Sophie Féréol
email: sophie.fereol@u-pec.fr

Nanoscale mechanical properties of chitosan hydrogels as revealed by AFM

Keywords: Atomic Force Microscopy, chitosan hydrogel gelation, Young's modulus distribution, 4 Discussion ..

Abstract: (201 words)

In the context of tissue engineering, chitosan hydrogels are attractive biomaterials because they represent a family of natural polymers exhibiting several suitable features (cytocompatibility, bioresorbability, wound healing, bacteriostatic and fungistatic properties, structural similarity with glycosaminoglycans), and tunable mechanical properties. Optimizing the design of these biomaterials requires fine knowledge of its physical characteristics prior to assess cell-biomaterial interactions.

In this work, using Atomic Force Microscopy (AFM), we report a characterization of mechanical and topographical properties at the sub-micron range of chitosan hydrogels, depending on physico-chemical parameters such as their polymer concentration (1,5%, 2,5% and 3,5%), their degree of acetylation (4% and 38,5%), and the conditions of the gelation process. Well-known polyacrylamide gels were used to validate the methodology approach for the determination and analysis of Elastic modulus (i.e.

Young's modulus) distribution at the gel surface.

We present elastic modulus distribution and topographical and stiffness maps for different chitosan hydrogels. For each chitosan hydrogel formulation, AFM analyses reveal a specific asymmetric elastic modulus distribution that constitutes a useful hallmark for chitosan hydrogel characterization. Our results regarding the local mechanical properties and the topography of chitosan hydrogels initiate new possibilities for an interpretation of the behavior of cells in contact with such soft materials.

Introduction

Regenerative medicine aims at restoring the function of lost, damaged, or diseased tissue via replacement or regeneration. The development and use of biomaterials for these aims is a founding paradigm of tissue engineering and a fast-growing research axis [START_REF] Kumar | Future biomaterials for enhanced cell-substrate communication in spinal cord injury intervention[END_REF][START_REF] Meco | Microscale Architecture in Biomaterial Scaffolds for Spatial Control of Neural Cell Behavior Frontiers in Materials[END_REF][START_REF] Rami | Physicochemical modulation of chitosan-based hydrogels induces different biological responses: Interest for tissue engineering[END_REF]. Following this, it is well established that cell responses and functions are critically influenced by not only biological, but also topological and biomechanical interactions between cells and biomaterials [START_REF] Glass | Tissue-engineered cartilage with inducible and tunable immunomodulatory properties Biomaterials[END_REF][START_REF] Zhou | Host Responses to Biomaterials and Anti-Inflammatory Design-a Brief Review[END_REF]. Such interactions are partly regulated by cell adhesion sites in adherent cells, thus implying cell-material interactions at the subcellular level [START_REF] Fereol | Prestress and adhesion site dynamics control cell sensitivity to extracellular stiffness[END_REF][START_REF] Ladoux | Physically based principles of cell adhesion mechanosensitivity in tissues[END_REF][START_REF] Skoog | Biological responses to immobilized microscale and nanoscale surface topographies[END_REF]).

Among the various biomaterials used for tissue engineering, hydrogels are of interest because they are highly hydrated, "tissue-like" materials, potentially providing a favorable medium for cell growth and differentiation. In particular, chitosan hydrogels with cavities are of specific interest for cell maturation, preserving paracrine cell signaling [START_REF] Perrard | Complete Human and Rat Ex Vivo Spermatogenesis from Fresh or Frozen Testicular Tissue[END_REF]. Furthermore, their physical and biochemical properties, including stiffness, morphology, microstructure and composition can be controlled [START_REF] Lee | Injectable hydrogels delivering therapeutic agents for disease treatment and tissue engineering[END_REF][START_REF] Li | Engineering neural stem cell fates with hydrogel design for central nervous system regeneration Progress in[END_REF][START_REF] Rami | Physicochemical modulation of chitosan-based hydrogels induces different biological responses: Interest for tissue engineering[END_REF]. Chitosan hydrogels are currently used as medical device (see for example the Novashield nasal stent marketed by Medtronic company (Medtronic 2017)), but are also envisioned for water treatment, cell/tissue maturation, croop and food preservation [START_REF] Gutiérrez | Chitosan Applications for the Food Industry[END_REF][START_REF] López-Velázquez | Gelatin-chitosan-PVA hydrogels and their application in agriculture[END_REF][START_REF] Pakdel | Review on recent progress in chitosan-based hydrogels for wastewater treatment application[END_REF][START_REF] Perrard | Complete Human and Rat Ex Vivo Spermatogenesis from Fresh or Frozen Testicular Tissue[END_REF]. The choice of this natural polymer family is founded by a number of suitable properties (biocompatibility, bioresorbability, bioactivity for tissue regeneration, haemostatic, bacteriostatic and fungistatic properties [START_REF] Crini | Chitine et chitosane: du biopolymère à l'application[END_REF][START_REF] Kim | Chitosan and its derivatives for tissue engineering applications[END_REF][START_REF] Yang | Chitin-based Materials in Tissue Engineering: Applications in Soft Tissue and Epithelial Organ[END_REF]. Chitosans are linear polysaccharides consisting of N-acetyl D-glucosamine and D-glucosamine residues linked by a β (1 -> 4) glycosidic linkage. D-glucosamine residues can be protonated at acidic pH, whereas N-acetyl glucosamine residues stay neutral. Polymers in the chitosan family differ by their degree of acetylation (DA, i.e. the fraction of N-acetyl glucosamine units), their molecular mass distributions and, at a finer scale, the intramolecular repartition of glucosamine and N-acetyl glucosamine residues. Our recent studies suggested that chitosan hydrogels are promising candidates as supporting material for various tissue engineering applications [START_REF] Aussel | Chitosan-based hydrogels for developing a small-diameter vascular graft: in vitro and in vivo evaluation[END_REF][START_REF] Montembault | A material decoy of biological media based on chitosan physical hydrogels: application to cartilage tissue engineering[END_REF]. Notably, the implantation of low-DA chitosan hydrogels in a fragmented form can be used as scaffolds for spinal cord injury and axon regeneration by preventing formation of a mature glial scar. This facilitates functional tissue regeneration and modulates the inflammatory response [START_REF] Chedly | Physical chitosan microhydrogels as scaffolds for spinal cord injury restoration and axon regeneration[END_REF]. Regarding the latter point, our results are consistent with the study of [START_REF] Vasconcelos | Macrophage polarization following chitosan implantation[END_REF] which reported that subcutaneous implantation in mice of a chitosan 3D porous scaffold with DA 5% induced an anti-inflammatory macrophage response (M2 polarization), whereas chitosan scaffolds with DA 15% favored a pro-inflammatory macrophagic phenotype (M1) [START_REF] Vasconcelos | Macrophage polarization following chitosan implantation[END_REF]. Such phenotypic transitions of macrophages are believed to be involved in tissue repair [START_REF] Novak | Phenotypic transitions of macrophages orchestrate tissue repair The[END_REF]. However, the underlying cellular mechanisms by which the properties of chitosan hydrogels modulate the macrophagic response remains unclear. These include biomechanical, topographical, composition and processing parameters. In order to better understand these mechanisms, it is important to determine the mechanical, topographical and structural properties of chitosan hydrogels at a pertinent scale, i.e. at the cellular scale, and more specifically at the cell adhesion site scale.

Thus, the aim of this present study is to connect the mechanical and topographical properties of chitosan hydrogels at sub-micron-range, depending on their polymer concentration Cp (% w/w), their DA, and their preparation route. For this, we used the Atomic Force Microscopy (AFM). Indeed, AFM is recognized to be a suitable device to characterize the surface properties of gels [START_REF] Denisin | Tuning the Range of Polyacrylamide Gel Stiffness for Mechanobiology Applications[END_REF][START_REF] Elosegui-Artola | Rigidity sensing and adaptation through regulation of integrin types[END_REF][START_REF] Schillers | Standardized Nanomechanical Atomic Force Microscopy Procedure (SNAP) for Measuring Soft and Biological Samples[END_REF], although a correct characterization by AFM of soft materials with surface rugosity is a challenge [START_REF] Dokukin | High-resolution high-speed dynamic mechanical spectroscopy of cells and other soft materials with the help of atomic force microscopy[END_REF][START_REF] Notbohm | Analysis of nanoindentation of soft materials with an atomic force microscope[END_REF][START_REF] Piner | Improved Imaging of Soft Materials with Modified AFM Tips[END_REF].

In

Chitosan hydrogel preparation

Highly deacetylated chitosan produced from squid pen was purchased from Mahtani Chitosan (batch type 114, DA 4%) and was filtered in solution as described in a previous work (Montembault et al. 2005b). A part of this polymer batch was then N-reacetylated, using acetic anhydride in hydro-alcoholic media [START_REF] Vachoud | Formation and characterisation of a physical chitin gel[END_REF]. Briefly, an hydro-alcoholic chitosan solution was prepared at a concentration of 0.5% (w/v) (with a water/1,2propanediol ratio of 1/1 [v/v]). Acetic anhydride was then diluted in 1,2-propanediol and this resulting acetylating mix was added dropwise to the chitosan solution. The amount of acetic anhydride added in the chitosan solution corresponded to the number of moles of amine sites to be reacetylated. After stirring for 3 h, the N-reacetylated chitosan was isolated by precipitation with aqueous ammonia, thoroughly washed with deionized water until neutral pH, and freeze-dried. The DA was analyzed by 1 H NMR spectroscopy, according to the method of Hirai [START_REF] Hirai | Determination of degree of deacetylation of chitosan by 1H NMR spectroscopy[END_REF]. The DAs of the initial chitosan and the Nreacetylated chitosan were 4% and 38.5%, respectively.

The number average and weight average molar masses (Mn and Mw) of chitosans were determined by size exclusion chromatography coupled online with a differential refractometer (Wyatt Optilab T-rEx) and a multi angle laser light scattering detector (Wyatt HELEOS), according to our previous works (Montembault et al. 2005b). The weight average molar masses were around 550 kg/mol for the two chitosans and the dispersity ratio Mw/Mn was close to 1.5. The reacetylation step did not change significantly the degree of polymerization of the chitosan (DPw~3400).

Chitosan physical hydrogels were prepared by using two different gelation routes. The first is the ammonia vapor route, which corresponds to a neutralization process performed by placing an aqueous chitosan solution in contact with ammonia vapors (generated by 200 ml of a 1M ammonia solution in the volume of a closed reactor of 5L) for 15 h. Different gels were obtained by varying the DA (4%, 38.5%) and polymer concentration Cp (1.5%, 2.5%, 3.5% w/w). A second gelation route consists of neutralizing chitosan aqueous solutions with a sodium hydroxide solution (2M for 2 hours), using a chitosan with a DA 4% at a concentration Cp 2.5%. All chitosan hydrogels were prepared following our published works [START_REF] Chedly | Physical chitosan microhydrogels as scaffolds for spinal cord injury restoration and axon regeneration[END_REF][START_REF] Fiamingo | Chitosan Hydrogels for the Regeneration of Infarcted Myocardium: Preparation, Physicochemical Characterization[END_REF]Montembault et al. 2005a;Montembault et al. 2005b), and then sterilized by autoclaving at 121°C for 20 minutes.

At the end of the hydrogel gelation process, in particular for hydrogels issued from the ammonia vapor neutralization route, a rigid and thin membrane covers the apical surface of the chitosan hydrogel [START_REF] Fiamingo | Chitosan Hydrogels for the Regeneration of Infarcted Myocardium: Preparation, Physicochemical Characterization[END_REF][START_REF] Sereni | Dynamic Structuration of Physical Chitosan Hydrogels[END_REF]. In order to characterize mechanically this apical membrane and the lateral surface, we manufactured our chitosan hydrogels within 8 mm thickness molds with a half circle shape with 35 mm diameter (see Figure 1) using a Petri dish and a Teflon insert. During gelation with ammonia vapors, the lateral surface of the half disk was not in direct contact with the base, preventing formation of the thin and dense layer. In practice, our half-moon chitosan hydrogels were cut in smaller pieces (~1,5 x 1,5 x 1,5 mm) using a scalpel. For AFM measurements, the sample is fixed on a glass coverslip with a double-sided adhesive in such a way as to orient toward the top the unaltered hydrogel surface to be assessed by AFM. AFM experiments were performed in water at room temperature.

AFM measurements

We used two different AFM devices, i.e. AFM ASYLUM MFP-3D-BIO, provided by Inc.

Oxford Instruments Asylum Research (U. S. A.), and JPK bioafm NanoWizard  3 and 4 (Germany). These different AFM benches were used to assess the force-distance curves with non-coated n-type silicon cantilevers (CSC38) provided by MikroMasch ® (Sofia, Bulgaria). The tips used were pyramidal probes with 20° half angle aperture and 350 µm cantilever length. The same calibration procedure was systematically performed to calculate the nominal spring constant k, based on the thermal noise approach (Hutter J.L.

1993). The mean nominal spring constant was about 0.072 ± 0.026 N/m.

Measurements on polyacrylamide gels were achieved considering a measuring point grid with 2 µm mesh over a 18×18 µm² surface in the gel center, i.e. with grid mesh size in the same range as used by Elosegui-Artola (Elosegui-Artola et al. 2014). For each Acrylamide/Bisacrylamide sample, three different zones of measurement at the gel surface were arbitrarily chosen, thus leading to the analysis of 300 spectroscopy force curves per sample.

Concerning chitosan hydrogel surfaces, AFM force spectroscopy measurements, including apical and lateral surfaces, were performed with a measurement point grid with 66.7 nm mesh size over an area of 1×1 µm² at the hydrogel surface. The analysis was carried out on 512 to 2560 force-spectroscopy curves per hydrogel sample area.

According to Bilodeau [START_REF] Bilodeau | Regular Pyramid Punch Problem[END_REF], for quadrilateral pyramid probe, the force-indentation depth relation is given by the following Hertz-based equation:

𝐹𝐹 = 3 4 𝐸𝐸 (1-𝜗𝜗 2 ) 𝛿𝛿 2 𝑡𝑡𝑡𝑡𝑡𝑡(𝛼𝛼) (1)
Where 𝐹𝐹 is the applied force, 𝐸𝐸 the elastic modulus, 𝛼𝛼 the half angle aperture and 𝛿𝛿 the indentation depth, 𝜗𝜗 is the Poisson's ratio assumed to be close to 0.4 for polyacrylamide gels according to values reported in the literature [START_REF] Alcaraz | Microrheology of human lung epithelial cells measured by atomic force microscopy[END_REF][START_REF] Gross | Simultaneous measurement of the Young's modulus and the Poisson ratio of thin elastic layers[END_REF][START_REF] Hutter | Characterization of atomic-force microscope tips[END_REF]), and 0.5 for chitosan hydrogels.

In addition, the contact point 𝑃𝑃 𝑐𝑐 can be found according to the following equation:

𝑃𝑃 𝑐𝑐 -ℎ = 𝑑𝑑 + 𝛿𝛿 = 𝐹𝐹 𝑘𝑘 + 𝛿𝛿 (2)
Where ℎ is the sensor position, 𝑑𝑑 and 𝑘𝑘 are the deflection and the spring constant of the cantilever, respectively (see figure SM1 in supplementary materials)

Using ( 1) and ( 2), we obtained the following equation:

3 4 𝐸𝐸 (1-𝜗𝜗 2 ) �𝑃𝑃 𝑐𝑐 -ℎ - 𝐹𝐹 𝑘𝑘 � 2 𝑡𝑡𝑡𝑡𝑡𝑡(𝛼𝛼) -𝐹𝐹 = 0 (3)
The elastic modulus 𝐸𝐸 and the contact point 𝑃𝑃 𝑐𝑐 are calculated by fitting the experimental curve 𝐹𝐹(ℎ) with equation (3) (see figure SM2 and SM3 in supplementary materials).

As we previously described in Féréol et al [START_REF] Fereol | Effect of cholesterol depletion on the viscoelastic properties of alveolar epithelial cells assessed by atomic force microscopy in large deformation Revue de composites et des matréiaux[END_REF], we have checked that the elastic modulus remained constant as indentation 𝛿𝛿 increased, to ensure that both polyacrylamide gels, and chitosan hydrogels behave like an elastic material with a purely linear behavior.

Due to the wide dispersion of elastic modulus values observed notably for chitosan hydrogels, we present our results with smoothed functions for elastic moduli distributions.

Thus, a Non-Parametric Probability Density Function (NPPDF) estimation using a kernel estimation based on a normal (Gaussian) function was determined with the Matlab ® builtin function (fitdist()) to fit the elastic modulus occurrence distribution (Mathworks 2020). For each gel, i.e. polyacrylamide gels and chitosan hydrogels, the bandwith of kernel smoothing window or Kernel smoothing parameter Ker was set following this formula:

𝐾𝐾𝐾𝐾𝐾𝐾 = 𝐸𝐸 𝑚𝑚𝑚𝑚𝑚𝑚 50 ⁄ (4)
Where Emax is the maximum value of the elastic modulus measured for each gel.

Rheometry measurements

Dynamic rheological measurements were performed on different chitosan hydrogels following the same procedure as described in Fiamingo et al. [START_REF] Fiamingo | Chitosan Hydrogels for the Regeneration of Infarcted Myocardium: Preparation, Physicochemical Characterization[END_REF]. Briefly, rheological measurements were carried out at room temperature by using an ARES rheometer (TA Instruments) operating with a plate-plate geometry (diameter 25 mm). The shear strain amplitude was monitored to ensure that the measurements were carried out within the linear viscoelastic domain at a strain amplitude of 0.5%, resulting in storage modulus (𝐺𝐺 ′ ) and loss modulus (𝐺𝐺 ′′ ) independent of the strain amplitude (see figure SM4 in supplementary materials). Angular frequency sweep measurements were carried out in the range from 100 rad/s down to 0.05 rad/s. G' is fairly constant with frequency in this range, as expected for gels, thus the values used hereafter were determined in the low angular frequency range. Rheometry measurements were repeated three times for each hydrogel type.

Results

Methodological validation with reference polyacrylamide gel

In order to validate both our experimental approach to characterize soft materials, and the analysis of AFM results with our data analysis software, we prepared and studied three different polyacrylamide gels following the protocol described by Elosegui-Artola et al.

( For each polyacrylamide gel, we calculated the mean elastic modulus value noted 𝐸𝐸 𝑚𝑚 , and the modal modulus value defined as the maximum of the distribution function and noted 𝐸𝐸 � . In all cases, we observed that the modal value 𝐸𝐸 � is rather close to the mean value 𝐸𝐸 𝑚𝑚 , indeed, the differences vary between -0.4 and 11.3% (see Table 1). These results also compare well with the reference data obtained by Elosegui-Artola et al. (see In conclusion, our results are in good agreement with various data found in the literature [START_REF] Denisin | Tuning the Range of Polyacrylamide Gel Stiffness for Mechanobiology Applications[END_REF][START_REF] Elosegui-Artola | Rigidity sensing and adaptation through regulation of integrin types[END_REF], validating our experimental protocol, as well as our AFM data analysis.

AFM Study of Chitosan Hydrogels

We performed the AFM analysis of elastic modulus values at both the lateral surface, and the apical surface of the chitosan hydrogels for three different polymer concentrations (Cp= 1.5%, 2.5%, 3.5% w/w), for two different DAs (4%, 38%), and for two different gelation routes (ammonia vapor neutralization or sodium hydroxide solution neutralization) [START_REF] Fiamingo | Chitosan Hydrogels for the Regeneration of Infarcted Myocardium: Preparation, Physicochemical Characterization[END_REF]). The specific sample with a concentration Cp= 2.5% and a DA of 4%, gelled with gaseous ammonia was used in a previous work and showed remarkable regenerative properties in the form of a suspension of a fragmented (micron-range) hydrogel, inducing a robust axonal regeneration after implantation in a rat spinal cord lesion model [START_REF] Chedly | Physical chitosan microhydrogels as scaffolds for spinal cord injury restoration and axon regeneration[END_REF].In this work, we added two similar chitosan hydrogel samples by varying the concentration, i.e. 1.5% and 3.5%. It is expected that the topographical, structural, and mechanical properties of chitosan hydrogel will be impacted by the chitosan concentration. Moreover, we also analyzed a sample with a higher DA of 38.5%, investigated previously in the same study [START_REF] Chedly | Physical chitosan microhydrogels as scaffolds for spinal cord injury restoration and axon regeneration[END_REF]. As previously reported increasing the DAs of chitosan strongly impacts the biological response of macrophages in vivo [START_REF] Chedly | Physical chitosan microhydrogels as scaffolds for spinal cord injury restoration and axon regeneration[END_REF][START_REF] Vasconcelos | Macrophage polarization following chitosan implantation[END_REF]. Finally, we used a comparable sample to examine the individual effect of the gelation method on the chitosan hydrogel mechanical properties, i.e., gelation of the chitosan solution in contact with sodium hydroxide aqueous solution vs gelation in a closed reactor in presence of ammonia vapor.

Due to the known differences [START_REF] Fiamingo | Chitosan Hydrogels for the Regeneration of Infarcted Myocardium: Preparation, Physicochemical Characterization[END_REF]) in structural and mechanical properties of chitosan hydrogels between the apical surface and the lateral surface (representative of bulk properties), we compared these two hydrogel regions by AFM. In the following, analyses and results are presented in order to distinguish between the bulk properties, those assessed on the lateral surface, and those of the apical surface of chitosan hydrogels.

Characterization of local mechanical properties on the lateral surface of chitosan hydrogels

Figure 3 shows, for each chitosan hydrogel sample, the elastic modulus distribution histograms superimposed with the NPPDF distributions (red lines), calculated as described previously. Whatever the tested sample, the elastic modulus distributions present a wide dispersion (see Figure 3 A-E) with standard deviations close to the mean 𝐸𝐸 𝑚𝑚 values (see Table 2). Figure 3 A-D also highlights an asymmetric distribution extended towards high modulus values, characterized by positive skewness values, s > 1 (see Table 2), where the skewness is given by the following formula: a softer (disentangled) hydrogel. In-plane shear rheometry induces a series-type mechanical coupling of all layers with an apparent macroscopic modulus ideally related to the moduli of all layers according to:

1/𝐺𝐺 ′ = 1 𝑒𝑒 ∑ 𝐾𝐾 𝑖𝑖 . 1 𝐺𝐺 𝑖𝑖 ′ 𝑖𝑖 (6)
Where 𝐾𝐾 𝑖𝑖 and 𝐺𝐺 𝑖𝑖 ′ are the thickness and shear modulus of the 𝑖𝑖 𝑡𝑡ℎ layer and 𝐾𝐾 = ∑ 𝐾𝐾 𝑖𝑖 𝑖𝑖 is the width of the gel sample. From this 'inverse rule of mixture' or Reuss law [START_REF] Reuss | Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle[END_REF], the impact of the softer layers should dominate the rheological response, resulting in lower 𝐸𝐸 𝑅𝑅 values. Actually, since the hydrogels exhibit a multilayered morphology with a dense and rigid external apical layer on top of softer internal layers, the AFM evaluation of the elastic modulus should yield a lower estimation of the elastic modulus of the dense membrane, since softer layers may also contribute to the indentation. In spite of this lower estimation, the elastic modulus of the apical surface stays in order of magnitudes higher than the rheology estimation that is representative of softer internal layers.

Influence of the polymer concentration Cp

As expected, for the samples prepared from the ammonia route with a DA of 4%, the values of 𝐸𝐸 � and 𝐸𝐸 𝑚𝑚 increase with the mass concentration Cp. In the same way, we observe that the ratio 𝐸𝐸 𝑚𝑚𝑚𝑚𝑚𝑚 /𝐸𝐸 � also increases with Cp, evidencing that the modulus distribution becomes more asymmetric at high Cp (see Table 2). In addition, the values of 𝐸𝐸 � can be related to chitosan concentration Cp (w/w) according to a power law function,

𝐸𝐸 � = 𝐸𝐸 0 �𝐶𝐶 𝑝𝑝 � 𝛽𝛽 ,
where 𝛽𝛽 is close to 4.4 (see Figure 6 A). Such values are significantly higher than in homogeneous polyacrylamide gels (𝛽𝛽~3 to 3.5) [START_REF] Abidine | Physical properties of polyacrylamide gels probed by AFM and rheology EPL[END_REF][START_REF] Adibnia | Universal aspects of hydrogel gelation kinetics, percolation and viscoelasticity from PAhydrogel rheology[END_REF][START_REF] Oyen | Mechanical characterisation of hydrogel materials[END_REF], which could result from the specific physical gel structure of chitosan hydrogels [START_REF] Popa-Nita | Continuum of structural organization from chitosan solutions to derived physical forms[END_REF], implying the role of entanglements [START_REF] Popa-Nita | Structure of Natural Polyelectrolyte Solutions: Role of the Hydrophilic/Hydrophobic Interaction Balance[END_REF][START_REF] Sereni | Dynamic Structuration of Physical Chitosan Hydrogels[END_REF]) -inherited from the polyelectrolyte chitosan solution -in the mechanical properties of hydrogels. Increasing polymer concentration would thus result in an increase in multiple physical interaction sites and entrapped entanglements, leading to a 'multiple' physical network with various interaction types.

Influence of the gelation route

Figure 3 F and columns 2 and 5 in Table 3 allow comparing the modulus distribution functions of hydrogel samples at the same polymer concentration Cp = 2.5% and DA of 4.0%, but with different gelation conditions (NaOH solution vs ammonia vapor).

We observe significantly higher values for the elastic moduli 𝐸𝐸 𝑚𝑚 and 𝐸𝐸 � resulting from the sodium hydroxide neutralization route, in comparison to the series of samples neutralized with ammonia vapor (𝐸𝐸 𝑚𝑚 and 𝐸𝐸 � are increased by a factor of 8 and 12, respectively). Thus, the sodium hydroxide solution route yields hydrogels with a higher modulus i.e. more cohesive structure. The difference between hydrogels obtained by one or the other gelation route is owed to different gelation kinetics. Indeed, neutralization with ammonia vapors requires the formation of vapors and condensation onto the chitosan solution surface, whereas neutralization with NaOH solution is followed by direct and fast diffusion through the formed hydrogel and the solution [START_REF] Enache | Kinetics of chitosan coagulation from aqueous solutions[END_REF]). Thus, neutralization with NaOH solution is faster, and could yield a more entangled hydrogel from the highly entangled polyelectrolyte chitosan parent solution [START_REF] Sereni | Dynamic Structuration of Physical Chitosan Hydrogels[END_REF]. Supplementary figures SM5 and SM6 display examples of the evolution of the gel width (e) during gelation of chitosan acetate solutions. Table TSM2 and TSM3 show the comparative characterization of gelation kinetics in terms of reaction parameter 𝜉𝜉 = 𝑒𝑒 √𝑡𝑡 .

Influence of the degree of acetylation DA

The impact of the degree of acetylation on the modulus distributions can be observed comparing Figure 3 B and 3 D obtained at the same polymer concentration Cp = 2.5%, using the same neutralization conditions (ammonia route), with chitosan of similar molar masses, but at two different DAs, i.e. 4% and 38.5%. An increase in the DA is related with a decrease in the modulus deduced from AFM spectroscopy. In solution, at a DA of 4%, chitosan is a strong polyelectrolyte [START_REF] Popa-Nita | Structure of Natural Polyelectrolyte Solutions: Role of the Hydrophilic/Hydrophobic Interaction Balance[END_REF][START_REF] Schatz | Typical physicochemical behaviors of chitosan in aqueous solution[END_REF]) with a high entanglement density and high hydrophilicity. At a DA of 38%, the density of charge is lower, thus the entanglement density also decreases, although the persistence length is partly preserved due to the steric contribution of acetyl groups [START_REF] Lamarque | Physicochemical behavior of homogeneous series of acetylated chitosans in aqueous solution: role of various structural parameters[END_REF].

Consequently, in the neutralized state, low DA hydrogels will preserve a higher entanglement density, formed by interchain interactions from a highly entangled solution. Moreover, we previously showed that low DA chitosan in the neutralized state were in the most hydrophobic conditions [START_REF] Becerra | Tuning the Hydrophilic/Hydrophobic Balance to Control the Structure of Chitosan Films and Their Protein Release Behavior[END_REF]). Thus, low DA chitosan hydrogels could entrap a higher entanglement density in a physical network formed with a higher density of hydrophobic junctions, resulting in a higher modulus for the hydrogels (see Table 2 and

Chitosan hydrogel family identification by their mechanical properties

In order to compare the characteristic mechanical behavior of chitosan hydrogels depending on three parameters, namely concentration, gelation route, and DA, we have reported the normalized non-parametric probability density function versus the normalized Young modulus distribution for each condition (see Figure 4). This graph highlights that gelation route or DA values seem to impact the shape of the Young modulus distribution, while parameter Cp associated to low DAs result in limited effect, and tend to preserve a similar shape of the normalized curves (see Figure 4).

Young's modulus and topography maps

In order to complete the previous mechanical characterization and assess the characteristic sizes of the hydrogel microstructure, we report in Figure 5 the Young modulus distribution maps over a 1×1 µm² surface together with the corresponding topographical maps of each chitosan hydrogel. In Figure 5

Characterization of local mechanical properties on the apical surface of chitosan hydrogels

The apical surface of hydrogel chitosan samples (i.e., the surfaces formed at first contact with the gaseous or liquid base) were analyzed by AFM following the same method described above for the lateral surfaces. Thus, Figure 6 A-E shows, for each sample, the elastic modulus distribution histograms superimposed with the continuous estimation of the probability distribution functions (NPPDF, red lines). As we already observed for the lateral surface, the elastic modulus distribution of chitosan hydrogels presents a wide dispersion (see Figure 6 A-E) with standard deviation values close to the mean 𝐸𝐸 𝑚𝑚,𝑚𝑚 values and skewness values > 1 (see Table 3). Again, all the samples studied on the apical surface show an asymmetric distribution extended towards high elastic modulus values of the histogram (see Figure 6). The elastic modulus corresponding to NPPDF peak values 𝐸𝐸 � 𝑚𝑚 are reported in Table 3. Considering low DA chitosan (4%) samples neutralized with ammonia vapor, the polymer concentration impacts the elastic modulus following a power law as observed for the lateral surface, although the absolute values are significantly higher at the apical surface (see Figure 7 A). When the DA increased from 4% to 38.5%, the elastic modulus 𝐸𝐸 � 𝑚𝑚 decreased by a factor of 4.6 (see Table 3), while for the lateral surface analyses the factor was close to 3.3. In order to compare apical and lateral surfaces, we have reported on the same graphs the normalized elastic modulus occurrence curves (NPPDF) from both surface type analyses in Figure 8. The apical surfaces exhibit higher elastic moduli, in agreement with the formation of a dense layer in contact with the base. Surprisingly, in the case of hydrogels neutralized with NaOH aqueous solutions, the apical surface modulus value is close to the value on the lateral surface, suggesting that the microstructure is similar in the apical and lateral surfaces, at least in the investigated depth range. Visually, or using an optical stereomicroscope it was possible to observe a clear apical membrane after slow neutralization with ammonia vapor, whereas this membrane was more difficult to exhibit in fast neutralization conditions (NaOH), possibly because the hard surface membrane could be much thicker and more diffuse (in this case, the lateral surface investigation could still be located in the dense superficial membrane).

In case of neutralization with ammonia vapor, we observe that the elastic modulus 𝐸𝐸 � of the lateral surface and 𝐸𝐸 � 𝑚𝑚 of the apical surface follow a linear relation (i.e. 𝐸𝐸 � 𝑚𝑚 ~36𝐸𝐸 � see

Discussion

In this work, Atomic Force Spectroscopy at the 66.7 nm resolution was carried out on physical chitosan hydrogels. The optimization of their mechanical properties requires the control of the gelation method, of the molecular parameters of chitosan (ex: degree of acetylation), and of the formulation parameters of the initial chitosan solution (ex: chitosan concentration).

Our contribution is a local characterization approach, which allowed us to exhibit various, measurable structural heterogeneities in chitosan hydrogels at multiple length scales, as revealed by our normalized curves and modulus maps obtained with AFM. The differences observed in the modulus values obtained with AFM and rheology may arise from the multi-layered structure of chitosan hydrogels [START_REF] Sereni | Dynamic Structuration of Physical Chitosan Hydrogels[END_REF], and the precise location of AFM analysis with respect to the hydrogel surface. In this regard, a high ratio of 𝐸𝐸 𝑚𝑚 (3𝐺𝐺 ′ ) ⁄ can be interpreted as reflecting a high modulus gradient of hydrogels. Thus, AFM is clearly shown to be a unique technique able to reveal heterogeneities and gradients in the mechanical properties of chitosan hydrogels at the nanometer to micron scales, a characterization that cannot be assessed via the rheological behavior of macroscopic hydrogels. Specifically, at the micron-range area, the neutralization route impacts the breadth of the distribution of elastic moduli: Ammonia vapor neutralization of low DA chitosan solutions yield hydrogels with a higher heterogeneity parameter (𝑆𝑆𝐷𝐷/𝐸𝐸 𝑚𝑚 ), in comparison with sodium hydroxide solution neutralization of gels at the same concentrations.

An increase of the DA strongly reduces such sub-micron scale heterogeneities, an indication that the observed modulus fluctuations for low DA hydrogels could be related to entanglement density fluctuations entrapped in the hydrogels. Indeed, during neutralization, chitosan chains switch from an extended conformation in the polyelectrolyte state to a more compact and disentangled conformation in the neutralized state. Gel formation only occurs if an entanglement network can persist entrapped in the gel. Thus, at low DA, a high charge density in chitosan solutions could favor strong conformation changes and disentanglements during neutralization, whereas the conformation of chitosan of a higher acetylation degree chitosan would be less sensitive to the neutralization state, maintaining a persistence length due to the steric hindrances of acetyl moieties.

Another important consequence of our nano-localized mechanical measurements is our ability to estimate the impact of the various parameters of chitosan formulations on the formation of different zones in the multi-layered hydrogels, at micron scale and/or higher length scales. Thus, we were able to characterize and compare the first-formed surface (apical), and the bulk (lateral surface) of hydrogels. A stiffer membrane is formed at the apical surface, as was previously observed, although this was never quantified before [START_REF] Fiamingo | Chitosan Hydrogels for the Regeneration of Infarcted Myocardium: Preparation, Physicochemical Characterization[END_REF][START_REF] Sereni | Dynamic Structuration of Physical Chitosan Hydrogels[END_REF]. We have found a scaling relation relating the mechanical properties of the bulk versus apical layer for hydrogel neutralization with ammonia vapor, for all investigated concentrations and DAs. Our results also show that the polymer concentration impacts the bulk and apical surface moduli of different hydrogel layers with a similar power law.

Further, an increase in the acetylation degree was found to induce a decrease of the chitosan hydrogel elastic moduli. Although a higher DA results in a more hydrophobic polymer in acidic solutions [START_REF] Popa-Nita | Structure of Natural Polyelectrolyte Solutions: Role of the Hydrophilic/Hydrophobic Interaction Balance[END_REF], an opposite trend is expected in the neutralized state, where a low DA yields a more hydrophobic hydrogel [START_REF] Becerra | Tuning the Hydrophilic/Hydrophobic Balance to Control the Structure of Chitosan Films and Their Protein Release Behavior[END_REF]. Thus, in the neutralized state, a low DA chitosan should favor hydrophobic interactions, also entrapping a higher entanglement density, thus resulting in a higher modulus.

Finally, our AFM-based mechanical characterization approach is pertinent to better understand hydrogel-cell interactions. Indeed, we have shown previously that alveolar macrophages are impacted, in terms of shape, spreading, height and cytoskeletal stiffness, by the mechanical properties of the substrate with elastic modulus values close to 10 kPa, 40 kPa, 160 kPa up to nearly infinite rigidity [START_REF] Féréol | Sensitivity of alveolar macrophages to substrate mechanical and adhesive properties[END_REF]). This sensitivity is regulated by the formation of macrophage adhesion sites [START_REF] Fereol | Prestress and adhesion site dynamics control cell sensitivity to extracellular stiffness[END_REF]). Concerning chitosan-based materials, several studies have shown that a change in DA is correlated with a change in the macrophage phenotype invading the hydrogel [START_REF] Chedly | Physical chitosan microhydrogels as scaffolds for spinal cord injury restoration and axon regeneration[END_REF][START_REF] Vasconcelos | Macrophage polarization following chitosan implantation[END_REF]. From our present results on chitosan hydrogel materials, changes in the DA are related to a change in mechanical properties in a range from 4 to 13 kPa, i.e. the range of sensibility of macrophages to substrate mechanical properties [START_REF] Féréol | Sensitivity of alveolar macrophages to substrate mechanical and adhesive properties[END_REF][START_REF] Sridharan | Material stiffness influences the polarization state, function and migration mode of macrophages[END_REF]. This could at least partly explain the macrophagic polarization mechanism in contact with chitosan hydrogels with different degrees of acetylation. In order to establish the specific impact of the mechanical properties of the substrate on macrophage polarization, further cellular studies are planned, varying the type of hydrogels, and the type of surface (apical or lateral) used for cell culture.

Conclusion

Atomic force spectroscopy is shown to be an ideal tool for the characterization of soft complex materials. In this work, we have developed a methodological approach and applied it to the characterization of multi-layered hydrogels obtained by neutralization of chitosan acetate aqueous solutions. At a sub-micron scale, we thus clearly demonstrate that the neutralization conditions (with ammonia vapors or NaOH liquid solutions), the molecular parameters of chitosan (degree of acetylation), and the processing parameters (chitosan concentration) affect the hydrogel local mechanical properties. We have interpreted this by invoking the dynamic effects related to disentanglement time during neutralization and gelation kinetics.

In addition, we characterized for the first time the elastic modulus of the thin membrane covering the apical surface of samples elaborated via the ammonia route. In contrast, for gels obtained via NaOH neutralization the elastic modulus value of the apical surface was not substantially different from that of the chitosan hydrogel bulk. The results of our microscale mechanical characterization of various formulations of chitosan hydrogels should initiate new possibilities for an interpretation of the behavior of cells in contact with such soft materials.

  1. Introduction ............................................................................................................... 2. Materials and methods ............................................................................................. 2.1. Polyacrylamide gel preparation .......................................................................... 2.2. Chitosan hydrogel preparation ........................................................................... 2.3. AFM measurements ......................................................................................... 2.4. Rheometry measurements ............................................................................... 3. Results ................................................................................................................... 3.1. Methodological validation with reference polyacrylamide gel ........................... 3.2. AFM Study of Chitosan Hydrogels ................................................................... 3.2.1 Characterization of local mechanical properties on the lateral surface of chitosan hydrogels ................................................................................................. 3.2.1.1 Influence of the polymer concentration Cp .......................................... 3.2.1.2 Influence of the gelation route ............................................................. 3.2.1.3 Influence of the degree of acetylation DA ............................................ 3.2.1.4 Chitosan hydrogel family identification by their mechanical properties 3.2.1.5 Young's modulus and topography maps ............................................. 3.2.2 Characterization of local mechanical properties on the apical surface of chitosan hydrogels .................................................................................................

Figure 1 :

 1 Figure 1 : (A): Image of chitosan hydrogel top view (𝐷𝐷𝐷𝐷: 4%, 𝐶𝐶 𝑝𝑝 : 3.5%), neutralized with ammonia vapor (B): Sketch of the chitosan hydrogel half circle shape, red squares represent zones assessed by AFM. «a» is the assessed area located at the level of the thin layer formed at the first neutralized surface of the hydrogel, i.e. apical surface, "b" is the assessed area located between 0.5 and 2 mm from the surface on the lateral surface of the hydrogel.

  Figure 2 A-C presents the distributions of elastic modulus for these three conditions. The red curves represent the continuous estimations of distribution functions (NPPDF) that fit and smooth the histograms of elastic modulus values.

Figure 2 :

 2 Figure 2 : Histograms of elastic modulus occurrence distributions versus elastic modulus values for three polyacrylamide gels assessed by AFM varying concentration of acrylamide (Acr) and bis-acrylamide (Bis). Red curve represents the non-parametric probability density function (NPPDF) using a kernel density estimation based on a normal distribution to fit and smooth the occurrence distribution of elastic modulus values.

Figure

  Figure 3 F).

Figure 3 :

 3 Figure 3 : (A-E) Histogram of elastic modulus and distribution functions for five chitosan hydrogels, varying their concentration Cp, DA and route of gelation assessed by AFM on their lateral surface (Measurements performed at a depth between 0.5 and 2 mm from the surface). The red curve represents the non-parametric probability density function (NPPDF) using a kernel density estimation to smooth the histograms. (F) Comparison of the normalized elastic modulus occurrence corresponding to these five hydrogels.

Figure 4 :

 4 Figure 4 : Normalized non-parametric probability density functions versus normalized young's modulus distribution (𝐸𝐸 𝐸𝐸 � ) ⁄ of five chitosan hydrogels assessed by AFM on lateral surfaces.

  A, D, G, J and M, the Young modulus distribution histograms calculated from their corresponding maps are in agreement with the Young modulus NPPDF calculated from all samples of the same condition (red curves) as shown in Figure3. The topography map of each sample is shown in Figure5 B, E, H, K and N, and the Young modulus distribution maps are shown in Figure5C, F, I, L and O. Variations in height and modulus maps do not appear to be correlated.

Figure 5 :

 5 Figure 5 : Topological and mechanical property maps of chitosan hydrogels (Lateral surfaces). (A, D, G, J and M): histograms of elastic modulus distributions for a given region (in blue), superimposed with the elastic modulus estimation of density probability functions performed with all studied samples (in red). (B, E, H, K and N): topography (relative height) of the hydrogel surface. (C, F, I, L and O): Elastic modulus distribution map on the hydrogel surface.

Figure 7 B

 7 Figure 7 B and Figure 8 A-D), whereas the NaOH route gelation yields 𝐸𝐸 � close to 𝐸𝐸 � 𝑚𝑚 (Figure 8 E). These results suggest that the gelation route and the gelation kinetics are

Figure 6 :

 6 Figure 6 : Histograms of elastic modulus assessed by AFM for the apical surfaces of five chitosan hydrogel types. The red curves represent the estimation of probability density function using a kernel density estimation.

Figure 8 :

 8 Figure 8 : Comparison between the normalized elastic modulus occurrence assessed by AFM of the chitosan hydrogel apical surfaces (red curve) and chitosan hydrogel bulk (blue curve).

  Acr 5.5% / Bis 0.03%), 13.69 ± 2.84 kPa (Acr 7.52% / Bis 0.16%) and 29.01 ± 6.18 kPa (Acr 12.0% / Bis 0.15%)[START_REF] Elosegui-Artola | Rigidity sensing and adaptation through regulation of integrin types[END_REF]).

), i.e. with following predicted elastic modulus values (𝐸𝐸 𝑚𝑚 𝐸𝐸𝐸𝐸 ± 𝑆𝑆𝐷𝐷) 1.99 ± 0.13 kPa (

Table 1 )

 1 [START_REF] Elosegui-Artola | Rigidity sensing and adaptation through regulation of integrin types[END_REF]. The relative differences in the values of elastic moduli (%) for (Acr 5.5% / Bis 0.03%), (Acr 7.52% / Bis 0.16%) and (Acr 12.0% / Bis 0.15%), are -37.8%, 0.2%, and -6.4%, respectively (see Table1). For the softest gel, i.e.

	(Acr 5.5% / Bis 0.03%), the discrepancy found can be explained as described by Schillers
	et al (2017), invoking an uncertainty in cantilever calibration and instrumental errors. Ad-
	ditional elements concerning the methodological validation are provided in supplementary
	materials.

Table 1 :

 1 Elastic modulus of three different polyacrylamide gels assessed by AFM and compared to those obtained by AFM inElosegui-Alberto et al (Elosegui-Artola et al. 2014) for the same formulations.

Table 2 :

 2 Young modulus and associated parameters of five chitosan hydrogels assessed by AFM on lateral surface and by rheometer device.

		Lateral Surface	C 1.5% / DA	C 2.5% / DA	C 3.5% / DA	C 2.5% / DA	C 2.5% / DA
				4.0%	4.0%	4.0%	38.5%	4.0% (NaOH)
		Number of data	1280	1587	768	584	1280
		Maximum value (𝑬𝑬 𝒎𝒎𝒎𝒎𝒎𝒎 ) (kPa)	27.4	237.6	2603.4	15.3	916.1
		Mean value (𝑬𝑬 𝒎𝒎 )(kPa)	4.7	26.3	317.0	4.1	213.3
	AFM	Standard deviation (kPa)	4.7	21.4	376	1.7	135.8
	device	Peak Value (𝑬𝑬 � ) (kPa)	1.9	13.0	85.0	3.9	158.8
		Skewness	2.4	2.0	3.1	1.3	1.7
		𝑬𝑬 𝒎𝒎 -𝑬𝑬 � 𝑬𝑬 𝒎𝒎	⋅(%)	58.9	50.7	73.2	4.6	25.6
		𝑬𝑬 𝒎𝒎𝒎𝒎𝒎𝒎 𝑬𝑬 �	14.2	18.3	30.6	4.0	5.8
		Kernel size (kPa)	0.6	5.3	58.3	0.3	20.5
	Rheometer	Storage shear modulus (𝑮𝑮 ′ ) (kPa) ± 0.2 (kPa)	0.25	1.1	2.45	2.54	1.95-
	device	Equivalent elastic modulus 𝑬𝑬 𝑹𝑹 = 𝟑𝟑𝑮𝑮 ′ (kPa) ± 0.6 (kPa)	0.75	3.3	7.35	7.62	5.85

Table 3 :

 3 Analysis of Young's modulus assessed by AFM at the apical surface of five chitosan hydrogels and associated methodological parameters.

		Apical Surface	C 1.5% / DA	C 2.5% / DA	C 3.5% / DA	C 2.5% / DA	C 2.5% / DA
			4.0%	4.0%	4.0%	38.5%	4.0% (NaOH)
		Number of data	512	2560	1024	1280	512
		Maximum Measured value (𝑬𝑬 𝒎𝒎𝒎𝒎𝒎𝒎 ) (kPa)	734.4	2325.3	56269.8	1323.4	2881.8
		Mean value (Eam) (kPa)	154.7	425.1	8812.3	248.0	338.4
	AFM device	Standard deviation (kPa) Peak (modal) value (𝑬𝑬 � 𝒎𝒎 ) (kPa)	133.5 57.9	237.9 398.7	9490.8 1747.9	205.2 87.2	333.8 174.2
		Skewness	1.48	2.93	1.64	1.46	2.96
		Kernel size (kPa)	14.7	46.5	1125.4	26.5	57.6

Figure 7 : (A) Elastic modulus peak values versus polymer concentration 𝐶𝐶 𝑝𝑝 after ammonia vapors neutralization. (B) Relation between elastic modulus peak values at the lateral surface and elastic modulus peak values at the apical surface.

With n the number of data.

Again, data processing provides the modal value 𝐸𝐸 � and the mean value 𝐸𝐸 𝑚𝑚 . As a result of asymmetry of distribution functions, we can observe significant differences between 𝐸𝐸 𝑚𝑚 and 𝐸𝐸 � (𝐸𝐸 𝑚𝑚 > 𝐸𝐸 � ); the ratio (𝐸𝐸 𝑚𝑚 -𝐸𝐸 � )/𝐸𝐸 � varying between 25% and 75% for the tested sample on the lateral surface except for the sample Cp= 2.5% / DA 38.5% where the relative discrepancy between 𝐸𝐸 𝑚𝑚 and 𝐸𝐸 � is only 5%, in agreement with a more symmetrical distribution, skewness = 1.3 (see Table 2). As a result, chitosan hydrogels generally exhibit broad and asymmetric modulus distributions that could be associated with a submicron range heterogeneous structure at low DAs (Popa-Nita et al. 2010) (see Figure 3 A-C and E). To go further, we assessed the macroscopic mechanical properties of all chitosan hydrogel samples with a plate-plate shear rheometer device (see Table 2). The real part of the complex shear modulus G' is used to calculate the equivalent elastic modulus obtained with the rheometer device, 𝐸𝐸 𝑅𝑅 ~ 3G' and can be compared with 𝐸𝐸 𝑚𝑚 and 𝐸𝐸 � obtained with AFM (see Table 2). The values of elastic modulus obtained by AFM (𝐸𝐸 𝑚𝑚 and 𝐸𝐸 � ) are generally higher than those obtained from rheology, except for the high DA (38.5%) sample. This could be related to the multi-layered structure of chitosan hydrogels, associated with the gradual slowing down in the neutralization kinetics with diffusion depth [START_REF] Enache | Kinetics of chitosan coagulation from aqueous solutions[END_REF][START_REF] Sereni | Dynamic Structuration of Physical Chitosan Hydrogels[END_REF]. At low DAs, the chitosan chain conformations in solution are strongly impacted by their charge density, thus, a slow neutralization kinetics will yield

Acknowledgments

We would like to acknowledge the « Ministère de l'Enseignement Supérieur et de la Recherche Scientifique » of Algeria for PhD funding attributed to AB, Satt-Lutech (financial support for MV salary) and Prof. Hugues Talbot, Université Paris-Saclay, for the helpful discussions.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Research Resource Identifiers (RRID)

Software: MATLAB, RRID:SCR_001622 Software: AMIRA 5.2, Advanced 3D Visualization and Volume Modeling, RRID:SCR_007353