M W D Cooper

S Kelly

M Bertolus

Atomic scale mobility of the volatile fission products Xe, Kr and I in cubic SiC

Keywords: Silicon Carbide, Fission Products, Diffusion, Density Functional Theory

Atomic scale mobility of the volatile fission products Xe, Kr and I in cubic SiC

Introduction

Silicon carbide (SiC) exhibits a very high melting point and good chemical stability making it suitable for high temperature applications. In particular, as a wide band gap semiconductor, it has been touted for applications in high temperature electronic devices [1] and is envisaged as an alternative to Si. Furthermore, it has a low neutron capture cross section making it an interesting candidate material in fission and fusion reactors. Low fission product mobility in SiC makes it a prime candidate material for a barrier in advanced high temperature reactor designs. For example, the tristructural-isotropic (TRISO) particle fuel design employs SiC in this role [4].

A significant body of work has been undertaken to study the release of radiologically important fission products from nuclear fuel. For example, rare gas fission products, Xe and Kr, are highly insoluble in the UO 2 matrix and are released from the fuel in significant quantities [5][6][7][8][9][10]. Similarly, highly volatile fission products, such as I and Cs, rapidly migrate out of the host UO 2 matrix [11,12]. Therefore, these fission products can provide a particular problem for retention and must be isolated through a barrier layer. The mobility of fission products in SiC has been studied experimentally [4,[13][14][15][16] and atomic scale simulations can be employed to develop a fundamental understanding of the underlying mechanisms. Density functional theory (DFT) has been successfully applied to the investigation of defect behaviour in a number of nuclear materials [17]. SiC exhibits a large number of polytypes, the most common being the cubic 3C and the two hexagonal 4H and 6H structures. The 3C structure is simpler to model, while most experimental results have been obtained on 6H-SiC. Wiktor et al. [18] have shown that the extrapolation of the formation energies of point defects obtained in 3C-SiC to the gap of the 6H structure is a good approximation, especially for carbon defects.

In DFT [18,[START_REF] Bertolus | Modélisation à l'échelle atomique de matériaux nucléaires du cycle du combustible[END_REF] and the GW [21] approximation carbon vacancies are predicted to be the most stable intrinsic defects in SiC. Unlike GW, DFT significantly underestimates the band gap. Nonetheless the same trends are predicted for the charge states and formation energies of intrinsic defects across the theoretical band gaps for both approaches. Therefore, DFT energies as a function of the Fermi level must be considered relative to the size of the bandgap.

The results of Wiktor et al. [18] indicated that the carbon vacancy is in the 2+ charge state over nearly the full theoretical band gap (1.38 eV), although at the top of the band gap the neutral carbon vacancy was predicted to be favourable. Previously Bertolus et al. [START_REF] Bertolus | Modélisation à l'échelle atomique de matériaux nucléaires du cycle du combustible[END_REF] and Charaf-Eddin and Pizzagalli [START_REF] Charaf-Eddin | [END_REF] used DFT to investigate the incorporation of a number of fission products into neutral defects of SiC, including Xe, Kr and I. The substitution of fission products onto the carbon sublattice was widely predicted to be very significantly more favourable than as an interstitial or on the Si sublattice. Similarly, Roma et al. [22] identified that Pd is preferentially accommodated on carbon sublattice either as a +2 or a neutral defect. Furthermore, the migration of Pd in SiC was also predicted to be restricted to vacancy-assisted migration on the FCC carbon sublattice when vacancies are present [23].

Here we investigate the mobility of Xe, Kr and I in 3C-SiC from their stable sites on the carbon sublattice by assuming a vacancy-assisted migration mechanism like that of Roma et al. [22]. This is justified because i) the most stable sites for these fission products are on the carbon sublattice, ii) the carbon vacancy is the most stable defect in SiC and iii) the highly unfavourable silicon vacancy is predicted to be converted to a carbon vacancy C Si antisite pair (see Figure 1).

This allows an analysis of fission product mobility that is based on the five frequency model for vacancy-assisted diffusion on the FCC carbon sublattice. The regimes over which diffusion via +2 or neutral carbon vacancies is suitable are also discussed.

Methodology

Calculation parameters

All DFT calculations were carried out using the projector augmented wave (PAW) method [26,27] as implemented in the Vienna ab initio Simulation Package (VASP) [28][29][30] with a plane wave cut-off energy of 600 eV. For carbon the 2s and 2p levels are treated as valence states (and level 1s is included in the core regions), whereas for silicon 3s and 3p are considered to be valence states (and the 1s, 2s and 3p levels constitute the core region). The parametrisation of Perdew, Burke and Ernzerhof (PBE) [31] for the Generalised Gradient Approximation (GGA) was used to describe the exchange-correlation interactions. Defect calculations were carried out on supercells of 3×3×3 sphalerite unit cells of SiC (216 atoms) with spin polarisation and no conservation of symmetry. The Brillouin zone was sample using a 2×2×2 k-point mesh generated using the Monkhorst-Pack scheme [32]. Electron relaxation was optimised in reciprocal space with force and total energy convergence criteria of 10 -8 eV Å-1 and 10 -8 meV respectively. The perfect crystal properties predicted here are compared to experimental results in Table 1, showing a good agreement. Similar calculation parameters were used previously by Wiktor et al. [18] to determine the positron lifetimes and the results showed a strong agreement with experiment. In addition, the insertion of Kr and Xe in SiC is correctly described using the PBE functional [START_REF] Bertolus | Modélisation à l'échelle atomique de matériaux nucléaires du cycle du combustible[END_REF].

The formation energy of a charged defect was calculated by:

E F = E tot (V X,q ) -n C µ bulk SiC -(n Si -n C ) µ bulk Si + 1 2 ∆H f (SiC) + q(E V BM + µ e ) (1)
where E tot is the energy of the defective supercell, µ bulk SiC is the energy per SiC pair in the bulk, the energy per atom in bulk Si is µ bulk Si . The Fermi level is given by µ e and E V BM is the energy of the valence band maximum. The formation enthalpy of SiC, ∆H f (SiC), is given by:

∆H f (SiC) = µ bulk SiC -µ bulk Si -µ bulk C (2)
where µ bulk C is defined as the energy of a carbon atom within the diamond structure. One issue with using the supercell approach for charged defects is the unphysical system charge that arises due periodic boundary conditions. A charge neutralising background jellium must, therefore, be used [33][34][35]. However, defect energies must be adjusted according to the interaction energy of a periodically repeating system containing a point charge, q, with the neutralising background jellium, as defined by the Madelung energy [33,34]:

∆E el (q) = αq 2 2 L ( 3
)
where α is the Madelung constant (α = 1.6381 for 3C-SiC), is permittivity of the medium and L is the supercell size length. and L are defined from the geometry optimised perfect cell (Table 1). To calculated the additional potential correction term ∆V the method of Taylor and Bruneval [36] is used, such that:

∆V = v bulk KS -v def ect KS (4)
where v bulk KS and v def ect KS are the averaged Kohn-Sham potentials for the perfect and defective supercells respectively.

Migration barriers are calculated using the nudged elastic band (NEB) method [37] in conjunction with the same DFT parameters described above. For each NEB calculation the initial and final stable configurations of a given transition are determined using geometry optimisation. Based on the linear interpolation of the initial and final atomistic configurations an initial guess of the lowest migration pathway, which is then minimised, is made at five discrete points. There are, as such, seven images of the lowest energy migration pathway including the initial and final configurations.

Five Frequency Model

Based on the justifications given in section 1 it assumed that fission product migration is restricted to the FCC carbon sublattice. The five frequency model governing vacancy mediated impurity diffusion on an FCC lattice assumes that the second nearest neighbour distance is great enough so the vacancy-impurity binding is very low and can be neglected beyond this distance [38]. Therefore diffusion can be broken down into five constituent individual jump frequencies [39,[START_REF] Mehrer | Diffusion in Solids[END_REF]:

• w 0 -vacancy-atom exchange rate in the host material. Vacancy migration in the bulk whereby the bulk is defined as any jump not involving the first nearest neighbour site with respect to the impurity. In Figure 2 w 0 is represented by the blue arrow between the second and third nearest neighbour positions on the carbon sublattice.

• w 1 -rotation rate of the impurity-vacancy pair. The jump of a vacancy around the impurity between two first nearest neighbour sites, as represented by the yellow arrow in Figure 2.

• w 2 -impurity-vacancy exchange rate. The jump of the impurity into a vacancy that is occupying a first nearest neighbour site, as indicated by the red arrow in Figure 2.

• w 3 -dissociation rate of the impurity-vacancy pair. The jump of the vacancy from a first nearest neighbour position to a second nearest neighbour site. The purple arrow in Figure 2 represents dissociation.

• w 4 -association rate of the impurity-vacancy pair. Vacancy migration from a second nearest neighbour position into a first nearest neighbour site with respect to the impurity as indicated by the green arrow in Figure 2.

Each of the above jump frequencies, w i , has an associated attempt frequency, v i , and energy barrier, E i , such that:

w i = v i .exp -E i k B T (5)
where k B is the boltzmann constant and T is the temperature. Generally, impurity diffusivity, D, can be described by:

D = 1 6 f α 2 pv 2 .exp -E 2 k B T ( 6
)
where α is the jump distance for the vacancy-impurity exchange and p is the probability of finding a vacancy in a first nearest neighbour site with respect to the impurity, which can be expressed as follows:

p = N.exp -(E f + E B ) k B T (7)
where E f is the bulk vacancy formation energy, E B is the impurity-vacancy binding energy and N is the number of first nearest neighbour sites with respect to the impurity. In the absence of interaction beyond the first nearest neighbour, the binding energy can be calculated by

E B = E 4 -E 3 .
As such, if the vacancy and impurity attract (E B < 0) the probability of finding a vacancy in a first nearest neighbour site is enhanced with respect to the bulk concentration. Equation 8shows that the correlation factor, f , as a function of w 1 , w 2 , w 3 and the escape probability, 7F3 2 [39]:

f = w 1 + 7F 3 w 3 /2 w 1 + w 2 + 7F 3 w 3 /2 (8)
Although an explicit form of the escape probability, 7F3 2 , is given in reference [39], the results of NEB calculations presented later show that for all cases studied here the association rate, w 4 , far exceeds that of bulk vacancy migration, w 0 . Consequently, every time the vacancy dissociates from the impurity it rapids re-associates and the escape probability, 7F3 2 , tends to zero so that:

f = w 1 w 1 + w 2 (9)
Therefore, in conjunction with strong vacancy-impurity binding, the migrating species can be treated as a bound pair with some special cases discussed below: a) if w 1 >> w 2 vacancy migration around the impurity is significantly greater than impurityvacancy exchange. This effectively randomises the position of the vacancy with respect to the impurity before the impurity jumps into the vacant site. As such, f → 1 in equation 6, so that the impurity diffusivity is expressed as:

D = 1 6 α 2 v 2 N exp -(E 2 + F f + E B ) k B T (10)
b) if w 2 >> w 1 the impurity-vacancy exchange rate is far greater than the other jump frequencies. Consequently, the motion of the impurity is highly correlated as it 'rattles' back and fourth between two adjacent lattice sites. Therefore, equation 9 gives f → w1 w2 and by assuming all attempt frequencies (v i ) are approximately equal to the Debye frequency the impurity diffusivity is expressed as:

D = 1 6 α 2 v 1 N exp -(E 1 + E f + E B ) k B T (11)
Long range diffusion is, therefore, dependent on the ability of the vacancy-impurity pair to reconfigure by rotation (w 1 ). c) if w 2 ≈ w 1 there is a combined correlated impurity-vacancy exchange/rotation mechanism, whereby f → 1 2 and the diffusivity is expressed as:

D = 1 12 α 2 v 1,2 N exp -(E 1,2 + E f + E B ) k B T (12)
This work is concerned firstly with identifying the stable configurations associated with the five frequency model and then determining all migration barriers between these configurations (E 0 , E 1 , E 2 , E 3 , E 4 and E 5 ). Based on the special cases outline above an analysis of the vacancyassisted migration mechanisms for Xe, Kr and I migration in cubic SiC is given.

Results and discussion

Formation energies and charge states

Formation energies are reported as a function of µ e in Figure 3 for a carbon vacancy and a first nearest neighbour carbon divacancy. Values are reported from the bottom of the band gap up to edge of the experimental band gap (2.39 eV), however, as the computational band gap is just 1.38 eV one must consider the defect energies at the top of the theoretical band gap as commensurate with top of the real life band gap (see section 1), as shown by comparison with GW results [21], which show the same trends from 0 < µ e < 2.39 as predicted by DFT from 0 < µ e < 1.38. Figure 3 indicates that over the calculated band gap the +2 charged supercell dominates for both the single carbon vacancy and the carbon divacancy. However, at the top of the theoretical band gap the neutral supercell becomes favourable. It is only when the Fermi level significantly exceeds that of the computational band gap that any negative charge states exist for carbon vacancy type defects.

As for the carbon vacancies, a Xe impurity occupying a carbon site, Xe C , is also dominated by the +2 charged supercell over the full calculated band gap (see Figure 4a). Alternatively, if the xenon impurity has an additional carbon vacancy in a first nearest neighbour carbon site the neutral charge state becomes favourable at the top of the band gap (see Figure 4b). Again one only encounters alternative charge states when µ e is significantly greater than 1.38 eV.

Due to similar chemistry the Kr formation energies are very similar to that of Xe; the +2 charged defects dominate over the the full computational band gap (see Figure 5). However, if a carbon vacancy occupies a first nearest neighbour carbon site to the Kr impurity the neutral supercell becomes favourable near the top of the computational band gap.

Figure 6 shows that the accommodation of I at a carbon site is also dominated by the the +2 charge state over nearly the full theoretical band gap. If the first nearest neighbour carbon site with respect to the impurity is vacant the +2 supercell is also more favourable over a broad range of Fermi levels. However, near the top of the theoretical band gap alternative valence states become favourable.

For all defects studied here that are involved in the five-frequency model on the carbon sublattice it is clear that the +2 charge state is dominant over a broad range of the computation band gap. However, the neutral charge state is important near the top of the bad gap for the formation of the migration mediating carbon vacancies as well as for the accommodation of the noble gases Xe and Kr. Therefore, all migration barriers involved in the five-frequency model will be examined in both the neutral and the +2 charged supercells.

Migration barriers of the five-frequency model

The stable configurations calculated in section 3.1 define the initial and final configurations for E 0 , E 1 and E 2 . Whilst the initial configurations for E 3 and E 4 is given by the impurity-vacancy first nearest neighbour configuration determined previously, the final configuration was calculated by energy minimisation of the impurity-vacancy second nearest neighbour configuration. Using these initial and final configurations the NEB method was used to calculate the energy barriers.

For summary the energy barriers associated with the five frequency model (i.e. E 0-4 ) for I, Xe and Kr are shown in Table 2. The charge neutral and +2 supercell cases are both reported. Firstly, one should note that in all cases E 4 < E 0 (or w 4 >> w 0 ) so that if the vacancy overcomes the binding energy with the impurity to reach a second nearest neighbour site it is highly likely that it will re-associate with the impurity rather than migrate into the bulk. Additionally, all cases exhibit strong binding energies (E 3 > E 4 ) in line with the limiting cases discussed at the end of section 2.2. Therefore, the relative height of the E 1 and E 2 energy barriers determine the specific limiting case.

Figure 7 shows the E 1 and E 2 barriers associated with the five frequency model for Xe in the neutral supercell regime, indicating E 1 > E 2 . Consequently, the extremely high dependency of the jump frequency on the energy barrier (equation 5) dictates that w 2 >> w 1 . The diffusivity is therefore determined by equation 11, such that E 1 is the only barrier that contributes to the activation energy. Although for the case of xenon in the +2 charged supercell the migration barriers are different, the same relative trends between barriers are predicted -i.e. w 2 >> w 1 . Therefore, the migration mechanism remains the same as for the neutral case and E 1 plays the dominant role in governing migration.

The energy barriers for carbon vacancy mediated Kr migration in 3C-SiC are shown in Figure 8. As with Xe, the migration mechanism for Kr in the neutral supercell is predicted to proceed through the rotation of a tightly bound vacancy-impurity pair where E 1 contributes to the activation energy. However, in the +2 charged supercell E 1 ≈ E 2 (at least within 0.04 eV) so that w 1 ≈ w 2 . In this case, the similar jump frequencies of impurity-vacancy exchange and rotation leads to a somewhat correlated motion, such that f → 1 2 and E 2 ≈ E 1 contributes to the activation energy (equation 12).

Figure 9 shows the energy barriers associated with the five frequency model for I in the neutral supercell regime, indicating that E 1 > E 2 or w 2 >> w 1 . In addition to the high binding energy, this reveals a migration mechanism that is again characterised by a tightly bound impurityvacancy pair that rotates through the lattice. The diffusivity is, thus, determined by equation 11.

Although the barriers are different, the same trends and mechanism are predicted for the +2 supercell.

In summary, nearly all of the cases studied exhibit a type b) migration mechanism (see section 2.2), whereby, the impurity rattles between the two carbon sites and the rotation of this tightly bound impurity-vacancy pair provides the means of diffusion. Kr in the +2 supercell exhibits some mixture of a) and b) type migration with a somewhat correlated diffusive motion. Based on these limiting cases the activation energies can be determined.

Activation energies

Table 3 summarises the activation energies for I, Xe and Kr for the neutral and +2 supercells calculated using equation 11 except for the case of Kr in the +2 charged supercell, where equation 12 is used. In the cases of the charged supercell the formation energy of the mediating carbon vacancy is dependent on the Fermi level, µ e , and, therefore, so is the activation energy. We have, thus, reported the activation energy as function of the Fermi level (see Table 3).

In line with previous simulations [18], it was predicted in section 3.1 that the transition between +2 and neutral carbon vacancies occurs at µ e = 1.33 eV (see Figure 3). This indicated that the +2 regime is expected to dominate over the majority of the bandgap. Thus, one may promote high activation energies by favouring n-type doping, so long as one does not raise the Fermi level to the top region of the band gap where neutral vacancies begin to dominate. In the p-doping regimes (i.e. near the bottom of the band gap) the activation energy is lowest in part to the low formation energy of the migration mediating carbon vacancies.

Xe has a higher activation energy than Kr across the entire band gap. Due to their similar inert chemistry this difference can be attributed to size effects. In the +2 regime it can be seen that, although the impurity-vacancy exchange barrier (E 2 ) is lower for Xe, the diffusion limiting impurity-vacancy rotation barrier (E 1 ) is in fact 0.46 eV lower for Kr. This is sufficient to ensure Kr has a lower activation energy in the +2 supercell despite the tighter binding (E 4 -E 3 ) for Xe. In the neutral supercell Kr has a more attractive binding energy in addition to a lower rate limiting diffusion barrier, thus, contributing an even lower Kr activation energy compared to that of Xe. These results indicate that Kr will diffusion more rapidly than Xe regardless of the Fermi level.

Over the majority of the band gap (+2 regime) I exhibits the highest activation energy, indicating that it will diffuse more slowly than the noble gases. Early results from experimental studies reflect this, in that I has been observed to be immobile in SiC up to 1400 • C [START_REF] Carlot | [END_REF], whereas, Xe exhibits limited mobility at 1350-1400 • C [START_REF] Gilabert | GdR MATINEX plenary meeting[END_REF]. However, Figure 10 indicates that at the very top the band gap it is possible that iodine mobility could exceed that of Xe. This is a consequence of the reduced E 1 barrier for I in the neutral cell compared to the +2 supercell, whereas, the converse is true for the noble gases (see Table 2). This highlights a key way in which the chemistry of a given species affects mobility as function of the Fermi level and indicates how doping can manipulate the efficacy of SiC for fission product retention.

Conclusions

Density functional theory has been applied to investigate the vacancy-assisted migration of fission products in 3C-SiC. Based on the stable carbon vacancies and the accommodation of fission products on the carbon sublattice, a justification is made for treating diffusion as limited to the FCC carbon sublattice. Furthermore, the +2 and neutral charge states are sufficient to describe the defects involved over the full theoretical band gap. All migration barriers involved in the five frequency model have been calculated for Xe, Kr and I in the +2 and neutral supercells.

Results indicate that over the majority of the band gap the activation energy for I exceeds that of Xe which exceeds that of Kr. It is expected therefore that SiC is most effective at preventing I mobility, as supported by preliminary experimental results [START_REF] Carlot | [END_REF][START_REF] Gilabert | GdR MATINEX plenary meeting[END_REF].

The activation energy for all species increases as a function of the Fermi level, indicating that n-type doping could be used to enhance the fission product retention properties of SiC. Raising the Fermi level reduces the stability carbon vacancies, thus, limiting their availability for assisting migration. Further work should be done to investigate the attempt frequencies involved in the five frequency model for a full description of fission product diffusivity. Additionally, models that incorporate more mechanisms involving longer range interactions must also be studied. Table 1: The bulk properties of 3C-SiC predicted using the DFT method in this work and from previous experimental work [START_REF] Lee | [END_REF][44][45]

Figures and Tables

Figure 1 :

 1 Figure 1: The formation energy for the carbon vacancy, a carbon vacancy CSi antisite pair and a silicon vacancy as a function of the Fermi level. Values are reported up to the experimental band gap limit of 2.39 eV. The calculated band gap limit of 1.38 eV is shown by the dotted line. Data for Figure taken in reference [18].

Figure 2 :

 2 Figure 2: The jumps involved in the the five frequency model are indicated using coloured arrows: i) w0 (blue) -vacancy migration in the bulk (beyond the first nearest neighbour), ii) w1 (yellow) -vacancy migration between two first nearest sites with respect to the impurity, iii) w2 (red) -the migration of the impurity into the vacancy, iv) w3 (purple) -vacancy migration from the first nearest neighbour site to the second nearest neighbour site, v) w4 (green) -vacancy migration from the second nearest neighbour site to the first nearest neighbour site. Silicon and carbon are represented by purple and turquoise spheres respectively. The red sphere indicates the impurity atom (Xe, Kr or I).

Figure 3 :

 3 Figure 3: The formation energy for a) the carbon vacancy and b) carbon divacancy as a function of the Fermi level. Values are reported up to the experimental band gap limit of 2.39 eV. The calculated band gap limit of 1.38 eV is shown by the dotted line.

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4: The formation energy for the accommodation of Xe at a) the carbon vacancy and b) carbon divacancy as a function of the Fermi level. Values are reported up to the experimental band gap limit of 2.39 eV. The calculated band gap limit of 1.38 eV is shown by the dotted line.

  .

		DFT (present work)	Experimental
	Lattice parameter	4.379 Å	4.36 Å [43]
	Band gap	1.38 eV	2.39 eV [44]
	Relative dielectric constant, r	9.72 Fm -1	9.72 Fm -1 [45]

Table 2 :

 2 The energy barriers for Xe, Kr and I associated with the jump frequencies of the five-frequency model, as shown in Figure2. Values are reported for the charge neutral and +2 supercells. Note that EB = E4 -E3.

	Neutral	Charged +2

Table 3 :

 3 The activation energy for I Kr and Xe in the charge neutral and 2+ supercells. These activation energies are also reported in Figure10. EB + E1 = 5.45E f + EB + E1 = 3.29 + 2µe Kr E f + EB + E1,2 = 4.60 E f + EB + E1 = 2.92 + 2µe I E f + EB + E1 = 4.65 E f + EB + E1 = 4.27 + 2µe

	Impurity	Neutral	Charged +2
	Xe	E f +

Acknowledgements R.W. Grimes and E. Vathonne are acknowledged for useful discussion. Part of this work was performed using HPC resources from GENCI (grant t2013086922).


Ph.D J Puibasset
email: puibasset@cnrs-orleans.fr

Adsorption-Induced Deformation in Nanopores: Unexpected Results Obtained by Molecular Simulations

The adsorption of a fluid in a nanoporous material induces deformations of the solid. The saturating regime, where the solid is filled with liquid, generally exhibits a linear relationship between the liquid pressure and the solid strain. This provides an experimental way to measure the elastic moduli of the solid walls. For large pores, the strain is determined by the pressure of the liquid saturating the pores and the mechanical properties of the porous solid. What happens at the nanometric scale, where liquid/matrix interfacial effects dominate? We have performed molecular simulations of a simple Lennard-Jones fluid confined between deformable nanoplatelets. The simulations provide the deformation of the nanopore as a function of the liquid pressure, in a way similar to what is done experimentally. The results show unexpected interface effects, which could be relevant to experimental data analysis.

INTRODUCTION

Adsorption-induced deformation of a nanoporous material concerns not only soft materials like biopolymers or aerogels [START_REF] Dušek | Responsive Gels: Volume Transitions I[END_REF]Scherer, Smith et al. 1995;Scherer, Smith et al. 1995;[START_REF] Thibault | Silica-Aerogel Thermal Expansion Induced by Submonolayer Helium Adsorption[END_REF][START_REF] Herman | Deformation of Silica Aerogel During Fluid Adsorption[END_REF][START_REF] Kulasinski | Poroelastic Model for Adsorption-Induced Deformation of Biopolymers Obtained from Molecular Simulations[END_REF][START_REF] Ogieglo | In Situ Ellipsometry Studies on Swelling of Thin Polymer Films: A Review[END_REF], but also stiff materials [START_REF] Meehan | The Expansion of Charcoal on Sorption of Carbon Dioxide[END_REF][START_REF] Bangham | The Expansion of Charcoal Accompanying Sorption of Gases and Vapours[END_REF][START_REF] Haines | Length Changes of Activated Carbon Rods Caused by Adsorption of Vapors[END_REF][START_REF] Amberg | A Study of Adsorption Hysteresis by Means of Length Changes of a Rod of Porous Glass[END_REF][START_REF] Scherer | Dilatation of Porous Glass[END_REF][START_REF] Dolino | Adsorption Strains in Porous Silicon[END_REF][START_REF] Fomkin | Adsorption of Gases, Vapors and Liquids by Microporous Adsorbents[END_REF][START_REF] Grosman | Influence of Elastic Strains on the Adsorption Process in Porous Materials: An Experimental Approach[END_REF][START_REF] Prass | Capillarity-Driven Deformation of Ordered Nanoporous Silica[END_REF][START_REF] Grosman | Influence of Elastic Strains on the Adsorption Process in Porous Materials. Thermodynamics and Experiments[END_REF][START_REF] Gor | Adsorption of N-Pentane on Mesoporous Silica and Adsorbent Deformation[END_REF][START_REF] Schappert | Unexpected Sorption-Induced Deformation of Nanoporous Glass: Evidence for Spatial Rearrangement of Adsorbed Argon[END_REF][START_REF] Balzer | Deformation of Microporous Carbon During Adsorption of Nitrogen, Argon, Carbon Dioxide, and Water Studied by in Situ Dilatometry[END_REF][START_REF] Grosman | Adsorption-Induced Strain of a Nanoscale Silicon Honeycomb[END_REF]. Beyond its importance for sequestration, storage or oil recovery [START_REF] Vandamme | Adsorption and Strain: The Co2-Induced Swelling of Coal[END_REF][START_REF] Brochard | Poromechanics of Microporous Media[END_REF], it is a fundamental issue to understand the interplay between surface effects and the adsorbed fluid; it has been suggested that deformation could contribute to the hysteresis in the adsorption-desorption isotherm [START_REF] Haines | Length Changes of Activated Carbon Rods Caused by Adsorption of Vapors[END_REF][START_REF] Amberg | A Study of Adsorption Hysteresis by Means of Length Changes of a Rod of Porous Glass[END_REF][START_REF] Grosman | Influence of Elastic Deformation of Porous Materials in Adsorption-Desorption Process: A Thermodynamic Approach[END_REF][START_REF] Grosman | Influence of Elastic Strains on the Adsorption Process in Porous Materials: An Experimental Approach[END_REF][START_REF] Grosman | Influence of Elastic Strains on the Adsorption Process in Porous Materials. Thermodynamics and Experiments[END_REF]. It is also a powerful tool to measure the elastic moduli -2 -Rev. 10/2015 of nanoporous systems [START_REF] Dolino | Adsorption Strains in Porous Silicon[END_REF][START_REF] Herman | Deformation of Silica Aerogel During Fluid Adsorption[END_REF][START_REF] Prass | Capillarity-Driven Deformation of Ordered Nanoporous Silica[END_REF][START_REF] Grosman | Adsorption-Induced Strain of a Nanoscale Silicon Honeycomb[END_REF].

Understanding the mechanical behavior of nanosized materials has attracted intense searches due to their potential applications. In the case of nanoporous materials, it is possible to use the capillary stress caused by an adsorbed fluid to induce a measurable deformation. A model has to be used to extract the pore moduli from experiments. Poromechanics is a consistent theory to model the mechanical coupling between fluids and solids, including adsorption-induced deformations [START_REF] Biot | General Theory of Three-Dimensional Consolidation[END_REF][START_REF] Coussy | Poromechanics[END_REF][START_REF] Brochard | Poromechanics of Microporous Media[END_REF][START_REF] Coasne | Poroelastic Theory Applied to the Adsorption-Induced Deformation of Vitreous Silica[END_REF][START_REF] Kulasinski | Poroelastic Model for Adsorption-Induced Deformation of Biopolymers Obtained from Molecular Simulations[END_REF], but more sophisticated models are required to take into account the inhomogeneous and anisotropic nature of the material [START_REF] Eriksson | Thermodynamics of Surface Phase Systems[END_REF][START_REF] Ash | Thermodynamics of the Effects of Adsorption on Interparticle Forces[END_REF][START_REF] Ravikovitch | Density Functional Theory Model of Adsorption Deformation[END_REF][START_REF] Günther | Sorption Strains and Their Consequences for Capillary Condensation in Nanoconfinement[END_REF][START_REF] Gor | Adsorption-Induced Deformation of Mesoporous Solids[END_REF][START_REF] Schappert | Unexpected Sorption-Induced Deformation of Nanoporous Glass: Evidence for Spatial Rearrangement of Adsorbed Argon[END_REF][START_REF] Diao | Monte Carlo Simulation of Adsorption-Induced Deformation in Finite Graphitic Slit Pores[END_REF][START_REF] Gor | Revisiting Bangham's Law of Adsorption-Induced Deformation: Changes of Surface Energy and Surface Stress[END_REF]. It is well-known that porous materials have smaller elastic moduli than the bulk [START_REF] Gibson | Cellular Solids: Structure and Properties[END_REF], but there is generally a disagreement between the measured pore-load moduli and that expected for the porous solid, despite the development of refined models taking into account the pore geometry [START_REF] Gor | Elastic Response of Mesoporous Silicon to Capillary Pressures in the Pores[END_REF][START_REF] Guyer | Theoretical Model for Fluid-Solid Coupling in Porous Materials[END_REF][START_REF] Liu | The Pore-Load Modulus of Ordered Nanoporous Materials with Surface Effects[END_REF][START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF].

The surface stress is dominant in nanometer size systems, and generally taken into account in the models to calculate the elastic constants of the solid. However, the interplay between surface stress and adsorption is not so well documented. We thus perform a "numerical experiment" of adsorption-induced deformation of a nanoplatelet. The advantages are the following: the geometry is perfectly known, and the elastic constants of the solid, taking into account the surface stress, is known too. The observed deformation can thus be compared to that expected from the porous solid modulus and a theoretical thermodynamic approach. The observed discrepancy suggests an influence of the adsorbed fluid on the surface stress of the solid.

The atomistic model and the thermodynamic approach are presented in the next section. In the third section we present the results and question the validity of the macroscopic approach.

MODEL AND NUMERICAL DETAILS

Solid. The platelet is chosen to be a fcc Lennard-Jones (12,6) solid, with parameters =73.2 kJ/mol and =0.3518 nm. The interactions are cut at 4. These values allow reproducing the mechanical properties of silicon, a material that has been used several times to study adsorption-induced deformation [START_REF] Dolino | Adsorption Strains in Porous Silicon[END_REF][START_REF] Grosman | Adsorption-Induced Strain of a Nanoscale Silicon Honeycomb[END_REF]. Note however that silicon is not a fcc solid, and that better potentials exist to reproduce its physical properties [START_REF] Lee | A Modified Embedded Atom Method Interatomic Potential for Silicon[END_REF]. The fcc Lennard-Jones solid is however accurate enough for our purpose. The bulk properties are determined in a simulation box containing 6 unit cells (3.26 nm) in each direction with periodic boundary conditions (the crystallographic axes are parallel to the simulation box). The Young modulus E and the Poisson coefficient  have been determined by Monte Carlo simulations in the isobaric ensemble where an external pressure is applied on the Proceedings Paper Formatting Instructions -3 -Rev. 10/2015 system and the average deformation is an output of the simulation. We obtain E = 165 GPa and  = 0.36 at 300 K. The shear modulus is not used in this work. Note that the symmetry of the solid being cubic, the mechanical properties are entirely given by E and 

The properties of the nanoplatelet are evaluated in a larger simulation box: L x = L y = 7 unit cells in the x and y directions (3.805 nm); a gap is introduced along the z direction so as to create two opposite surfaces (see Fig. 1, left). The thickness h of the nanoplatelet is 6 unit cells (h = 3.26 nm), and the dimension L z = 10 nm. The distance between the walls is thus H = 6.74 nm. The wall thickness is quite small (compared to typical nanoporous silicon for instance, 5-6 nm), in order to emphasize surface stress effects. The gap is however typical of nanoporous materials. The elastic properties of the platelet have been determined in the framework of the standard Monte Carlo simulations in the isobaric ensemble, where only the dimensions parallel to the nanoplatelet are allowed to vary, while L z is fixed. The cubic symmetry of the solid reduces to the tetragonal symmetry for the nanoplatelet, which requires the determination of 4 parameters to get the compliance matrix: E x = 162 GPa, E z = 180 GPa,  yx = 0.457,  zx = 0.339, and  xz = 0.335 at 353 K. Note that these elastic moduli take into account the surface stress. Calculations are performed at 353 K, just above the freezing point of the Lennard-Jones model. Using standard grand canonical Monte Carlo simulations, the pressure of the (bulk) liquid phase has been determined versus its chemical potential  (see Table 1). Note that we have considered  values above and below (metastable liquid) its bulk saturating value, because, in the system we want to study, the fluid is confined (Puibasset 2005). The pressure of the liquid phase thus ranges from -116 to +210 bar.

Method. The method relies on the measurement of the deformation of the solid induced by the pressure of the adsorbed fluid (see Fig. 1, right). We use the standard semi-grand canonical Monte Carlo algorithm to let the simulation box fluctuate in the x and y directions while the chemical potential of the fluid is imposed through the pressure of the surrounding gas. The external pressure on the simulation box is set to zero: the system is free to relax, so that the solid (which deforms) accommodates the fluid pressure.

Phenomenological model. The aim of this section is to relate the expected average deformation of the simulation box with the fluid pressure, in the framework of a simple thermodynamic approach. The quantities to be considered are: the pressure of the liquid adsorbed on the platelet, P L ; the fluid-wall surface tension , and the elastic moduli of the platelet previously determined without adsorbed fluid. At equilibrium, the overall constrain on the simulation box walls parallel to the z axis is zero since the external pressure in the semi-grand canonical ensemble is set to zero (free walls). As a consequence  xx =  yy = (H P L -L x L y )/h;  zz = -P L where  is the solid-fluid surface tension. Deformations along the x and y directions are given by:

  xx =  yy = (1- yx )  xx /E x - zx  zz /E z = [(1- yx )H/(E x h) + zx /E z ] P L -(1- yx ) L x L y /(E x h
). The surface tension, given by the excess amount of adsorbed liquid, is essentially constant because the liquid is barely compressible. The solid deformation is thus expected to be linear with the liquid pressure; the inverse of the slope is [(1- yx )H/(E x h) + zx /E z ] -1 = 113 GPa. Note that the fluid pressure has two additive effects on the solid: through the simulation box (a positive pressure tends to dilate the nanoplatelet in the x and y directions), and directly on the solid (a positive fluid pressure along z induces a nanoplatelet dilatation along x and y given by the Poisson ratio).

RESULTS AND DISCUSSION

For each given chemical potential, we have measured the fluctuations of the system size in directions x and y (see an example in Fig. 2). The fluctuations are of the order of 10 -3 L x , which means that they are not negligible compared to the average deformation of the nanoplatelet, as expected in nanometer size systems. Long simulation runs are thus required to reach an accuracy of 5% in the determination of the solid strain.

The average strain has been determined for different values of the chemical potential. The results are given in Table 1. As can be seen, the solid deforms under the influence of the adsorbed fluid. For high chemical potential values, the solid expands, while for low chemical potential values the solid shrinks. This is qualitatively expected from the observation that the fluid pressure acts directly on the solid (along z) and through the simulation box (parallel to the nanoplatelet). The observed deformation is of order 10 -4 , typical of solid strain. The simulation results are shown as a function of the liquid pressure in Fig. 3. As can be seen, the observed strain follows essentially a linear behavior, except for the lowest pressure point, which however corresponds to the stability limit of the stretched liquid. At coexistence, where the liquid pressure is essentially zero, the observed deformation is very small: the solidfluid surface tension is thus small compared to the solid stiffness. How do the simulations compare with the phenomenological model depicted in previous section? The prediction of the model is given as a solid line in Fig. 3, where we have omitted the (constant) surface tension term. The simulations qualitatively follow the expected behavior (linear), but a significant disagreement is observed between the slopes. The inverse of the slope of the simulation results is approximately 270 GPa, while the prediction gives 113 GPa. Many papers in the literature mention disagreements between the elastic moduli determined from adsorption-induced deformation measurements and bulk values. Two major origins are invoked. On one hand, the origin is attributed to finite size effects due to the small wall thicknesses in nanoporous materials. On the other hand, one can also invoke the dependence of the solid (surface) stress with the presence of the adsorbed fluid.

Since in our simulations the elastic constants have been determined for the nanoplatelet itself, finite size and surface stress effects cannot be invoked to explain the disagreement. Two hypotheses are proposed to explain the results: a strong dependence of the fluid-substrate free energy with the chemical potential of the fluid, or a significant variation of the surface stress of the solid in presence of the fluid. The small compressibility of the adsorbed liquid seriously disfavors the first hypothesis. However, quantitative analysis is under consideration. The second argument has already been invoked to explain some features of the nitrogen adsorption hysteresis in porous silicon [START_REF] Grosman | Influence of Elastic Deformation of Porous Materials in Adsorption-Desorption Process: A Thermodynamic Approach[END_REF][START_REF] Grosman | Influence of Elastic Strains on the Adsorption Process in Porous Materials: An Experimental Approach[END_REF][START_REF] Grosman | Influence of Elastic Strains on the Adsorption Process in Porous Materials. Thermodynamics and Experiments[END_REF].

CONCLUSION

This paper focused on the comparison between the adsorption-induced deformation of a nanoplatelet given by atomistic simulations, and that predicted from the elastic constants of the nanoplatelet determined without fluid. The results show a strong disagreement which could reveal interplay between surface stress and fluid adsorption.

ACKNOWLEDGMENTS

The author acknowledges fruitful discussions with A. Grosman and E. Rolley on experimental and theoretical issues regarding adsorption-induced deformation.

Figure 1 .

 1 Figure 1. General presentation of the simulation box; L z is constant, while L x and L y are allowed to fluctuate (isobaric ensemble). Left: an external pressure (arrows) is imposed to measure the elastic moduli of the nanoplatelet. Right: a fluid at imposed chemical potential is introduced; the external pressure is set to zero; the arrows materialize the internal pressure of the fluid.

Figure 2 .

 2 Figure 2. Fluctuations of the nanoplatelet dimension L x during a Monte Carlo simulation run. 1 MC step corresponds to 1000 moves per atom.

Figure 3 .

 3 Figure 3. Symbols: Monte Carlo simulation results of the nanoplatelet deformation as a function of the fluid pressure in the liquid phase (the line is a guide to the eye). Solid black line: theoretical prediction based on the thermodynamic approach (see text).

TABLE 1 :

 1 Monte Carlo simulation results.

	ln(activity)	-11.175	-10.83	-10.485	-10.200	-9.930	-9.375
	P L (bar)  xx =  yy	-119 -5.65×10 -5 -1.85×10 -5 -65	-1.9 8.86×10 -6	52.1 2.80×10 -5	113 4.99×10 -5	211 8.91×10 -5

Rev. 10/2015

Proceedings Paper Formatting Instructions

Rev. 10/2015


Karine Nozeret
email: karine.nozeret@gmail.com

François Loll
email: floll@mnhn.fr

Mouta Gildas

Christophe Cardoso
email: christophe.escude@mnhn.fr

Alexandre S Escudé

Boutorine

Escudé

Alexandre S Boutorine
email: alexandre.boutorine@mnhn.fr

Interaction of fluorescently labeled pyrroleimidazole polyamide probes with

Keywords:

fixed and living murine and human cells

Introduction

The observation of the dynamics of a native double-stranded DNA in living cells by fluorescence microscopy is a serious challenge for cellular biology [START_REF] Boutorine | Fluorescent Probes for Nucleic Acid Visualization in Fixed and Live Cells[END_REF]. The FISH (Fluorescence in situ hybridization) method is based on the fixation of cells and the denaturation of DNA, thus it is incompatible with living cells [START_REF] Nath | A Review of Fluorescence in Situ Hybridization (FISH): Current Status and Future Prospects[END_REF][START_REF] Levsky | Fluorescence in situ hybridization: past, present and future[END_REF][START_REF] Didion | Invaders: Recognition of Double-Stranded DNA by Using Duplexes Modified with Interstrand Zippers of 2-O-(Pyren-1-yl)methyl-ribonucleotides[END_REF]. Imaging of native DNA has been achieved using quite complicated methods as the incorporation of fluorescent nucleotides during DNA replication [START_REF] Sadoni | Nuclear Organization of Mammalian Genomes: Polar Chromosome Territories Build up Functionally Distinct Higher Order Compartments[END_REF][START_REF] Manders | Direct Imaging of DNA in Living Cells Reveals the Dynamics of Chromosome Formation[END_REF] or the fusion of fluorescent proteins (such as GFP or similar) to endogenous DNA binding proteins [START_REF] Wang | Visualizing genetic loci and molecular machines in living bacteria (Biochemical Society Linked Focused Meetings)[END_REF][START_REF] De Vos | Four-dimensional telomere analysis in recordings of living human cells acquired with Controlled Light Exposure Microscopy[END_REF][START_REF] Sugimoto | Construction of three quadruple-fluorescent MDA435 cell lines that enable monitoring of the whole chromosome segregation process in the living state[END_REF]. The recent achievements in the live cell imaging are based on the use of two natural DNA recognition systems, the TALE motif [START_REF] Miyanari | Live visualization of chromatin dynamics with fluorescent TALEs[END_REF][START_REF] Ma | Visualization of repetitive DNA sequences in human chromosomes with transcription activator-like effectors[END_REF] and the CRISPR/Cas9 system [START_REF] Chen | Dynamic Imaging of Genomic Loci in Living Human Cells by an Optimized CRISPR/Cas System[END_REF][START_REF] Anton | Visualization of specific DNA sequences in living mouse embryonic stem cells with a programmable fluorescent CRISPR/Cas system[END_REF][START_REF] Ma | Multicolor CRISPR labeling of chromosomal loci in human cells[END_REF]. However, these approaches require transgenic techniques that can modify the genetic nature of the cells.

Recently, we have used fluorescently labeled synthetic Nmethylpyrrole-N-methylimidazole (Py-Im) polyamides that bind specifically to the minor groove of double-stranded DNA for imaging major satellite sequences, which form the basis of pericentromeric heterochromatin foci, in living mouse cells [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF]. This approach does not necessitate genome modifications; the polyamides easily penetrate into the cells without toxicity and specifically recognize their target native dsDNAs.

Fluorescent polyamide probes were synthesized, characterized and successfully applied for living cell imaging. However, several unexpected problems were discovered: i) fluorophore conjugation decreased polyamide affinity for DNA; ii) several fluorophores affected the nuclear penetration of the probes and iii) a quick fluorophore bleaching under the conditions of microscopic observation was revealed.

The present work aims at better understanding the different factors that affect the feasibility of this approach: DNA sequence, fluorophores, cell type, culture medium. We first designed, synthesized and characterized polyamide probes targeting pericentromeric repeats that are found in the human genome. Then we investigated, using mouse and human cells as models, how polyamide probes penetrate into cells and enable the labeling of pericentromeric heterochromatin foci.

A R T I CL E I NFO

A B ST R A C T

Materials and methods

Materials and reagents

Monomers for polyamide synthesis: 4-(Boc-amino)-1-methyl-1H-pyrrole-2-carboxylic acid, 4-(Boc-amino)-1-methyl-1Himidazole-2-carboxylic acid, N-Boc-ß-alanine and N-Boc-γaminobutyric acid were purchased from Bachem (Germany) and PolyPeptide Laboratories (France). Activating reagent HATU (2-(1H-7-azabenzotriazol-1-yl)-1,1,3,3-tetramethyl uronium hexafluorophosphate) and HOAT (1-hydroxy-7-azabenzotriazole) were from "Molekula" (UK). Boc-ß-ala-Pam (Boc-ß-alanine-(4carbonylaminomethyl)-benzyl-ester-copoly-(styrene-divinylbenzene) resin was from Merck. N-Hydroxysuccinimide esters of fluorophores Cy3 (Cy3-NHS), Cy5 (Cy5-NHS), Oregon Green (OG-NHS), Rhodamine (Rh-NHS) and fluorescein-NHS, as well as fluorescein-5-isothiocyanate were from FluoProbes. Other reagents (salts, monomers and organics) were purchased from Sigma-Aldrich, Acros, Merck, Fluka and Fisher Scientific, and solvents from Carlo Erba. Target oligonucleotides for physicochemical studies and all the oligonucleotide probes were purchased from Eurogentec (Seraing, Belgium). DMEM High glucose Glutamax-supplemented and RPMI 1640 Glutamaxsupplemented culture media were from Gibco, fetal bovine serum -from Eurobio, imaging DMEMgfp medium from Euromedex, Denhart solution and Rutin -from Sigma-Aldrich, blocking reagent -from Roche.

Reverse-phase HPLC analysis and purification were performed on Agilent Technologies 1200 analytical and preparative chromatographs piloted by Agilent ChemStation software. Mass spectrometry analysis by electrospray Q-TOF (ESI Q-TOF MS) was performed on a Q-Star instrument (Applied Biosystems, Courtaboeuf, France) in the positive mode; analyses were performed in methanol. UV-Vis spectra and thermal denaturation curves were obtained on an Uvikon XL UV-visible spectrophotometer (Secomam, Nova Analytic Company) with 12 quartz cells installed in a mobile thermostated support piloted by ThermAlys software (DuDoTec GmbH). A thermostat Julabo F25, piloted by Easy Temp Professional software, was used to monitor the temperature. Polyacrylamide gels were scanned on a Typhoon 9410 (Amersham) fluorescence scanner with a laser excitation at 532 nm and an emission filter at 526 nm. CD spectra were recorded on a Jasco J-810 spectropolarimeter. Fluorescence spectra were recorded on a SPEX Fluorolog II (Jobin-Yvon -Horiba) spectrofluorometer.

Polyamide synthesis and characterization

The synthesis of polyamides has been done according to the method by Krutzik and Chamberlin [START_REF] Krutzik | Synthesis of DNA-binding polyamides. Robust solid-phase methods for coupling heterocyclic aromatic amino acids[END_REF][START_REF] Krutzik | Rapid solid-phase synthesis of DNA-binding pyrrole-imidazole polyamides[END_REF] with several modifications [START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF]. The products were purified and characterized as it was described previously [START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF]. The interactions of each polyamide with their target DNA fragments have been studied by polyacrylamide gel electrophoresis using "gel retardation" method, by thermal denaturation of complexes "target duplexpolyamide" and by circular dichroism spectroscopy.

Synthesis of fluorophores bearing isothiocyanate groups

Insertion of amino group. N-hydroxysuccinimide esters of the fluorophores (OG-NHS or Rh-NHS, 10 µmoles) were dissolved in dry DMF (50 µL). A solution of BOC-diaminopropane (40 µmoles) in dry DMF (50 µL) and diisopropyle ethylamine (DIPEA, 15 µL) were added, well mixed and the mixture was incubated overnight at room temperature. The product was purified by preparative reversed-phase HPLC and the solvent evaporated. The BOC protection was removed by incubation with 20% trifluoroacetic acid in dichloromethane during 90 min followed by evaporation of the solvent. The product was transformed in amino form by dissolution in 10% triethylamine in dichloromethane for 1 h at room temperature followed by the evaporation of the solvent. The yield was 98%.

Insertion of the isothiocyanate group. Amino-modified fluorophores (5,6 µmoles) were dissolved in absolute ethanol (150 µL), then carbon disulfide (56 µmoles) and triethylamine (5,8 µmoles) were added and the mixture was incubated 90 min at room temperature. Then the mixture was cooled to 0°C and di-tert-butyl dicarbonate (5,5 µmole in 2 µL of the absolute ethanol) and 4dimethylamionopyridine (0,14 µmoles in 1 µL of the absolute ethanol) were added under stirring. The mixture was stirred overnight at room temperature. The solvents were evaporated and the products purified by preparative reversed-phase HPLC [START_REF] Munch | A new efficient synthesis of isothiocyanates from amines using ditert-butyl dicarbonate[END_REF]. Yields were 44% for Rh-ITC and almost quantitative for OG-ITC.

Murine cell culture experiments [15]

The NIH-3T3 or MEF cell lines were grown in T75 culture flasks at 37 °C in 5% CO2 atmosphere in Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% fetal bovine serum (FBS). Every 2 to 3 days, cells were trypsinized for 5 min at 37 °C and resuspended in fresh medium.

For experiments with fixed cells, 10 5 cells resuspended in the culture medium (300 µL) were deposited on 22x22 mm coverslips cleaned with a plasma cleaner Femto v4 (Diener electronic GmbH) with an even thickness of 0.17±0.01 mm (Thermo Fisher Scientific Menzel) and deposited in 6-well plates. After 2 hours, a fresh medium (2 mL) was added to each well and cells were further grown until 70% confluence on the following day. The coverslips were washed three times in PBS, fixed with 4% paraformaldehyde (PFA) in PBS for 10 minutes at room temperature and washed three times with PBS. Fixed cells were stored at 4 °C.

For experiments with live cells, 3x10 4 cells resuspended in the culture medium (200 µL) were deposited on glass gridded ibiTreat µ-slides (Ibidi, Biovalley). After 24 hours, the medium was removed and replaced with a solution containing fresh medium (199 µL) and fluorescent polyamide solution (1 µL, 400 µM) in DMSO for a final polyamide concentration of 2 µM. Cells were incubated at 37 °C (5% CO2) for 24 h. Before fluorescent microscopy, the cells were washed twice with PBS to remove excess compounds and the PBS was replaced under sterile conditions with modified media for imaging DMEM gfp (Euromedex) supplemented with Rutin (16 µM) and incubated 30 min at 37 °C.

Human cell culture experiments

The Human cell line RPE-1 was cultivated in T75 culture flasks containing 10 mL of liquid medium RPMI (Roswell Park Memorial Institute medium) supplemented by 10% FBS under controlled atmosphere (5% CO2, 37°C). Every 2 to 3 days the cells were treated with a trypsin solution 5 min at 37°C, diluted and resuspended in a fresh medium.

All the experiments with the fixed and living human cells have been done according to the same protocols as for the murine ones, except the number of cells per sample. For the fixed cells, this number was 5×10 4 while for the living cells -1.5×10 4 .

Labeling of fixed cells in situ.

On the day of the experiment coverslips were fixed to 26×76 mm glass slides using rubber cement. Three types of experiments were performed.

For the combined visualization of fluorescent polyamides and DAPI, the fluorescent polyamide staining was first performed by incubating the slides in the dark for 30 min at room temperature in a solution containing PBS 1X (199 µL) and the fluorescently labeled polyamide solution (1 µL, 400 µM) in DMSO for a final polyamide concentration of 2 µM. Then cells were washed briefly with PBS before the post-fixation step which consisted in incubating the cells with 2% PFA in PBS (100 µL) for 10 min, then rinsing three times in PBS/0.05% TritonX-100. The nuclear DNA staining was performed by addition of a DAPI solution (70 nM, Sigma-Aldrich) for 5 min at room temperature, then, after a brief washing step in PBS, the coverslips were mounted by removing the rubber cement and turning the coverslips upside down onto a clean 26×76 mm slide. A drop of PPD8 mounting medium (Sigma-Aldrich, 1 mg/mL solution in PBS/90% glycerol, pH 8 adjusted with carbonate/bicarbonate buffer, pH 9.6) was deposited. Finally, the slides were pasted by varnish and stored at 4°C for a short storage or at -20°C for a long one.

For the combined visualization of fluorescent polyamides and FISH probes, the cells were permeabilized with Triton X-100 in PBS (0.1%), rinsed three times with PBS, treated with 0.1 N HCl for 2 min, rinsed twice, equilibrated 5 min in 2X SSC and treated with 2X SSC/50% deionized formamide at room temperature for at least 30 min prior to hybridization. The "mouse" FISH probe was a mixed DNA/LNA oligonucleotide targeting murine major satellite (5'-gACgACtTGaAAaATgACgAAaTC-3', where small letters indicate LNA modifications) labeled with Cy3 at its 3'-end. The "human" FISH probe was a full LNA oligonucleotide 5'tttgtgatgtgtg-3' ("PCY") also labeled by Cy3 at 3'-terminus and targeted to positions 17-29 of the human α-satellite repeat sequence consensus. The hybridization solutions were prepared upon diluting the oligonucleotide probe to a final concentration of 1 µM in a hybridization solution (2X SSC, pH 5.6, 50% deionized formamide, Denhart solution, 10% dextran sulfate, 0.1% SDS). The hybridization solution (45 µL) was added to the coverslip on the slide. The coverslip was covered with Krups paper and heated for 3 min at 85°C, then slowly cooled to 37°C at a rate of 1° C/s. This was performed in an in situ PCR apparatus (MJ Research). Each slide was washed twice in 2X SSC at 63 °C and once in 2X SSC at room temperature. The fluorescent polyamide staining was then performed as described above. The slides were mounted without further DNA staining.

For the combined visualization of polyamide probes and proteins by immunocytochemistry, the cells were permeabilized by 0.1% Triton X100 solution in PBS during 5 min at room temperature and following washing twice by PBS. After saturation in 1.5% "blocking reagent" solution with 0.05% Tween 20 in 2X SSC, pH 6.3, the cells were incubated with primary antibodies during 90 min at room temperature in a humid chamber, washed 3 times by 0.1% Triton X100 in PBS, then incubated with secondary antibodies 45 min at room temperature in a humid chamber in the dark and washed 3 times by 0.1% Triton X100 solution in PBS.

All the antibodies were diluted in 1% " blocking reagent" in PBS. The primary antibodies were the following: for detection of murine centromeres -rabbit polyclonal anti-CenpB (clone H65, 1/200, Santa Cruz), for detection of pericentromeresrabbit polyclonal anti-H3K9me3 (1/400, Upstate, Millipore). The secondary antibodies were the goat anti-rabbit antibodies labeled either with Cy3 or with Cy5 (Jackson ImmunoResearch).

In the immuno-FISH experiments, after immunochemical labeling the cells were post-fixed in 2% PFA in PBS during 10 min, washed 3 times by 0.1% Triton X100 in PBS and the FISH protocol was then applied. For simultaneous detection of both FISH and polyamide probes, the FISH protocol was applied first and followed by treatment with the fluorescent polyamide probes. [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF] Images were recorded with a Zeiss epifluorescence inverted microscope (Axio Observer ZI) equipped with a Hamamatsu ORCA R2 camera, a plan apochromatic 63x1.4 NA oil-immersion objective and the following filters set: 49 shift free for Hoechst or DAPI (G365/FT395/BP44/50), 38 HE shift free for FITC (BP470/40, FT495, BP525/50), home-made sets for Cy3 (BP 546/10, FF555, BP 583/22) and for Cy5 (BP643/20, FF660, BP684/24). Immersion oil of refractive index 1.518 at 23°C was used. The light source was LED illumination (wavelengths: 365 nm, 470 nm or 625 nm) except for Cy3 where a metal halide lamp HXP120 was preferred. The Zen software was used for image acquisition.

Image acquisition

Results and discussion

Polyamides and target sequences

Hairpin pyrrole-imidazole polyamides are peptide-like oligomers that are able to specifically recognize DNA sequences and to bind to the minor groove of a double-stranded DNA. The recognition rules are well known and quite simple [START_REF] Dervan | Recognition of the DNA minor groove by pyrrole-imidazole polyamides[END_REF]. Polyamides can easily penetrate into living cells and interact with the target native DNA sequences [START_REF] Blackledge | Programmable DNA-binding small molecules[END_REF]. After labeling by fluorophores, they can be used for direct fluorescent imaging of the DNA repeats in fixed and living cells [START_REF] Boutorine | Fluorescent Probes for Nucleic Acid Visualization in Fixed and Live Cells[END_REF][START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF][START_REF] Hirata | Structural Evaluation of Tandem Hairpin Pyrrole-Imidazole Polyamides Recognizing Human Telomeres[END_REF]. We previously designed and characterized synthetic polyamide probes targeting major satellite DNA, a sequence that is highly abundant in the pericentromeric regions of mouse chromosomes [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF][START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF]. These fluorescent probes were able to stain specifically pericentromeric heterochromatin foci, called chromocenters, in fixed cells [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF]. The visualization of chromocenters was obtained for the first time in live cells using the fluorescein isothiocyanate conjugated probe. For the present study, the F1 polyamide (Fig. 1A) was conjugated to various other fluorophores (analogs of Cy series, Rhodamine, Oregon Green 488). Some of these conjugations involved coupling to the polyamide with an isothiocyanate group instead of N-hydroxysuccinimide or azide groups as active moieties.

The most abundant tandemly repeated sequence in the human genome is called a-satellite. It is present at both centromeres and pericentromeres. We have designed a 14 nucleotide probe (called PCY) for a-satellite DNA based on the conservation of the target sequence within numerous a-satellite DNA [START_REF] Wu | Sequence definition and organization of a human repeated DNA[END_REF][START_REF] Waye | Structure, organization, and sequence of alpha satellite DNA from human chromosome 17: evidence for evolution by unequal crossing-over and an ancestral pentamer repeat shared with the human X chromosome[END_REF][START_REF] Vissel | Human alpha satellite DNA -consensus sequence and conserved regions[END_REF]. This probe labels large pericentromeric regions on almost all chromosomes, as revealed by FISH experiments (see further). The work performed in mouse cells suggested that target sequences as short as 6 bp may be sufficient for enabling tight and specific binding of the polyamide probes and successful visualization of pericentromeric repeats in live cells. Nevertheless, we were interested in investigating the possibility of using longer polyamides. We chose as a model a truncated version of the target sequence of the PCY probe:

5'TTTGTGATGT 3' 3'AAACACTACA 5'

We designed a series of polyamides with different hairpin lengths for the recognition of sequences ranging from 6 to 9 bp [START_REF] Syed | Targeted Suppression of EVI1 Oncogene Expression by Sequence-Specific Pyrrole-Imidazole Polyamide[END_REF]. Previous work from the the group of Sugiyama has shown that replacing one or several N-methylpyrroles by balanine units can make the polyamide molecules more flexible and adaptable to the DNA minor groove [START_REF] Syed | Targeted Suppression of EVI1 Oncogene Expression by Sequence-Specific Pyrrole-Imidazole Polyamide[END_REF][START_REF] Han | Effect of single pyrrole replacement with β-alanine on DNA binding affinity and sequence specificity of hairpin pyrrole/imidazole polyamides targeting 5′-GCGC-3′[END_REF]. Therefore, such molecules were also included in our design. Fig. 1B summarizes all the molecules together with the DNA duplex target sequence used for the in vitro studies.

The differences between the structures of human polyamides were in the length of the hairpin (from 4 to 7 monomer pairs), the number of the b-alanine moieties (from 0 to 2) and their positions (only in the C-domain of each polyamide or both in its N-and Cdomains) (Fig. 1B). The identity of all the polyamides and probes was confirmed by mass-spectrometry (Tables S1 andS2, Supplementary materials).

Studies of the interaction of human polyamides with their target DNA in vitro

We studied first the interaction between synthesized polyamides and a synthetic DNA fragment containing the target DNA sequence in vitro (Duplex H, Fig. 1B). Several physicochemical methods were applied, such as DNA thermal denaturation, gel-shift experiments and circular dichroism of the complexes, as it was described in our previous publication [START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF]. The results were compared with those obtained in similar experiments performed using a control Duplex C (Fig. 1C) without any binding sites for the polyamides.

Table 1 shows the results obtained by thermal denaturation and gel-shift experiments. The apparent dissociation constants of the complexes were calculated from the gel-shift data [START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF]. The experimental results are in the Supplementary Materials (Fig. S1 andS2). All the polyamides form stable complexes with their target duplex (Duplex H); the apparent dissociation constants varied from 70 to 430 nM. The best affinity was demonstrated by the longer polyamides Hb2 and Hb3 (6-7 monomer pairs) containing two b-alanine residues in the C-terminal domain of the hairpin. A weak non-specific interaction with the non-cognate duplex (Duplex C) was revealed by thermal denaturation (maximal increase of the duplex denaturation temperature DTm upon complex formation was less than 5°C), but it was not seen in gel shift experiments. When a polyamide was in excess (>2 times), a second retarded band with a lower mobility was observed (Fig. S1, Supplementary Materials). It can be due to the formation of a triple complex "DNA/2 polyamides" when two halves of each polyamide are located in the minor groove of the target duplex in an antiparallel orientation (Fig. S3, Supplementary Materials).

G A G G A A A A C T G A A A A A G G T G G A A A A T T T A G C T C C T T T T G A C T T T T T C C A C C T T T T A A A T C

T A A T C A A T T T G T G A T G T G T C A T T A T G A T T A G T T A A A C A C T A C A C A G T A A T A C

The comparison of different polyamide structures shows that the insertion of a b-alanine synthon instead of Nmethylpyrrole into the C-terminal part of hairpins is favorable for the polyamide affinity (Hb1, Hb2 et Hb3). In contrast, the insertion of the ß-alanine residue into the N-terminal part of the polyamides (Hbb1, Hbb2 et Hbb3) seems to be unfavorable and decreases the polyamide affinity.

The circular dichroism experiments revealed slightly different forms of spectra for the different DNA-polyamide complexes (Fig. S4, Supplementary materials). However, when compared with the model spectra profiles published by the group of Gursky [START_REF] Surovaya | Binding of bis-linked netropsin derivatives in the parallel-stranded hairpin form to DNA[END_REF], these profiles are more similar to those ones when the polyamides maintain hairpin antiparallel conformation in the duplex minor groove [START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF][START_REF] Halby | Head-to-head bis-hairpin polyamide minor groove binders and their conjugates with triplex-forming oligonucleotides: Studies of interaction with target doublestranded DNA[END_REF].

Polyamide labeling by fluorophores, physico-chemical and fluorescent properties of the synthesized probes.

Taking into account our previous results [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF][START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF], we decided to label all the polyamides by fluorescein isothiocyanate. The labeling method was the same as in the mentioned publications. The studies of the interaction between the probes and their target DNA by gel shift and thermal denaturation methods also revealed a strong decrease of the affinity after the fluorophore conjugation. In the gel shift experiments, the formation of a complex resulted in the retardation of the duplex migration with an increase of the polyamide concentration. However, no distinct bands of duplexes and complexes were observed and the smear between the bands did not permit to calculate apparent dissociation constants of the complexes (data not shown).

Table 2 shows the results of the experiments on the thermal stability of the DNA-probe complexes. A strong decrease of the melting temperature of these complexes was observed compared to those of non-labeled polyamides, which demonstrates a decrease of the affinity upon labeling as it was observed for the murine probes [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF][START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF].

The circular dichroism spectra of the DNA-probe complexes have a similar form as the complexes of non-labeled polyamides thus indicating the same binding mode and conformation (Fig. S5, Supplementary Materials). However, the spectrum amplitudes, especially for short polyamides, are not so high as those of the free polyamides. It is in agreement with our previous results obtained with "murine" probes [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF][START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF]. Table 2. Increase of the dissociation temperatures of the duplexes H and C (DTm) upon their complex formation with the polyamide probes labeled by fluorescein. Similar to the mouse fluorescein-labeled probes, the human fluorescent polyamides demonstrate a high increase of the fluorescence emission upon the formation of the complex with the target DNA. The highest emission increase (17 times) has been obtained for the complex of duplex H with the labeled polyamide Hb1 (Fig. 2). A weak non-specific interaction with the noncognate duplex leads to the increase of the fluorescence, but with much less intensity (Table 3, Fig. 2). Hb2-FITC × 9,5 × 3,5

Hb3-FITC × 3 × 1, 1
Hbb2-FITC × 2,9 × 1, 2
H1-FITC × 1,9 × 1, 1
Hbb3-FITC × 1,5 × 1, 1
Hbb1-FITC × 1,4 × 1,1
The fluorescence emission increase upon interaction of fluorescent polyamides with the target DNA correlates with (but does not follow) the affinity of the targeting polyamides determined by thermal denaturation and gel shift methods (Tables 2 and3).

The interaction of murine polyamide probes with murine fixed and living cells

In our previous communication [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF], we selected two most affine polyamides targeted to murine DNA sequences. We labeled them different fluorophores and demonstrated that the probes are able to stain chromocenters in fixed murine cells MEF and NIH-3T3. In living cells, only the probes labeled with the fluorescein isothiocyanate (FITC) were able to visualize specifically the pericentromeric heterochromatin foci. In the present work, we approved the probes' specificity, studied the roles of the fluorophore nature and tried to apply several treatments known to improve cell penetration of the synthetic probes. Fig. 3 shows images of fixed NIH-3T3 murine cells stained with 2 µM polyamide probes F1-Cy3 and F4ß-Cy5 during 30 min. A punctuated labeling pattern typical of chromocenters is observed. Similar images were obtained with the polyamides labeled by fluorescein, fluorescein isothiocyanate, different cyanine and coumarin dyes [START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF] (data not shown). We note here that this pattern is obtained provided a post-fixation is performed. This suggests that the interaction of the probes with their target is very labile and does not resist the washing steps that are required for removing unbound probes in those experiments.

In order to prove the specificity of the staining, we compared the localization of the polyamide probes and that of the known markers of centromeric and pericentromeric regions. We used DAPI (who is a marker for chromocenters in murine cells), a Cy3-labeled chimeric LNA/DNA oligonucleotide (SatMaj, 5'-gACgACtTGaAAaATgACgAAaTC-3'-Cy3, lower-case letters indicate LNA units) targeted to one of the pericentromere repeated sequences, and an anti-H3K9me3 antibodies detected then by immunofluorescence method. For negative control, the histone CenpB, which is a centromere marker, was also stained using immunofluorescence detection with anti-CenpB antibodies (Fig. 4). As it is seen on the Fig. 4, the polyamide probe F1-FITC perfectly co-localizes with all the pericentromere markers. Quantitative analysis of the scan data demonstrates that 87% of the F1-FITC signal colocalize with the DAPI signal (19 nuclei, Pearson coefficient 0,82), 97% -with the H3K9me3 signal (16 nuclei, Pearson coefficient 0,88) and 98% -with the Sat Maj (10 nuclei, Pearson coefficient 0,65). In contrast, the signal of centromere-specific histone CenpB does not co-localize with that of pericentromere-specific probes (Fig. 4,D4). There is a low probe signal and no signal co-localization with the pericentromere markers when the DNA-binding polyamide F1 is replaced by another one F2 that possesses a low affinity for the targeted DNA sequence (see [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF][START_REF] Nozeret | Synthesis of mouse centromere-targeted polyamides and physico-chemical studies of their interaction with the target double-stranded DNA[END_REF], fig S6).

In the living cells, according to our previous data, FITC appeared to be a suitable fluorophore to label the polyamides for the visualization of pericentromere regions [START_REF] Nozeret | Polyamide Fluorescent Probes for Visualization of Repeated DNA Sequences in Living Cells[END_REF]. All the other fluorophores (cyanines, coumarins, rhodamines) strongly affect the nuclear penetration of the polyamide probes. Fig. 5 demonstrates a typical example of the cellular distribution of the cyanine-labeled probes in NIH-3T3 murine cells. The polyamides labeled by Cy3 or Cy5 penetrate into the cell but stay in the cytoplasm and do not enter into the nucleus. The distribution of the probes is not uniform and the formation of aggregates is observed. FITC probes allowed a specific visualization of the targeted pericentromeric sequences in murine live cells, in contrast to probes where fluorescein was conjugated with N-hydroxysuccinimide or azide groups (Figure S7, Supplementary). Therefore, we undertook the synthesis of several other fluorophores bearing this isothiocyanate group for the polyamide coupling. Thus, we synthesized several cyanine fluorophores, analogs of Cy series and other known fluorophores (Rhodamine, Oregon Green 488) with an isothiocyanate group instead of N-hydroxysuccinimide or azide groups as active moieties. Among them, only the probes labeled by the Oregon Green 488 isothiocyanate (OG-ITC) (Fig. 6 and S8, Supplementary Materials) demonstrated a similar punctuated staining of the murine pericentromere repeats. Several factors may limit the penetration of probes into the cell nuclei in a fluorophore dependant manner. The first of them if the formation of aggregates. Hargrove et al. [START_REF] Hargrove | Characterization and Solubilization of Pyrrole-Imidazole Polyamide Aggregates[END_REF] used an addition of 2-hydroxypropyl-β-cyclodextrin to the medium in order to solubilize pyrrole-imidazole polyamide aggregates. We tried to use this method to improve the nuclear penetration of our probes. Fig. 7 shows that with the addition of 3 mM 2hydroxypropyl-β-cyclodextrin, the aggregation was strongly reduced but not completely suppressed and the nuclear penetration of the probes was not improved. This also holds true for the use of a medium deprived of fetal bovine serum. Another one is the permeability of the nuclear membrane. We decided to incubate the cells with the Cy5-labeled probes in the presence of detergents (0,05% Tween 20 or 0,01% Saponine). This resulted in the penetration of the fluorescent material into the nucleus, but its distribution was not punctuated and the cells changed their morphology. They became rounded and granule-like (Fig. S9, supplementary materials). Although cells are likely no more viable at this step, such an experiment shows that nuclear entry is not sufficient for enabling the labeling of heterochromatin using Cy5-modified probes. The same was true for Cy3-labeled probes. One explanation for this observation may be the lower affinity of these probes for their target, which may not be sufficient for enabling observation of the targeted DNA in living cells. We also tried to generate micro-pores in the cell membranes using electroporation method with Amaxa© system, but we did not obtain better nuclear penetration, in contrast, high level of cell death has been observed when electroporation method has been applied (data not shown).

Finally, we must mention that photobleaching represents a serious limit when one want to undertake labeling of nuclear structures in live cells. This bleaching can be attributed to the generation of free radicals under the UV irradiation. Our initial attempts led us to chose for observation of living cells a special medium DMEM gfp , depleted of two radical-generating vitamins (riboflavin and pyridoxal) in the presence of 16 µM rutin, a natural flavonoid from plants that captures and eliminates free radicals from the medium (Fig. 6) [START_REF] Bogdanov | Anti-fading media for live cell GFP imaging[END_REF]. This resulted in an apparent increased life time of the signal, probably by decreasing the radical production and quenching produced radicals. Nevertheless, it was not possible to extend the observation over a few seconds under the fluorescence microscope, due to a quick bleaching of the fluorescent signal (Figure S10, Supplementary materials).

In conclusion, the imaging of the DNA in living murine cells with fluorescent polyamide probes appeared to be very sensitive not only to the structure of the polyamides and targeted DNA sequence, but also to the nature of conjugated fluorophores. All the fluorophores after conjugation strongly decreased the polyamide-DNA affinity and the majority of them had limited the nuclear penetration and aggregated in the cytoplasm. Thus, the main question remains the fluorophore nature. More stable fluorophores that do not prevent the nuclear penetration and do not stimulate the probe aggregation are needed.

Interaction of human polyamide probes with human fixed and living cells

Recent data from our group suggest that human αsatellite centromeric repeats are able to associate and to form nuclear structures similar to murine chromocenters [START_REF] Ollion | Proliferation-dependent positioning of individual centromeres in the interphase nucleus of human lymphoblastoid cell lines[END_REF][START_REF] Ollion | Dynamique de l'organisation nucléaire des séquences d'ADN répétées centromériques humaines au cours du cycle cellulaire[END_REF]. In particular, a FISH probe targeting numerous α-satellite repeats labels foci in the nucleus of human cells (Fig. 8). We decided to study the interaction of human probes with fixed and living RPE-1 human cells. Fig. 9 shows a typical example of human cell imaging after incubation of fixed RPE-1 cells with 2 µM Hb1-FITC probe during 30 min. As it is seen on the picture, all the DNA in the nuclei is stained by the probe. Thus, a total non-specific staining is observed. Very similar images were obtained for all the human probes in both RPE-1 and GM12878 cell lines (data not shown).

Like for murine cells, we compared the labeling patterns provided by the FISH probe for α-satellite repeats and by the newly synthesized polyamide probes targeting the same sequences. As it is seen on the Fig. 8, the Hb1-FITC polyamide probe stains fixed nuclei from RPE-1 cells in a similar way as does DAPI, but does not stain the foci that are revealed with the FISH probe. A similar staining was obtained using all the α-satellite targeted polyamide probes, suggesting that the polyamide probes do not achieve specific staining of their target sequences. Although the probes did not appear to be suitable for imaging heterochromatin foci in living human cells, none of the probes showed cytotoxicity. There was no difference in the morphology and the proliferation of the cells treated or nontreated by the polyamide probes. Concerning the cellular penetration, three types of images were obtained (Fig. 10). We performed several additional experiments in order to better understand the difference between both our experimental systems. When human RPE-1 living cells were treated with murine polyamide probe F1-FITC, a uniform staining of DNA in the cell nuclei was observed (Fig. 11). Zoomed photos 4, 5 and 6 show one cell in division with the visible chromosome segregation. It means that the short polyamide probes can be used as efficient non-toxic markers of the intracellular DNA in living cells for observations in dynamics. A similar uniform staining of DNA was observed when living murine NIH-3T3 cells were treated with the human polyamide probe Hb1 (Fig. S12, Supplementary Materials), while the F2-FITC probe, which did not reveal chromocenters in fixed murine cells, formed aggregates in the cytoplasm on living murine cells.

Taken together, these results demonstrate that sequencetargeted polyamide fluorescent probes are promising tools for DNA imaging in mammalian cells but that specific staining of pericentromeric heterochromatin using such probes is highly dependent on the nature of the polyamide sequence and of the attached fluorophore. The newly synthesized polyamides targeting α-satellite sequences displayed high affinity for their target which could be enhanced by replacement of a single pyrrole residue by a b-alanine residue, while increasing the length of the polyamide could have a detrimental effect.

Conjugation of fluorophores resulted in a strong reduction of the affinity for the target, but some of the probes still bind efficiently to target DNA in vitro and show fluorescence enhancement upon binding. Nevertheless, while most probes targeting major satellite repeated sequences specifically stain pericentromeric heterochromatin in fixed murine cells, asatellite-targeted probes only revealed uniform staining all genomic DNA. This observation may be the result of: i) a different accessibility of DNA at the targeted chromatin in fixed human cells, ii) the higher polymorphism of human DNA repeats [START_REF] Vissel | Mouse major (γ) satellite DNA is highly conserved and organized into extremely long tandem arrays: implications for recombination between nonhomologous chromosomes[END_REF][START_REF] Lee | Human centromeric DNAs[END_REF] or iii) the lower relative density of binding sites for the polyamide probes in pericentromeric DNA compared to the rest of the genome in human cells (for human cells: one every 33 bp on pericentromeric DNA, one every 50 bp for the rest of the genome; for murine cells: one evry 10 bp for pericentromeric DNA, one in 31 bp for the rest of the genome).

Experiments conducted in living cells demonstrated the absence of major cytotoxicity of polyamide probes: cells with labeled DNA are viable and can still proliferate. Nevertheless, the suitability of such probes for DNA imaging in cellulo is influenced by their composition or, more precisely, by the nature of the polyamide and the fluorophore. Nuclear penetration is favored by the use of isothiocyanate derivatives of fluorescein or Oregon Green and by the use of short polyamides containing a b-alanine residue instead of a pyrrole residue in the C-terminal part of the polyamide hairpin. Photobleaching of these fluorophores remains a problem if one wants to make longer observations of living cells.

Future work could aim at improving the relative specificity of human probes for pericnetromeric DNA with respect to the rest of the genome. New tandem constructions via conjugation of two to four hairpin polyamides by a flexible linker may be envisioned, following the recent publications of Sugiyama's group [START_REF] Kawamoto | Development of a New Method for Synthesis of Tandem Hairpin Pyrrole-Imidazole Polyamide Probes Targeting Human Telomeres[END_REF][START_REF] Kawamoto | Targeting 24 bp within Telomere Repeat Sequences with Tandem Tetramer Pyrrole-Imidazole Polyamide Probes[END_REF]. This approach works well in fixed cells for imaging of telomere repeats, but for living cells, according to our preliminary data (data not shown), formation of aggregates is observed. It should be interesting to modify the structure of the tandems by making them more hydrophilic, for example, by linking the hairpins with oligo(ethylene glycol) linkers. The other problem is the fluorophore nature. It is worth trying more photostable molecules than fluorescein, for example, described by Wagenknecht et al [38,

Figure 1 .

 1 Figure1. The model target DNA sequences and the pyrrole-imidazole polyamides used for the probe synthesis: A, for murine major satellite repeats, B, for human a-satellite repeats. The target DNA sequences (in red) and the pyrrole-imidazole polyamides used for the probe synthesis are shown. Duplex 1 is a fragment from murine pericentromeric repeats, Duplex H is a model dsDNA fragment derived from human a-satellite repeats for in vitro studies. Duplex C is a control duplex without any binding sites for all the murine and human polyamides.

1 *Figure 2 .

 12 Figure 2. Fluorescence spectra of the human probe Hb1-FITC in the absence of DNA (1), in the presence of the non-cognate duplex C (2) and of the target duplex H (3) in Tris-HCl buffer (10 mM, pH 7.5), 50 mM NaCl, 50 mM KCl and 1 mM MgCl2. DNA and probe concentrations are 2 µM. Excitation at 480 nm.

Figure 3 .

 3 Figure 3. Images of fixed murine cells NIH-3T3 stained with 2 µM F1-Cy3 (1-3) and F4ß-Cy5 (4-6) during 30 min. 1 and 4, bright field; 2, F1-Cy3 staining; 5, F4ß-Cy5 staining; 3, overlay of 1 and 2; 6, overlay of 4 and 5. Scale bar: 10 µm.

Figure 4 .

 4 Figure 4. Images of nuclei in fixed murine cells NIH-3T3 stained with 2 µM F1-FITC (A1, B1, C1) during 30 min and then treated with pericentromere-specific markers DAPI (A2), H3K9me3 (B2) and oligonucleotide probe SatMaj (C2), as well as with centromere-specific marker CenpB (C3). The images were overlaid as it is indicated on the pictures: A3, F1-FITC (green) + DAPI (red); B3, F1-FITC(green) + H3K9me3 (red); D1, F1-FITC (green) + SatMaj (red); D2, F1-FITC (green) + CenpB (red); D3, SatMaj (red) + CenpB (green). An arbitrary axe was drawn on each overlay image and the fluorescence intensity of both signals was measured along this axe. The intensity profiles along the axes shown in A3, B3, D1 and D2 are shown in column 4. Scale bar: 10 µm.

Figure 5 .

 5 Figure 5. Images of living cells NIH-3T3 treated with 2 µM F1-Cy3 (A) and F4β-Cy5 (B) during 24 h. 1, fluorescence; 2, overlay of the images with the fluorescence of F1-Cy3 (A2) and F4β-Cy5 (B2) in red and cells in bright field in gray. Some aggregates are indicated by the arrows. Scale bar: 10 µm.

Figure 6 .

 6 Figure 6. Images of living cells NIH-3T3 treated with 2 µM F1-FITC (1-3) or F1-OG-ITC (4-6) during 24 h in 3T3 medium without fetal bovine serum in the presence of 16 µM rutin (to decrease bleaching) and DMEMgfp. 1, 4, bright field; 2, 5, fluorescence; 3, 6, overlay of both images. Scale bar: 10 µm.

Figure 7 .

 7 Figure 7. Images of living cells NIH-3T3 treated with 2 µM F1-Cy3 during 24 h in the presence of 3 mM 2-hydroxypropyl-β-cyclodextrin (A) and in the 3T3 medium deprived of fetal bovine serum (B). 1, bright field; 2, fluorescence; 3, overlay of both images. Some aggregated are indicated by the arrows. Scale bar: 10 µm.

Figure 9 .

 9 Figure 9. Images of fixed RPE-1 cells treated with 2 µM Hb1-FITC during 30 min in PBS solution. 1, bright field; 2, fluorescence; 3, overlay of both images. Scale bar: 10 µm.

Figure 8 .

 8 Figure 8. Images of nuclei of fixed human cells RPE-1 incubated with 70 nM DAPI (1), 2 µM Hb1-FITC (2), and 1 µM LNA oligonucleotide PCY (3). For LNA hybridization, the cellular DNA was denatured by heating at 85°C. The images were overlaid as it is indicated on the pictures: 4, Hb1-FITC/DAPI, 5, Hb1-FITC/PCY. An arbitrary axe was drawn on each overlay image and the fluorescence intensities of both signals were measured along this axe. The intensity profiles are shown on pictures 6 and 7, green Hb1-FITC, blue DAPI and red PCY. Scale bar: 10 µm.

Figure 10 .

 10 Figure 10. Images of living RPE-1 cells treated with 2 µM polyamide probes during 24 h in RPMI+10% FBS medium. 1, fluorescence; 2, overlay of bright field and fluorescence images. A, Hb1-FITC; B, H1-FITC; C, Hb2-FITC. Scale bar: 10 µm.

First, the

  probes Hb1-FITC and Hbb1-FITC reveal identical staining profiles: a uniform labeling of nucleus without any visible structures. A dividing cell with uniformly stained separating chromosomes is seen on the Fig 10A (one more proof of the absence of toxicity and a DNA-specific, but not a sequencespecific staining). Second, H1-FITC (without ß-alanine residue) shows a much lower nuclear penetration and a small aggregate formation (Fig 10B). So, the role of the b-alanine residue is not limited to bringing flexibility into the polyamide structure but it is also useful for improving the cell penetration. Finally, all the probes longer than 4 pairs of monomers (Hb2-FITC, Hbb2-FITC, Hb3-FITC et Hbb3-FITC) aggregate and do not penetrate into the nuclei (Fig 10C and S11, Supplementary Materials).

Figure 11 .

 11 Figure 11. Images of living human RPE-1 cells treated with 2 µM murine polyamide probe F1-FITC during 24 h in RPMI medium with 10% FBS. 1,4. bright field; 2,5, fluorescence; 3,6; overlay of bright field and fluorescence images. 1-3, several cells in the field, 4-6, zoom from another field demonstrating a dividing cell. Scale bar: 10 µm.

Table 1 .

 1 Increase of the dissociation temperatures of the duplexes H and C (ΔTm) upon their complex formation with the polyamides and apparent dissociation constants of the complexes "Duplex H / polyamide" determined by gel shift experiments. Melting temperature of the duplex H alone was 64°C. *Melting temperature of the complex was close to the upper limit of the instrument's operational temperature (85°C).

	Polyamide	DTm in a complex	DTm in a complex	Dissociation constant of the
		with the Duplex H a , °C	with the Duplex C, °C	complex with the Duplex H (Kd), µM
	Hb1	≥ 20*	4	0,17 ± 0,02
	Hb2	≥ 20*	4,5	0,07 ± 0,004
	Hbb2	16	3	0,085 ± 0,005
	Hb3	15	2	0,09 ± 0,01
	Hbb1	14	3	0,38 ± 0,01
	H1	12,3	2	0,43 ± 0,015
	Hbb3	12	1	0,38 ± 0,01

a

Table 3 .

 3 Increase of the fluorescence emission intensity (fold) of the polyamide probes upon their interaction with the target (H) and non-cognate (C) DNA duplexes. Conditions -see legend to figure2

	Probe	Duplex H	Duplex C
	Hb1-FITC	× 17	× 4,5

39]. In order to reduce the masking of the target-bound probe signal by the background fluorescence, new fluorophores drastically changing the wavelengths of the fluorescent emission upon interaction with DNA could be used[START_REF] Shaya | Rational Design of Push-Pull Fluorene Dyes: Synthesis and Structure-Photophysics Relationship[END_REF][START_REF] Dziuba | Rational Design of a Solvatochromic Fluorescent Uracil Analogue with a Dual-Band Ratiometric Response Based on 3-Hydroxychromone[END_REF].

Acknowledgments

This work was supported by MNHN, INSERM and CNRS. K.N. had a PhD scholarship from the National Museum of Natural History, Paris. We thank Drs. Alain Blond, Arul Marie and Mr. Lionel Dubost for NMR and mass spectra. Special thanks to Dr. Loïc Ponger for his help in the selection of the human α-satellite sequences.

Conflict of interest

The authors declare no conflict of interest.

Supplementary Material

Supplementary materials are available at the WEB-site