG2k>170 mg/ml) have been obtained from initially isotropic suspensions. A rise of the virus concentration up to the I/N * phase coexistence results in the helical bundle growth within N * domains. Since the virus self-assembly causes the evolution of a surrounding matrix from the N * to pure I, passing the I/N * phase coexistence, helical superstructures are metastable as they only exist in the timescale of the N * phase existence inside a sample matrix. As mentioned above, aggregation of helical bundles occurs when suspensions turn to be isotropic. With increasing PEG2k concentration viruses crystallize into periodic smectic fibrils from the N * phase.

Figure 9 depicts experimentally obtained phase diagrams at room temperature for twocomponent mixtures of viruses with PEG8k (e) or PEG2k (f). Adding neutral polymer to fdY21M matrix results in a widening of the I/N * phase coexistence region, compared to polymer-free suspensions [39]. The binodal of the I/N * phase transition in two-component (fdY21M/PEG) mixtures have been deduced from polarizing microscopy images taken 15 minutes after the polymer has been introduced in viral suspensions, and these mixtures have been placed inside the optical glass cells, assuming that the amount of viruses incorporated into self-assemblies is negligible compared to the number of free viruses. The duration of the matrix evolution from a pure N * to a pure I phase depends on the initial virus and polymer concentrations and could be up to one month long. This relatively slow growth kinetics favors our future investigations of helical bundle structures that can be stabilized by a cholesteric matrix for at least a few days in the case of using PEG2k as a depletant.

3.2.3.

Investigations of the helical bundle structure

To study our new helical superstructures, we have probed the nature of particle order within helical bundles by SAXS. For this purpose, we have used the synchrotron x-ray beam (SWING, synchrotron Soleil). The range of investigated scattering vectors q corresponds to inter-rod distances of about one virus diameter. Figure 10 illustrates typical diffraction patterns of concentrated (sedimented) by gravity forces smectic fibrils and helical bundles (inserts in [a]) with their averaged scattering profiles (a). These profiles display the presence of sharp (100) Bragg diffraction peaks, whose positions in reciprocal space are at q100~0.08 Å -1 for bothsmectic fibrils and helical bundles.

The scattering profile obtained for helical bundles (formed from the N * matrix with C PEG2k =31.2 mg/ml and the initial virus concentration C ᴼ fdY21M =50.5 mg/ml) displays several Bragg peaks, whose positions in reciprocal space relative to the position of the main (100) peak are 1: √4: √7: √9: √12 (fig. 10 b). The presence of a sharp 𝑞 210 = √7 × 𝑞 100 peak proves local hexagonal packing of rods within helical superstructures [40]. For smectic fibrils only main (100) Bragg diffraction has been detected. Bragg diffraction at 𝑞 110 = √3 × 𝑞 100 , which also characterizes hexagonal order, has not been experimentally found either for smectic fibrils or helical bundles. It may be related to the low scattering intensity of the peaks at higher q (compared to q100) as well as the presence of relatively high background intensity at lower q (compared to q200) for samples prepared from the N * matrix (fig. 10 a,b).

For hexagonally packed colloids, the mean distance between centers of two adjacent particles 𝑠 = 4𝜋 √3×𝑞 100 -1 can be directly obtained from the position of the main (100) Bragg peak. For our helical self-assemblies, there is a slight variation on q100 peak positions as well as inter-rod distances, and q100 values correspond to the mean inter-rod distances of about 9.0 nm. Taking to account the virus diameter of 7 nm, the distance between the two neighbor rods 𝑠 0 = 𝑠 -2𝑟 𝑣𝑖𝑟𝑢𝑠 is around 2 nm, which is smaller than PEG2k coil size (𝑠 0 < 2𝑅 𝑔 , R g =1.8 nm [38]). This value is in agreement with the depletion theory [20], which excludes the polymer from self-assembled superstructures formed under effective attraction.

The line shape analysis of (100) Bragg peaks has been done to calculate the typical translational correlation length associated with particle positional order within self-assemblies. The X-ray beam resolution function is approximated by a Gaussian distribution with a full width at half maximum (FWHM) of its scattering profile equal to1.0×10 -3 Å -1 (see Appendix I). After the subtraction of a background contribution to scattering intensity, as shown by dashed magenta lines in figure 10 (c), FWHMs of (100) peaks have been manually determined as described in Appendix I.

Figure 10. Typical synchrotron X-ray scattering averaged radial profiles obtained after azimuthal integration of corresponding scattering patterns (inserts in the plots) of helical bundles (HB) and smectic fibrils (SmFib) (a). The polymer (CPEG2k) and initial virus (𝐶 𝑓𝑑𝑌21𝑀 0

) concentrations are indicated on the plots. The presence of sharp Bragg diffractions at q100~0.080 (Å -1 ) evidences longrange positional order of particles within both -helical bundles and smectic fibril. The presence of sharp q210=0.211 (Å -1 ) proves hexagonal packing of the particles within helical bundles. The scattered intensity as a function of q/q100 better visualizes the hexagonal particle organization within

helical bundles (b). Zoomed normalized by maximum intensity (I0) q100 peaks with indicated by dashed lines background scattering and normalized direct beam scattering profiles (c). Subtracted normalized q100 peaks fitted with Lorentzian function with indicated manually determined correlation lengths ξ (d).

Translational correlation lengths have been calculated as 𝜉= 2𝜋 𝐹𝑊𝐻𝑀(𝑞 100 )

. The measured correlation length between viruses incorporated in smectic fibrils (for which long-range hexagonal order of particles has been proved in our group by B. Sung et al [36]) is ξ=0.35 μm. In the case of helical bundles, correlation lengths have similar values as the one found for smectic fibrils, and they are from 0.38 to 0.63 μm (fig. 10 d). The instrumental resolution of correlation length measurements is 𝜉max=0.63 μm and it is limited by the FWHM of the direct beam. Experimentally obtained correlation lengths for helical bundles and smectic fibrils are close to this limit. Thus, the range of translational correlations extends over the distances, which are around one order of magnitude higher compared to virus diameter. It shows that particles within these self-assemblies have long-range translational order.

Consequently, the presence of sharp Bragg diffraction peaks (fig. 10) is a solid proof of longrange positional order of particles within helical bundles. Positions of these Bragg diffractions with respect to q100 as 1: (√3): √4: √7: √9: √12 evidence a local hexagonal packing of viruses within helical superstructures, which is typical for all known virus assemblies (including liquid-crystalline phases) with long-range positional order [18], [36], [40].

Then, a full-wavelength retardation plate or λ-plate has been used to determine the optical sign (positive or negative) of a birefringent bundle through polarized light microscopy. λ-plate has been inserted into the microscope optical pathway at a 45 o angle of its slow axis γ concerning the transmission orientations of the polarizer and analyzer (P and A respectively). It induces an elliptical polarization vector to green, red and blue waves of the polarized white light. Thus, for an isotropic background, only blue and red wavelengths can be polarized by the retardation plate, which allows their passing thought an analyzer of the microscope. It results in a magenta color (fig. 11 a). When a Chapter 3 birefringent object and retardation plate are inserted into the optical pathway, red (when object slow wave n is oriented along γ) or blue (when n is perpendicular to γ) waves exhibit linear polarization behavior, which prevents their passing through an analyzer, and it results in second order blue or first order yellow colors correspondingly (fig. 11 b-c). For fd virus self-assemblies, a slow wave has the same orientation as the main rod axis. In this way, depending on the virus orientation in reference to the position of the λ-plate slow axis, different colors can be observedsecond order blue for the rods oriented parallel compared to γ (fig. 11 b) or first order yellow for perpendicularly oriented rods (fig. 11 c). Consequently, depending on the self-assembly color, we can conclude about the virus orientation within the structure. Our experimental findings illustrated by figure 12 show that, when the main helix axis (𝑛 ̅) of the helical bundle is oriented nearly parallel to γ, it has a blue color (angle 45 o ), while after the change of the bundle orientation on 90 o , it changes the color from blue to orange. In combination with results obtained by polarizing microscopy, it signs about a nearly parallel orientation of viruses compared to the main bundle axis (N). Due to the presence of virus twist at the structure edges, the colored λ-plate image of the twisted ribbon with well-known particle orientation (fig. 5 b) [16] will depend on the focal depth at which it has been taken. Thus, at the twisted ribbon middle, when it is oriented along γ, a presence of mainly orange (yellow with low intensity) color of the ribbon, with some magenta regions, where viruses are optically isotropic has been observed (fig. 12 d). Figures 12 (b) and (e) schematically illustrate the particle orientation (with corresponding colors) within the helical bundle and middle section of the twisted ribbon as deduced from optical microscopy images when λ-plate has been used. Unfortunately, the contrast decrease between the background and self-assemblies has been observed for helical bundles compared to twisted ribbons. It can be explained by the presence of a N * birefringent matrix around helical bundles, in which rods usually are oriented along the main helix axis. It results in the presence of blue (45 o ) or orange (-45 o ) colors not only for helical superstructures but also for a sample background.

Figure 12. Polarizing microscopy images of the same single helical bundle and the corresponding DIC image (~0 о ) or λ-plate colored images (±45 o ), for various angular orientation of the main helix axis (𝑛 ̅) related to the crossed polarizers (a). The DIC microscopy image of the twisted ribbon formed at the presence of PEG8k (c) and the λ-plate colored image of the same ribbon taken at its middle section. In both cases λ-plate colored images have been obtained for verifying of virus orientation within self-assemblies. The retarded optical path results in fast (first order yellow, perpendicular virus orientation compared to γ) and slow (second order blue, parallel virus orientation compared to γ) axes. In an isotropic medium, it leads to a magenta background, while the background of N * matrix depends on its relative virus director orientation compared to γ. Schematic illustration of the twisted ribbon middle section (e) and helical bundle (b) with indication of virus orientation (n) (viruses are presented by cylinders) as deduced from optical microscopy results.

In this section, we have used SAXS and optical microscopy methods for the investigation of the virus organization within helical bundles. Our experimental results have proved the existence of long-range hexagonal order of rod-like particles within new helical superstructures with their orientation along the main bundle axis (fig. 10,12).

3.2.4.

Helical bundle handedness and periodicity

When the virus organization within helical bundles has been explored, we have extended our research on quantifying the helicity (pitch and handedness) of our superstructures. Thus, for all detected single helices, their periodicity, called helical bundle pitch, has been measured using a ruler tool in ImageJ software (fig. 13 a). The pitch shows the distance of one complete helix turn, measured parallel to the main helix axis. As mentioned in section 3.2.1 of this chapter, the I/N * interface of a sample matrix confines helical bundles during their growth. Consequently, it induces helical pitch decreasing with time. Experimentally pitches from 1.4 to 7.2 μm have been measured for helices formed in fdY21M/PEG2k mixtures. These values in most cases are smaller compared to ones found in fdY21M/PEG8k mixtures (P>5μm, fig13b), and pitch decrease is expected with decreasing depletant size (Rg of the used polymer) from theoretical considerations, which describe a depletion driven helix formation [41]. Besides, depending on the amount of a N * matrix in fdY21M/PEG2k mixtures, we have noticed two different populations of helical bundles with average pitches 1.9±0.3 and 4.3±2.5 μm (fig. 13 a) for cholesteric-rich (T<15 days after sample preparation, big tactoids) or cholesteric-poor (T>15 days, small tactoids) matrices correspondingly. Error bars have been determined as full widths at half maximum of the Gaussian fits of corresponding distributions.

In the case of confinement effect on existed helices in a N * matrix, we have expected to see only a pitch decrease without significant changes in the helix width (helical bundle can reduce the width on the values smaller than its core diameter dcore, dcore<<Whelix). Experimentally, wide pitch distributions have been detected for a fixed helix width. For example, at Whelix=1.5 μm measured pitches change from 1.5 to 6 μm (fig. 13 b). At the same time, a helical bundle width as a function of the helical pitch has shown a linear decrease with pitch decreasing (fig. 13 b). Not only the compression of the existing helices by the I/N * interface, but also the growth of new bundles with P~2 μm from cholesteric-poor viral suspensions at t>15 days may cause this trend. Helical bundle handedness investigation has been done by capturing DIC microscopy images at different focus depths. Before describing experimental results, let's consider limitations for the helix handedness determination. The first of them lies in the helical bundle length. Thus, for the helices with lengths lower than one full turn (pitch), handedness determination is impossible because, for short bundles, optical microscopy does not allow us to determine the direction (handedness) of the turn at their length ~ P/2 (fig. 14 c,g). Another limit is related to the axial (focal) resolution of our optical setup (microscope). Similar to the lateral resolution in the plane perpendicular to the optical axis (z), axial or longitudinal resolution (along the z-axis) is determined only by the numerical aperture of the objective [42] and for standard wide field microscope can be calculated using following equation

𝐷 𝑧 = 𝜆 × 𝑛 𝑁𝐴 2
where Dz is the axial resolution, λ is the wavelength of illuminating light, n is the refractive index of the medium between the coverslip and the objective front lens element, and NA is the objective numerical aperture. With assumption that our samples have been illuminated with the wavelength λ=0.5μm and by taking experimentally used NA=1.4 and n=1.33 for a sample aqueous medium, we can calculate the maximal longitudinal resolution Dz(max)=0.34 μm. Thus, to be able to recognize two opposite sides (the bottom and top parts) of the helical bundle separately, there should be at least 0.34 μm distance between them. This distance can be considered as a helix core, and it limits the ability to determine helical bundle handedness via optical microscopy. Helical bundle core diameter can be calculated as dcore=Whelix-2Wbundle, where Whelix and Wbundle are helix and bundle widths. In figure 13 (c) we can clearly see that a very small fraction of detected bundles (around 15%) are above the longitudinal resolution limit. Consequently, experimental handedness determination for the majority of helical bundles has been impossible, and these helices appear as "achiral" 2D structures.

Experimentally, for helical bundles with dcore≥0.34 μm, opposite handednesses (i.e. left-or right-) have been detected. Several examples of left-and right-handed bundles are presented in figure 14 (d,h). To make conclusions about the relationship between particle chirality and chirality of selfassembled helices, higher statistics on their handedness determination would have been needed.

Conclusions

In this chapter, we have demonstrated the existence of 1D helical bundles in a mixture of hard rods and nonadsorbing polymer. The formation of these superstructures critically depends on both depletant and rod concentrations. Their growth has been observed only within the Cholesteric liquid crystalline phase at a small range of polymer concentrations (fig. 9 e). An increase in the depletant concentration leads to the growth of lamellar crystalline structures. The surrounding environment limits the stability of helical bundlesthese chiral self-assemblies are stable only within the N * phase and during their growth exhibit confinement by the I/N * interface followed by their aggregation within an isotropic matrix. The twist of particles condensed into helical bundles is forbidden in a perpendicular direction to the long virus axis due to geometrical frustrations. As a result, similar to chiral hexagonal platelets [18], the intrinsic chirality of viral colloidal rods induces their continuous twist in a parallel direction to the long rod axis, which has been proved by optical microscopy (fig. 12).

Particle order within helical bundles has been probed using synchrotron SAXS. Multiple Bragg diffraction peaks have been detected with their positions in reciprocal space relative to the position of the main q100 peak as 1: (√3): √4: √7: √9: √12. It shows local hexagonal particle packing within helical bundles, typical for previously obtained in our group self-assemblies [18], [36]. The position of the main Bragg diffraction peak (100) at q~0.08 (A -1 ) evidences that inter-rod distances for viruses incorporated into helical bundles are smaller than the depletant coil diameter (s 0 ~2 nm, s 0 <2Rg).

Long-range positional order of particles within helical superstructures has been proved by the calculated from sharp q100 peaks translational correlation lengths, which is around one order of magnitude higher compared to the virus diameter. Similar to chiral crystalline platelets, the formation of two enantiomeric forms of helical bundles (left-and right-handed) has been observed.

The crucial limit for investigations of helical bundles is, therefore, their metastability.

Stabilization of these self-assemblies out of the cholesteric phase could provide a promising system of macroscopic crystalline helices, and it is the main goal for their future studies.

Introduction

Filamentous viruses are often used not only as a good model system of colloidal rods, but also as scaffolds for chemical functionalization and biological engineering [1]- [3]. Prior studies have reported that self-assembly of bacteriophages, mainly modified by phage display, results in the formation of chains with various lengths [4], rings [5], or radial structures [6]. These works are based on the genetic engineering of viruses, minor proteins (P3 and P9), which have been changed and specifically fused with polypeptide sequences exhibiting specific affinity for a given target. Note, that in this chapter, the term self-assembly is used only for describing a process of self-driven complex particle formation from individual (viral) building blocks, and it is not related to the formation of liquid crystalline phases or macroscopic structures, which have been described in previous chapters.

Here, their formation will be associated with the term self-organization.

Recently in our group has been developed a simple, robust, and effective method of bioconjugation between nanobeads of noble metals and M13 filamentous viruses [7]. Rod-like M13KE and M13C7C viruses, exhibiting exposed disulfide groups at their proximal ends (P3 proteins), bind to metallic nanobeads (Au, Pt, or Ag) via specific noble metal-sulfur chemistry. In this way, scepter-like (one virus attached by its tip to one nanobead) hybrid colloids have been produced via a reaction between viruses and metallic nanobeads. Protocols for the hybrid colloid production using gold nanobeads (AuNBs) have been developed. Thus, to obtain scepter-like colloids with high reaction efficiency(>90% of reacted viruses, with ~90% of scepter-like particles), the excess of 3

AuNBs per virus has to be used. The detailed protocol for the production and purification of these Then, these colloids have been self-assembled with green M13C7C body labeled viruses (gM13C7C) into AB2 type bicolored diblocks (rM13C7C-AuNB-gM13C7C). Single-particle microphases usually is diverse according to the volume ratios of polymer constituents. Thus, threeblock polystyrene/polybutadiene/polystyrene copolymer at up to 12% volume fraction of the minority component, its melt is in the form of uniform spheres, which transforms into uniform cylinders of practically infinite length at a volume fraction increasing up to 30%. In both cases, the majority component forms the continuous matrix. In the composition range of 35-65% of either component, the microphases have lamellar character [12].

Similar to copolymers, we expect that segregation of different colloidal blocks may be obtained when they are physiochemically incompatible. The advantage of using viral rods lies in the possibility of their direct visualization via optical microscopy. One of the simple ways to achieve an incompatibility between viral blocks is to use the hydrophilic\hydrophobic feature. Knowing that filamentous bacteriophages are hydrophilic, the simplest way to obtain hydrophobic phage is to cover its capsid with thermoresponsive poly-N-isopropylacrylamide (PNIPAM), which becomes hydrophobic at temperatures higher than TCSL (Lower Critical Solution Temperature). Then, selfassembly of raw and covered with PNIPAM viruses to metallic nanoparticles can produce hybrid colloids, which may form amphiphilic liquid crystals at T>TCSL [7]. In this way, spherical micelles or colloidal bilayers may be obtained from colloidal suspension with increasing particle concentration at T>TCLS.

Another way to achieve incompatibility between different rod-shaped colloids during their self-organization is to use for self-assembly blocks of different lengths (aspect ratio) in order to obtain asymmetric diblocks. As described in Chapter 2, filamentous viruses in their Smectic phase jump between adjacent smectic layers, overcoming an energy barrier related to the lamellar organization, called smectic ordering potential. This potential is periodic, with its minimum located at the middle of the smectic layer and the maximum (energy barrier)at the interlayer spacing (see fig. 1 of Chapter 2). The virus length characterizes the layer spacing of their Smectic phase, and usually, the layer spacing is nearly the same as the virus contour length [13]. In the case of introducing longer than the layer spacing virus (guest particle, L>Llayer) into a smectic matrix, it results in its faster dynamics compare to particles, which form a matrix [14]. Moreover, with time the size mismatch results in the segregation of guest longer viruses within defects present in a Smectic liquid crystalline phase [15]. Thereby, due to the mismatch in virus lengths, segregation of rods with different lengths is expected in other viral systems. Considering hybrid colloids made of two viral blocks of different lengths (asymmetric diblocks), block segregation with the formation of smectic layers of different L Layer may be obtained in resulting smectic suspensions. Nowadays, thanks to biological engineering, filamentous virus strains that differ only in their length have been obtained. Thus, these viruses can be used for producing asymmetric viral diblocks via their conjugation with metallic nanobeads. Since the strategy of diblock segregation based on the block length difference doesn't require additional virus modifications (such as their surface coating for changing hydrophilicity, as described above), it has been selected for our investigations.

Consequently, to promote the formation of diblocks, the efficiency of the reaction between tannic acid capped 11.1 nm AuNBs and fd or M13 viruses of different lengths is the first step of our investigations presented in this chapter. Viruses that have a highest ability to react with AuNBs will be selected for the formation of hybrid colloids. In order to sterically stabilize AuNBs involved in these colloids at high ionic strengths, the protocol for AuNB surface coating with a neutral molecular oligomer will be developed. Finally, the self-organization of hybrid colloids (scepter-like particles, symmetric and asymmetric diblocks) will be investigated under depletion attraction, as well as in their aqueous suspensions at low ionic strength. viruses with the sequencing of the phagemid pBluescript KS (-) plasmid. As expected, miniM13 has a single mutation at nucleotide 1655 of the pBluescript sequence [16].

Results and discussions

For investigations based on self-assembly and self-organization of hybrid colloids, filamentous viruses with exposed cysteine groups in their minor coat proteins (table 4.1) and different contour lengths, such as M13K07 (LM13K07=1.2 μm [17]), M13C7C (LM13C7C=1.0 μm [7]), fd-wt or fdY21M (Lfd=0.9 μm [18]), and miniM13 (LminiM13=0.35 μm, measured by TEM in our group, see Appendix III), have been selected for bioconjugation with AuNBs. Viruses with lengths of 0.9 μm and above have been produced and purified using a standard protocol [19], as described in Chapter 1. All these bacteriophages, as well as many other viruses, consist of DNA and a protein shell (called a capsid). As long as the viral DNA must encode all information about the protein shell structure and DNA replication, there are limits to how small DNA can make a fully "functioning" virus. For the miniM13 system, whose genome is around three times shorter (miniM13 used here contains 2404 nucleotides in its DNA [16]), compared to wild type M13, which has 6407 nucleotides [20], these limits were circumvented through the use of helper plasmid [21], [22] in E.Coli cells which makes miniM13 production more complicated and less efficient. Thus, Dr. Brown and co-workers have developed a production method of miniM13, whose contour length has been reduced to values about 0.35 μm [16]. This miniM13 can be grown from a single, stable E.Coli bacterial strain using a helper phage system. For this purpose, Dr. Brown has used helper plasmid (pSB4434) retained a double-stranded origin of replication and the chloramphenicol antibiotic resistance gene. This plasmid encodes information for the production of M13 coat proteins but is itself defective for packaging [23]. Thus, miniM13 is encoded by a single-stranded (ss) DNA (pSB4434), a deletion derivative of the phagemid pBluescript KS(-) with ampicillin-resisting genes [16]. Consequently, during miniM13 production, in culture media containing both chloramphenicol and ampicillin, only surviving E.Coli cells should be those with both the helper plasmid and miniM13 phage DNA. For the production of the miniM13 phage, we have followed the protocol developed in Dr. Brown's lab [16]. Thus, a single colony of the E.Coli bacteria strain S2188 harboring pSB4423 helper plasmid and miniM13 ssDNA has been grown in rich culture media with chloramphenicol (15 μg/ml) and ampicillin (200 μg/ml) with their following purification by centrifugation and dialysis [16]. All biological materials (bacteria containing plasmids) were obtained as a gift from Dr. Brown.

After production miniM13, its DNA has been extracted, and its ssDNA sequence has been compared

to the sequence of the phagemid pBluescriptKS(-) (can be found in genbank with accession number X52326). As expected, the miniM13 ssDNA sequence has a single mutation (G to A transition at nucleotide 1655) compared to the pBluescript one (fig. 2a) [16]. Since the helper plasmid encodes the formation of coat proteins for miniM13, no matches have been found between the miniM13 DNA and M13 one. Helper pSB4434 plasmid is a pACYC18440 plasmid whose HindIII-SalI fragment has been replaced with M13 DNA fragment from gene II (coding P2 protein) through gene IV (coding P4 protein) [23]. Consequently, pSB4434 encodes the formation of the same coat proteins as ssDNA of wild type M13 viruses. In this way, there should not be a difference between structures of P3 proteins located on M13 and miniM13 proximal ends. However, we should still consider that the DNA, which is inside the miniM13 capsid, differs from one of the other M13 viruses. It could affect the interactions between virus coat proteins and ssDNA and, as a result, change virus flexibility, structural stability, or even coat protein conformations.

4.2.1.

The influence of filamentous bacteriophage strain on bioconjugation with AuNBs To select best viruses for their self-assembly into asymmetric diblocks, we have investigated the ability of various virus strains with different contour lengths to react with 11.1 nm tannic acid stabilized AuNBs. For this purpose, the reaction efficiency of fd-wt (L=0.88 μm [18]), M13KO7 (L=1.2 μm [17]), and miniM13 (L=0.35 μm, see Appendix III) viruses has been compared to the one obtained for M13C7C strain in the same experimental conditions (ionic strength, virus/AuNB ratio, duration of the reaction). The detailed protocol for the reaction between AuNBs and filamentous viruses is described in Chapter 1. TEM images of obtained AB type hybrid colloids with these viruses are illustrated in figure 3. As mentioned above, M13C7C forms week covalent bonds between sulfur (cysteine of P3 protein) and noble metals (including Au) [24]. Thus, at stoichiometric molar ratio It can be explained by the difference of its ssDNA [16] compared to other M13 or fd viruses, which could affect the P3 coat protein conformation, i.e. miniM13 ability to react with AuNBs. Moreover, after miniM13 production and purification [16], removing all byproducts remains a challenge. Thus, purified miniM13 isotropic suspensions are colored in the light yellow color (other viral suspensions are transparent), and during miniM13 storage, some of contaminants can sediment by the gravity force (can be partially removed from the suspension with time). Still, even after long miniM13 suspensions storage, these byproducts have been detected by TEM (fig. 4) after negative staining of the suspension with 1% uranyl acetate solution, which reacts with amino groups of viruses or DNA making them visible with electron microscopy. Consequently, these spherical contaminants are organic and probably have a biological origin (it could be globular proteins). Moreover, we cannot eliminate the presence of thiols in their composition. Thus, these contaminants could decrease a miniM13 reaction yield with AuNBs. Since M13C7C shows the highest reaction efficiency (fig. 3), this virus strain will be used as one of the blocks for the production of asymmetric diblocks. Then, in order to increase the difference between two block lengths, miniM13, despite its drawbacks, and fd-wt virus strains are chosen as the second blocks to produce asymmetric diblocks consisting of one short (miniM13 or fd-wt) and one long (i.e. M13C7C) viruses attached to the same AuNB. Results of their production are discussed in the following paragraph.

(

Production of asymmetrical AB2 type hybrid particles

Similar to heterofunctional bicolored diblocks [7], the production of AB2 type hybrid colloids with different block lengths consists of 2 steps (fig. 5), which are the conjugation of the short (fd-wt or miniM13) virus proximal end with 11.1 nm AuNB and assembly of obtained AB type structures ([Short virus]-AuNB) with the long virus (M13C7C).

The production of [Short virus]-AuNB hybrid colloids has been performed in different ways, depending on the virus strain used. In the case of fdWT-AuNB hybrid colloid production, we have used high initial AuNB molar excess (α0=NAuNB/NfdWT=3) at virus concentration lower than their overlapping concentration C * (Cfd-wt=0.033 mg/ml, C * fd-wt=0.039 mg/ml) and the ionic strength of 40mM. As a result of AuNB conjugation with fd-wt, can be produced around 0.9 mg of fdWT-AuNB particles from 30 ml of the reaction mixture. After removing free AuNBs by small speed centrifugation steps, fdWT-AuNB colloids have been concentrated by ultracentrifugation. Then the resulting pellet has been re-dispersed in a small amount of 0.16mM Tris buffer (see Chapter 1) to the virus concentration of about 1 mg/ml. The virus concentration has been calculated from the AuNB light absorption at λ=400 nm and λ=520nm, as described in Chapter 1.

In the case of miniM13 viruses, due to their lower reaction efficiency with AuNBs (fig. 3) initial AuNB/miniM13 ratio has been decreased to (α0=NAuNB/NminiM13=1.8). Around 61% of miniM13 have been bound to AuNBs after their reaction at the ionic strength of 40mM and CminiM13=0.040 mg ml (C * miniM13=0.365 mg/ml). Since sedimentation coefficients of 11 nm AuNBs and miniM13-AuNB hybrid colloids have very close values (see Appendix III), to remove unreacted AuNBs by centrifugation, 20% of glycerol has been added to the suspension after its dialysis against 0.16mM buffer. Thus, free beads have been removed by 7 rounds at 15,000g for 30min. Still, except hybrid colloids, around 40% of unreacted miniM13 have been present in the supernatant. To separate free miniM13 and miniM13-AuNB colloids, glycerol has been removed by 8 hour dialysis against 0.16mM Tris buffer. After that, hybrid colloids have been purified by 3 rounds of ultracentrifugation at 100,000g for 1h (free miniM13 stays in a supernatant). MiniM13-AuNB pellet has been redispersed in a small amount of 0.16mM Tris buffer. As a result of these purification procedures, we can prepare around 0.1 mg of hybrid miniM13-AuNBs from 30ml of AuNB suspension with the same particle concentration as has been used for fdWT-AuNB production. However, we still have found remains of unreacted miniM13 and AuNBs in the purified miniM13-AuNB suspension, which are about 10% and 7% correspondingly. After the production of [Short virus]-AuNB scepter-like colloids, we have performed their self-assembly with M13C7C. For this purpose, 1 μm long M13C7C viruses have been added step-bystep to suspensions of [Short virus]-AuNB hybrid colloids in order to obtain stoichiometric [Short virus]-AuNB/M13C7C molar ratio (N[Short-virus]-AuNB=NM13C7C). This molar ratio has been quantitatively checked by TEM (particles counting). Experimental conditions have been optimized by increasing ionic strength (as described in paragraph 1.4.2. of Chapter 1) to the final ionic strength of 40 mM with added 2 mM TCEP. For M13C7C self-assembly with scepter-like particles, the virus concentration has been kept at around 1 mg/ml [24] to favor interactions between two viral blocks.

Structure distributions and TEM images of obtained asymmetric diblocks are provided in figure 6. In this way, we have produced about 2 mg of fdWT-AuNB-M13C7C, and 0.4 mg of miniM13-AuNB-M13C7C asymmetric diblocks from 30 ml of AuNB (CAuNB=3.43×10 12 particles/ml). Due to the presence of higher van der Waals attraction between AuNBs compared to raw viruses, hybrid colloids are not stable at high ionic strength. For the long-term storage of hybrid colloids, the repulsive forces between AuNBs have to be increased. So, we have dialyzed our hybrid colloids against 0.16 mM Tris buffer in order to increase the range of their electrostatic repulsion. The structural stability of asymmetric diblocks in aqueous suspensions has been checked with time by TEM. We have found that fdWT-AuNB-M13C7C diblocks are stable in aqueous suspensions and don't show any disassembly within 14 days of storage. In contrast to them, miniM13-AuNB-M13C7C diblocks don't have this stability, and after 7 days of storage at 4 ᴼ C in 0.16mM Tris buffer with CM13=2.9 mg/ml, they have disassembled into single miniM13 and M13C7C viruses, free AuNBs, miniM13-AuNB and M13C7C-AuNB scepter-like particles (fig. 7a). Moreover, branched chain/train-like colloidal oligomers have been formed during this time. Figure 7 (b-c) depicts TEM images of colloidal oligomers, which have been obtained via reaction between distal virus ends and AuNB incorporated (or not) into hybrid colloids. Mainly these colloidal oligomers have been formed by conjugation of AuNBs with M13C7C viruses, and only their small fraction contains both virus strains. The instability of miniM13-AuNB-M13C7C compared to fdWT-AuNB-M13C7C diblocks could be related to the presence of the biological byproducts associated with the production of miniM13 viruses (fig. 4), which could react with AuNBs and replace viruses from hybrid colloids due to reasons discussed above. To avoid limitations in the use of hybrid particles at high ionic strength (AuNB aggregation), an unreacted surface of AuNBs could be sterically stabilized by its coating with a polymer layer. For this purpose, polyethylene glycol oligomer with one thiol terminal group CH3(OC2H4)12SH (next PEG12-SH) and molecular weight of 576.7 g/mol (𝑅 𝑔 = 0.02 × 𝑀𝑤 0,56 = 0.7 𝑛𝑚 [25]) has been selected for reaction with a water-exposed AuNB surface in order to coat it by a very thin polymer layer, which helps to eliminate AuNB aggregation at high ionic strengths.

4.2.1.

Production of hybrid particles with sterically stabilized AuNBs

The steric stabilization of hybrid colloids consists of 2 steps (fig. 8): the virus conjugation with 11.1 AuNBs at their proximal ends, and PEGylation of AuNBs via reaction of Au with terminal thiol groups of PEG12-SH oligomer. Before PEGylation, diluted suspensions of hybrid colloids (Cvirus≤C * ) have been dialyzed against Tris/HCl buffer with I=20mM for 8 hours. PEG12-SH stock solution with C0(PEG12-SH)=0.7mg/ml has been prepared by dissolving the PEG12-SH oligomer purchased from PurePEG in distilled water. PEG12-SH has been added in excess of about 8500 molecules per 11.1nm AuNB and reaction has been proceeded for 14 hours at room temperature and 300 rpm stirring. After reaction, the excess of unreacted PEG12-SH has been removed by 8 hours dialysis against Tris buffer with ionic strength up to 110mM, and at least one ultracentrifugation run at 215,00 g for one hour followed by a pellet redispersion in about 20 ml of Tris buffer. Then, hybrid colloids with sterically stabilized AuNBs have been concentrated by another ultracentrifugation run at 215,00 g for one hour. To obtain target virus concentration, precipitated structures have been redispersion in a small amount of the same buffer. For PEGylation, the excess of polymer molecules has been calculated as follows. Let's assume that PEG12-SH polymer is in good solvent and its molecules can be considered as spheres. In this situation, after reaction with surface of AuNBs, PEG12-SH oligomers are chemically attached to Au surface via their thiol groups though weak covalent binding, and the reaction terminates when PEG molecules are close-packed on the surface with a "mushroom" conformation (fig. 9). With the assumption of the close packing of polymeric "mushrooms" (90.7% of a total surface area is available for the polymer grafting [26]) and taking into account the surface, PEGylation, these hybrid particles show high colloidal stability at I=110mM. fdY21M-AuNB(PEG12) and M13C7C2-AuNB(PEG12) hybrid colloids have been kept for months at Cvirus>2 mg/ml without structure degradation. Unfortunately, asymmetric fdWT-AuNB-M13C7C do not have this stability over time. Thus, during storage, a disassembling of asymmetric diblocks takes place with the release of free viruses and free AuNBs (fig. 10). This may be caused by ligand exchange in which the reaction between PEG12-SH and AuNBs leads to the replacement of viruses by thiolated PEG. It makes virus binding weaker compared to not PEGylated asymmetric diblocks.

Consequently, only symmetric hybrid colloids can be sterically stabilized using the described above PEGylation protocol. The successful PEGylation of asymmetric diblocks requires future investigations of the influence of various factors (such as PEG excess, reaction duration and purification procedure) on their stability.

4.2.2.

Self-organization of hybrid colloids with sterically stabilized AuNBs under depletion interactions

The selective reaction between AuNBs and PEG12-SH allows us to produce symmetric hybrid colloids (scepter-like particles and diblocks) with sterically stabilized AuNBs. Thus, we have used these particles for studying their self-organization under effective attraction. Depletion interactions have been chosen for self-organization in order to minimize the amount (mass) of hybrid colloids needed for the formation of structures with liquid crystalline phase organization (by the opposition of mesophases in bulk). For example, to obtain a Smectic phase in 1 ml of viral suspension at I=0.16 mM, at least 6.5 mg of viruses have to be used, while adding neutral polymer to the isotropic suspensions of viruses may cause the formation of filaments with SmA phase organization [28] or fibrils of SmB phase [29] (depending on the induced attraction range, i.e. polymer size) at the initial virus concentration of only 1 mg/ml. It makes a big advantage in the case of using hybrid colloids since their mass after production is in order of milligrams.

To induce the self-organization of particles, the soft effective attraction has been achieved by adding large hydrophilic polymer Dextran500k (Dextran, Mw=500 kDa, Rg=17.6 nm [30]). As already shown by Dogic's group [28], [31], liquid-like colloidal membranes and twisted ribbons obtained for Smectic phases of raw fdY21M and M13KE/M13C7C viruses [13], [32]. Single colloids (sterically stabilized hybrid colloids made of fluorescently labeled viruses and 11.1nm AuNBs, which have been added in tracer amount into suspensions) visualized thanks to fluorescence microscopy evidence nearly frozen particle dynamics within hybrid smectic fibrils (fig. 12 c), which is a sign of particle positional order within these structures.

Moreover, hybrid smectic fibrils with the same particle dynamics within their structure have been formed under depletion by using smaller depletant -PEG8k with the radius of gyration Rg=4 nm [33]. We have probed the nature of particle order within these hybrid smectic fibrils by SAXS. For this purpose, we have used the synchrotron x-ray beam (SWING, synchrotron Soleil).

Figure 13 illustrates a typical diffraction pattern of concentrated by sedimentation hybrid smectic fibrils (left) with their scattering profile (right). Due to the presence of AuNBs (involved into hybrid colloids) in our colloidal system, the scattering profile of hybrid smectic fibrils displays the typical form factor for spherical gold nanoparticles. The presence of the sharp (100) Bragg diffraction peak with the position in reciprocal space located at q100=0.072 Å -1 has been also detected. By assuming hexagonal order of particles, we have calculated the mean inter-particle distance between the centers of two neighbor particles as 𝑠 = 4𝜋 √3×𝑞 100 -1 , and we found that 𝑠 =10.0 nm, which corresponds to the close packing of AuNBs. Thus, the distance between surfaces of two adjacent viruses is s 0 =3 nm (𝑠 0 = 𝑠 -2𝑟 𝑣𝑖𝑟𝑢𝑠 , 2𝑟 𝑣𝑖𝑟𝑢𝑠 =7 nm).

4.2.3.

Self-organization of asymmetric diblocks into periodic Smectic phase In this section, we will focus on the effect of the block asymmetry on the self-organization of hybrid colloids. For this purpose, we will use fdWT-AuNB-M13C7C asymmetric diblocks as building blocks for a Smectic phase formation. Since AuNB PEGylation affects the stability over time of asymmetric hybrid particles (see section 4.2.3), in order to avoid the aggregation of AuNBs involved in these diblocks, they have been stabilized by electrostatic repulsion. Thus, working at low ionic strength, we have looked for the length segregation of viral blocks within a Smectic phase.

To prepare suspensions of asymmetric diblocks, they have been dialyzed against 0.16mM

Tris/HCl buffer (pH 6.5) and concentrated by ultracentrifugation. In this way, we do not fully control the ionic strength of the suspension (see Chapter 2), but we keep it low enough to prevent AuNB aggregation. Thus, we have concentrated asymmetric diblocks to the virus concentration of 17.4±0.6 mg/ml, at which a Smectic phase has been formed (fig. 15). Due to the presence of AuNBs in the interlayer spacing, the contrast between the virus-rich (smectic layer) and virus-poor (interlayer spacing) regions is higher compared to a Smectic phase formed by raw viruses at the same range of particle concentrations (see Chapter 2). Thus, similarly to the discussed above hybrid smectic fibrils, we are able to visualize the lamellar texture of asymmetric diblock suspensions by BF microscopy (fig. 14). So, we have measured the layer spacing as an average value over at least 10 FFT of the BF microscopy images (taken at the different regions of the glass cells 24 hours after sample preparation) and obtained LLayer=0.95 μm. This value is nearly the average of the contour lengths of the two viruses, which compose our asymmetric diblocks (Lfd-wt=0.88 μm, LM13C7C=1.0 μm). Moreover, direct measurements of the layer spacing of the lamellar texture visualized by BF or DIC microscopy has been done in ImageJ using a "line" with a width of 45 pixels (~3 μm) and oriented perpendicular to smectic layers, as it is illustrated in figure 16 Furthermore, the absence of block segregation has been confirmed by dynamics of individual particles within the Smectic phase made of asymmetric diblocks. For this purpose, bicolored asymmetric diblocks consisting of body labeled with fluorescent dye viruses (red M13C7C and green fd-wt) have been added in a tracer amount (1 body labeled virus per 10 4 raw ones) to the suspension of asymmetric hybrid colloids. Single-particle tracking shows that diblocks exhibit hopping-type diffusion within smectic layers, which signs about the formation of the Smectic-A phase. Green fd-wt and red M13C7C blocks involved in two different asymmetric diblocks have been detected

within the same smectic layers (fig. 17), which directly proves the lack of length segregation of viral blocks in the resulting Smectic-A phase. It may be related to the fact that the relative difference in viral block lengths is only 0.12 μm, of about 10%, which could be not enough for their segregation, since this value can be compatible with the interlayer spacing. Consequently, to obtain the asymmetric diblock segregation, we have to increase the length difference for two blocks by using miniM13 and M13C7C blocks. Unfortunately, our experimental results show that miniM13-AuNB-M13C7C diblocks are unstable in time, and their synthesis in a large amount is a time-consuming procedure due to the low reaction yield and the extensive purification procedure (see section 4.2.1). Thus, stabilization of these hybrid colloids after their preparation is needed for investigations of their selforganization into a Smectic liquid crystalline phase, which may provide us a system of segregated rod-like colloids.

Conclusions

In this chapter, virus-based hybrid colloids have been created using a previously developed in our group bioconjugation method of filamentous bacteriophages with gold nanobeads [7]. The influence of virus strains on the reaction yield has been explored not only for M13 viruses of different lengths but also for fd bacteriophages. These biological rods have been used for the synthesis of asymmetrical hybrid colloids, which consist of two viruses of different lengths linked together by 11.1 nm AuNB. A final yield of about 50% of filamentous viruses associated in asymmetric colloids has been achieved (fig. 6). Structural stability with time of fdWT-AuNB-M13C7C and miniM13-AuNB-M13C7C colloids has been studied, and experimental results obtained by quantitative TEM observations show that diblocks formed by miniM13 and M13C7C viruses are not stable and disassemble in aqueous suspensions (fig. 7). Thus, it is not possible to study the self-organization of these asymmetric colloids without their previous stabilization. fdWT-AuNB-M13C7C particles show high structural stability and have been used in investigations focused on their possible block segregation via self-organization into the Smectic-A phase at low ionic strength. Unfortunately, the difference in block lengths has been not sufficient to observe their segregation, i.e. fdWT-AuNB-M13C7C self-organize into a Smectic phase in which both virus strains can be located within the same smectic layer (fig. 17). It has been proved both by measuring layer spacing as well as by singleparticle tracking. We expect that a higher asymmetry in the block lengths (as the use of miniM13-AuNB-M13C7C hybrid colloids) could lead then to some segregation of the two blocks in a Smectic phase.

Moreover, we have developed the approach for the steric stabilization of AuNBs involved in hybrid colloids at high ionic strengths via reaction of Au with PEG12-SH oligomer. Stabilization procedure has been not yet optimized for asymmetric fdWT-AuNB-M13C7C colloids since it leads to their disassembly, but symmetrical M13C7C2-AuNB or fdY21M-AuNB particles after their PEGylation show high structural stability for months. It is extremely useful for investigating their self-organization, as a depletion mechanism requires relatively high ionic strengths, but at the same reduces the amount of material needed for the structure growth (hybrid colloids) by a factor 10. Using virus self-organization from isotropic suspensions under depletion interactions, we have studied resulting phase diagrams of two-component mixtures of hybrid colloids with Dextran 500k at the ionic strength of 110 mM. These particles differ in the phase behavior compared to raw viruses in the same experimental conditions. So, adding Dextran500k to isotropic suspensions of hybrid colloids induces their self-organization into hybrid smectic fibrils with positional particle order instead of self-

Conclusions and perspectives

In this thesis, we have focused on the self-organization of virus-based colloidal particles into various morphologies, including liquid crystalline phases and macroscopic hierarchical architectures.

For this purpose, the nature of interactions between viral colloids has been tuned using very low ionic strength, neutral polymers, and virus bioconjugation with gold spherical nanoparticles. Structures of formed self-organized morphologies as well as their phase behavior have been investigated using optical microscopy and small angle X-ray scattering (SAXS) techniques.

We began by studying the phase behavior of highly repulsive rod-shaped viruses in very low ionic strength suspensions, as described in Chapter 2. We have shown that the presence of thick electrical double layers around viral particles results in a unique phase behavior. We have found that the high electrostatic repulsion between viral particles destabilizes the Smectic-A phase. Our highly repulsive system undergoes a direct from the Cholesteric to Smectic-B phase transition by increasing particle concentration and the existence of the glass transition is not typical for this system of colloidal rods, as proved by single particle tracking and SAXS techniques. The concentration needed for the formation of the Smectic-B lamellar phase has been shifted to a relatively low virus concentration (C>6.2 mg/ml) due to the strong increase of the rod effective diameter. Unfortunately, we have found that the obtained Smectic-B phase from very low ionic strength suspensions evolves with time to the Cholesteric phase due to a continuous increase of the suspension ionic strength. We believe that this increase of the ionic strength is induced by byproducts of a bacteria (E. Coli) life cycle, which cannot be completely removed from the system of filamentous bacteriophages after their production. The preventing of the E. Coli growth in very low ionic strength aqueous suspensions of viruses may provide the stable in time colloidal lamellar liquid crystalline phase with a relatively low virus concentration. In long-term perspectives, this Smectic phase can be used as a transmission diffraction grafting for various photosensitive devices, as was already proposed for more concentrated smectic phases of filamentous phages [1], [2].

As a next step, we have changed interactions between viral colloids from highly repulsive to attractive ones by adding nonadsorbing polymer molecules into their suspensions, which act as and AuNBs (yellow spheres) periodic layers(left) and the scheme of the reflectivity of a typical 1D photonic crystal with indicated photonic bandgap (right) [6].

Since gold nanoparticles involved in virus-based hybrid colloids can support localized surface plasmon resonance, obtained hybrid smectic fibrils and a Smectic phase formed by these particles could find applications in biological sensing [5], cloaking devices [6], solar energy conversion [7], or different photonic devices [1]. Thus, hybrid virus-based colloids organized into morphologies with periodic structures can be used as a one-dimensional photonic crystal, in which alternating virus/gold layers have varying dielectric constants and refractive indexes [7].

When light propagates in the perpendicular direction compared to gold layers (fig. 1), 1D

virus/Au photonic crystals may work on different regimes depending on the ratio between the structure periodicity (defined by LLayer) and the wavelength of incoming light. Thus, incoming light with a particular wavelength range could be not allowed to propagate through the periodic texture of 1D photonic crystal and it can be totally reflected. Such a forbidden wavelength range is named the photonic bandgap (PBG). The position of PBG depends on the periodicity (LLayer), refractive indexes, and thicknesses (virus length and gold diameter) of photonic crystal components. The wavelength located in the middle of PBG, called center of the bandgap, for the photonic crystal composed of layers with thicknesses a and b and corresponding refractive indices n1 and n2 can be calculated as

𝜆 𝑐 = 2(𝑛 1 ×𝑎+𝑛 2 ×𝑏) 𝑚
, where m is a positive integer [8]. For our specific virus/Au system with assuming that the dielectric constant of viruses is nearly the same as for proteins or DNA (nv=1.45) and knowing that for gold nAu~0.2 (for λ>600 nm) [9], the position of the bandgap is 𝜆 𝑐 = 2900 𝑚 nm for periodic lattices made of 1μm long viruses and AuNBs with a diameter of 10 nm. The position of the bandgap decreases to 𝜆 𝑐 = 1019 𝑚 for lattices made of 350 nm long viruses and the same AuNBs. Tuning the position of the PBG driven by either change of the effective refractive index or the thickness of layers is widely used in sensing [6], [10]. Moreover, the tunability of PBG position (i.e. LLayer changes) can be exploited for the fabrication of optical switching components [11] or optical buffers [12]. Thus, for the fabrication of periodic textures, positions of PBG can be varied by using hybrid colloids composed of virus strains and AuNBs of different lengths and diameters, respectively. Using equation AIII.5 for 11.1 nm AuNBs, and AIII.7 for rod-shaped colloids, we can calculate sedimentation coefficients of these particles in their aqueous or 20% water/glycerol dispersions. Table AIII.1 illustrates results of these calculations. According to these calculations, we chose 20% glycerol suspensions for separation of free AuNBs from miniM13-AuNB colloidal particles since the difference in their sedimentation coefficients and, as a result, in applied accelerations is higher compared to aqueous ones. However, the concentrating of miniM13-AuNB colloids should be done in their aqueous suspensions in order to minimize both the centrifugation time and applied acceleration, which helps to avoid aggregation of involved in these colloids AuNBs.

Experimentally, to minimize the loss of miniM13 hybrid colloids, free AuNBs have been removed from their suspensions using 7 centrifugation runs at 15,000g for 30min. MiniM13-AuNB colloids have been concentrated in their aqueous suspensions by ultracentrifugation at 100,000g for 1h.

Figure 2 .

 2 Figure 2. (Top) Image of hard-sphere suspensions illuminated from behind by the white light. The samples are contained in cells of cross-section 1cm×1cm and are numbered from 2 to 10 in order of increasing sphere volume fraction. (Bottom) Phase diagram established according to the visual observations of the samples. The two horizontal axes indicate the measured volume fraction of PMMA sphere core фс and the effective hard-sphere (PMMA core covered with thin polymer layer) volume fraction

Figure 3 .

 3 Figure 3. Schematic interaction energy versus interparticle distance profiles of van der Waals attraction between colloidal spheres of radius R.

Figure 5 .

 5 Figure 5. Schematic illustrations of the liquid isotropic (left) and Nematic (right) phases (a). The red arrow indicates the averaged particle orientation within the ordered Nematic phase, called a director. Schematic illustrations of excluded volumes of two identical rods with length L and diameter D (b-c). Red dashed regions which enclose rods illustrate the excluded volumes equal to πLD 2 for parallel particle orientation (b) and 2L 2 D for perpendicular particle orientation (c).

Figure 6 .

 6 Figure 6. Schematic illustration of the depletion mechanism for pair of colloidal spheres (grey) with radius R in a solution of neutral polymer, presented as small spheres (blue) with radius δ, and the corresponding interaction potential (red solid line) between two big colloids. Voverlap the overlap volume of colloid excluded layers.

Figure 7 .

 7 Figure 7. Schematic representation of a filamentous phage (top). Filamentous viruses are semiflexible monodisperse rods with a diameter of 7 nm and variable length (from 0.35 to 1.2 μm), which depends on the bacteriophage strain. Transmission electron microscopy (TEM) image of the M13 wild-type virus with a length of 1 μm (bottom). Distal and proximal virus terminus cannot be discriminated by TEM.

Figure 8 .

 8 Figure 8. Polarizing microscopy image of Cholesteric (left) [61], differential microscopy image (DIC) of Smectic [32] (middle), and Columnar [20] (right) phases formed by fd viruses in aqueous dispersions with increasing rod concentration. Bottom schemes illustrate virus organization within different liquid crystalline mesophases: Chiral Nematic phase with twisted orientationally ordered particles, lamellar Smectic phases with 1D (SmA) and hexagonal 2D (SmB) positional order of particles, and Columnar phase, which consists of arrays of tubes in which particles have short-range positional order and are hexagonally organized.

Figure 9 .

 9 Figure 9. Phase diagrams for fd viruses as a function of the ionic strength. The Isotropic/Cholesteric phase transition (a) [9], where open and filled circles indicate phase boundaries and dashed region corresponds to phase coexistence. The Cholesteric/Smectic and the Smectic/Columnar phase transitions (b) [33] where blue filled triangles correspond to the Columnar (Col) phase, open inverted triangles to the Smectic (SmA and SmB) phase, and red triangles to the Cholesteric phase. Dashed lines indicate the phase boundaries.

Figure 10 .

 10 Figure 10. (a) Time sequence of an overlay of fluorescence and DIC microscopy images showing labeled particles jumping between smectic layers. The layer spacing is LLayer=0.9 μm. (b) Displacement of a given particle in the direction parallel (red) and perpendicular (black) to the director. The green lines indicate the time for which one particle stays in a given layer [68]. (c) Typical scattered intensity profile obtained by SAXS probing interred side-to-side distance.

Figure 11 .

 11 Figure 11. Scheme of the bioconjugation on virus body (a) and the virus proximal end (b). The full body conjugation has been achieved by reaction between the amine and NHS ester activated compounds (a). Tip conjugation via reaction between disulfide groups that are located only at proximal virus end and gold (Au), platinum (Pt), and silver (Ag) nanobeads (b). The left images are TEM images of formed scepter-like hybrid colloidal particles consisting of one metallic nanoparticle

Figure 1 .

 1 Figure 1. Schematic illustration of the steps carried out during infection of the E.Coli with bacteriophages. The graph on the right illustrates experimentally obtained growth curves for different virus strains.

Figure 2 .

 2 Figure 2. Excitation (unfiled plot) and emission (filed plot) spectra of the green Alexa-488(left) and red Dylight550 (right) fluorescent dyes used for virus body labeling.

Figure 3 .

 3 Figure 3. Scheme of the reaction corresponding to the functionalization of virus capsid with two types of fluorescent dyes. The reaction takes place between surface amino groups and ester groups of the dyes.

Figure 4 .

 4 Figure 4. UV-Vis spectra for stock suspension of 11.1 nm AuNBs used in this thesis.

Figure 5 .

 5 Figure 5. Production of AB2 type hybrid colloids using 11.1 nm AuNBs and M13C7C with initial virus excess of 1/α=NM13C7C/ NAuNBs=2. The fraction of M13C7C is defined by f(M13C7C)=N/Ntot, where N is the number of M13C7C incorporated into Au-M13C7Cn type colloids and Ntot is a total amount of M13C7C viruses.

  Parafilm spacer between them (thickness varies from 20 to 100μm depending on the parafilm stretching) (fig.4). Cells have been sealed by an ultraviolet cured glue (NOA81, Epotecny). One side of cylindrical quartz or glass capillaries have been pre-sealed by flame and UV cured glue, filled with approximately 20 μl of suspension, and then sealed from another side. During a glue hardening under the UV lamp, the main part of the samples has been protected from UV light by covering with some aluminum foil to avoid any photo-bleaching of fluorescent dyes grafted on the virus surface or heating suspensions by light.

Figure 6 .

 6 Figure 6. Side (left) and top (right) view on the optical microscopy cell. For optical microscopy observations, viral dispersions have been placed inside homemade glass cells or cylindrical capillaries (diameter ~ 1.0 mm; Mark-Röhrchen). To avoid the observation of dried samples, thicknesses of all glass cells have been measured before each observation thanks to the objective piezo z-positioner, incrementally moving (step interval: 0.1-0.2 μm) from the coverslipside (bottom) to the slide glass-side (top) of the cell (inverted microscope). For cylindrical capillaries, the suspension levels have been marked after their preparation. A systematic decrease of the cell thickness or the suspension level inside capillary with time signals us about their drying, and these samples have been excluded from any investigations. For refractive index matching of cylindrical capillary curved walls, they have been emerged inside the water bath during observations via optical microscopy.

Figure 7 .

 7 Figure 7. (Left) Scheme of the Optosplit II Andor. The emission wavelength recovered from a mixture of viruses labeled with green or red fluorescent dyes split into two channels by using a dichroic mirror. (Right) Fluorescence images as results of the beam split for red and green body labeled particles in the same field of view taken at the same time.

Tris/

  HCl buffer stock has been prepared by adding 10 ml of 1M HCl and 20 ml of 1M Tris solutions to 970 ml of distilled water by mass. This mixture has Tris and HCl analytical concentrations equal to C s T 20.0 mM and C s HCl 10.0 mM respectively and pH 8.2 at T=20°C. By taking to account that [T + ]=[Cl -]=C s HCl and [H + ]<<[Cl -]>>[OH -] the total ionic strength calculated as

Figure 8 .

 8 Figure 8. Experimentally obtained at 25°C

Figure 9 .

 9 Figure 9. Calculated concentration of dissolved and hydrated carbon dioxide at wide range of pH for low ionic strength buffer with CHCl=8.00×10-2 [mM] and CTris=0.16[mM].

Figure 1 .

 1 Figure 1. Differential interference contrast microscopy image of the fd Smectic phase (a). The high contrast narrow black-white lines are the gaps between smectic layers. A plot of the fd density ρ(z) with the half-width of the gap between two layers σ, layer spacing LLayer (b) [5], and corresponding smectic ordering potential Ulayer (c). Red dashed lines indicate the middle of the smectic layers.

Figure 2 .

 2 Figure 2. Sketch of the Nematic liquid crystalline phase (a), glass state formed within this phase with overlay of particle electrical double layers (b), and schematic illustration of the lamellar SmB phase with a layer spacing LLayer (c) for suspensions of colloidal rods. Rods represent colloid bodies and blue shells around themtheir electric double layers. Bottom insertions are low-resolution polarizing

  4) with the virus concentration 𝐶 𝑣 in [ 𝑚𝑔 𝑚𝑙 ⁄ ], the molecular weight of this virus 𝑀 𝑣 , and the fraction of free counterions 𝑄.

Figure 3 .

 3 Figure 3. Calculated curves and experimental data of the surface charge of fd bacteriophage versus pH. Curve 1 (-----), as calculated from the number of ionizable amino acids of the coat protein; curve 2 (---), as calculated from the number of ionizable residues in the coat protein and in DNA; curve 3 ( ), as calculated from the contribution of residues on the outside of the virus (terminal amino group, Glu 2, Asp 4, Asp 5, Lys 8, Asp 12, Glu 20) [29].

Figure 4 .

 4 Figure 4. Fractions of free counterions Q (solid squares) and the corresponding concentrations of free counterions (open circles) calculated for fd-wt using Manning's model for thick (к0r~1, blue symbols) or thin (к0r<<1, red symbols) cylinders and Trizac's model for salt-free suspensions (Cs<<Cc, black symbols) as a function of the virus concentration in Tris buffer with Ibuffer=0.16mM and pH 6.5. The dashed green line indicates Cs=Ibuffer=0.16mM for comparison.

  C c , Trizac, C s <<C c C c , Manning ( 0 r<<1) C c , Manning ( 0 r~1)

10 𝐶Figure 5 .

 105 Figure 5. Picture of the dialysis device used for establishing experimentally the relation between suspension height and virus concentration, with the illustration of the height (H) measurement (left).Volume-height dependence for the dialysis device with a diameter of 10 mm (right). Black dots indicate experimentally measured volume-height data and red linetheir fit with a linear function.

Figure 6 .

 6 Figure 6. DIC microscopy images illustrating fd-wt suspension before (a) and after dialysis (b) against 0.16mM Tris/HCl "buffer" with corresponding virus concentrations Cin(fd-wt)=32.8 mg/ml and C(fd-wt)=15.8 mg/ml. Red arrows indicate the layer spacing Llayer of formed Smectic phase observed t=7 days after sample preparation. Iridescent suspension bulk with C(fd-wt)=7.5 mg/ml, t=1 day, illuminated with visible light (c) Polarizing microscopy images of the texture observed for the 1.0 mm cylindrical capillary (d-f) and DIC microscopy images of the texture observed for the 100μm thick glass cell (g-h) with C(fd-wt)= 7.5 mg/ml. The light-green arrow indicates cholesteric pitch P. Images illustrate the time evolution form birefringent to fingerprint suspension texture inside the capillary (or from periodic Smectic to not lamellar textures inside the cell). Glass cells contain planar cholesteric domains (cholesteric helix axis is parallel to the incident light) which leads to the absence of the fingerprint texture. Time indicates the elapsed time after samples have been removed from a dialysis bag. For a-b, f-g scale bars indicate 10 μm and 400 μm for c-e.

Figure 7 .

 7 Figure 7. Experimental phase diagrams for the fd-wt phages after their short-term dialysis of about 1 week against 0.16mM ionic strength "buffer" as a function of virus concentration. Samples observations have been done 1 (a) 7 (b) 14 (c) and 21(d) days after their preparation. Dashed lines indicate the phase boundaries and are a guide for the eyes. Magenta regions indicate the virus concentration ranges, where the suspensions evidence strong time evolution. Black squares correspond to the experimentally measured LLayer for the Sm phase and red circles to the measured cholesteric pitch. Open red circles represent the iridescent cylindrical capillaries and open black squaresglass cells with the N * phase. Blue squares indicate I/N * phase coexistence and magenta squaresthe Isotropic phase. Open red circles and open black squares as well as blue or magenta squares do not carry information about the LLayer or cholesteric pitch but indicate the concentrations, where they have been observed. Error bars present dispersion of the measured [Pitch, LLayer and C(fd-wt)] values.

Figure 8

 8 Figure 8 Time evolution of the fd-wt suspension measured heights with the corresponding concentrations of the particles inside dialysis devices, during long-term dialysis against a big reservoir of 0.16 mM Tris/HCl "buffer". Initial concentration of viruses is Cin(fd-wt)=40.2 mg/ml (a) and Cin(fd-wt)=15.4 mg/ml (b). Virus concentrations (right axis) were calculated from the corresponding heights (left axis) as has been described above (eq. 2.9-2.10). Blue circles indicate direct concentration measurements by spectrophotometry. Heights have been fitted with the equation 𝐻 = 𝐻 𝑒𝑞 -(𝐻 𝑒𝑞 -𝐻 𝑖𝑛 )𝑒𝑥𝑝 -2𝑡/𝑡 𝑒𝑞 .

Figure 9 .

 9 Figure 9. Schematic illustration of the virus concentrating procedure using Amicon ® Ultra centrifugal regenerated cellulose filters with an average pore size of 30kDa. For separation of the filtrate from the equilibrated virus suspension, several 2-minute runs of centrifugation with the used acceleration of 2kg have been done.

Figure 10 .

 10 Figure 10. The optical iridescence of the dialysis device, which contains equilibrated fd-wt smectic suspension with Ceq=6.6 mg/ml (a) and of the 1.0 mm cylindrical capillary filled with this suspension (b), both illuminated with visible light. Overlay of DIC (grey) and fluorescence (green) microscopy images (c) with periodic smectic layers at C=15.1 mg/ml. Typical particle trajectories found in the N* (d) and SmB (f) phases and experimental phase diagram for the equilibrated fd-wt phages after long-term dialysis against 0.16mM Tris/HCl "buffer", pH 6.5 as a function of virus concentration (e). Red symbols indicate the measured cholesteric pitch and black rectangles indicate the measured layer spacing (observations t=1 day after sample preparation). Chiral nematic phase [e(I)] has been identified by its typical fingerprint texture observed using polarizing microscopy. The layered texture observed by DIC microscopy in [e(II)] is characteristic of the Smectic phases. The solid line indicates the phase boundaries and is a guide for the eyes. Error bars indicate data dispersion from the average virus concentration and cholesteric pitch.

Figure 11 (

 11 a) presents the diffraction 2D patterns of the suspensions with virus concentrations 8.2, 6.4, 5.6, and 4.5 mg/ml, indicated on the top of each image.

  performed after baseline subtraction as described in Appendix I, results in the presence of sharp peaks with relatively small full widths at half maximum (FWHM) for samples with virus concentrations C(fd-wt)≥6.4±0.1 mg/ml compared to peaks obtained for C(fd-wt)<6.4±0.1 mg/ml (fig.11. e) (detailed description of the manual FWHM determination can be found in Appendix I). It shows the existence of the transition between phases with liquid-like and positional particle orders at C(fd-wt)=6.4 mg/ml. In combination with the layered structure (positional correlations along the viruses), evidenced by DIC microscopy (fig.10 c) and hexagonal particle order, this defines the SmB phase as depicted in the fig.2 (c) for C(fd-wt) ≥6.4±0.1 mg/ml. The positions of q100 diffraction have been extracted and plotted as a function of the virus concentration as shown in fig.11 (d). The determination of q 100 for the lowest particle concentrations ( C ≤ 2.8mg/ml ) has not been possible due to its position at too low angles and the presence of central diffuse scattering from the direct beam.

Figure 11 .

 11 Figure 11. Typical synchrotron X-ray scattering patterns of the liquid crystalline phases at I=0.16 mM (a) with their averaged radial profiles (b) for the virus concentrations 8.2 (black line), 6.4 (blue line), 5.6 (red line) and 4.5 mg/ml (green line). The corresponding concentrations are located on the top of each scattering pattern. The presence of multiple Bragg diffraction peaks(q 100 :q 110 :q 200 :q 210 = 1: √3: √4: √7) for C(fd-wt)≥6.4 mg/ml proves hexagonal packing of the viruses within SmB phase while for suspension with C (fd-wt)<6.4 mg/ml) only q100 peak is detected (c).Log-log scale representation of the virus concentration dependence of the q100 Bragg diffraction position (left ordinate) and corresponding distance between the centers of two neighbor particles s (right ordinate) calculated for hexagonally packed viruses (d). The black line is a fit characterizinga 2D swelling law according to 𝑞 100 = 𝜂 × 𝐶 1/2 with 𝜂 = 3.83 × 10 -2 . Red data points correspond to sharp peaks with FWHM~0.35nm -1 and blue data points to the wide peaks characteristic of liquidlike order with FWHM>0.016 nm -1 . The virus concentration dependence of the FWHM of the main

Figure 12 .

 12 Figure 12. Typical trajectories (a) tracked for immobile particles attached to the glass surface (magenta) and for the particles within the SmB phase (virus concentration 12.1 mg/ml) (black) with their probability distributions (b, c). Parallel positions (z) have been normalized by the LLayer=0.9 μm.

Figure 13 .

 13 Figure 13. Deviation of the 𝜎 𝑟𝑒𝑎𝑙 from the 𝜎 𝑒𝑥𝑝 for real and experimental probability distributions described by the Gaussian functions for their various 𝜎 𝑒𝑥𝑝 /𝜎 𝑃𝑆𝐹 ratios.

Figure 14 .[ 40 ]

 1440 Figure 14. Experimentally obtained probability distributions fitted with Gaussian function (a), deconvoluted probability distributions P(z)real (b) of the particles located within smectic layers and corresponding smectic potentials (c). Presented data (a-c) corresponds to suspensions at t=1 day after sample preparation (virus concentrations are indicated in the plots). Smectic potentials (d)corresponds to suspensions with C(fd-wt)=12.1 mg/ml at different times after sample preparation.

Figure 15 .

 15 Figure 15. Standard deviations 𝜎 𝑒𝑥𝑝 extracted from the Gaussian fits of the corresponding probability distributions 𝑃(𝑧) 𝑒𝑥𝑝 and calculated with eq.2.16 𝜎 𝑟𝑒𝑎𝑙 standard deviation as a function of virus concentration at t=0 day after sample preparation (a) and as a function of time after sample preparation (t=0 day) for C(fd-wt)=12.1 mg/ml.

𝑆𝑖𝑂 2 ( 18 𝑆𝑖𝑂 2 ( 19 Figure 16 .

 21821916 Figure 16. Schematic illustration of the obligate aerobic (I), obligate anaerobic (II) and facultative anaerobic (III) bacteria (illustrated as gray spheres) distribution through their water dispersions, in which one of their sides is exposed to the air (O2), which creates the O2 gradient as shown by the black arrow.

Figure 1 .

 1 Figure 1. Schematic illustration of filamentous phage chirality at different length scales. Chiral amino acids (a) as constituents of α-helical coat proteins (b), which are helicoidally organized to the viral capsid (c). Corkscrew virus conformation of the whole virus body (d), and the macroscopic cholesteric phase (e) formed by these viruses.

Figure 3 .

 3 Figure 3. All-atom representation of the M13 virus surface (a). The distance of 3.3 nm corresponds to the coat protein periodicity. Surface accessible to a sphere of radius 0.5nm, rolling on the allatom representation (b). Colors correspond to the electrostatic potential (red: negative, blue: positive). Coarse-grained representation (c). Stacked light gray spheres (radius of 2.5 nm) representthe core of the virus, while dark gray spheres (radius of 0.6 nm) represent protruding amino acids (each sphere corresponds to 4 amino acids). Red spots correspond to point charges (located at 0.1 nm distance from the virus surface). Black lines show the tangent to a right-handed molecular helix identified on the virus surface (𝜑~41 ᴼ )[31].

Figure 4 .

 4 Figure 4. Cryo-TEM image of the CdSe/CdS nanorod suspension after addition of the depletant (top view [a]). The high-resolution TEM image shows the mutual crystallographic alignment of the wurtzite CdSe/CdS nanorods, where bright spots are columns of CdS (b) [33].

  (b) schematically represents the virus organization within a twisted ribbon. The direction of the twist within these self-assemblies is similar to the one observed in the N* phase of viruses, and it propagates in the perpendicular direction compared to the virus long axis. Consequently, handednesses of twisted ribbons and the N * phase are the same for the given virus and have the same origin[16].

Figure 5 .

 5 Figure 5. Overlaid DIC (red) and fluorescence (green) microscopy images of a liquid-like colloidal membrane (a), twisted ribbon (b) containing a low volume fraction of fluorescently labeled rods, and polarizing microscopy image of stacked membranes (c) with their schematic structure representations as deduced from optical microscopy [16], [27]. Scale bars are 5 μm.

Figure 6 .

 6 Figure 6. DIC microscopy images of achiral (a) left-and right-handed (b) crystalline hexagonal platelets, their stacks (c), smectic fibrils (d), and columnar fibers (e) with corresponding schematic representations of these structures [18], [36]. In the inserts (c-d) are presented overlays of DIC (grey) and fluorescent (red) microscopy images of each structure, where the tracer amount of red bodylabeled viruses has been introduced. Scale bares are 5 μm for a and 2μm for b-d.

Figure 7

 7 depicts the growth kinetics of helical bundles and evidences the decrease with time of the tactoid size during virus self-assembly. After a viral matrix evolves to the pure I phase, depletion of free viruses results in the coexistence of many viral-based morphologies, such as twisted ribbons and hexagonal platelets (fig.8 a-b).

Figure 7 .

 7 Figure 7. DIC microscopy images of the helical bundle growth within the N * tactoid in a twocomponent mixture consisting of fdY21M viruses and PEG8k with initial concentrations of CfdY21M =14,8 mg/ml and CPEG8k =20,2 mg/ml. The time scale in the left corners of the images indicates the time after the observation beginning (lag time from sample preparation time is n10300 min). Yellow dashed line indicates tactoid (nematic droplet) boundaries, and it is a guide for the eyes. Scale bars are 10 μm. Observations have been done in our group by B. Sung within the same tactoid on the different focal depth z=0 μm for images at t=0-2200 min and z=7 μm for images at t=2600-2900 min.

Figure 8 .

 8 Figure 8. DIC microscopy images showing the time evolution of suspensions (a) with the initially I/N * coexisting (C fdY21M =14,8 mg/ml and C PEG8k =20,2 mg/ml) and (b) pure N * (C fdY21M =20.1 mg/ml and CPEG8k =23.9 mg/ml) matrix. Aggregation of self-assembled structures occurs with a time-induced isotropic matrix and can also lead to the formation of twisted ribbons and hexagonal platelets in fdY21M/PEG8k two-component mixtures. Overlay of DIC (gray) and Fluorescence (red) microscopy images of self-assemblies obtained from fdY21M/PEG2k mixtures (c) and their aggregates formed within the isotropic matrix at a long time (d). Dashed squares indicate structure-free regions of the sample and their zooms are presented next to the corresponding images. The white arrow indicates a virus directorwithin the N * phase. Scale bars are 10μm.

Figure 9 .

 9 Figure 9. DIC microscopy images of the hexagonal platelet (side (a) and top (b) views), helical bundle (c) and smectic fibrils (d). Phase diagrams as a function of initial virus concentration obtained using PEG2k (e) and PEG8k (f) as depletants. Solid lines indicate the binodal for I/N * phase coexistence of fdY21M/PEG mixtures (Tris/HCl/NaCl buffer, pH 8.2, I=260mM [e] or I=110mM [f]) at the beginning of virus self-assembly and they are a guide for the eyes. Black squares correspond to the hexagonal platelets formed from an initially isotropic matrix, blue trianglesfor smectic fibrils, and red circles for helical bundles formed from initially pure N * (filled symbols) or I/N * (half-filled symbols) matrix. Scale bars are 2 μm.

Figure 11 .

 11 Figure 11. Schematic illustration of the λplate behavior in polarized white light when light is passing through an optically isotropic sample (a), a birefringent sample with its slow axis (main rod axis) n oriented along (b) and perpendicular (c) to the slow axis of λ-plate (γ). Magenta, blue and yellow squares indicate observed colors.

Figure 13 .

 13 Figure 13. Distribution of the helical bundle pitches measured for the samples at least 15 days after their preparation (t>15 days) and less than 15 days after the preparation (t<15 days) with corresponding average pitch values (Pav), where the meaning of error bars is the FWHM of the Gaussian fit (black solid line) (a). The relation between helical bundle width and pitch (b) measured as illustrated in the scheme. The relation between measured helical bundle width and core diameter, calculated as dcore=Whelix-2Wbundle (c). A dashed red line indicates the longitudinal resolution of the optical microscope.

Figure 14 .

 14 Figure 14. Schematic representations of the left-(top (a) and tilted side (b) views) and right-handed (e-f) helical bundles with corresponding schematic illustrations of their top view z-projections (c, g).Black curved arrows indicate the handedness. Helical bundles with opposite handednesses, as shown by capturing DIC microscopy images at different focal depths (z) perpendicular to the main helix axis (d,h). Red (d) and white (h) arrows indicate the helical bundle part, which is in focus at a given focaldepth.

  hybrid colloids is described in Chapter 1. By increasing AuNB size at a fixed amount of particles, the number of attached viruses to the same AuNB increases (fig.1 a). Thus, as a product of the reaction between 50 nm AuNBs and large excess of M13 viruses, star-like colloids with around 20 viruses attached to the same AuNB (AB20 type hybrid colloids, where A and B indicate the number of AuNB and viral rods involved in the structure, respectively) have been produced (fig.1 b). Based on these findings, methods to control the average amount of attached viruses to the same AuNB have been developed by tuning the AuNB size, virus/AuNB excess ratio, and/or ionic strength used for bioconjugation. Moreover, the approach of virus self-assembly with AB type hybrid colloids has been established to produce diblocks (AB2 type colloidal particles) with body labeled viruses by fluorescent dyes of different types. For this purpose, a body labeled M13C7C with a red fluorescent dye (rM13C7C) has been conjugated with AuNB to produce scepter-like hybrid colloids (rM13C7C-AuNB).

Figure 2 .

 2 Figure 2. Comparison of the experimentally obtained ssDNA sequencing from produced miniM13

Figure 3 .

 3 Figure 3. Distributions of hybrid colloid fractions for various viruses after their bioconjugation with 11.1 nm tannic acid capped AuNBs at the ionic strength of 60mM with CTCEP=2mM and stoichiometric α=NAuNB/Nvirus=1 molar ratio (left). Virus concentrations used for reactions are Cfd-wt=0.20 mg/ml, CM13C7C=0.11 mg/ml, CM13K07=0.14 mg/ml and CminiM13=0.25 mg/ml. The fraction of hybrid colloids with a given amount of attached viruses (or valency, n) to the same AuNB is defined by 𝑓(𝑣𝑖𝑟𝑢𝑠) = 𝑁/𝑁 𝑡𝑜𝑡 , where N is the number of viruses incorporated into hybrid colloids with a given valency n and Ntot is the total number of viruses, including unconjugated ones (i.e. n=0). The average number of viruses per conjugated AuNB <n> is determined from Gaussian fits of the distributions and indicates the bioconjugation ability of a given virus strain with AuNBs. TEM images of formed AB type colloids for the four studied virus strains (right).

  NAuNB=Nvirus where N is the number of particles) M13C7C bioconjugation results in the formation of AuNB-M13C7C (50.1%), AuNB-(M13C7C)2 (45.8%), and AuNB-(M13C7C)3 (4.1%) hybrid colloids at the ionic strength of 60 mM with the addition of 2 mM TCEP. Unreacted (free) viruses have not been detected in M13C7C/AuNB reaction mixture. It results in an average number of M13C7C per one reacted AuNB <n> of 1.48, which has been determined from the Gaussian fit of the structure distribution (fig.3). As expected, M13C7C viruses have the highest reaction efficiency due to the presence of two extra cysteine moieties, which forms disulfide (Cys-Cys) constrained peptides between the 2 nd and 11 th positions of N-terminal of P3 protein (table4.1) compared to other M13 or fd viruses. In the same experimental conditions, the fd-wt strain shows similar reaction efficiency with an average number of fd-wt per one reacted AuNB of 1.37 and 4% of unreacted viruses.Unexpected results have been obtained for the long M13K07 mutant with the same P3 protein as for fd-wt. Bioconjugation of M13K07 results in more than half (55.4%) of unreacted viruses. Relatively low reaction efficiency also shows the miniM13 mutant (<n>=0.87) with 32% of unreacted viruses.

Figure 4 .

 4 Figure 4. TEM image of miniM13 phage with biological contaminations present in short virus suspensions after their purification. Yellow arrows indicate the byproducts which cannot be removed by purification steps from miniM13 suspensions after their production.

Figure 5 .

 5 Figure 5. Schematic representation of the key steps to produce asymmetric hybrid colloids with two viral blocks of different lengths (a), including: (1) conjugation between short viruses [Short virus] and 11nm AuNBs at the proximal end resulting in the formation of [Short virus]-AuNB scepter-like particles; (2) self-assembly of [Short virus]-AuNB scepter-like particles with long viruses [Long virus] in stoichiometric conditions (N[Short virus]-AuNB=NLong virus) resulting in the formation of [Short virus]-AuNB-[Long virus] asymmetric diblocks. The dimensions of Short and Long virusschematic illustrations are not to scale.

Figure 6 .

 6 Figure 6. The yield of virus self-assembly into asymmetric colloidal diblocks fdWT-AuNB-M13C7C (a) and miniM13-AuNB-M13C7C (d) obtained at the ionic strength of 40mM and presented as fractions of different structures calculated by f(virus)=Nv/Ntot, where Nv is a number of viruses involved in a given structure and Ntot is total virus number. The reaction results in a 45% yield of fdWT-AuNB-M13C7C and a 40% yield of miniM13-AuNB-M13C7C asymmetric diblocks. TEM images of the fdWT-AuNB-M13C7C (b,c) and miniM13-AuNB-M13C7C (e-h) asymmetric hybrid colloids.

Figure 7 .

 7 Figure 7. Fractions of miniM13-AuNB-M13C7C asymmetric colloidal diblocks calculated as f(virus)=Nv/Ntot, where Nv is the number of viruses involved in the structure and Ntot is the total virus number obtained after reaction (t=0 day) and after 7 days of suspension storage at 4 o C (t=7 days) (a). The decrease of diblock and triblock fractions in combination with free virus and scepter-like particle fraction increase evidence disassembly of asymmetric miniM13-AuNB-M13C7C colloids with time. TEM images of branched colloidal polymers formed by blocks with different lengths as a result of the asymmetric diblock suspension dissociation and re-assembly during storage (b,c).

Figure 8 .

 8 Figure 8. Schematic representation of the key steps to produce hybrid colloids with sterically stabilized AuNBs (a), including: (1) conjugation of viruses and 11.1 nm AuNBs at their proximal end, which, by varying virus/AuNBs ratio, results in formation of AB or AB2 type hybrid colloids; (2) grafting of water exposed AuNB surface with an excess of neutral polymer containing terminal thiol group (PEG12-SH). TEM images of AB (b) and AB2 (c) type colloids with sterically stabilized AuNBs.

Figure 9 .

 9 Figure 9. Schematic illustration of polymer molecules (black chains) with Flory radius RF grafted to the gold surface. The distance between the centers of two neighbor polymers at their close packing is D=2R F. The curvature of AuNB spherical particle is neglected in the scheme.

(Figure 11 .

 11 Figure 11. Phase diagrams as a function of polymer concentration obtained using Dextran500k and different types of hybrid colloids as well as raw fdY21M viruses (a). Inserts in (a) are schematic representations of the used colloidal particles for studying their self-organization. Dashed lines indicate transitions between the different observed structures and they are guides for the eyes. Red squares correspond to the isotropic matrix (no self-organization of the rod-like particles), blue romps to twisted ribbons, magenta rompto colloidal membranes and black squaresto smectic fibrils formed from the Isotropic matrix. DIC microscopy mages of twisted ribbon (b), liquid-like colloidal membranes (c) formed from fdY21M isotropic suspensions. Bright-field (BF) microscopy image (d) and overlay of DIC and fluorescent microscopy images (e) of individual smectic fibrils formed from (M13C7C)2AuNB(PEG12) suspension in which has been added a tracer amount of sterically stabilized fluorescently labeled bicolored (green and red) diblocks. In the overlaid images (e) we can see a single red scepter-like structure or single virus (left bottom corner) and a triblock consisting of two red and one green blocks (right top corner) Schematic representation of the smectic fibril formed by the self-organization of symmetrical diblocks (f). Red dashed zones indicate the location of AuNBs in the interlayer spacing.

Figure 12 .

 12 Figure 12. Bright-field microscopy images of hybrid smectic fibrils formed from isotropic suspensions of fdY21M-AuNB(PEG12) (a) or (M13C7C)2-AuNB(PEG12) (b) and their fast Fourier transform images, which show the presence of several peaks related to the presence of AuNBs periodic layers with high contrast (Dark regions in bright field microscopy images). Typical trajectories for the particles involved in hybrid smectic fibrils (c). The lack of significant motion signs about SmB like particle organization. Insert in c illustrates an overlay of DIC and fluorescence microscopy images, where (M13C7C)3-AuNB (consisting of two green and one red blocks) is involved in the Smectic-B fibril.

Figure 13 .

 13 Figure 13. Typical synchrotron X-ray scattering radial profile (left) obtained after azimuthal integration of the corresponding scattering pattern (right) of hybrid smectic fibrils formed under depletion attraction induced by adding PEG8k as a depletant. The red dashed line indicates the form factor of the scattering intensity related to the presence of AuNBs in the system. The presence of the sharp Bragg diffraction peak at q=0.072 Å -1 proves long-range positional order of particles within hybrid smectic fibrils.

Figure 14 .

 14 Figure 14. Bright-field microscopy images of merging hybrid smectic fibrils with a branched structure formed under depletion attraction from fdY21M-AuNB(PEG12) (a) and (M13C7C)2-AuNB(PEG12) isotropic suspensions. Dark regions (high light absorption) correspond to the periodic layers of AuNBs. A widening of the width distributions of hybrid smectic fibrils measured 15 minutes, 1, 7 and, 14 days after their preparation (c,d). Solid lines are the fits with the lognormal distribution function of the experimental data.

Figure 15 .

 15 Figure 15. DIC (left) and BF (right) microscopy images of the Smectic phase formed in suspensions of fdWT-AuNB-M13C7C asymmetric diblocks at low ionic strength and C(virus)=17.4±0.6 mg/ml.

  (a). Layer spacing has been determined as a distance between two maximums or minimums of the directly measured grey levels (indicated by magenta arrows in fig.16a). Direct measurements (fig.16a, left) have not shown the presence of the two different layer spacings in the smectic suspension of asymmetric diblocks (black curve). It has evidenced the absence of the segregation for blocks with different lengths, i.e. the formation of the smectic layers with two different layer spacings.

Figure 16 .

 16 Figure 16. Direct measurements (black line) of the layer spacing (LLayer, indicated by magenta arrows) using the lamellar texture of the Smectic phase observed by BF microscopy (a, right image) and simulations (sinusoidal functions [LLayer=L]) for viruses with a contour length L of 0.9 (red line) and 1.0 (blue line) μm (a). Average of the 10 FFT radial integration curves obtained from the BF microscopy images of the Smectic phase formed by fdWT-AuNB-M13C7C asymmetric diblock (b, left) and the typical FFT image (b, right).

Figure 17 .

 17 Figure 17. Overlaid DIC and fluorescence microscopy images of the SmA phase formed in suspensions of fdWT-AuNB-M13C7C asymmetric diblocks with added tracer amount of fluorescently labeled bicolored asymmetric diblocks (with green fdWT and red M13C7C block) at low ionic strength and C(virus)=17.4±0.6 mg/ml with the schematic representation of formed SmA phase where AuNBs are illustrated by yellow spheres, fdWT block by green and M13C7Cby red cylinders (a). Illustration of bicolored asymmetric diblocks positions within smectic layers at different times, where dashed white lines indicate the interlayer spacing and are guides for the eyes. At times 2.6 s and 5.8 s, green and red blocks have been detected within the same layer, which proves the lack of block segregation.

  depleting agents. Thus, in Chapter 3, we have shown how the formation of 1D original chiral superstructures, which we have called helical bundles, can be induced by introducing neutral polymers into Cholesteric suspensions of hard viral rods. The structure of these chiral architectures, as well as their stability with time, have been investigated. We have found that the helical bundle van der Waals attractions between introduced gold nanoparticles (which are linked with viruses and form virus-based hybrid colloids) and induced depletion interactions.Moreover, in Chapter 4 the influence of virus strains with different contour lengths on the reaction yield with gold nanobeads has been investigated. Based on our experimental results, bacteriophages with different lengths have been used for producing asymmetric virus-based hybrid colloids. Thus, hybrid colloids with weak (M13C7C and fd-wt viral blocks with lengths of 1.0 and 0.9 μm) and high (M13C7C and miniM13 viral blocks with lengths of 1.0 and 0.35 μm) asymmetries have been obtained. In contrast to stable in time hybrid colloids with weak asymmetry, highly asymmetric virus-based diblocks show to be unstable and disassemble with time. Stable hybrid colloids with weak asymmetry have been used to study the possible segregation of their blocks via self-organization into the Smectic-A phase. Unfortunately, the difference in block lengths has not been sufficient to observe their segregation in smectic layers of different spacings, as proved by measuring a unique layer spacing (LLayer) and by the location of individual viral blocks within smectic layers. We assume that a higher asymmetry in the block length involved in virus-based hybrid colloids could lead to some segregation of two blocks in a Smectic phase. Thus, to study possible length segregation of colloidal blocks, our short-term goal is to stabilize virus-based colloidal diblocks with high asymmetry in their aqueous dispersions.

Figure 1 .

 1 Figure 1. Scheme of the 1D photonic crystal consisting of filamentous bacteriophage (grey cylinders)

Table 0 .

 0

	Virus	Mutation compared to fd-wt strain	Contour length, L (μm)	Persistence length, P (μm)	Total negative charge per virus at pH 8.2
	fd-wt	-	0.88	2.8	8800
	fdY21M	P8: Tyr21→Met21	0.92	9.9	8800
	M13	P8: Asp12→Asn12	0.88	2.8	6160
	M13K07	P8: Asp12→Asn12	1.2	2.8	8400
	M13K07Y21M	P8: Asp12→Asn12 Tyr21→Met21	1.27	9.9	8400
	miniM13	P8: Asp12→Asn12	0.35	2.8	2450
	M13C7C	P8: Asp12→Asn12 P3: extra cysteines	1.0	2.8	7000

1. Summarized properties of the different fd and M13 bacteriophage strains

Chapter 1 Experimental Materials and Methods Contents 1.1. Introduction

  ..........................................................................................................................

	3, we introduce the effective attraction between viral rods via depletion
	mechanism. The neutral polymers are selected to induce virus self-organization into the structures
	with positional particle order. Virus self-organization is initiated by adding polymer into the
	Cholesteric liquid crystalline phase with the formation of original chiral architectures. The structure,
	stability with time, and chirality (handedness) of the resultant morphologies are studied using SAXS
	and optical microscopy techniques. Phase diagrams of virus/polymer two-component mixtures are
	determined and compared for two different polymer sizes.
	In the last Chapter, we increase van der Waals attraction between colloids by changing the
	physical properties of investigated viral particles. For this purpose, we use bioconjugation of virus
	proximal ends and gold nanobeads for introducing gold into viral particles, which induces additional
	attraction. Moreover, thanks to the reaction of gold nanobeads with bacteriophage strains of different
	lengths, we introduce weak asymmetry into virus-based colloids. We study the self-organization of
	hybrid colloids consisting of one (scepter-like particles) or two (diblocks) viruses attached to the same
	gold nanobead under high electrostatic repulsion or soft effective attraction. The effect of introduced
	into colloidal diblocks weak asymmetry is used for investigation of possible length segregation of the
	respective blocks in the lamellar Smectic-A phase formed at high electrostatic repulsion. The self-
	organization of symmetrical hybrid colloids (scepter-like particles and diblocks) is studied in their
	virus/polymer two-component isotropic mixtures. The structure of resultant self-organized
	architectures via depletion mechanism, as well as corresponding phase diagrams, are established
	using SAXS and optical microscopy techniques.
	In general conclusions, we summarize all the results obtained during the self-organization of
	viral colloids, including raw viruses and hybrid virus-based particles.

1.2. Virus production and purification

  ......................................................................................

1.3. Preparation of chemically modified fluorescent viruses

  ...................................................

1.4. Preparation of hybrid virus-based colloids

  ........................................................................ 1.4.1. Production of the AB type hybrid colloids ................................................................... 1.4.2. Production of the AB2 type hybrid colloids .................................................................

1.5. Optical microscopy techniques: sample preparation and observation

  ...........................

1.6. Small-angle X-ray scattering

  ...............................................................................................

1.7. Preparation of Tris buffer solutions with millimolar ionic strength range

  ....................

1.8. Preparation of the 0.16mM Tris/HCl buffer

  ......................................................................

1.9. Preparation of samples with depletion interactions between particles

  ...........................

1.10. References

  .............................................................................................................................

Table 1 .

 1 1. Calculated overlap concentrations of different filamentous viruses.

	Virus strain	L, μm	Mv×10 10 mg/mol Cv * , mg/ml
	fd-wt/fdY21M 0.88 [6]	1.64	0.039
	miniM13	0.35[15]	0.56	0.365
	M13C7C	1.0 [16]	1.85	0.043
	M13K07	1.2 [7]	2.22	0.021

Table 1 .

 1

2. Calculated concentrations of each ionic species in the low ionic strength buffer, and their limiting molar conductivity (λ°) values at 25°C

Ionic species Concentration, [mM] Equation used for concentration calculation λ°, [S×cm 2 /mol]

	H +	3.16 × 10 -4	(1.11)	349.6 [21]
	OH -	3.18 × 10 -5	(1.12)	199.1 [21]
	HCO3 -	7.64 × 10 -2	(1.13)	44.5 [21]
	CO3 2-	1.36 × 10 -5	(1.14)	138.6 [21]
	Cl -	8.00×10 -2	(1.8)	76.3 [21]
	T

+

1.56 × 10 -1

(1.15) 29.7

[19]

Chapter 3 Self-assembly of viral rod-like particles into helical superstructures Contents 3.1. Introduction

  References ..............................................................................................................

	3.4.

............................................................................................................ 3.1.1. Depletion interactions ....................................................................................... 3.1.2. Twist between filamentous bacteriophages in their Cholesteric liquid crystalline phase................................................................................................ 3.1.3. Virus self-assemblies formed under depletion interactions ..............................

3.2.

Results and discussions .......................................................................................... 3.2.1. Influence of the PEG size on the helical bundles growth stability ................... 3.2.2. Phase diagrams of fdY21M/PEG mixture ........................................................ 3.2.3. Investigations of the helical bundle structure ................................................... 3.2.4. Helical bundle handedness and periodicity .................................................... 3.3. Conclusions ............................................................................................................

Table . 4

 . .1. Experimentally obtained by polymerase chain reaction (PCR) amino acid sequence of the P3 minor protein for M13 and fd virus strains.

	Virus strain		P3 protein form experimental DNA sequence
	fd-wt/fdY21M/M13/M13K07	H2N-A	ETVESCLAKP HTENSFTNVW…
	M13C7C	H2N-A<CDPVREATCGGG>ETVESCLAKP HTENSFTNVW …
	Expected P3 protein sequence [24]

  which occupies one PEG12 molecule 𝑆 𝑃𝐸𝐺12 = 𝜋𝑅 𝐹 2 = 9.07(𝑛𝑚 2 ), where RF=√6 × Rg = 1.7 𝑛𝑚, by neglecting the AuNB surface occupied by filamentous viruses, we can calculate the maximal number of PEG12 molecules, which can be attached to the same AuNB as

		𝑁 0 (𝑃𝐸𝐺) = 0,907 ×	𝑆 𝐴𝑢𝑁𝐵 𝑆 𝑃𝐸𝐺	=	2 4𝜋𝑟 𝐴𝑢𝑁𝐵 𝜋𝑅 𝐹 2	(4.1)
	where SAuNB is the surface area of AuNB with the radius rAuNB.
	Thus, for 11.1 nm AuNB N0(PEG12)=171 molecules/AuNB. Using the excess of 50 compared to
	N0(PEG12) [27], the experimental excess of PEG12SH molecules which has been used for steric
	stabilization of 11.1 nm AuNBs is 𝛼 𝑃𝐸𝐺 = 50 × 𝑁 0 (𝑃𝐸𝐺) = 8531 molecules/AuNB.
	In suspensions of hybrid colloids, the concentration of AuNBs has been measured by light
	absorption, and PEG12-SH mass needed for 1 ml of hybrid colloid suspension is calculated as
		𝑚(𝑃𝐸𝐺) =	𝐶 𝐴𝑢𝑁𝐵 𝛼 𝑃𝐸𝐺 𝑁 𝐴	× 𝑀 𝑃𝐸𝐺	(4.2)
						t=0 days, N tot =203
		50				t=4 days, N tot =223
						t=7 days, N tot =258
		40				t=10 days, N tot =276 t=14 days, N tot =233
	(virus)	30
	f	20
		10
		0
		Free virus	Monoblocks	Diblocks	Triblocks
	Figure 10. Fractions of fdWT-AuNB(PEG12)-M13C7C asymmetric colloidal diblocks calculated as
	f(virus)=Nv/Ntot, where Nv is a number of viruses involved in this structure and Ntot is a total virus
	number obtained after PEGylation (t=0 day) and after 4, 7, 10, 14 days of suspension storage at 4 o C.
	AuNBs/virus ratio stays the same for all TEM observations. Decrease of diblock and triblock fractions
	in combination with the increase of the free virus fraction evidence disassembly of the asymmetric
	fdWT-AuNB(PEG12)-M13C7C colloids with time.
	Using this simple procedure fdY21M-AuNB scepter-like particles, symmetric M13C7C 2 -
	AuNB and asymmetric fdWT-AuNB-M13C7C diblocks have been sterically stabilized. After AuNB

Table AIII .

 AIII 1. Summery of calculated and applied centrifugation conditions for a suspension of height 8 cm.

	Object	Solvent	Sedimentation coefficient (s)	Theoretical time × acceleration
	miniM13		3.41×10 -12	361kg×90 min
	11.1nm AuNB	Water	1.25×10 -10	15kg×90 min
	miniM13-AuNB		1.95×10 -11	76kg×90 min
	miniM13		1.63×10 -12	904kg×90 min
	11.1nm AuNB	20% glycerol	6.58×10 -11	23kg×90 min
	miniM13-AuNB		9.37×10 -12	158kg×90 min

Chapter 2 with the initially SmB phase starts from the suspension meniscus (air/liquid interface), and it gradually propagates through all capillary with time (fig. 17 b). Similar texture evolution, which usually propagates from the entrance of the cuvette (air/liquid interface) to the dispersion bulk, has been detected by K. Kang and J. K. G. Dhont in their experiments (fig. 17 c) [25]. Besides, the bacteria growth mostly located at liquid/air interface can also explain why the suspension placed inside samples with a higher ratio of the glass surface area to solution volume but a lower area of the air/liquid interface (glass cells) evolve slower than inside samples with a lower glass surface area to solution volume ratio and higher area of the air/liquid interface (cylindrical capillaries).

DIC microscopy image taken at the suspension meniscus at t= 7days after capillary preparation (a).

The cylindrical-shaped objects in the liquid phase boundary are bacteria. Polarized microscopy images of the liquid(birefringent)/air(black) interface for the same capillary at different time after its preparation (b): birefringent capillary at t=0-1 day, the beginning of the fingerprint texture formation close to the capillary meniscus at t=6 days, and well-established fingerprint texture at t=7 days.

Polarized optical microscopy images of the cuvette with a thickness of 1 mm filled with fd-wt suspension with C(fd-wt)=13.6 mg/ml (I=0.16mM) at different time after its preparation [25]. The entrance to the cuvette (space between two black squares on the left side of each image) is about 1 mm.

tracking of green and red blocks individually allows experimentally to have access to the dynamics at the single-particle level [7]. We can use the production method of bicolored diblocks as a general strategy for other diblock preparation. Thus, new hybrid particles consisting of linked together blocks with different physical (hydrophilicity, charge, flexibility) [8] or shape (blocks with different aspect ratios) [9] properties can be obtained. [7].

Figure 1. Schematic representation of filamentous bacteriophage bioconjugation with gold nanobeads (AuNBs) (a). The amount of conjugated viruses with the same AuNB is varying by increasing AuNB diameter in presence of large excess of viruses. TEM images and corresponding schemes of hybrid colloids experimentally obtained via conjugation of M13C7C viruses and AuNBs with various diameters (red values). Reactions have been done by Cheng Wu (former Ph.D. student of our group) at the ionic strength of 200mM

A difference in physicochemical properties of blocks involved in complex structures (AB2 type colloids, colloids with grafted flexible polymer or block copolymers) may induce their segregation during collective self-organization [10]- [12]. Thus, blocks of block copolymers segregate into different phases in their melts if polymer segments are chemically incompatible.

Considering that constituents within a given copolymer chain are molecularly connected, their phase segregation will be restricted to submicroscopic dimensions. The morphology of the resulting Chapter 4 organized structures with liquid-like order, such as twisted ribbons and colloidal membranes formed from two-component mixtures of raw viruses with the same depletant (polymer) [31]. Obtained hybrid smectic fibrils consist of periodic virus layers separated by layers of AuNBs. Formation of these smectic fibrils is induced by van der Waals interactions between AuNBs, which favor their segregation into the layers. Besides, these attractive interactions lead to the merging with time of different hybrid smectic fibrils resulting in both branched and wider fibrils, which have never been observed for usual smectic fibrils made of raw viruses.

Overall, here we present a method to create materials with periodic layers of gold nanobeads.

Since noble metals have unique properties, in particular, they can support localized surface plasmon resonance, these periodic layers of AuNBs separated by viral layers can find applications in biological sensing [34], cloaking devices [35], or solar energy conversion [36]. Moreover, after the stabilization with time of miniM13-AuNB-M13C7C colloids, their self-organization and possible segregation can be studied thanks to optical microscopy methods. It may provide a system with regular layers of different lengths, which could find an interest in fundamental studies of the segregation process as well practical applications in optics. growth has been observed only within the Cholesteric liquid crystalline phase at a small range of polymer concentrations. The surrounding environment limits the stability of these chiral superstructures, and as soon as a suspension matrix during bundle growth evolves to the isotropic phase, helical bundles aggregate. As has been proved by optical microscopy and SAXS, within helical superstructures viruses are oriented along the main bundle axis and exhibit long-ranged hexagonal order. Investigations focused on the chirality of these self-organized helices show the formation of two enantiomeric forms of bundles (left-and right-handed). Unfortunately, using these chiral superstructures is limited by their metastability, and the quantitative characterization of helical bundle chirality raises a challenge. The stabilization of helical bundles out of the Cholesteric phase could provide a promising system of macroscopic helices, which is the main perspective for their future study. Thus, weighty chirality investigations of self-organized macroscopic helices will not be limited by their stability and could provide fundamental information about the chirality amplification in these superstructures. In long-term perspectives, stabilized helical bundles could be used as templates [3], [4] for the synthesis of rigid inorganic macroscopic helices with target physical properties (such as electrical permittivity, hydrophobicity, charge) dictated by chemical compounds used for their mineralization.

In the last Chapter of the thesis, we have increased the complexity of the attraction in our viral system by introducing gold nanoparticles into self-assembled hybrid virus-based colloids. These virus-based hybrid colloids have been obtained using the previously developed in our group bioconjugation method between the proximal end of filamentous bacteriophages and gold nanobeads.

Various hybrid colloids consisting of one (scepter-like particles) or two (diblocks) viruses attached to the gold nanobead have been produced. We have developed an approach for the steric stabilization of gold nanobeads involved in virus-based hybrid colloids at high ionic strengths. It allows us to investigate the self-organization of hybrid colloids under soft effective attraction, which requires to screen electrostatic repulsion between them. Depletion driven self-organization of symmetrical virusbased colloids (scepter-like particles and diblocks) has been induced in their isotropic suspensions, and phase diagrams of two-component virus/polymer mixtures have been established using optical microscopy. We have found that hybrid virus-based colloids differ in the phase behavior compared to raw viruses in the same experimental conditions. In contrast to raw virus/polymer two-component mixtures, for which structures with liquid-like particle order have been obtained, the self-organization of hybrid colloidal particles under the same experimental conditions leads to the formation of hybrid smectic fibrils with positional particle order. These new hybrid smectic fibrils consist of periodic virus layers separated by layers of gold nanobeads, and their growth is induced by a combination of Appendix I A1.

Direct beam parameters

Synchrotron experiments for fd-wt suspensions at I=0.16mM have been performed at the ESRF-ID02 beamline with used a sample to detector distance 5 m and wavelength λ = 0.775 Å, while for self-assemblies formed under depletion interactions from fdY21M/PEG2k two-component mixtures, the SOLEIL-SWING beamline with used a sample to detector distance 2 m and wavelength λ=0.827 Å has been used. The x-ray beam resolution functions are approximated as a Gaussian distribution. The azimuthal integration of direct beam scattering patterns results in the manually measured full widths at half maximum (detailed description of the manual FWHM measurement method can be found in section A3 of this Appendix) of 3.1x10 -4 Å -1 for ESRF-ID02 beam (5 m, λ=0.775 Å) and 1.0x0 -3 Å -1 for SOLEIL-SWING beam (2 m, λ=0.827 Å).

Figure AI.1. Synchrotron X-ray radial intensity profiles of the direct beams (ESRF-ID02 [left] and SOLEIL-SWING [right]

) fitted with a Gaussian function. Inserts are their radial intensity profiles.

A2.

Background subtraction for q100 Bragg diffraction peaks

For SAXS investigations performed in Chapter 2 and Chapter 3, radial profiles after azimuthal integration of corresponding X-ray scattering patterns have a background scattering (coming mostly from the central scattering of the direct beam) at the range of q where (100) Bragg diffraction peaks have been detected. In order to find the center of the q100 peak, a linear background has been subtracted from experimentally obtained (raw) intensities, as shown in figure AI.2 for low ionic strength suspensions. The raw scattered intensity (I) at given q value can be expressed as a sum of background (Ib) and real (I * ) intensities (I=Ib+I * ). To find the position of the q100 peak, real radial intensities have been fitted with Gaussian (for samples with particle positional order) or Lorentzian (for samples with particle liquid-like order) functions using Origin. Positions of peak centers were extracted from the fits.

FWHM determination for q100 Bragg diffraction peaks

To analyze the width of q100 peaks, which carries information about particle order within probed viral suspensions or their two-component mixtures with neutral polymer, the manual measurements of the full width at half maximum (FWHM) has been performed. For this purpose, the distance between the peak center (position of q100 peak) and its right shoulder has been measured at half maximum of its intensity (I0/2), called half-width at half maximum (HWHM), as depicts figure AI.3. The advantage of measuring HWHM (and not directly FWHM) lies in the higher background intensity at lower q, which induces higher noise to the left peak shoulder compared to the right one (fig.AI.2. a,c), especially at low virus concentrations (and low q100) in the 0.16mM fd-wt suspensions, described in Chapter 2. Thus, FWHM has been calculated as twice HWHM. For

Figure AI.3. Schematic illustration of the q100 peak manual HWHM determination from real radial intensity profiles obtained after background subtraction (a), where Io is a maximum of the intensity and the red arrow indicates HWHM measured at the half of maximal intensity. Real radial intensity profiles for which the precise determination of HWHM is not possible due to the low signal-to-noise ratio (b).

Appendix II A1.

Convolution of two Gaussian functions

Let's consider two Gaussian functions centered at xc=0 (eq.AII.1)

where 𝜎 is a standard deviation of the Gauss distribution The convolution of two functions is an integral that expresses the amount of the overlap of one function g(x) as it is shifted over another function f(x) and can be written as

However, the usual approach is to use the convolution theorem [1], which defines the convolution via Fourier transformed functions 𝐹[𝑓(𝑥)]. Thus, convolution can be written as

where

is Fourier transformation of the function Using Euler's formula, properties of the sin and even cos functions (𝑠𝑖𝑛(𝑛𝜋) = 0;

), the Fourier transform of the Gaussian (eq.AII.1) can be written as

Using the standard form of the integral (eq.AII.5) [2] we can find the Fourier transformed Gaussian (eq.AII.6)

Eq. AII.6 shows that the Fourier transform of the Gaussian is Gaussian with same standard deviation.

The convolution of two Gaussians centered at xc=0 can be found using inverse Fourier transformation

Application of the Eurel's formula with taking to account 𝑠𝑖𝑛(𝑛𝜋) = 0 and using the integral (eq.AII.8) we can write convoluted Gaussians as followed (eq.AII.9)

(AII.9)

After comparison of the eq.AII.9 with eq.AII.1 we can clearly see that the convolution of two Gaussians results in a Gaussian function with the standard deviation 𝜎 𝑐𝑜𝑛𝑣 (eq.AII.10) A2.

Calculation of the sedimentation coefficient of miniM13 based colloids

Centrifugation is one of the most commonly used methods of separation and concentration of colloidal particles. In our experimental research, centrifugation has been often used for purification and concentration of raw viruses as well as for virus-based hybrid colloids. For this purpose, depending on the investigated system, various accelerations have been applied. Cheng Wu, a former student of our group, numerically calculate accelerations for 1μm long viral colloids (raw viruses and hybrid colloids) and spherical nanobeads in aqueous dispersions [2]. Here, based on his calculations, we will find sedimentation coefficients as well as needed accelerations for sedimentation of miniM13 viruses and its hybrid colloids in aqueous and 20% glycerol mediums.

In a much shorter time compared to the duration of centrifugation, particles reach terminal velocity, which determines as

where a is the applied acceleration and S is the sedimentation coefficient of the particle.

With time, particles dispersed in a medium migrates through the suspension height (l) until they reach the bottom and precipitate as a pellet. It is possible if the centrifugation will proceed for long enough time (t), which depends on the sedimentation coefficient at fixed acceleration (eq.AIII.2).

Thus, colloidal particles can be separated by centrifugation thanks to the difference in their sedimentation coefficients (by varying centrifugation time at fixed acceleration or by varying acceleration at fixed centrifugation time, see eq.AIII.2). Consequently, to determine conditions for miniM13 centrifugation (acceleration and time), in the case of experimentally fixed suspension height, calculations of sedimentation coefficients for different particles have to be done.

where t is the centrifugation time and l is the suspension height.

When centrifugation is performed for a colloidal particle, there is a centrifugal force (FC), and a drag force (FD) acting on it (in this situation, gravity of particles is negligible compared to other forces). When a particle reaches terminal velocity, these forces become equal [2]. For spherical particles they can be determined as

where 𝜌 𝑁 is the density of the spherical nanoparticle (for Au 𝜌 𝑁 = 19.4kg/m 3 ), 𝜌 𝑆 is the density of the solvent, D is the sphere diameter, 𝜂 is the dynamic velocity of the solution (for the water 𝜂 = 0.00100 Pa×s, for the 20% glycerol/water mixture 𝜂 = 0.00198 Pa×s), and S is the sedimentation coefficient.

Thus, the sedimentation coefficient for a spherical particle can be calculated as [2] 𝑆(𝑠𝑝ℎ) = (𝜌 𝑁 -𝜌 𝑆 ) × 𝐷 2 18𝜂 AIII.5

The terminal velocity for rods with the length L and diameter d during their sedimentation via centrifugation with applied centrifugal force Fc can be determined as [2], [3] 𝑣 For aqueous suspensions of miniM13 viruses, parameters of the system are: the length L=0.35μm, the diameter d=7nm, the raw virus density 𝜌 𝑚𝑖𝑛𝑖𝑀13 =1.285×10 3 kg/m 3 , the density of solvent (water) 𝜌 𝑆 =1.00×10 3 kg/m 3 and the dynamic velocity of the water 𝜂 = 0.00100 Pa×s. In the case of using colloidal dispersions in 20% (by volume) glycerol/water mixture, the solvent density increases to 𝜌 𝑆 =1.06 ×10 3 kg/m 3 and the dynamic velocity of the 20% glycerol/water mixture is 𝜂 = 0.00198 Pa×s. Using equation AIII.7, the sedimentation coefficient can be calculated for raw viruses as well as for virus-based rod-shaped hybrid colloids, such as AB type particles. To do so, let's assume that an AuNB on the tip of this hybrid colloid is homogeneously spread on the surface of the rod, and the resulted rod keeps the same length as original one [2]. Also, this resulted rod keeps the same volume and mass as original AB type hybrid colloid, which are

AIII.8

Thus, the volume of hybrid miniM13-AuNB particle is 1.42×10 -23 m 3 , and its mass is 3.12×10 -20 kg.

Consequently, the density of miniM13-AuNB is 𝜌 𝐴𝐵 = 2.20×10 3 kg/m 3 . The diameter of the resulted rod can be calculated as [2] 𝑑 𝐴𝐵 = √ 𝐷 2 3𝐿 + 𝑑 2 AIII.9