Jasna Kovačič
email: jasna.kovacic@mf.uni-lj.si

Bojan Božič

Saša Svetina

Budding of giant unilamellar vesicles induced by an amphitropic protein β 2 -glycoprotein I

β 2 -glycoprotein I (β 2 GPI) is a plasma protein capable of binding reversibly to membranes, and is classified among the amphitropic proteins. Part of the protein intercalates into the outer membrane leaflet, altering the difference between the preferred areas of the membrane leaflets, which results in membrane shape transformations. Budding, as a specific example of such shape transformations, was studied using giant unilamellar vesicles. Our aim was to identify the vesicle parameters that influence the degree of membrane budding by studying this process qualitatively and quantitatively. A simple theoretical model has been developed and assessed against the experimental observations. The results show that β 2 GPI binds in a concentration dependent manner, causing transitions between vesicle shapes with increasing numbers of buds. Higher numbers of buds are characteristic of larger and/or more flaccid vesicles. When the vesicle membrane is strained, a higher β 2 GPI concentration is needed to produce the same effects as on the unstrained vesicle. Vesicles were found to be highly individual in their behaviour, so each was treated individually. Specific vesicle behaviour was found to be the consequence of the neck between the main vesicle body and the buds, which could be either open, closed for the exchange of solution, or closed for the exchange of both solution and membrane.

Introduction

The class of proteins defined as amphitropic [START_REF] Burn | Amphitropic proteins: a new class of membrane proteins[END_REF] can translocate reversibly from the cytosol/plasma into the membrane of cells. Three membrane binding motifs have been proposed and described in detail [START_REF] Johnson | Amphitropic proteins: regulation by reversible membrane interactions (Review)[END_REF]: (i) a lipid clamp that regulates the association of a protein with a specific lipid headgroup, (ii) a covalently bound lipid anchor that embeds in the membrane and (iii) an amphipathic helix that is embedded in the membrane parallel to the membrane surface, in such a way that the hydrophobic face of the helix orients towards lipids and the polar face to the aqueous phase. β 2 -glycoprotein I (β 2 GPI) is an amphitropic protein of type (iii) but a structurally distinct binding motif with a patch of positive charges and a hydrophobic loop inside this patch. β 2 GPI is a 50 kDa plasma protein. Its crystal structure reveals five domains connected in an elongated fish-hook shape (Fig. 1a). While the first four domains are regular short consensus repeats, the fifth domain differs structurally and functionally [START_REF] Bouma | Adhesion mechanism of human β2-glycoprotein I to phospholipids based on its crystal structure[END_REF]. It contains a 20 nm 2 large patch containing 14 positively charged amino acid residues and a hydrophobic loop that consists of seven amino acid residues. The loop is approximately 1.5 nm long, 1.2 nm wide and 0.9 nm deep (Fig. 1a), and the area of the cross section of the loop of about 1 nm 2 . These characteristics indicate that the fifth domain is implicated in the membrane binding which is mediated by strong electrostatic interactions between its positive charges and the negative charges of the lipid polar headgroups [START_REF] Steinkasserer | Activity, disulfide mapping and structural modeling of the fifth domain of human β2-glycoprotein I[END_REF]. Binding of β 2 GPI does not take place in the absence of the latter. The affinity increases with increasing molar fraction of negatively charged lipids in the membrane and decreases with increasing ionic strength of the medium [START_REF] Wurm | β2-glycoprotein-I (Apolipoprotein H) interactions with phospholipids vesicles[END_REF][START_REF] Willems | Role of divalency in the high-affinity binding of anticardiolipin antibody β2-glycoprotein I coplexes to lipid membranes[END_REF][START_REF] Harper | Characterization of β2glycoprotein I binding to phospholipid membranes[END_REF][START_REF] Wang | The insertion of human apolipoprotein H into phospholipid membranes: a monolayer study[END_REF][START_REF] Gamsjaeger | Membrane binding of β2-glycoprotein I can be described by a two-state reaction model: an atomic force microscopy and surface plasmon resonance[END_REF]. The association is further strengthened by hydrophobic interactions in which the hydrophobic loop of the fifth domain is anchored into the outer phospholipid leaflet of the membrane (Figs. 1b and1c).

The biological role of β 2 GPI is not certain, but it is believed that when inserted in the membrane it is recognized by antiphospholipid antibodies (aPL) [START_REF] Galli | Anticardiolipin antibodies directed not to cardiolipin but to a plasma protein cofactor[END_REF] which are associated with antiphospholipid syndrome, an autoimmune disease [START_REF] Mcneil | Antiphospholipid antibodies are directed against a complex antigen that includes a lipid-binding inhibitor[END_REF]. One possible example of β 2 GPI involvement in cellular processes is the formation of apoptotic blebs on cells losing transmembrane lipid asymmetry at the beginning of apoptosis. Abundant quantities of β 2 GPI were detected in the blebs [START_REF] Casciola-Rosen | Surface blebs on apoptotic cells are sites of enhanced procoagulant activity: Implications for coagulation events and antigenic spread in systemic lupus erythematosus[END_REF], suggesting that β 2 GPI plays a role in vivo in budding and vesiculation of membranes. It could thus act as an immunological marker for macrophages when removing liposomes or apoptotic cells [START_REF] Connor | Exposure of phosphatidyserine in the outer leaflet of human red-blood-cells -relationship to cell-density, cell age, and clearance by mononuclear-cells[END_REF]. In an earlier study of interactions of β 2 GPI

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with giant unilamellar vesicles (GUVs) [START_REF] Ambrožič | Budding, vesiculation and permeabilization of phospholipids membranes -evidence for a feasible physiologic role of β2-glycoprotein I and pathogenic actions of anti-β2glycoprotein I antibodies[END_REF], buds were observed to form on the surface of GUVs. Shape transformations of GUVs could thus constitute a promising tool with which to probe the effects of this type of protein on membranes, in particular by quantitative evaluation of the shape behaviour of flaccid GUVs in their presence. It is our purpose to identify the vesicle parameters crucial to influencing vesicle behaviour in the presence of β 2 GPI. The approach introduced in this study may also be of use in studies of the effects of a variety of other proteins that have been identified to directly bind and deform membranes, e.g. proteins involved in membrane traffic processes [START_REF] Farsad | Mechanisms of membrane deformation[END_REF].

The outline of the paper is as follows: we first present a theoretical background for mechanisms by which the binding of amphitropic proteins to the outer leaflet of membranes affects vesicle shapes. This provides a lead for designing the most informative experiments.

The description and outcome of the necessary control experiments are presented in the Supplementary information. The results of the dependence of budding of GUVs on β 2 GPI concentration are examined critically in the Discussion by comparing them with the predictions of the proposed model.

Theoretical background

Vesicle budding is a specific example of vesicle shape transformations. The fact that amphitropic proteins affect vesicle shape indicates a coupling between their binding properties and the elastic energy of the membrane. This coupling is manifested by the mutual interdependence of the number of bound proteins and the vesicle shape. Here we shall treat this problem by minimizing free energy of the system (G), which is the sum of the elastic energy of the phospholipid membrane (W) and the free energy of the membrane bound proteins (G p )

G = W + G p . (1)
In defining W we shall take into account that we are concerned with the shape behaviour of flaccid vesicles, i.e. vesicles with excess membrane area with respect to the vesicle volume. Because the membrane is composed of two phospholipid leaflets, the relevant terms of the elastic energy of the vesicle membrane are the membrane-local [START_REF] Helfrich | Elastic properties of lipid bilayers -theory and possible experiments[END_REF] and nonlocal [START_REF] Helfrich | Blocked lipid exchange in bilayers and its possible influence on shape of vesicles[END_REF][START_REF] Evans | Minimum energy analysis of membrane deformation applied to pipet aspiration and surface-adhesion of red-blood-cells[END_REF][START_REF] Svetina | Lipid bilayer elasticity and the bilayer couple interpretation of red-cell shape transformations and lysis[END_REF][START_REF] Miao | Budding transitions of fluidbilayer vesicles -the effect of area-difference elasticity[END_REF] bending energies, expressed as

2 0 0 2 0 2 0 2 1 ) ( 2 1 ) ( 2 1 A A A h k dA C C C k W r c ∆ - ∆ + - + = ∫ , (2)

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where k c and k r are the local and nonlocal bending moduli of the bilayer, respectively, C 1 and C 2 are the principal curvatures of the membrane and C 0 is its spontaneous curvature.

Integration is over the preferred membrane area A 0 . ΔA is the difference between the areas of the outer and the inner leaflets and is given by

0 2 1 ) ( dA C C h A + = ∆ ∫
, where h is the distance between the neutral surfaces of the membrane leaflets, and ΔA 0 the preferred (equilibrium) difference between the areas of the outer and the inner leaflets.

The preferred membrane area, A 0 , and the preferred area difference, ΔA 0 , can be expressed in terms of the number of molecules of membrane components and their areas.

Since biological membranes and thus experimental membrane systems are multicomponent, there is a possibility of multiple species of phospholipids in the membrane. We shall treat the case in which the proteins are inserted into the outer leaflet of the symmetrical and laterally homogeneous bilayer membrane. The element of the protein inserted into the outer leaflet increases the preferred area of that leaflet while the preferred area of the inner leaflet remains the same. A 0 and ΔA 0 depend therefore on the number of bound proteins (N P ). The preferred areas of the outer and inner leaflets are then

∑ = = 2 1 , 2 , 2 , 0 n i i i L N A A + A P N P and ∑ = = 1 1 , 1 , 1 , 0 n i i i L N A A ,
respectively, with A L,i the area of the i-th component of n 2 species of phospholipid molecules in the outer leaflet and of n 1 species of phospholipid molecules in the inner leaflet, N 2,i and N 1,i the numbers of the i-th component of n 2 and of n 1 species of phospholipid molecules in the outer and the inner leaflets, respectively, and A P the effective area of the protein insertion. The

vesicle preferred area is then [19] ) ( 2 1 A 1 , 0 2 , 0 0 A A + = (3)
and the preferred area difference is

1 , 0 2 , 0 0 A A A - = ∆ . ( 4
)
The protein insertion also affects the spontaneous curvature of the outer leaflet and, consequently, of the membrane (C 0 ). By taking into consideration the approximation that C 0 depends on the intrinsic curvatures of the protein (C P ) and phospholipid molecules (C L,i ) of the i-th component of n 2 species of phospholipid molecules in the outer leaflet and of n 1 species of phospholipid molecules in the inner leaflet, the spontaneous curvatures of the outer and inner leaflets are

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 2 , 0 , , 1 , 2 2 , 0 / ) ( 2 A C A N C A N C p p p i L i L n i i + = ∑ = (5)
and

C 0,1 = 1 , 0 1 , , , 1 / ) ( 1 A C A N n i i L i L i ∑ = . ( 6
)
The spontaneous curvatures of the two leaflets thus differ, with a consequent non-zero bilayer spontaneous curvature [START_REF] Svetina | Lipid bilayer elasticity and the bilayer couple interpretation of red-cell shape transformations and lysis[END_REF] ) ( 2

1 2 , 0 1 , 0 0 C C C + = , (7)
and C 0 is proportional to the difference C P -C L . The elastic energy of the system (W) is equal at given N p and A p , if A 0,1 , A 0,2 and C 0 of different membranes are equal, regardless of the number of membrane components. For the sake of simplicity we therefore define the mean area of phospholipid molecules

2 1 , 2 , / 2 N N A A n i i i L L ∑ = =
, where N 2 is a total number of phospholipid molecules in the outer leaflet of the membrane.

The free energy of proteins bound to the membrane (G p ), can be written in the form [START_REF] Hill | An introduction to statistical thermodynamics[END_REF] G p = -εN p -kT(N 0 lnN 0 -N p lnN p -(N 0 -N p )ln(N 0 -N p )) , [START_REF] Wang | The insertion of human apolipoprotein H into phospholipid membranes: a monolayer study[END_REF] where ε represents the energy of the interaction between the protein and the membrane, N 0 is the maximal number of its binding sites, k is Boltzmann constant and T the absolute temperature.

The equilibrium configuration of the vesicle can be obtained by minimizing Eq. 1.

Minimization with respect to the number of bound proteins (N p ) is considered first where bound proteins are in equilibrium with the external protein solution. This equilibrium is obtained by equating the chemical potential of bound proteins with that of free proteins

∂G/∂N p = μ 0 + kTln(c/c 0 ) , (9)
where μ 0 and c 0 are constants and c is the protein concentration of the outer solution. From Eq. 9 N p is obtained as a function of c

with

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT K D,0 = c 0 kT e ε µ + -0 . ( 12
)
K D,0 is a shape independent part of the binding constant.

Minimization with respect to vesicle shape can be carried out at fixed values of vesicle volume and of numbers of lipid molecules and of proteins inserted in the membrane. Since G P does not explicitly depend on vesicle shape, only W has to be minimized. The result of the minimization of W is the vesicle shape and the relation between ΔA and ΔA 0 [START_REF] Heinrich | Nonaxisymmetric vesicle shapes in a generalized bilayer-couple model and the transition between oblate and prolate axisymmetrical shapes[END_REF][START_REF] Miao | Budding transitions of fluidbilayer vesicles -the effect of area-difference elasticity[END_REF][START_REF] Jarić | Vesicular instabilities -the prolate-tooblatetransition and other shape instabilities of fluid bilayer-membranes[END_REF]. The number of inserted molecules depends on vesicle shape, because the elastic energy depends on N p . Therefore K D (Eq. 11) depends on ΔA, i.e. on vesicle shape. The vesicle shapes at relatively large ΔA 0 values are approximated well by a spherical main vesicle body and spherical buds that may also be arranged as strings [START_REF] Božič | Shapes of phospholipid vesicles with beadlike protrusions[END_REF]. The fact that vesicle shapes, that are compositions of spheres, may have only two different radii is taken into account [START_REF] Svetina | Membrane bending energy and shape determination of phospholipid vesicles and red blood cells[END_REF].

We first determine how budding progresses as a function of the external concentration of the amphitropic protein, by approximating the vesicle shapes as being composed of the main spherical body and n spherical buds. At fixed vesicle volume and solution concentration, its shape and N p depend only on n because the radii of spheres and the corresponding difference between the areas of the outer and the inner leaflets (ΔA) depend only on the number of buds. ΔA is expressed by 8πhR v + n8πhR n , with R v the radius of the main spherical body and R n the radius of the bud. By assuming that the number of buds is an increasing function of the concentration, the number of buds increases from n buds to n + 1 buds at concentrations at which the free energies of the system (Eq. 1), calculated separately for n and n + 1 buds, assume equal values. In this procedure N p is obtained from Eq. 10 separately for shapes with n and n + 1 buds. The budding is found to depend on the degree of flaccidness, which is conveniently measured by the reduced volume, defined as the ratio of vesicle volume (V) to volume of the sphere with the same membrane area (A 0 ),

v = 3 0 4 3 R V π ( 13
)
where R 0 is the radius of a sphere with the same membrane area (

π 4 / 0 0 A R = ).
The dependence of the number of buds (n) on the reduced volume (v), on the radius of a sphere with the same membrane area (R 0 ) and on the reduced concentration (c/K D,0 ), is shown in Fig.

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reduced because area and volume redistribute. At given c/K D,0 , for spherical vesicles (v close to 1) significantly less pronounced shape transformations (lower n) are predicted than for flaccid vesicles (v < 1). Vesicles with higher v have smaller buds than those with lower v but the same number of buds. At a given value of v the final number of buds is limited, because of the limited maximal number of binding sites on the vesicle. Fig. 2b shows the dependence of the number of buds (n) on reduced concentration (c/K D,0 ) for different values of vesicle size (R 0 ). It is evident that, at a given β 2 GPI concentration, larger vesicles can produce more buds than smaller vesicles. At larger R 0 more buds are formed, due to an increase in ΔA 0 which increases proportionally to R 0 2 (Eq. 4) because N P is approximately proportional to N 2 , while ΔA at the same shape increases proportionally to R 0 .

Design of the experiment

The purpose here is to study the properties of the binding of β 2 GPI to membranes and the influence of such binding on the shape of an individual vesicle, observed under a phase contrast microscope. Shape transformations of the chosen vesicle should not be disturbed by other vesicles, e.g. due to β 2 GPI induced aggregation of anionic vesicles [START_REF] Gushiken | Polymorphisms β2-glycoprotein I: phospholipids binding and multimeric structure[END_REF]. Also the lipid:β 2 GPI ratio should be in favour of β 2 GPI. A procedure to isolate chosen vesicles from the pool of vesicles by transferring them in the desired solution was therefore employed [START_REF] Božič | Shapes of phospholipid vesicles with beadlike protrusions[END_REF][START_REF] Mally | Mechanisms of equinatoxin II-induced transport through the membrane of a giant phospholipid vesicle[END_REF][START_REF] Ambrožič | Budding, vesiculation and permeabilization of phospholipids membranes -evidence for a feasible physiologic role of β2-glycoprotein I and pathogenic actions of anti-β2glycoprotein I antibodies[END_REF], modified because in our experiments we were interested in the β 2 GPI concentration dependence of shape transformations of vesicles. β 2 GPI, in this case, was injected into the solution with the isolated vesicle so that the outer concentration increased only slowly with time.

Shape transformations should be as extensive as possible in order to observe them under the microscope. The phase diagram in Fig. 2a shows the dependence of the number of buds on v and c/K D,0 , and it can be seen that the shape transformations are more pronounced for flaccid vesicles, which were therefore used in our experiments. The use of flaccid vesicles is also advantageous because the curves are steeper in the region of lower v and thus the accuracy of its value is not so critical for the dependence of budding on c/K D,0 .

Determination of vesicle dimensions is one of key elements of the study. Vesicles floating in the solution are hard to follow and observe microscopically, and it follows that their size and flaccidity cannot be easily characterized. In order to determine their shape, vesicles were stabilized by falling to the bottom of the observation chamber. This is achieved

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by creating a difference in density between the fluids inside and outside the vesicle, using different sugars with equal osmolarities but different specific weights.

Materials and methods

Preparation of β 2 GPI

β 2 GPI was purified from pooled human plasma and checked by polyacrylamide gel electrophoresis [START_REF] Čučnik | Concomitant isolation of protein C inhibitor and unnicked ß2-glycoprotein I[END_REF]. Prior to use it was dialyzed against 0.22 M glucose solution, first in a 2 L flask with vortexing for 2 hours and then in a fresh glucose solution overnight at + 4°C. The pH value was 8.7 where affinity of β 2 GPI towards membrane is sufficiently high [START_REF] Wang | The insertion of human apolipoprotein H into phospholipid membranes: a monolayer study[END_REF]. The pH remained stable for several hours.

Preparation of flaccid vesicles

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We used giant unilamellar vesicles (GUVs) composed of 80 mol% neutral POPC and 20 mol% negatively charged POPS. The lipid composition was chosen in order to allow β 2 GPI to bind to the vesicles in an electrostatic manner. Preparation of flaccid vesicles took place in two stages: (i) GUVs were prepared using electroformation according to a modification of the method [START_REF] Angelova | Preparation of giant vesicles by external ac electric fields: kinetics and applications[END_REF]. The protocol for preparation of GUVs was described in ref. After the end of each injection the pipette was kept in the pit to avoid disturbing the vesicle.

The whole experimental procedure lasted about an hour and during this time no influence of evaporation on v was detected. All experiments were conducted at room temperature. See Supplementary information for details on control experiments.

Results

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Shape transformations of individual flaccid vesicles were monitored. 17 vesicles were examined, of which about 50 % underwent no visible shape transformations, some of which formed protrusions, e.g. tubes. The largest group of vesicles however formed buds. Five of these were selected for detailed analysis for having buds sufficiently visible to be reliably counted. The radius of the ring around the rim of the vesicle (R v ), the distance from the rim of the vesicle to the substrate (Z) (the method of their determination is presented in the Supplementary information) and the final number of buds (n f ) for these vesicles (A -E) are listed in Table 1. The radius of a sphere with the same membrane area (R 0 ) and the reduced volume (v), calculated from the foregoing parameters, as described in the Supplementary information, are also listed.

The time course of budding of vesicle B after the start of β 2 GPI injection is shown in Vesicles with smaller v in general exhibited more buds on strings than those with higher v.

The latter usually had only one or a few buds on a string and tended to bud individually from many sites. It was also observed that later in time (not shown) some buds detached from the main vesicle body or from each other.

The time dependence of the number of buds (n) formed by membranes of vesicles A to E is shown in Fig. 4. The dashed curve shows the increase of β 2 GPI concentration averaged over the whole chamber volume, i.e. as if it were uniformly distributed at all times. n increased with β 2 GPI concentration for all vesicles, in steps according to the injection intervals, eventually reaching a plateau. For some vesicles (like A and B) the steps were very steep. Buds were formed successively following injection steps. However, some vesicles, like vesicle D, did not start budding before the second injection interval. There was a time lag in the onset of budding after the start of injection, and budding was still occurring after the injection stops. The behaviour of vesicles is characterized by R 0 and v. For example, case B had significantly higher final number (n f ) of buds and significantly lower v than case D which had a similar R 0 . For vesicles with higher v and the same R 0 , n f was lower at the same protein

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concentration, indicating that more β 2 GPI had to be embedded in the membrane to create the same number of buds. Moreover, larger vesicles (higher R 0 ) also produced more buds than smaller vesicles with the same v. R v was observed to depend on n for all vesicles A to E (Fig. 5). R v at the beginning and during the process of budding was measured where a decrease in that radius could have been observed after an increase in n.

Discussion

The previous qualitative study of the formation of buds on the surface of giant unilamellar vesicles (GUVs) in the presence of β 2 GPI and their dependence on the vesicles' state led to the suggestion that buds form because insertion of β 2 GPI into the outer membrane leaflet increases the area of that leaflet, resulting in curvature enhancement and consequent vesicle shape transformations [START_REF] Ambrožič | Budding, vesiculation and permeabilization of phospholipids membranes -evidence for a feasible physiologic role of β2-glycoprotein I and pathogenic actions of anti-β2glycoprotein I antibodies[END_REF]. In our research we investigated the shape behaviour of individual vesicles when introduced to a solution with β 2 GPI at increasing concentrations in a more quantitative way by defining vesicle parameters. First we will discuss the adequacy of the experimental methods. The experimental work will then be analyzed with respect to the theoretical modelling of the shape behaviour of vesicles after the insertion of proteins in the outer membrane leaflet.

GUVs serve as an in vitro membrane system as they are cell-sized and can be observed and manipulated under the microscope [START_REF] Luisi | Giant vesicles: Perspectives in supramolecular chemistry[END_REF]. However, their use has some drawbacks. They differ from each other (size, flaccidity, lipid composition of both membrane leaflets) because of their inhomogeneity in the original solution as a result of the preparation procedure. Because of their difference, different shape transformations (buds, tubes of different lengths and widths, no shape transformations) are observed during the injection experiment. As shown in Fig. 2a, flaccidity has an important impact on the shape of protrusions. If reduced volume (v) is high enough no shape transformations are formed within the experimental conditions. Also, at higher v smaller buds are observed which eventually could be observed as tubes. It was observed in our experiments that only the most fluctuating vesicles formed buds and the least fluctuating did not change shape. Because of many different possibilities for the shapes of protrusions, the number of investigated vesicles forming countable buds could not be very large. However, because it was our intention to analyze behaviour of individual vesicles in order to recognize crucial vesicle parameters that

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influence their behaviour and not to study the effect on the whole population of vesicles, the need for a high statistical number of cases was not necessary.

While size and v could readily be determined, the initial preferred area difference (∆A 0 ) is not easy to establish. Their behaviour is thus to some extent unpredictable. The evidence for unpredictability of vesicles behaviour on account of different initial ∆A 0 seems to be reflected by different time lags of the beginning of budding after the start of injection (Fig. 4); this cannot be explained on the basis of their different radii. Because of different initial values of ∆A 0 , a different period of time must pass for β 2 GPI to reach a sufficient concentration to reach the ∆A 0 needed to produce a bud leading to the conclusion that the larger the initial ∆A 0 the shorter the time lag. Another drawback of the method is the lack of information about the distribution of β 2 GPI molecules throughout the pit of the observation chamber during three consecutive injection intervals because of the unknown rate of liquid mixing. However, based on an injection control experiment of the examination of homogeneity of β 2 GPI solution shown in Fig. S3 (Supplementary information), we concluded that the concentration became homogenous before the start of the next injection interval.

A model was proposed having the simplest possible structure that still captures the essential elements of the treated system. The model presumes spherical vesicles with a homogenous surface density of bound proteins. The latter affects not only the preferred area difference (∆A 0 ) but also the spontaneous curvature of the membrane (C 0 ). Both describe the observed shape transformations but in our model we assumed that the effect of ∆A 0 prevails over the effect of C 0 . Flip-flop between the leaflets is very slow so we could assume that the preferred areas of membrane leaflets are conserved on the experimentally relevant time scales [START_REF] Döbereiner | Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory[END_REF]. According to the bilayer couple hypothesis [START_REF] Sheetz | Biological membranes as bilayer couples. A molecular mechanism of drug-erythrocyte interactions[END_REF][START_REF] Svetina | Membrane bending energy and shape determination of phospholipid vesicles and red blood cells[END_REF], protrusions (buds, tubes, tethers, etc.) of higher membrane curvature on the membrane of the main vesicle body form in order to reduce the difference between ∆A and ∆A 0 and thus the area difference elasticity term of Eq. 2. ΔA depends on the vesicle shape whereas ∆A 0 depends on the molecular occupancy of the two layers and their interaction with the surroundings. These two quantities are generally not identical. The model accounts for the importance of the coupling between vesicle shape and the number of bound proteins (N p ). It assumes that the shape of a vesicle and the number of bound proteins are interdependent. The initial transition of the vesicle shape resulting in the first bud cannot be calculated accurately from the proposed model. All the theoretical results are thus presented from the first bud onwards.

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The model predicts the dependence of the number of buds on R 0 and v as shown in Figs. 2a and2b. A phase diagram presented in Fig. 6 ). For the model parameters therefore we chose values of the ratio between the maximal number of binding sites and the total number of phospholipid molecules in the outer leaflet (N 0 /N 2 = 0.012), the mean area of phospholipid molecules (A L = 0.6 nm 2 [START_REF] Cevc | Phospholipid bilayers[END_REF]), the ratio between nonlocal and local bending moduli of the bilayer (k r /k c = 3), and reduced concentration (c/K D,0 = 10). The reduced concentration was selected according to the conditions close to saturation, i.e. 10 times K D,0 . At this high protein concentration, the theoretically predicted number of buds was approximated closely to a final number of buds, and the shape of the main vesicle body was approximated to a sphere. We took as an adjustable parameter the effective area of the crosssection of the inserted portion of the protein (A p ) obtained from Eq. 4, which influences ΔA 0 , and tried to obtain as good as possible fit with experimental points by varying its value. The position of the curves is greatly dependent on A p . At values of A p larger than that estimated, the curves would shift towards the left, because transitions would occur sooner. A p was, in our case, determined to be about one tenth of the area of the cross-section of the whole inserted portion of the protein. The membrane area thus responsible for ΔA 0 is smaller than that of the whole inserted portion of the protein. The result suggests that only the keel-like part of the inserted portion of the protein (Fig. 1c) reaches the neutral surface of the leaflet and is thus responsible for the increase of ΔA 0 . The theoretical predictions of the number of buds agree with experimental results of most vesicles (vesicles A, B, D and E) sufficiently well for the chosen parameters. However the predicted value of n f for vesicle C deviates slightly from the observed value (discussed later).

The radius of the main vesicle body at the rim (R v ) was determined, as well as the number of buds (n). The dependence on n of the experimental values of R v for vesicles A-E is presented in Fig. 5, showing that R v decreases with increasing n. This observation does not fit

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with the proposed theoretical model, which predicts a slight increase of R v with bud formation, because the formation of buds involves relatively more increase in vesicle area than in volume. The observations can be understood if it is taken into account that gravity causes a vesicle lying on the substrate to flatten, so that R v is larger than that of a sphere with the same membrane area (Fig. S1a -Supplementary information). The decrease in R v with increasing n can be explained by the fact that the volume and membrane area of the newly formed bud are accompanied by their decrease in the main vesicle body. The latter then reforms its shape stepwise from a sphere section into a sphere, which involves an increase in the effective reduced volume of the main vesicle body. When the latter attains the shape of a sphere, the predicted outcome is practically the same as that obtained by the simple theoretical model (Fig. S1b -Supplementary information).

The dependence of R v on n obtained from measured data for vesicle B (circles) is compared with possible theoretical interpretations (curves) of vesicle behaviour (Fig. 7). The theoretical reasoning described in the section on theoretical background predicts a decrease in R v represented by the dashed curve. This decrease is quite rapid so that the shape of the sphere is reached at n = 6, whereas the experimental dependence of R v on n is much less steep. An attempt is made to interpret the vesicle behaviour by assuming partially closed and closed necks between the main vesicle body and buds. An example is presented by the solid curve. It is assumed that, during the formation of a string of three buds on the first budding site (Fig. 3), the neck is partially closed so that membrane, but not solution inside the vesicle, can be exchanged between the main vesicle body and buds. R v decreases more slowly than in the case of exchange of both membrane area and solution. It appears that the neck of the first budding site then closes completely (denoted by an arrow at n = 3), indicating that neither the volume nor the area could be exchanged and that the budding from this budding site stopped.

When the second budding site opens, the shift of R v is again larger (between n = 3 and 4).

During the formation of another string of five buds on the second budding site the neck is, as previously assumed, partially closed and R v thus decreases correspondingly slowly. An arrow positioned at n = 8 indicates another possible neck closure. When the third budding site opens, the shift of R v is again larger (between n = 8 and 9) and decreases slowly until formation of the last bud (n = 19) when the shape of the main vesicle body assumes the shape of a sphere. The partial neck closure can be explained by an assumption that solution molecules inside the vesicle cannot move through the neck from the main vesicle body to a protrusion while the membrane components can. The plausible rationale for a total prevention of movement of all molecules through the neck is that the neck gets too narrow. The reason

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for the neck closure cannot be totally clarified. This interpretation considering closed and partially closed necks was therefore used only to describe observed phenomena properly. A similar interpretation can also be employed to explain the smaller final number of buds (n f ) observed on vesicle C than is predicted theoretically. Budding of this vesicle may have stopped prematurely because the energy barrier for a new bud was too high after the neck closed at some point. However, in this case it may also be that undetected tethers or other protrusions were formed in addition to buds, resulting in a smaller final number of buds.

The interpretation represented by the solid curve in Fig. 7 is consistent with the rapid increase in number of buds seen in Fig. 4 in cases A and B. The predicted dependence of n on c/K D,0 for vesicle B is shown in Fig. 8. The lower curve represents the beginning of budding of the initial vesicle that ends at n = 3. When budding begins on the second budding site, it does not continue on the same curve but rather jumps (shown by a lower arrow) to the middle curve which corresponds to a now different effective reduced volume of the main vesicle body. This is because the main vesicle body acts as a separate entity and its effective reduced volume is larger, as discussed previously. As the budding continues at the second budding site, the number of buds predicted for the current concentration is already greater than 1 and the number of buds immediately increases to a total of six or seven. The budding continues on the solid section of the middle curve as long as the neck closes again. The analogous interpretation applies when the third budding site opens, with the result that the possible interpretation of budding jumps to the upper curve. The budding continues on the solid section of the upper curve where at n = 19 a spherical shape is reached. In accord with the interpretation of the steep increase of the number of buds seen in Fig. 4 for vesicles exhibiting long strings of buds (A and B), and in vesicles where budding is individual (D and E), the number of buds increases in steps.

Conclusions

The notion that β 2 GPI induces shape transformations of vesicles preferentially by forming buds and strings of buds is confirmed in this study. The extent of budding is an increasing function of β 2 GPI concentration. The occurrence of budding can be rationalized by assuming that part of β 2 GPI is inserted only into the outer leaflet of the bilayer, thus increasing the preferred difference between the areas of the outer and the inner leaflets (ΔA 0 ).

The contribution to ΔA 0 of each bound β 2 GPI was estimated to be about one tenth of the area of the cross-section of its inserted portion, meaning that only a part of it reaches into the The radii of spheres with the same membrane area (R 0 ) are 20 µm (upper curve), 15 µm (middle curve) and 10 µm (lower curve). The reduced volume (v) is 0.9. The cartoons show the shapes of vesicles with various numbers of buds. Note the size of buds is smaller at higher numbers of buds.

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Fig. 4: The time dependence of the observed number of buds (n) on vesicles A to E (Table 1)

during the injection of β 2 GPI in three intervals (0 -900 s overall). The dashed curve represents an average concentration of β 2 GPI which rises according to the injections (0 s -150 s, 300 s -450 s and 600 s -750 s).

2 .

 2 Fig. 2a is a phase diagram showing the dependence of the number of buds (n) on reduced volume (v) and reduced protein concentration (c/K D,0 ). Each zone limited by two neighbouring curves defines a certain number of buds. At each transition n is increased by one. Every time the vesicle undergoes a transition from n to n + 1 buds, the bud size is A C C E P T E D M A N U S C R I P T

4. 1 .

 1 Materials and equipment Purified β 2 GPI was isolated and donated by the Department of Rheumatology, University Medical Centre, Ljubljana, Slovenia. D(+)-glucose and D(+)-sucrose were from Fluka, Switzerland. Phospholipids POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and POPS (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine) were obtained from Avanti Polar Lipids, USA. Bovine serum albumin (BSA) was from Sigma, USA. Rat blood for the isolation of haemoglobin was donated by the Institute of Pathophysiology, Faculty of Medicine, University of Ljubljana, Slovenia. The ingredients of acid-citrate -dextrose (1:1) anticoagulant, citric acid and dextrose were from Fluka, Switzerland, and sodium citrate was from Riedel-de Haën, Germany. All the solutions were prepared in double-distilled and sterile water. An Olympus IMT2 (USA) inverted microscope, (40x objective, NA = 0.55), was used for phase contrast microscopy. It was equipped with a black and white CCD camera Hammamatsu, C4742-95 (Japan) for image acquisition. Images of vesicles were analyzed with Hammamatsu Hokawo 210 and Image J version 13.6b softwares. The dimensions of the intercalated part of β 2 GPI as shown in Fig. 1 were analyzed by RasWin software. Protein solutions were injected into the pit of the observation chamber by a Genie Plus syringe pump (Kent Scientific, USA).

[ 14 ]

 14 . GUVs prepared in such a manner are preferentially spherical, 30 to 60 µm in diameter, filled with 0.2 M sucrose solution and surrounded by isoosmolar glucose/sucrose (1:1) solution. The GUVs were stored at a room temperature for a day to allow time to get rid of abnormalities (tethers, tubes, etc.) that might have resulted during the procedure in electroformation. (ii) Selected GUVs were then transferred using a micropipette into a hyperosmolar (0.22 M) glucose solution to give suitable flaccid vesicles which were recognized by the distinct membrane fluctuations. See Supplementary information for details on preparation of flaccid vesicles, determination of shapes of flaccid vesicles and the influence of gravity and micropipette transfer technique.4.4. Injection experimentsA pipette (diameter 480 μm), tightly connected by a thin rubber tube to a syringe pump, was inserted into the pit of the observation chamber containing the vesicle under examination in 40 μL of 0.22 M glucose solution. The micropipette was filled with 50 μM β 2 GPI in 0.22 M glucose solution. The tip of the pipette was placed in the upper corner of the pit at the maximal distance from the vesicle, which was as a rule released from the pipette close to the other end at the entrance to the pit. β 2 GPI was then injected at three intervals as follows. 5 μL of β 2 GPI were injected into the solution containing the examined vesicle over 150 s followed by a pause of 150 s to allow the concentrations to equalize. The images of the vesicle during the injection interval were recorded by a camera mounted on a microscope.

Fig. 3 .

 3 Fig. 3. Budding started to be visible after a time lag of 207 s. During this time the vesicle did not change shape. Buds were then ejected in a consecutive way from multiple membrane sites like strings of buds, as indicated on the image at 600 s. The first budding series, occurring in the time interval 207 s -221 s, shown by an arrow at twelve o´clock position, consisted of three buds. The second series, of 5 buds (236 s -278 s), occured at five o´clock position, and the third, out of 11 buds (317 s -606 s), at eight o´clock position. The sizes of the buds in the second and third budding series were smaller than those in the first. Other vesicles exhibited similar behaviour, except that occasionally, e.g. vesicle C, strings of buds grew in parallel.

AFig. 1 :

 1 FIGURE CAPTIONS

Fig. 2 :

 2 Fig. 2: Theoretically predicted dependence of the number of buds (n) on the reduced volume (v), the radius of a sphere with the same membrane area (R 0 ), and the reduced concentration (c/K D,0 ) obtained by solving Eqs. 2 and 10. The model parameters are chosen as A p = 0.1 nm 2 , A L = 0.6 nm 2 , N 0 /N 2 = 0.012, k r /k c = 3. The equilibrium area difference between outer and inner leaflets without intercalated proteins is taken to be equal to the area difference of the sphere (8πhR 0 ). (a) The curves of the phase diagram show the transition between n and n + 1 buds for R 0 = 20 μm. (b) The number of buds (n) as a function of c/K D,0 for vesicles of different sizes.

Fig. 3 :

 3 Fig.3:A typical example of shape deformations of flaccid vesicles during injection of β 2 GPI (vesicle B from Table1is presented). The time from the beginning of injection is indicated.

Fig. 5 :Fig. 6 :Fig. 7 :

 567 Fig. 5: The dependence of the observed radius of a vesicle at the rim (R v ) on the number of buds (n) for vesicles A -E.

Fig. 8 :

 8 Fig.8: Theoretical predictions of the dependence of the (total) number of buds (n) on reduced concentration (c/K D,0 ) for the same model parameters as in Fig.7. The possible steep increase in the number of buds for vesicle B is illustrated. The lower curve represents the start of budding up to n = 3. After that, budding continues with a jump (shown by a lower arrow) to the middle curve where the number of buds immediately increases for three to four buds. The solid section of the curve depicts the actual course of budding. The dashed section of the curve depicts the imaginary budding path if the jump had not occurred for vesicles with

  Fig. 1

  combines the effects of parameters R 0 and v on the number of buds. The experimental data (squares) for vesicles A-E were located on this phase diagram. By solving Eqs. 2 and 10 the curves that indicate the theoretically predicted number of buds for certain model parameters were also added to the phase diagram, to test whether the experimental observations of the final number of buds (n f , Table1) are in accord with theoretical predictions. If we consider maximal binding of β 2 GPI to planar phospholipid membranes (= 0.17 μg/cm 2 )[START_REF] Willems | Role of divalency in the high-affinity binding of anticardiolipin antibody β2-glycoprotein I coplexes to lipid membranes[END_REF] and the mass of one β 2 GPI molecule (=

	3 . 8	⋅	10	-	11	ng), we can calculate the maximal number of proteins (i.e. the maximal number of
	binding sites) on a vesicle with a typical radius of 20 μm (N 0 =	02 . 1 ⋅	10	8

  Table 1 is presented). The time from the beginning of injection is indicated.

	Arrows (at 600 s) show three budding sites with multiple buds ejected from the membrane.
	Three buds were produced on the first budding site (207 s -221 s), five on the second budding
	site (236 s -278 s), and 11 on the third budding site (317 s -606 s). Certain images of the
	main vesicle body are out of focus in order to show in focus protrusions which are normally

present below the rim of the main vesicle body, i.e. on the substrate due to gravity. * designates the onset of budding.

Table 1 :

 1 Experimentally based and theoretically determined values of vesicle parameters.

	Values are means ± standard deviation.
	vesicle	R v (μm)	Z (μm)	nf	R0 (μm)	v
	A	21.7 ± 0.35	3.4 ± 1	21 19.65 ± 0.4	0.83 ± 0.015
	B	18.2 ± 0.3	3.4 ± 1	19 16.6 ± 0.35	0.84 ± 0.02
	C	20.65 ± 0.35	7.65 ± 1		9 19.6 ± 0.35	0.895 ± 0.015
	D	16.85 ± 0.35	10.2 ± 1		6 16.5 ± 0.35	0.95 ± 0.015
	E	11.4 ± 0.

Acknowledgements

We thank Prof. Blaž Rozman, PhD (Department of Rheumatology, University Medical Centre, Ljubljana, Slovenia) for providing purified β 2 GPI, Prof. Robert Zorec, PhD (Institute of Pathophysiology, Faculty of Medicine, University of Ljubljana, Slovenia) for providing rat blood, Prof. Jure Stojan, PhD (Institute of Biochemistry, Faculty of Medicine, University of Ljubljana for providing images of β 2 GPI embedded in the membrane. We are also grateful to Janja Majhenc, PhD (Institute of Biophysics, Faculty of Medicine, University of Ljubljana) for valuable discussions. This work was supported by Slovenian Research Agency through Grant No. P1-0055.


Christoph Held

Thorsten Neuhaus

Gabriele Sadowski
email: g.sadowski@bci.tu-dortmund.de

Compatible solutes: Thermodynamic properties and biological impact of ectoines and prolines

Keywords: osmolyte, aqueous solution, activity coefficient, osmotic coefficient, solubility, PC-SAFT, modeling, measurement, ectoine, urea

Compatible solutes like ectoine and its derivatives are deployed by halophile organisms as osmolytes to sustain the high salt concentration in the environment. This work investigates the relation of the thermodynamic properties of compatible solutes and their impact as osmolytes. The ectoines considered in this work are ectoine, hydroxyectoine, and homoectoine. Besides solution densities (15-45°C) and solubilities in water

(3-80°C), component activity coefficients in the aqueous solutions were determined in the temperature range between 0 and 50°C. The latter are important for adjusting a certain water activity and therewith a respective osmotic pressure within a cell. The characteristic effect of ectoines is compared to that of prolines, as well as to that of incompatible solutes as salts and urea. The experimental results show that the influence on the activity (coefficient) of water is quite different for compatible and incompatible solutes; whereas compatible solutes cause decreasing water activity coefficients, incompatible solutes lead to an increase in water activity coefficients. Based on this quantity, the paper discusses the impact of various osmolytes on biological systems and contributes to the explanation why some osmolytes are more often and at other temperatures used than others. Moreover, it was found that the anti-stress effect of an osmolyte is weakened in the presence of a salt.

1Introduction

Many microorganisms are known to live under high-stress conditions. Stresses can be caused e.g. by very high or very low temperatures, by non-neutral pH values, or by extreme salt concentrations. To live in environments with extreme salt concentrations, various microorganisms produce so-called osmolytes which are organic compounds of low molecular weight. In contrast to electrolytes they do not influence the cellular metabolism, are non-toxic, and therefore also known as "compatible solutes". One of the most-investigated compatible solutes is ectoine which is deployed e.g. by the halophilic microorganism Halomonas elongata.

Since 1998, ectoine is also produced at an industrial scale by so-called "bacterial milking". Due to its stabilizing effect to biological cell membranes, today ectoine is used e.g. in skin-protection and health-care applications and is an important additive of more than 200 biochemical, medical, and cosmetic products.

The influence of osmolytes like ectoine on biological solutions (e.g. protein systems) has already been earlier investigated phenomenologicaly. Several beneficial effects of ectoine against denaturizing stresses were observed, e.g. by Kolp et Galinski (protection against heat, urea, and freezing), by Galinski and Truper (protection against salt stress) and others.

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Concerning the protection against salt stress, there already exist some general observations: halophilic/halotolerant microorganisms (1) produce different osmolytes or

(2) pump in ions from the environment to protect themselves against salt stress.

Moreover [START_REF] Schnoor | Characterization of the synthetic compatible solute homoectoine as a potent PCR enhancer[END_REF], at least one organism (Halomonas Elongata) even produces different osmolytes at different temperatures. Moreover, it is well accepted that the ability of a molecule to act as biological osmolyte is mostly determined by the properties of the osmolyte/water binary system. However, a detailed investigation of the thermodynamic properties of those systems is so far missing.

From the thermodynamic point of view, the the osmolyte reduces the chemical potential (activity) of water and therewith increases the osmotic pressure. As these two quantities are strongly related to the water activity coefficients, this quantity will be examined (measured and modeled) throughout this work.

This paper will present new experimental data and thermodynamic modeling of osmolyte solutions and will use this approach to quantitatively estimate and explain the impact of osmolytes to aqueous systems. In particular the following thermodynamic properties of ectoine solutions will be investigated: solution density which is important for the design of apparatus and reservoirs, activity coefficients which reveal interactions with other system components and determine e.g. the osmotic pressure in a cell, and water solubility which is required to function in biological systems.

Fig. 1 shows the different ectoine derivatives considered within this work:

hydroxyectoine, which has an additional hydroxyl group and homoectoine with an additional methylene group inserted into the ectoine ring.

Fig. 1 The compatible solute ectoine (left) and two derivatives, the hydroxyectoine (middle) and the homoectoine (right).

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As ectoine is often compared to the amino acid L-proline, it is also considered within this work. Moreover, we will compare the effect of ectoines to those of other substances (salts, urea) which are known as incompatible solutes.

2Experimental work

2.1Materials and Reagents

Ectoine, hydroxyectoine, homoectoine were obtained from the bitop AG in Witten, Germany with high purity (>99 %). They were used as obtained. For the calibration of the osmometers, solutions of sodium chloride (Merck, >99.5%) were applied. All solutions were prepared gravimetrically by weighing with an uncertainty of 0.01 mg.

Water from the Millipore purification system was used for the preparation of all aqueous solutions.

2.2Density Measurements

Densities of ectoine solutions in water were determined with a vibrating-tube densimeter "DMA 602" from Anton Paar Germany GmbH (Ostfildern, Germany) at ambient pressure and temperatures between 15 and 45°C. For the measurements, a utube is filled with the fluid of interest and set into oscillation by an electromagnetic field. Densities are obtained by measuring the eigenfrequency of the filled u-tube. The apparatus was calibrated with air and deionized water (data taken from). According to the manufacturer, the maximum uncertainty of this apparatus is within ±1.5•10 -6 g/cm³.

2.3Measurements of water activity coefficients

The measurements were performed with a vapor-pressure osmometer at temperatures In order to also determine activity coefficients at the freezing point we used the cryoscopic osmometer "K-7400" by Knauer (Berlin, Germany). This method is based on the freezing-point depression caused by a solute dissolved in water. The first step of the measurement is to supercool the solution without freezing it. The freezing is afterward initiated by vibrating and the freezing-point temperature is measured. The freezing-point depression compared to the freezing point of pure water is a measure for the osmolality of the solution and thus for osmotic and water-activity coefficients, respectively. The K-7400 allows for measurements at maximum concentrations of 2.0 mol/kg. According to Knauer, the experimental uncertainty (relative standard deviation) is below 1%.

Before carrying out the measurements, the two osmometers had to be calibrated. This was done with sodium chloride solutions of different molalities (0.05 -1.2 mol/kg for the vapor-pressure osmometer, 0 -0.45 mol/kg for the freezing-point osmometer).

Thereby, reference values from literature were used. Experiments for the ectoines in water were performed at 0°C, 30°C, and 50°C, respectively. All measurements were repeated until a constant temperature difference could be observed.

2.4Solubility measurements

The solubility of the solutes considered in this work was determined gravimetrically as also described earlier, e.g. in. First, the substances were filled into glass vials (20 ml) and purified water from the Millipore system was added to an extent that a supersaturated solution was obtained. These vials were placed into a rotary oven with a temperature deviation of ±0.3 K. After equilibration (48 h), a sample of 2 ml solution

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was withdrawn using a preheated syringe with a syringe filter (poresize 0.45 µm). The sample was weighed with an accuracy of 0.01 mg. After solvent evaporation in a drying chamber this sample was reweighed. In order to assure for total evaporation of the solvent, the sample was placed back into the drying chamber and was reweighed again after 24 h. At the point where no further weight decrease was observed the concentration of the sample (the solubility) was obtained from the weight difference of the sample before and after solvent evaporation.

3Thermodynamic modeling

One aim of this work is the modeling of the various thermodynamic properties of aqueous ectoine solutions which may also contain electrolytes. Properties of interest are solution density, vapor-pressure depression (water activity coefficient), solute activity coefficient and solubility. For this purpose, we applied the ePC-SAFT equation of state.

This model has already proven its flexibility and excellent performance in modeling complex systems containing amino-acids, polymers , polar compounds, associating compounds, pharmaceuticals, and electrolytes.

The ePC-SAFT model is based on a perturbation theory. This type of theories uses a reference system which is easy enough to derive analytical expressions for the thermodynamic quantities (e.g. Helmholtz energy) but already covers the most-relevant properties of a molecule. As the thermodynamic behavior of a molecule is to a remarkable amount determined by its volume (which causes repulsive forces), a very often used reference for a real molecule is the so-called hard sphere. This is a spherical molecule having a fixed volume and no attractive interactions with other molecules.

Deviations from that reference system, as e.g. from spherical shape or attractive interactions (e.g. due to van der Waals forces, hydrogen bonds, or charges) are usually considered as independent perturbations of the reference system and are described by additional contributions to the Helmholtz energy. ePC-SAFT considers the hard chain (a chain of spherical segments) as reference system instead of the hard-sphere system and

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is therefore in particular suitable for describing non-spherical and chain-like molecules as those considered in this work.

The residual Helmholtz energy a res (deviation from ideal-gas state) is thus obtained as the sum of the contribution of the reference system hard chain (hc) as well as the contributions originating from the various perturbations: To describe a pure substance i, the model requires at maximum five parameters which have a physical meaning: the number of segments m seg , the diameter of the segments σ i , the van der Waals-interaction (dispersion) energy between two segments of different molecules u i /k B . In case of associating molecules, one can define N association sites per molecule characterized by the association energy ε AiBi /k B and the association range κ AiBi .

For gases or liquids, these parameters are usually determined by fitting to purecomponent thermodynamic properties as e.g. liquid-density or vapor-pressure data. For solids, as e.g. amino acids or salts these parameters can be fitted to solution data (densities, vapor pressures, activity or osmotic coefficients).

For application to mixtures, conventional Berthelot-Lorenzcombining rules are used for two components i and j:

( ) 3) is a binary parameter that can be used to correct for deviations from the geometric mixing rule of the dispersion energy. This parameter (if required) is determined by fitting to binary data, e.g. to activity coefficients or solubilities.

ij i j 1 2 σ = σ + σ ( ) ij i j ij u u u 1 k = ⋅ - k ij in eq. (

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Eq. is applied in this work to water/ion, water/ectoine, water/proline, and water/urea interactions. van der Waals interactions between two ions are neglected. Furthermore, according to our previous work, the k ij parameter between water and an ion is set to zero.

Since amino-acid solutions could previously be described accurately using PC-SAFT without considering the charges of the zwitterions , the charge-charge interactions among the biomolecules are also neglected here for the modeling.

Once the residual Helmholtz energy a res of a system is known, other properties can be derived, e.g. fugacity coefficients:

res i i B ln ln Z k T µ ϕ = -
with the real gas factor Z being:

res B a k T Z 1     ∂       = + ρ   ∂ ρ      
The residual chemical potential µ res of component i in Eq. is obtained by: res res

res res N B B i j j 1 B B i j a a k T k T a Z 1 x k T k T x x -         ∂ ∂         µ     = + -+ -     ∂ ∂             ∑
The fugacity coefficients obtained from Eq. can be used to calculate activity coefficients. Rational activity coefficients γ * of the solutes i reported in this work are normalized to infinite dilution and already converted into molality scale (for details see e. g. Ref.

). They are obtained by: ( ) ( )

m i i *,m i ,m i i m m 0 ∞ ϕ γ = ϕ →
where φ i m is the fugacity coefficient of component i in the mixture, and φ i ∞,m (m i → 0) is the fugacity coefficient of the same component at infinite dilution. Water activity coefficients (WAC) are calculated by:

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In contrast to the rational activity coefficients γ * , the water activity coefficients γ w are normalized to the pure-component state, i.e. the fugacity coefficient of water φ w in the mixture is related to the fugacity coefficient of pure water, φ 0W .

For the calculation of solubilities we applied the phase-equilibrium condition between the liquid and the solid phase. Assuming a pure solid phase and neglecting the influence of the difference in liquid and solid heat capacities, the mole fraction of the solute in the liquid phase (its solubility) can be calculated by:

L SL L 0i 0i i L SL i 0i h T x exp 1 RT T     ϕ ∆   = ⋅ - -     ϕ       φ 0i L / φ i L
is the ratio of the fugacity coefficients of component i (e.g. the ectoines) as pure substance and in the mixture, respectively. Δh 0i SL is the melting enthalpy and T 0i SL the melting temperature of the pure ectoines. As ectoines decompose before melting, these properties cannot be determined experimentally. Therefore, a group contribution method was applied to estimate Δh 0i SL and T 0i SL as it was done earlier for solubility calculations in amino-acid systems.

4Experimental results

4.1Solution densities

The density of aqueous solutions of ectoine, hydroxyectoine, and homoectoine was measured at various ectoine concentrations at a minimum of two different temperatures between 15 and 45°C and at atmospheric pressure. The results are summarized in Tab.

1.

Tab 1: Experimental densities of aqueous solutions of ectoine(E), hydroxyectoine(HyE), and homoectoine(HoE) in water between 15 and 45°C at ambient pressure.

ectoine hydroxyectoine homoectoine

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4.2Solubilities in water

The experimental determined solubilities of the considered systems are listed in Tab. 2.

The gravimetrical method has already been proven for application in aqueous aminoacid systems at similar conditions. Our experimental solubility data in the previous work agreed with literature data within 3 %. The solubility of the ectoines in water was measured between 3 and 80°C. While the ectoine solubility possesses a strong temperature dependence, the solubility of hydroxyectoine in water does almost not change between 3 and 40°C. This might be ascribed to the additional hydroxyl group within hydroxyectoine leading to stronger association forces between this solute and water, in particular at low temperatures. The associative interaction is known to decrease with increasing temperature thereby compensating for the commonly known solubility benefit at increasing temperatures.

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4.3Activity and osmotic coefficients

Microorganisms produce osmolytes to adjust the water activity (which prevents from getting lost of the water) and to compensate for the osmotic pressure in the habitat.

Often, the ideal osmotic pressure is used in literature which is defined as:

ideal solute RT n V π =
where n solute and V denote the mole number of solute molecules and the system volume at the temperature T, respectively. However, the real osmotic pressure of the system can remarkably deviate from this value which is described by the osmotic coefficient Φ:

real ideal π π = ⋅ Φ
which is defined as:

( )

w w w ln x ln x Φ = γ
Here, γ w and xw are the activity coefficient and the mole fraction of water, respectively.

However, in this work we apply a simplified expression which is commonly used in literature:

( )

w w w solute ln x M m Φ = - ∑ γ ν A C C E P T E D M A N U S C R I P T

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Thus, all experimental water activity coefficients presented in this work are calculated from Eq. . The measurement signal of the vapor-pressure osmometer stems from a boiling-point difference between the water/solute drop and the pure water drop. This quantity can be converted into the osmotic coefficient by: b,solution b w 0w

eb solute solute T T K m - Φ = ⋅ ν ∑
In contrast, cryoscopic measurements yield the freezing point difference between pure water and the ectoine solution (see e.g.) which can again be used to obtain the osmotic coefficient:

f f ,solution 0w w cryo solute solute T T K m - Φ = ⋅ ν ∑
In Eq. and K eb and K cryo are the ebullioscopic (0.52 K•kg•mol -1 ) and the cryoscopic (-1.86 K•kg•mol -1 ) constants of water, respectively. T f and T b refer to freezing-point and boiling-point temperatures of pure water (0w) and the solution, respectively.

In this work the osmotic coefficients of the binary solutions water/ectoine, water/hydroxyectoine, and water/homoectoine were measured at temperatures between 0 and 50°C and concentrations between 0 and 2 mol/kg. The osmotic coefficients determined this way could be measured within a maximum deviation of 2 %.

The osmotic coefficients of the investigated ectoine systems are given in Tabs. 3 -5.

Whereas the experimental data in Tab. 3 was measured with the freezing-point osmometer, the data in Tabs. 4 (30°C) and 5 (50°C) was obtained by vapor-pressure osmometry. Applying Eq. then allows for the determination of water activity coefficients which will be the main-focussed property in the discussion part of this work.

Besides the activity coefficient of water, the rational solute activity coefficients are also of interest in many applications. Applying the Gibbs-Duhem relation allows for the conversion of osmotic-coefficient data into rational solute activity coefficients. For that purpose, the estimated osmotic coefficients were first approximated by a power series:

n i i i 1 1 A m = Φ -= ∑ A C C E P T E D M A N U S C R I P T

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and then converted into the rational solute activity coefficients by applying: 16) and ( 17) is the molality of the solute. In Eq. ( 16), the A i values are adjustable parameters and n refers to the number of parameters needed to represent the experimental osmotic coefficients. For ectoine at 30°C, A 1 , A 2 , and A 3 were found to be 0.085, 0.024. and -0.009, respectively.

( ) ( ) m * 0 1 ln 1 dm m Φ - γ = Φ -+ ∫ m in Eqs. (

Tab 3: Experimental osmotic coefficients of aqueous ectoine (E), hydroxyectoine (HyE),

and homoectoine (HoE) solutions at the respective freezing point depression ∆T f . Solute activity coefficients were obtained by Eq. .

mE Φ ∆T f γ * E mHyE Φ ∆T f γ * HyE mHoE Φ ∆T f γ * HoE [mol/kg] [-] [K] [-] [mol/kg] [-] [K] [-] [mol/kg] [-] [K] [-] 0.

5Parameter estimation for ePC-SAFT

Within ePC-SAFT, the ectoines are considered as chains consisting of identical uncharged spheres. The azotic group and the carboxylic group were assumed to have each one association site mimicking the proton donator site (acidic group) and the proton acceptor site (azotic group, Fig. 1). The hydroxyl group of hydroxyectoine was considered as an additional association site. All association-site types were assumed to have the same energy and volume parameters (ε AiBi and к AiBi ). Urea was modeled having For solubility calculations (see. Eq. ), the melting enthalpy and melting temperature had to be determined. In the case of urea, melting data was found in literature which was directly taken for the solubility calculations. For amino acids, these properties are not available but they could be estimated applying the group-contribution method of Marrero and Gani. However, this method does not seem to be appropriate for ectoines. Just to give an example, due to this method the estimated melting temperatures of the considered ectoines turned out to be 380 -420 K, respectively. On the other hand, differential scanning calorimetry measurements have shown that the decomposition point of ectoine is about 550 K, i.e. higher than the estimated melting point. Because of that, the melting parameters were fitted to experimental solubility data.

In order to describe all the data types with only one parameter set, a temperaturedependent binary interaction parameter k ij was used with T given in Kelvin:

ij ij,25 C ij,T k (T) k k (T 298.15K) °= + ⋅ -
This procedure is commonly used (see e.g. Ref.) when accurate fits for solubility data are desired. Note, that Eq. is applied to all properties calculated with ePC-SAFT (densities, activity coefficients, solubilities). The same k ij,T is applied for ectoine and homoectoine, whereas k ij,T could be set to zero for hydroxyectoine and urea. Summing up, a total of five ePC-SAFT pure-component parameters, the binary k ij parameter, and the two melting properties are necessary for modeling the above-mentioned thermodynamic properties of the considered solutes in aqueous solution. This compares to our previous work dealing with amino-acid solutions. The parameters of the ectoines and urea are summarized in Tab. 6. The observed deviations between modeled and measured data (absolute average deviations AAD and absolute relative deviations ARD) are also summarized in Tab. 6, calculated by:

A C C E P T E D M A N U S C R I P T

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT ( ) NP calc exp k k k 1 calc NP k exp k 1 k 1 AAD y y NP y 1 ARD 100 1 NP y = = = -   = ⋅ -     ∑ ∑
Solution densities, osmotic coefficients, and the solubility behavior of the considered systems can be accurately described with PC-SAFT. The absolute relative deviations ARD over all considered systems are very small (ARD density = 0.15 %, ARD osmotic coefficient = 1.63 %) with the highest error appearing for the solubility data (ARD solubility = 8.47 %).

Presumably, this is caused by the experimental uncertainty (3 %) as well as by the simplification used in equation (Eq. ). To sum up, PC-SAFT is a suitable approach for modeling thermodynamic properties over a large concentration and temperature range using solely one parameter set per solute.

6Discussion

In general, the ectoines possess -like the amino-acid prolinea negatively charged carboxylate group attached to a cyclic ring structure that contains -in contrast to proline -a delocalized positive charge. The competition of hydrophilic (polar groups) and hydrophobic forces (nonpolar groups) influences the water-water and water-solute interactions. This influence can be revealed by activity or osmotic coefficients. In the following, especially the activity coefficients of water will be discussed for the different ectoine systems. Furthermore, they will be compared to those in aqueous solutions containing incompatible solutes (inorganic salts, urea) on the one side and to amino acids, which are known to also be compatible solutes, on the other side. Finally, also the salt influence on aqueous ectoine solutions will be investigated. In each subchapter, experimental results will also be compared to the thermodynamic modeling with PC-SAFT.

6.1Thermodynamic properties of ectoine systems

Thermodynamic properties of aqueous ectoine solutions discussed in this work are liquid densities, osmotic and activity coefficients, and solubilities. The knowledge of

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density data is crucial in the engineering domain. This is due to the fact that the solution's volume (the reciprocal solution density) determines the dimension of apparatuses or reservoirs. Fig. 2 shows solution densities at 25°C. Obviously, homoectoine and ectoine similarly influence the density behavior of the system. Only the hydroxyectoine causes higher solution densities leading to higher cellular weights at concentrated hydroxyectoine solutions. This is valid for all measured temperatures.

Furthermore, the accurate description with PC-SAFT shows the quality of the equation of state modeling applying the parameters in Tab. 6.

Fig. 2 Solution densities of aqueous ectoine solutions at 25°C. Symbols represent experimental data (squares: ectoine, circles: hydroxyectoine, triangles: homoectoine), lines are calculations with PC-SAFT.

Osmotic coefficients determine the osmotic pressure in a solution, i.e. solutes which cause high osmotic coefficients also cause high osmotic pressures (see Eq. ) making them powerful anti-stress agents in extremophile bacteria. Moreover, osmotic coefficients directly determine the water activity coefficients (WAC) (see Eq. ). Fig. 3 illustrates the WAC values in ectoine solutions at 30°C. Obviously, all ectoines cause water activity coefficients lower than unity, which means that the osmotic coefficients are bigger than unity. This latter is important as it becomes obvious from Eq. that the anti-stress effect would be decreased by low osmotic coefficients. However, the deviations from unity are not very pronounced which is characteristic for aqueous solutions containing biomolecules (e.g. amino acids).

Among the ectoine types experimental WAC values at 30°C decrease in the order "hydroxyectoine > homoectoine > ectoine" as can be observed in Fig. 3, i.e. the smallest compatible solute (ectoine) causes the strongest non-ideal behavior in the solution and thus is the most effective osmolyte. This behavior is accurately captured by the PC-SAFT model (see Fig. 3).

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Fig. 3 Water activity coefficients of aqueous ectoine solutions at 30°C. Symbols represent experimental data (squares: ectoine, circles: hydroxyectoine, triangles: homoectoine), lines are calculations with PC-SAFT.

To evaluate the temperature dependence of the anti-stress effect of ectoines, the activity coefficients of water in ectoine, hydroxyectoine, and homoectoine solutions were investigated at other temperatures than 30°C, namely at 50°C and at the solutions' freezing points, respectively. decrease with increasing temperature whereas for ectoine and homoectoine solutions the WAC is found to increase with elevated temperature. This means that with increasing temperature the strength of the anti-stress effect is weakened for ectoine but augmented for hydroxyectoine. This supports the experimental observation that microorganisms like Halomonas elongata to a high extent produce ectoine at ambient conditions but at elevated temperatures a remarkable amount of hydroxyectoine. Another/additional explanation might be the temperature dependence of the enzymatic activity.

6.2Comparison of ectoines and prolines

Because of the similar chemical structures it is obvious to compare the chemicophysical properties of ectoines and prolines. One osmolyte that is often produced to sustain salt stress, is the amino acid L-proline. However, proline is rather employed by halotolerant microorganisms whereas the ectoines act as osmolytes especially in halophile organisms, i.e. in surroundings with high salt concentrations. In contrast, the

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amino acid L-hydroxyproline is not known to be found as an anti-stress agent in microorganisms. In this chapter, the thermodynamic properties of aqueous proline solutions are compared to those of ectoines in water to detect possible differences between these similar solutes. Fig. 5 illustrates that the WAC in solutions of ectoine and proline at 30°C show a qualitatively similar dependence on solute molality: the WAC values always decreases with increasing solute concentration. Moreover, the two pairs ectoine/proline and hydroxyectoine/hydroxyproline influence the WAC values in a similar way: hydroxyectoine and hydroxyproline behave almost ideally in water as the activity coefficients are very close to unity. This might be ascribed to the additional OH-group which seems to make the hydroxy solutes more water like. Therewith, the pronounced ambition of water molecules to build hydrogen bondings is satisfied and there is no need for reorientation efforts. Furthermore, we have shown earlier that the addition of polar groups to amino acids (-SH, OH, peptide bonds) causes increased WACs. In contrast, ectoine as well as proline cause activity coefficients which decrease more strongly with increasing molality. These observations also thermodynamically confirm that proline -due to its similar chemical structureis an osmolyte which behaves almost equally compared to ectoine. However, ectoine is produced by halophile organisms (moderate to high salt concentrations) while proline is rather used by halotolerant (low to moderate salt concentrations) ones. This might be due to the fact that ectoine is a better anti-stress agent than proline (see Fig. 5). However, the osmoticcoefficient data cannot explain why hydroxyectoine is produced by microorganisms against stress situations whereas hydroxyproline is not. The reason for this might be another thermodynamic property: the solubility in water. In order to be highly flexible and to survive in extremely concentrated aqueous systems with high osmotic pressures, the microorganisms have to produce a large amount of the compatible solute. Moreover, this amount of substance has to be soluble in the cell as

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the solute would otherwise precipitate thereby loosing its anti-stress effect. This means that a good solubility in water is a prerequisite for acting as osmolyte. At ambient conditions all ectoines have a very high solubility in water (ca. 7 mol/kg, Tab.

whereas hydroxyproline possesses only a solubility of about 2 mol/kg at 25°C (Fig. 6b).

This value would certainly be further decreased in the presence of other solutes in the organism. In addition to the possibility of non-existing metabolic pathways for the formation of hydroxyproline its comparatively small solubility might be a reason that microorganisms produce hydroxyectoine instead of hydroxyproline. As it is crucial to know the solubility of the ectoines also at other temperatures we investigated the solubility of each ectoine between 3 and 80°C. It can be observed in Fig. 6 that the solubility of ectoine strongly increases with temperature increase whereas the solubility of hydroxyectoine only weakly depends on the system's temperature.

Whereas the solubility of biomolecules like ectoine are in general accurately modeled with PC-SAFT (see Fig. 6a or Refs.) the temperature-independent behavior of hydroxyectoine and hydroxyproline solubilities in water leads to exceptional high deviations of the model calculations (16 % deviation between experiment and PC-SAFT, see Tab. 1). However, this is rather an exception as can be seen in Ref. or in Fig. 6a, respectively.

Comparison of ectoines and salts

Almost every microorganism possesses ion pumps. However, instead of pumping in inorganic ions, they often rather produce compatible solutes against stresses although this consumes extra energy. Obviously, in contrast to compatible solutes inorganic salts negatively affect the cell milieu. In addition to that there is also a distinct difference in the thermodynamic properties. In order to survive under salt-stress conditions a certain

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water activity has to be adjusted which -at given concentration -only depends on the activity coefficient of water.  Compared to a one-molal ectoine solution (thin grey line in Fig. 7), 2 m NaCl or 3.5 m KCl would be necessary to establish the same activity coefficients, respectively. This makes the ectoine much more effective from thermodynamic view.

 Moreover, the accumulation of high amounts of salt (2 or 3.5 mol/kg) is wellknown to be poisonous (especially Na + ) to marine organisms.

 Beyond thermodynamics -organic compounds might be metabolized if not needed any more which is not possible for high amounts of salts (those have to be flushed out).

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All this might explain the production of compatible solutes like ectoine instead of pumping in ions from outside the organism as protection against salt stress.

Comparison of ectoine with urea

In contrast to the ectoines and proline, urea is well-known to be an incompatible solute.

This means, that urea destabilizes protein structures. One reason might be the strong interaction of urea with peptide groups or aromatic side chains. However, in analogy to water/salt systems, the incompatible character of urea might also be caused by its influence on the osmotic behavior of the solution. It becomes obvious from Fig. 8 that, in contrast to the ectoine solutions, water activity coefficients directly increase by adding urea. This means that urea is a very ineffective anti-stress agent which seems to be characteristic for incompatible solutes. The same osmotic behavior was observed for glycine solutions in which water activity coefficients are higher than unity. To give an example, a 2 molal urea solution causes an osmotic coefficient of 0.93 which is more than 25 % lower compared to an equimolal ectoine solution (see Tab. 4), i.e. the osmotic pressure within a cell containing urea will be remarkably reduced compared to cells containing ectoine.

Fig. 8 Water activity coefficients of aqueous ectoine and urea solutions at 30°C. Symbols represent experimental data (squares: ectoine, circles: urea), lines are calculations with PC-SAFT.

6.5Salt influence on aqueous ectoine solutions

The importance of understanding the phase behavior of "simple" binary ectoine/water systems was illustrated in the previous chapters. However, biological solutions never contain one solute only.

To study the influence of electrolytes on the thermodynamic behavior of ectoine solutions, also osmotic coefficients of aqueous solutions containing both, ectoines as well as salt, were investigated. Here, we applied the vapor-pressure osmometer for the experimental investigations at 30°C. Tab. 7 summarizes the experimental results of these ternary systems at potassium chloride concentrations of 0.5 and 1 mol/kg. Fig. 9 shows the influence of hydroxyectoine (Fig. 9a) and of potassium chloride (Fig. 9b) on water activity coefficients at 30°C. Just as in the binary ectoine/water systems where WACs are always decreased by the ectoines (Fig. 3), the addition of hydroxyectoine to aqueous KCl solutions (Fig. 9a) causes also decreased WAC values.

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This means that increased osmotic pressures can be realized in cells containing salts (KCl) also by adding ectoines (independent of salt concentration). Moreover, this also gives a first hint to the effect of osmolytes in more complex systems: obviously, hydroxyectoine influences solutions by increasing their osmotic coefficients independent of the presence of other solutes. This supports the statement of other authors () that the ability of a molecule to act as biological osmolyte is mostly determined by the properties of the osmolyte/water binary system.

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Fig. 9b shows the salt influence to binary osmolyte/water systems. It can be observed that the addition of salt to aqueous hydroxyectoine solutions strongly increases the WACs in such ternary systems. As the addition of salt to pure water also causes increased WACs this is an expected experimental result. This means that increasing salt concentrations defeat the benefit of ectoines as anti-stress agents. Thus, from thermodynamic point of view, the cell should avoid accumulating salts. This might explain why microorganisms do not produce ectoines and simultaneously pump in inorganic compounds. However, it is possible that other salts do not cause such unfavorable effects which still has to be investigated.

In order to evaluate the applicability of ePC-SAFT to these complex multi-solute solutions, the activity coefficients and osmotic coefficients were predicted for these systems (no parameter fitting). Fig. 9 exemplarily illustrates the model predictions in hydroxyectoine/KCl/water solutions at 30°C. With the hydroxyectoine parameters given in Tab. 6 and the KCl parameters as determined earlier the influence of KCl on WAC of hydroxyectoine/water solutions can be predicted with ePC-SAFT at several temperatures and concentrations. Fig. 9a shows that the WACs even at both salt concentrations (0.5 and 1 mol/kg) are predicted by the model quantitatively, i.e. the results are based on the binary salt/water and ectoine/water systems only and no adjustable parameters k ij between ions and hydroxyectoine had to be applied. This

shows that ePC-SAFT is a suitable model for describing the liquid-phase properties of solutions containing biomolecules or salt and even of multi-solute solutions.

7Summary

In this work we investigated interactions in aqueous solutions containing the compatible solutes ectoine, hydroxyectoine, and homoectoine. Whereas the latter is a synthetic compound, ectoine and hydroxyectoine are produced by halophilic organisms against salt stress. In the first part of the work we presented for the first time solution densities between 15 and 45°C, solubilities between 3 and 80°C, and activity coefficients between freezing point and 50°C. Furthermore, the influence of KCl on activity coefficients in aqueous hydroxyectoine solutions at 30°C was measured.

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Based on these data, comparisons between the different kinds of ectoines were carried out showing that the smallest osmolyte (ectoine) causes the lowest water activity coefficients and thus has the best anti-stress effect. It could be observed that all thermodynamic properties between ectoine and proline as well as between hydroxyectoine and hydroxyproline are very similar except the comparably low solubility of the latter solute. This might explain the fact that organisms do not produce hydroxyproline to protect themselves against salt/pressure stresses.

Comparing the influence of urea (an incompatible solute) and salts to the one of ectoines and prolines (compatible solutes) on the thermodynamic properties of aqueous solutions revealed pronounced differences. Whereas salts and urea increase the WAC, all ectoines and prolines were shown to reduce these WAC values even at small concentrations. Thus, osmolytes cause much higher osmotic pressures than incompatible solutes at the same concentrations. That means that, e.g. less ectoine is necessary to establish a certain osmotic pressure (i.e. low water activity) compared to urea. This makes the osmolytes unique compared to salts or urea and explains why organisms avoid pumping in ions but rather produce organic compounds like the ectoines.

In the last part of the work the ternary system water/KCl/hydroxyectoine was investigated. It could be shown that the anti-stress effect of hydroxyectoine in the binary system without salt is qualitatively the same as for the ternary systems with added salt.

That supports earlier findings, that the ability of a molecule to act as biological osmolyte is for the most part already determined by the properties of the binary osmolyte/water systems.

Finally, the thermodynamic model PC-SAFT has been applied for the modeling of solution densities (ARD density = 0.15 %) as well as for vapor-liquid (ARD osmotic coefficient = 1.63 %) and solid-liquid (ARD solubility = 8.47 %) phase behavior of aqueous ectoine solutions. PC-SAFT was shown to accurately describe all the thermodynamic properties with only one single parameter set per solute. One exception is the modeling of hydroxysolute solubilities which show an almost temperature-independent solubility behavior; this cannot be captured well with PC-SAFT (up to 16% deviation between model and experiment). Moreover, it is possible to predict the salt influence on aqueous

  al. (protection against activation of zymogens), by Schnoor et al. (PCR enhancer), by Goller and

  between 30 and 50°C. Experimental activity coefficients at the freezing point were obtained by a cryoscopic osmometer. The vapor-pressure osmometer "Osmomat O70" by Gonotec (Berlin, Germany) used in this work allows for measurements in one-solvent solutions at concentrations between 0.005 and 3.0 mole solute per kg water [mol/kg]. It was already applied earlier (Held et A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT al.) to determine solvent activity coefficients in amino-acid solutions. Measurements can be performed at temperatures up to the boiling point of the solvent. The measuring cell of the Osmomat O70 consists of two thermistors placed in a tempered watersaturated atmosphere. With the help of a syringe, a droplet is placed at the end of each of the thermistors: one droplet being water, the other one being the aqueous solution of the solute of interest. Being at the same solvent pressure, the temperature difference between the two droplets is detected. This value can be converted into the osmotic coefficient or the solvent activity coefficient.

A

  C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT two association sites. The same model was used for water which has already been applied earlier (parameters in Ref.).In this work, the five ePC-SAFT parameters (segment number, segment diameter, dispersion-energy parameter, association-energy parameter, and association range) for the associating ectoines were determined by fitting to our own experimental liquiddensity (Tab. 1) and osmotic-coefficient (Tabs. 3-5) data at 25°C. To determine the pure-component parameters for urea, solution-density and osmotic-coefficient data from literature was applied (seeTab 6).

Fig. 4

 4 Fig. 4 Temperature dependence of water activity coefficients of one molal aqueous ectoine solutions between freezing point and 50°C. Symbols represent experimental data (squares: ectoine, circles: hydroxyectoine, triangles: homoectoine), lines are calculations with PC-SAFT.

Fig. 4

 4 Fig. 4 illustrates the influence of temperature on water activity coefficients in one molal ectoine solutions. Experimental results show a remarkably different behavior of ectoine systems with varying temperature: the WAC values of hydroxyectoine solutions slightly

Fig. 5

 5 Fig. 5 Water activity coefficients of aqueous ectoine and proline solutions at 25°C. Symbols represent experimental data (full squares: ectoine, full circles: hydroxyectoine, open squares: proline, open circles: hydroxyproline), lines are calculations with PC-SAFT.

Fig. 6

 6 Fig. 6 Solubilities of ectoine/L-proline (a) and hydroxyectoine/L-hydroxyproline (b) in water between 0 and 80°C. Symbols represent experimental data (squares: ectoine, circles: hydroxyectoine, triangles: proline, rhombi: hydroxyproline), lines are calculations with PC-SAFT.

Fig. 7 Fig. 7 

 77 Fig. 7 Water activity coefficients at 30°C. circles: NaCl solution, triangles: KCl solution, squares: ectoine solution. Symbols are experimental data from this work (ectoine) and from Lobo and Quaresma for the salts. The thin grey line is the activity coefficient of water caused by 1 mol ectoine per kg water.

  Fig. 2

  R I P T

		ACCEPTED MANUSCRIPT
	T	m E	density	T	m HyE	density	T	m HoE	density
	[K]	[mol/kg]	[kg/m³]	[K]	[mol/kg]	[kg/m³]	[K]	[mol/kg]	[kg/m³]
	288.17	0.0882	1002.63	288.17	0.0097	998.86	288.15	0.4000	1014.53
	288.17	0.1757	1006.17	288.17	0.0293	999.89	288.15	0.8000	1028.44
	288.17	0.3484	1013.22	288.17	0.0876	1003.23	288.15	1.2000	1041.47
	288.17	0.6864	1027.21	288.17	0.2601	1012.44	288.15	1.4000	1047.59
	288.17	1.3383	1055.30	288.17	0.7513	1040.64	298.15	0.4000	1011.97
	288.17	2.5408	1110.84	288.17	2.0917	1121.41	298.15	0.8000	1025.63
	298.24	0.0882	1000.54	298.20	0.0097	997.43	298.15	1.2000	1038.45
	298.24	0.1757	1003.99	298.20	0.0293	998.47	298.15	1.4000	1044.45
	298.24	0.3484	1010.94	298.20	0.0876	1001.53
	298.24	0.6864	1024.84	298.20	0.2601	1010.97
	298.24	1.3383	1052.66	298.20	0.7513	1038.09
	298.24	2.5408	1106.99	298.20	2.0917	1117.32
	318.17	0.0882	993.69	318.23	0.0097	990.64
	318.17	0.1757	997.08	318.23	0.0293	992.24
	318.17	0.3484	1003.95	318.23	0.0876	994.40
	318.17	0.6864	1017.45	318.23	0.2601	1004.07
	318.17	1.3383	1044.87	318.23	0.7513	1026.72
	318.17	2.5408	1098.37	318.23	2.0917	1110.24

Table 6 :

 6 PC-SAFT parameters for ectoine (E), hydroxyectoine (HyE), homoectoine (HoE), and urea as well as deviations between model and experimental data.

	_____________________________________________________________________________________________________________________________________________
	Parameter	Unit Abbr.	E	HyE	HoE	Urea
	_____________________________________________________________________________________________________________________________________________
	segment number	[-]	m seg	1.250	8.389	2.217	4.244
	segment diameter	[Å]	σ	5.050	2.532	4.333	2.446
	dispersion energy	[K]	u / k B	530.00	352.56	392.98	368.23
	association sites	[-]	N	2	3	2	2
	association energy [K] ε hb AiBi /k B 3500.00	2000.00	3500.00	3068.31
	association volume [-]	κ hb AiBi	0.09	0.09	0.09	0.001
	melting temperature [K]	T 0 SL	511.45	750.41	665.76	405.80*
	melting enthalpy	[K]	h 0 SL / R 1918.78	1462.59	1187.49	1636.91*
	interaction parameter [-]	k ij,25°C	2.933•10 -3 -5.240•10 -2	-4.136•10 -4 -4.380•10 -2
	at 25°C
	interaction parameter [-]	k ij,T	5.787•10 -4 -	5.787•10 -4	-
	solution density
	T-range	[K]		288-318	288-318	288-298 298-303**
	ARD	[%]		0.08	0.34	0.03	0.11
	AAD	[kg/m³]	0.82	3.47	0.32	1.12
	solubility
	T-range	[K]		276-353	276-313	293-353 291-346**
	ARD	[%]		2.15	17.36	5.90	3.89
	AAD	[mol/kg]	0.20	1.25	0.58	0.98
	osmotic coefficients
	T-range	[K]		T m -323	T m -323T m -323 288-323**
	ARD	[%]		1.91	0.49	2.49	0.07
	AAD	[-]		0.021	0.005	0.026	<0.001
	* Experimental melting parameters directly taken from without further adjustment.
	** Experimental data taken from literature: solution densities, solubilities, and osmotic coefficients at
	25°C and between 30 and 50°C.

  Tab 7: Experimental water and osmotic coefficients of aqueous KCl/hydroxyectoine solutions at 30°C. Solute activity coefficients γ * were obtained by the ePC-SAFT model.

		30°C, 0.5 m KCl				30°C, 1 m KCl
	m HyE	Φ	γ water	γ * KCl	γ * HyE	m HyE	Φ	γ water	γ * KCl	γ * HyE
	[mol/kg]	[-]	[-]	[-]	[-]	[mol/kg]	[-]	[-]	[-]	[-]
	0.401	0.929 1.0014 0.630 0.986	0.204	0.928 1.0021 0.594 0.967
	0.799	0.962 1.0008 0.626 0.996	0.400	0.931 1.0020 0.591 0.971
	1.200	0.990 0.9996 0.623 1.009	0.600	0.941 1.0016 0.588 0.976
	1.600	1.007 0.9986 0.619 1.026	0.791	0.957 1.0009 0.586 0.981
	Fig. 9 (a) Water activity coefficients of aqueous hydroxyectoine solutions containing
		different concentrations of potassium chloride at 30°C. Symbols represent
		experimental data (squares: 0.5 m KCl, circles: 1 m KCl), lines are
		predictions with ePC-SAFT.
		(b) Water activity coefficients of aqueous potassium chloride solutions
		containing different concentrations of hydroxyectoine at 30°C. Symbols
		represent experimental data (circles: 0.4 m HyE, squares: 0.8 m HyE),
		lines are predictions with ePC-SAFT.

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ectoine solutions with ePC-SAFT, i.e. the calculations are based on binary water/salt and water/ectoine data only and do not require any additional adjustable parameters.

8Acknowledgements

The authors gratefully acknowledge the financial support by the German Society of Industrial Research (AiF) with Grant 162958N/1. We also want to thank Thorsten

Beierling and Zhenhua Liu for their help with the parameter estimation and with the vapor-pressure measurements. Greek symbols

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Research highlights -Compatible solutes strongly decrease the water activity coefficient whereas incompatible solutes (urea, salts) do not. -The lower the water activity coefficient the better the protection against osmotic stresses. -Among the considered compatible solutes, ectoine causes the best protection.

-This beneficial impact of compatible solutes does not depend on the presence of other molecules (e.g. salts).