Matthieu Vandamme

Coupling between adsorption and mechanics (and vice versa)

Adsorption can deform porous solids, and mechanical stresses or strains can impact the adsorption process: this mini-review is dedicated to this coupling. After introducing some frameworks used to predict adsorption-induced strains, the question of how important it is to take into account the impact of mechanics on the adsorption process is addressed. Finally, some specific complexities (e.g., of the microstructure, or of the mechanical behavior of the adsorbent) that the community aims at integrating into the prediction of adsorption-induced strains are addressed.

Introduction

The fact that adsorption can deform solids has been known for centuries, but has been the subject of renewed interest in the last decade or so, since the discovery that some metal-organic frameworks (MOFs) can exhibit large deformations upon adsorption. As I will try to address in this mini-review, not only does adsorption impact the mechanical response of the adsorbent, also does the mechanical response of the adsorbent impact the adsorption process: the coupling between adsorption and mechanics is a two-way coupling.

Depending on the size of their pores, porous bodies are referred to as microporous (i.e., with a pore size below 2nm), mesoporous (i.e., with a pore size between 2nm and 50nm), or macroporous (i.e., with a pore size greater than 50nm). The physics through which in-pore fluid can deform a porous body depends on this pore size: capillary effects (i.e., effects due to the presence of menisci between various phases of the in-pore fluid) and Gibbs-Bangham-like effects (i.e., deformations induced by adsorption on solid surfaces) in mesoporous materials, or pore filling (rather than surface covering) in microporous solids. Note that, even in macroporous solids (in which fluid is not adsorbed but behaves like a bulk phase), in-pore fluids can deform the body, through their pressure variations (see, e.g., [1]).

One can already find in the recent literature an extensive review of adsorption-induced deformations in porous solids [START_REF] Gor | Adsorption-induced deformation of nanoporous materials[END_REF], which I will partly complement with some most recent works. I also want to mention a recent review on the computational chemistry of soft porous crystals [START_REF] Fraux | Recent advances in the computational chemistry of soft porous crystals[END_REF].

In this mini-review, I will first introduce some frameworks used to estimate adsorptioninduced strains, before tackling the notion of the two-way coupling between adsorption and mechanics, and moving to specific complexities incorporated in the modeling of adsorption-induced deformations.

Some frameworks to predict adsorption-induced strains

The discussion in this section is quite generic and disregards specific complexities of the material, which will be addressed later in the manuscript.

A first pore-scale approach to predict adsorption-induced strains is a thermodynamic one, which consists in identifying the energy to minimize in the so-called osmotic ensemble, which is the 2 right thermodynamic ensemble to address adsorption-induced deformations [START_REF] Escobedo | Novel pseudoensembles for simulation of multicomponent phase equilibria[END_REF]. Through this approach, Ravikovitch and Neimark [START_REF] Ravikovitch | Density functional theory model of adsorption deformation[END_REF] first showed that adsorption induces a mechanical stress (sometimes called 'adsorption stress') whose magnitude is equal to the solvation pressure and can be obtained from the grand potential of the adsorbed fluid. For mesoporous materials, an alternative pore-scale approach, more mechanistic, consists in considering the concept of surface stress, which is being successfully used in electro-chemistry in particular (see, e.g., [START_REF] Kramer | Surface-stress induced macroscopic bending of nanoporous gold cantilevers[END_REF]).

To estimate the adsorption-induced deformations of an anisotropic mesoporous silica body made of parallel cylindrical channels, both the thermodynamic approach [START_REF] Balzer | Adsorption-induced deformation of hierarchically structured mesoporous silica Effect of Pore-Level Anisotropy[END_REF] and the surface stress approach [START_REF] Gor | Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress[END_REF] were used recently. The two approaches are compared in [START_REF] Gor | Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress[END_REF]: above capillary condensation, they yield identical results, while, below capillary condensation (i.e., in the film regime), they provide qualitatively similar but quantitatively different responses. To me, this difference might at least partly be due to the fact that the input parameters for the two works are different: for instance, the relation between thickness of adsorbed film and relative pressure is given by the BET model in [START_REF] Gor | Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress[END_REF], while it is given by the DBdB theory in [START_REF] Balzer | Adsorption-induced deformation of hierarchically structured mesoporous silica Effect of Pore-Level Anisotropy[END_REF].

There exist other approaches, at a macroscopic scale, aiming at predicting adsorption-induced strains through adaptation of the poromechanical framework. Here again, one can divide those approaches into more thermodynamic ones (e.g., [START_REF] Brochard | Poromechanics of microporous media[END_REF][START_REF] Kulasinski | Poroelastic model for adsorption-induced deformation of biopolymers obtained from molecular simulations[END_REF][START_REF] Zhang | Mechanics of adsorption-deformation coupling in porous media[END_REF] ) or more mechanistic ones (e.g., [START_REF] Vermorel | Enhanced continuum poromechanics to account for adsorption induced swelling of saturated isotropic microporous materials[END_REF], in the sense that it introduces an apparent porosity). For this type of approaches again, as explained in [START_REF] Gor | Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress[END_REF], with different approaches, similar predictions can be obtained.

a. Notion of pore-load modulus

With most pore-scale approaches, the effect of adsorption is translated into a stress, which then needs to be translated into a strain, for which purpose an elastic modulus is needed. To this effect, there exists the notion of pore-load modulus , which relates a strain to a pressure of fluid in the pore through: = / . A pore-load modulus is only valid for a specific direction and a specific loading [START_REF] Gor | Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress[END_REF]. For transverse isotropic membranes of porous silicon exhibiting a random honeycomb structure, by using n-heptane above capillary condensation, Rolley et al. [START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF] measured pore-load moduli and showed that their magnitudes are consistent with elastic properties measured by direct stretching of the membrane: pore-load moduli can be used to measure elastic properties of the porous material.

With finite-element modeling (FEM), Rolley et al. [START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF] showed that, to retrieve the correct elastic properties of those same membranes, the elastic modulus of the solid walls must be about 2 to 6 times smaller than the bulk modulus of bulk silicon, depending on the direction considered: they attributed this discrepancy to finite-size effects and defects of the solid walls. In contrast, based on adsorption measurements with argon and n-hexane on Vycor (i.e., an amorphous mesoporous silica glass with worm-like channels), Gor et Gurevich [START_REF] Gor | Gassmann theory applies to nanoporous media[END_REF] succeeded in calculating the response of their porous material by considering that the bulk modulus of the solid skeleton is close to the bulk modulus of a solid Vycor matrix, as back-calculated from the dry moduli of Vycor using an elastic effective medium theory. How to translate elastic properties of the solid skeleton into pore-load modulus or elastic properties of the porous material in presence of fluid, although well established for macroporous materials, appears, for nanoporous materials (i.e., for materials with a pore size below 100nm [START_REF] Thommes | Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution[END_REF]), to be system-dependent [START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF].

Recently, Puibasset [START_REF] Puibasset | Adsorption-induced deformation of a nanoporous material: Influence of the fluid-adsorbent interaction and surface freezing on the pore-load modulus measurement[END_REF] found out that, in presence of fluid, the apparent pore-load modulus can differ from the one expected by considering the properties of the solid wall to be those of the bulk non-porous solid, even though, on the dry material, a correct value is retrieved. The difference is attenuated if the fluid-wall interaction is attenuated. He attributes the discrepancy to a surface effect, namely a variation of the surface stress in presence of fluid, which he correlates to surface ordering. Therefore, I would not rule out that relating pore-load modulus to properties of the solid skeleton in the generic case could be improved through a better understanding of the solid-fluid interactions at the solid surfaces.

Impact of mechanics on the adsorption process

If adsorption can deform a solid, deformations can also impact the sorption process, as already observed experimentally with porous membranes [START_REF] Grosman | Influence of elastic strains on the adsorption process in porous materials: An experimental approach[END_REF]. Consequently, in the generic case, the adsorbed amount of adsorbate should be considered to depend not only on the chemical potential of the adsorbate and the temperature , but also on mechanical stresses or strains. Whether considering this dependence is important is the topic of the next two sections (for what concerns estimations of adsorption-induced strains or of adsorbed amounts) before moving to other topics relevant to this coupling.

a. Importance of considering how adsorption depends on strains to estimate adsorption-induced strains

When adsorption occurs on surfaces, the surface stress , which deforms the solid surface, is related to the excess adsorbed amount Γ through Shuttleworth's equation [START_REF] Shuttleworth | The surface tension of solids[END_REF]:

= Γ
where is the surface strain of the solid surface. In a generic case (i.e., valid for micropores, mesopores, or macropores), the volumetric stress induced by the presence of the fluid is related to the amount of fluid in the body through [START_REF] Brochard | Poromechanics of microporous media[END_REF]: = where is the volume strain of the body. Those (Lagrangian) equations clearly show that, if the fluid induces a stress and deforms the porous body, this is because the adsorbed amount depends on the volume/surface strain. Consequently, how adsorption depends on strains is of prime interest to correctly estimate adsorption-induced strains.

For what concerns adsorption on solid surfaces, the celebrated Bangham model [START_REF] Bangham | The swelling of charcoal. Part V. The saturation and immersion expansions and the heat of wetting[END_REF], which is valid for a wide variety of cases, states that:

∝ ∆ such that strains should be proportional to variations ∆ of surface energy. However, theoretically, strains should be proportional to variations of surface stress. Recently, this discrepancy was explained, and is in fact rooted in how adsorption depends on strains: in the framework of the BET model, Gor and Bernstein [START_REF] Gor | Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress[END_REF] showed that, if the energy of adsorption of first layer does not depend on the stretch of the surface, then variations of surface energy and of surface stress are equal, thus making it possible to retrieve Bangham's law. Their results suggest that Bangham's law should be verified for small strains and small molecules with non-specific interactions. In contrast, if this energy of adsorption of the first layer depends on the stretch of the surface, the authors show that you can predict contractions at low gas pressures, which are indeed observed experimentally.

To capture non-trivial dependency of the adsorbed amount on strain and its consequences on strains, Kolesnikov et al. [START_REF] Kolesnikov | Effects of enhanced flexibility and pore size distribution on adsorption-induced deformation of mesoporous materials[END_REF], who calculate adsorption and deformation of a mesoporous film with cylindrical pores from a direct minimization of the appropriate thermodynamic potential in the osmotic ensemble, consider that the interaction between solid and fluid can depend on the pore radius. Like Gor and Bernstein [START_REF] Gor | Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress[END_REF], they conclude that taking into account this dependence is necessary to capture non-monotonic strain isotherms.

b. Importance of taking into account how adsorption depends on strains to estimate adsorption

Reversely, taking into account the dependence of adsorption on strains/stresses can be important to correctly estimate adsorbed amounts, with qualitatively significant impacts: deformations are shown to be the reason for observed negative adsorptions [START_REF] Evans | Origins of negative gas adsorption[END_REF][START_REF] Krause | A pressure-amplifying framework material with negative gas adsorption transitions[END_REF], and in presence of fluid mixtures the deformability of the adsorbent can impact the selectivity (e.g., [START_REF] Mahynski | Tuning flexibility to control selectivity in soft porous crystals[END_REF]). Quantitatively, Kolesnikov et al. [START_REF] Kolesnikov | Effects of enhanced flexibility and pore size distribution on adsorption-induced deformation of mesoporous materials[END_REF] showed that, in a mesoporous material, taking into account the flexibility of the adsorbent is necessary to explain why, above capillary condensation, increasing the relative pressure still makes it possible to increase the adsorbed amounts: adsorbed amounts increase not only by pore filling, but also by deformation of already-filled pores. Experimentally, on microporous carbons, micropores were shown to contribute to the adsorption isotherm on the full range of vapor pressures, even when micropores are already filled [START_REF] Balzer | Deformation of microporous carbons during N2, Ar, and CO2 adsorption: Insight from the density functional theory[END_REF].

In a converse manner, stresses applied to the adsorbent can also impact adsorbed amounts: experiments show that, on compacted coal powders [START_REF] Hol | Applied stress reduces the CO2 sorption capacity of coal[END_REF], applying effective stresses up to 35MPa can expel from 5% to 50% of the CO2 initially present in the sample. Even if most of the fluid was expelled from in-between the coal grains, subsequent analysis confirmed that the stresses indeed expelled some fluid that was adsorbed in the coal matrix [START_REF] Espinoza | Adsorptivemechanical properties of reconstituted granular coal: Experimental characterization and poromechanical modeling[END_REF].

Whether taking into account this effect is required to properly estimate the adsorbed amounts depends on the magnitude of the applied stresses or of the adsorption-induced strains. Just to provide an order of magnitude, typically for a microporous solid such as coal, the relative variation of adsorbed amount is estimated to be equal to about 10 times the strain [START_REF] Espinoza | Measurement and modeling of adsorptive-poromechanical properties of bituminous coal cores exposed to CO2: Adsorption, swelling strains, swelling stresses and impact on fracture permeability[END_REF].

c. Impact of adsorption on mechanical properties

Adsorption can modify the apparent elastic properties of the adsorbent and lead to either an apparent stiffening or an apparent softening of the adsorbent [START_REF] Mouhat | Softening upon adsorption in microporous materials: A counterintuitive mechanical response[END_REF][START_REF] Kulasinski | Impact of moisture adsorption on structure and physical properties of amorphous biopolymers[END_REF]. The apparent stiffness of the adsorbent is a function of the stiffness of the dry adsorbent and of how the adsorption isotherm depends on both the strain of the adsorbent and the chemical potential of the adsorbate [START_REF] Brochard | Poromechanics of microporous media[END_REF]. Confinement also modifies the mechanical properties of the fluid, as observed experimentally [START_REF] Schappert | Influence of the Laplace pressure on the elasticity of argon in nanopores[END_REF] or theoretically [START_REF] Gor | Adsorption stress changes the elasticity of liquid argon confined in a nanopore[END_REF].

A way through which adsorption can modify the mechanical properties of the adsorbent is through its impact on the microstructure: Perrier et al. [START_REF] Perrier | Poromechanics of adsorption-induced swelling in microporous materials: a new poromechanical model taking into account strain effects on adsorption[END_REF] showed that, in microporous materials, the apparent porosity can vary significantly upon the adsorption, and hence impact the poroelastic properties of the material. For a sandstone, whose dry mechanical behavior is nonlinear, variations of the elastic moduli with relative humidity could be explained by the impact of the variation of relative humidity on solvation pressure and hence effective stress [START_REF] Yurikov | Sorption-induced deformation and elastic weakening of Bentheim sandstone[END_REF]. Note however that, even in absence of nonlinearity or rearrangement of the microstructure, adsorption can impact the drained moduli of the porous material [START_REF] Mouhat | Softening upon adsorption in microporous materials: A counterintuitive mechanical response[END_REF].

d. Modeling the coupling between adsorption and mechanics

Since adsorption induces strains, and since strains impact adsorption, one should take into account this two-way coupling into the modeling. Such coupling can be particularly significant in microporous solids, in which the adsorption stress depends strongly on the pore size [START_REF] Ustinov | Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions[END_REF]. One way to capture this coupling, when employing a thermodynamic approach, is to minimize the appropriate thermodynamic potential ensemble with respect to both parameters characterizing the adsorption process and parameters characterizing the deformation process. Such approach was adopted for a mesoporous material made of cylindrical pores [START_REF] Kolesnikov | Effects of enhanced flexibility and pore size distribution on adsorption-induced deformation of mesoporous materials[END_REF], for MOFs [START_REF] Bakhshian | Theoretical model and numerical simulation of adsorption and deformation in flexible metal-organic frameworks[END_REF] or for cellular solids [START_REF] Guyer | Theoretical model for fluid-solid coupling in porous materials[END_REF]. This last work, formulated at a mesoscopic scale, shows that the solid-fluid interaction can lead to a hysteresis of the adsorption strain isotherm. For nanoporous crystalline materials with rotatable ligands shared between neighboring cages, a statistical mechanical model that captures the coupling was developed [START_REF] Simon | Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties[END_REF], which includes energy penalization for the rotation of a ligand and an energy of an adsorbed molecule that depends on the rotation of the ligands: the model captures inflections, steps, and hysteresis.

Specific complexities for prediction of adsorption-induced strains

In this section I address recent complexities that the community aims at integrating into models to predict adsorption-induced strains.

a. Complexity of the pore space: size, morphology Porous materials are characterized by a pore size distribution (PSD). Since the solvation pressure (and hence the adsorption-induced strains) depends on the pore size, using strain isotherms as an additional input to adsorption isotherms to back-calculate PSDs was proposed [START_REF] Ustinov | Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions[END_REF][START_REF] Kowalczyk | Using in-situ adsorption dilatometry for assessment of micropore size distribution in monolithic carbons[END_REF]. Another question relevant to the adsorption-induced deformation of generic materials is that of the shape of the pores, which can be more complex than slit, spherical, cylindrical, or hexagonal pores. To this respect, adsorption-induced deformations were recently studied in wedge-shaped graphitic pores [START_REF] Zeng | A Monte Carlo study of adsorption-induced deformation in wedge-shaped graphitic micropores[END_REF].

The PSD can evolve in a complex manner upon adsorption, due to the inhomogeneity of the microscopic deformations, as was shown numerically for a microporous carbon in presence of methane [START_REF] Obliger | Poroelasticity of methane-loaded mature and immature kerogen from molecular simulations[END_REF]. The PSD being in fact stress-dependent, Siderius et al. [START_REF] Siderius | Relationship between pore-size distribution and flexibility of adsorbent materials: statistical mechanics and future material characterization techniques[END_REF] showed that how the PSD evolves over the adsorption process theoretically contains information related to the flexibility and deformation characteristics of the adsorbent. One question that arises when adsorption occurs in a material in which pores are sufficient close to each other is whether the deformation of (or adsorption in) one pore occurs independently of what happens in the neighboring pores: indeed, some adsorption superlattice formation of the adsorbate in a metal-organic framework was observed [START_REF] Cho | Extra adsorption and adsorbate superlattice formation in metal-organic frameworks[END_REF].

b. Anisotropy

The stress induced by adsorption can be anisotropic (e.g., in a cylindrical pore, adsorptioninduced stresses are not identical in the axial and in the radial directions [START_REF] Balzer | Adsorption-induced deformation of hierarchically structured mesoporous silica Effect of Pore-Level Anisotropy[END_REF][START_REF] Gor | Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress[END_REF]). Also, pores can be organized in an anisotropic manner, or the mechanical behavior of the material can also be anisotropic. Consequently, there exist various potential sources of anisotropy because of which adsorption at the microscopic scale can lead to a macroscopically anisotropic deformation. In coal for instance, the anisotropy of the adsorption-induced strains was shown to be mostly due to the anisotropy of the mechanical behavior, while the adsorption stress itself is mostly isotropic [START_REF] Espinoza | A transverse isotropic model for microporous solids: Application to coal matrix adsorption and swelling[END_REF]. Anisotropic effects can also add or counterbalance each other: in silica struts containing parallel cylindrical mesopores [START_REF] Balzer | Adsorption-induced deformation of hierarchically structured mesoporous silica Effect of Pore-Level Anisotropy[END_REF], the cylindrical pore geometry makes the axial adsorption-induced stress about 3 times larger than the radial one but, as consequence of the anisotropy of the mechanical properties of the porous struts, deformations at the scale of a strut are roughly isotropic.

c. Beyond the linearity of the mechanical behavior of the solid

The simplest elastic behavior of a solid material is a linear one: stresses and strains are linearly related, following Hooke's law. But many materials do not follow Hooke's law, as is the case for instance for cracked media (upon compression, cracks close so that the stiffness of the material increases), or for polymeric solids. For wood for instance, whose elastic behavior is also nonlinear, adsorption-induced strains were modeled by taking explicitly into account the complexity of the free energy of the dry porous solid [START_REF] Kulasinski | Poroelastic model for adsorption-induced deformation of biopolymers obtained from molecular simulations[END_REF]. Molecular simulations can help explore the complexity of the free energy landscape: for another mechanism inducing flexibility in a MOF, namely the swing effect in ZIF-8, Coudert [START_REF] Coudert | Molecular mechanism of swing effect in zeolitic imidazolate framework ZIF-8: Continuous deformation upon adsorption[END_REF] showed with the help of quantum chemistry calculations and first-principles molecular dynamics that the flexibility is not a bistable system, but that the deformation evolves continuously with the pore loading.

For some MOFs like MIL-53, depending on the environmental conditions (temperature, stress, partial pressure of the adsorbate), two configurations of the adsorbent with very distinct strains can be observed (sometimes called 'large pore' and 'narrow pore' configurations), around which the material behaves in a linear elastic manner. The osmotic framework was adapted to such cases [START_REF] Coudert | Thermodynamics of guest-induced structural transitions in hybrid organic-inorganic frameworks[END_REF], under the assumption that each configuration is rigid. For the same family of materials, by considering a free energy of the dry porous material which exhibits two wells, the features of the energy landscape (i.e., the depth of the two wells) were shown to impact the transitions between the two configurations and the phase transitions of the pore fluid [START_REF] Shen | Molecular simulation of capillary phase transitions in flexible porous materials[END_REF].

d. Upscaling

Upon adsorption, the porous adsorbent deforms at several scales: for instance, in a monolithic silica sample with hierarchical porosity, strains at the scale of the pore lattice and at the macroscopic scale of the sample can both be measured [START_REF] Morak | Quantifying adsorption-induced deformation of nanoporous materials on different length scales[END_REF] and differ from each other. In a material containing pores with a variety of sizes, deformations should vary from pore to pore. Since many models to predict adsorption-induced strains are formulated at the pore scale, the question arises of how to translate strains at this scale into strains at the macroscopic scale of the sample.

Even though the variations of the volume of the sample are sometimes assumed to be equal to the variation of volume of the pores (e.g., in [START_REF] Kolesnikov | Effects of enhanced flexibility and pore size distribution on adsorption-induced deformation of mesoporous materials[END_REF]), note that it is generally not the case, as the volume of the solid skeleton can vary as well. When the geometry of the pores is well defined, one can find out how stresses/strains at the pore scale translate into strains at a larger scale by using the finite element method (FEM), as was done for an anisotropic mesoporous silica body made of parallel cylindrical channels [START_REF] Balzer | Adsorption-induced deformation of hierarchically structured mesoporous silica Effect of Pore-Level Anisotropy[END_REF][START_REF] Gor | Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress[END_REF]. For the nanoporous crystalline MIL-53, to upscale information on the breathing transition from the scale of the individual cage to the scale of a whole crystal, a Hamiltonian-based model was proposed [START_REF] Triguero | Understanding adsorptioninduced structural transitions in metal-organic frameworks: From the unit cell to the crystal[END_REF]. When some information is known about the microstructure, one can try to inject this information in the prediction of the adsorption-induced strains: such was done for instance for a synthetic activated carbon with a bi-modal distribution of pore sizes, for which models of adsorption-induced deformations were derived, that take explicitly into account the fact that the sample contains both nanopores that adsorb fluids and macropores that contain bulk fluid [START_REF] Perrier | Extended poromechanics for adsorption-induced swelling prediction in double porosity media: Modeling and experimental validation on activated carbon[END_REF].

In practice, many materials are composite or heterogeneous. As a consequence of this heterogeneity, an additional complexity in the upscaling process is that adsorption-induced deformations can be heterogeneous, as was observed for coal in presence of methane, through 3D digital image correlation of X-ray microtomography images [START_REF] Nie | Quantitative investigation of anisotropic characteristics of methaneinduced strain in coal based on coal particle tracking method with X-ray computer tomography[END_REF]. On composite materials with a coreshell microstructure, in which an adsorbing core is surrounded by an elastic binder, the presence of the binder was shown to decrease the magnitude of the adsorption-induced stresses and strains [START_REF] Coudert | Adsorption deformation of microporous composites[END_REF]. Also, if the adsorbing core can be subjected to adsorption-induced structural transitions, the presence of the binder impacts the pressures at which those transitions occur [START_REF] Coudert | Adsorption deformation of microporous composites[END_REF]. One way to decipher how adsorption-induced strains at the scale of the microscopic phases translate macroscopically into a strain of the macroscopic composite sample is to use FEM, as shown in [START_REF] Evans | Macroscopic simulation of deformation in soft microporous composites[END_REF] on composite microporous materials.

Concluding comments

In this mini-review, I covered not only how adsorption impacts the mechanical behavior of the adsorbent and deforms it, but also how mechanics (i.e., strains or stresses) impacts the adsorption process and the importance of taking into account this coupling. There exist several well-established frameworks to model adsorption-induced strains, and a trend in the modeling of adsorption-induced deformations is to take into account as much as possible of the complexity of actual materials, in terms for instance of microstructure (pore size distribution, pore morphology, heterogeneity,…) or of mechanical behavior of the adsorbent (anisotropy, non-linearity,…).

A recent and very complete review of adsorption-induced deformations in microporous and mesoporous materials. Covers both experimental and theoretical achievements, and applications of adsorption-induced deformations. * C. Balzer, A.M. Waag, S. Gehret, G. Reichenauer, F. Putz, N. H?sing, O. Paris, N. Bernstein, G.Y. Gor, A.V. Neimark, Adsorption-induced deformation of hierarchically structured mesoporous silica Effect of Pore-Level Anisotropy, Langmuir. 33 (2017) 5592-5602. doi:10.1021/acs.langmuir.7b00468. A manuscript that presents data on deformation of hierarchical Si system made of anisotropic struts containing parallel cylindrical mesopores in presence of N2 at 77K and aims at explaining those data through modeling based on the thermodynamic concept of adsorption stress. Modeling original because captures anisotropy of adsorption stress by minimizing appropriate potential with respect to both radial and axial dimensions of cylindrical pores. Model upscaled from scale of strut to scale of sample by superposition. * G.Y. Gor, P. Huber, J. Weissmüller, Elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress, Physical Review Materials. 2 (2018). doi:10.1103/PhysRevMaterials.2.086002. Manuscript devoted to the modeling of adsorption-induced deformations in anisotropic material made of parallel cylindrical mesopores. Modeling based on concept of surface stress, developed for both specific and non-specific adsorptions. Includes a comparison between modeling approaches based on thermodynamic concept of adsorption stress and concept of surface stress. * J. Puibasset, Adsorption-Induced Deformation of a Nanoporous Material: Influence of the Fluid-Adsorbent Interaction and Surface Freezing on the Pore-Load Modulus Measurement, The Journal of Physical Chemistry C. 121 (2017) 18779-18788. doi:10.1021/acs.jpcc.7b06888 Manuscript dedicated to the notion of pore-load modulus, studied by molecular simulations of thin solid layers. Shows that, on dry system, apparent stiffness of solid layer is consistent with what is expected from bulk properties of solid. In contrast, in contact with liquid, apparent stiffness of solid layer significantly larger than expected from bulk properties of solid. Relates this increase to a surface effect. ** G.Y. Gor, N. Bernstein, Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress, Phys. Chem. Chem. Phys. 18 (2016) 9788-9798. doi:10.1039/C6CP00051G. Manuscript that shows that, in framework of BET model, if energy of adsorption of first layer does not depend on the stretch of the surface, variations of surface stress are equal to variations of surface energy, which explains Bangham's law. * A.L. Kolesnikov, N. Georgi, Y.A. Budkov, J. Möllmer, J. Hofmann, J. Adolphs, R. Gläser, Effects of Enhanced Flexibility and Pore Size Distribution on Adsorption-Induced Deformation of Mesoporous Materials, Langmuir. 34 (2018) 7575-7584. doi:10.1021/acs.langmuir.8b00591. Manuscript dedicated to modeling of adsorption-induced deformations of mesoporous solids, in the spirit of the thermodynamic approach based on adsorption stress. Interest and originality of model in fact that captures the full coupling between adsorption and strain: below capillary condensation, equilibrium found by minimizing the correct energy, for each pore size, in terms of pore radius and in terms of thickness of adsorbed film. * F.-X. Coudert, A.H. Fuchs, A.V. Neimark, Adsorption deformation of microporous composites, Dalton Transactions. 45 (2016) 4136-4140. doi:10.1039/C5DT03978A. Manuscript dedicated to modeling of adsorption-induced strains in composite materials made of soft adsorbing cores surrounded by non-adsorbing elastic matrix. Shows that presence of elastic binder attenuates adsorption stress at scale of sample and shifts partial pressures at which adsorptioninduced structural transitions occur (if soft adsorbing core prone to adsorption-induced structural transitions). * E. Rolley, N. Garroum, A. Grosman, Using capillary forces to determine the elastic properties of mesoporous materials, Physical Review B. 95 (2017) 1-7. doi:10.1103/PhysRevB.95.064106. Experimental work which focuses on deformation of anisotropic mesoporous silicon membranes with a random honeycomb structure, above capillary condensation. Shows that elastic properties obtained from pore-load measurements are consistent with direct measurement of elastic properties, but cannot be simply retrieved from geometry of solid walls by considering that those walls behave like bulk material. Discrepancy attributed to finite-size effects and to defects in the walls.

Conflict of interest

The author declares no conflict of interest.


Dr Marianne Latinus
email: marianne.latinus@univ-tours.fr

Helen Cléry

Frédéric Andersson

Frédérique Bonnet-Brilhault

Pierre Fonlupt

Marie Gomot

Latinus Marianne

Cléry Helen

Andersson Frédéric

Bonnet-Brilhault Frédérique

Fonlupt Pierre

Gomot Marie

Inflexibility in Autism Spectrum Disorder: Need for certainty and atypical emotion processing share the blame

Keywords: autism, cognitive flexibility, emotion, facial expression, fMRI, WCST, setshifting, faces, inferior parietal sulcus. Latinus -4

Introduction

Patients with Autism Spectrum Disorder (ASD) display difficulties in changing strategy and adapting their perspective during daily activities, especially during social interactions. ASD is characterized by two main diagnostic criteria: persistent deficits in social communication and restricted, and repeated patterns of behavior, interests and activities (RRB). Although ASD diagnosis requires this dyad of symptoms to co-occur, research in the field is traditionally dissociated into two main domains (socio-emotional and cognitive), while their interactive effects, e.g. the cognitive control of social information, remain largely unexplored. This schematic partition is possibly due to the prevalent view of the brain as organized into either affective or cognitive components (see the meta-analysis of social and non-social processes in ASD by Di [START_REF] Martino | Functional brain correlates of social and nonsocial processes in autism spectrum disorders: an activation likelihood estimation meta-analysis[END_REF]. However, based on the proposition that the neural basis of emotion and cognition should be viewed as strongly non-modular [START_REF] Pessoa | On the relationship between emotion and cognition[END_REF], research in ASD would benefit moving beyond the dual process approach towards more realistic models emphasizing their interactions [START_REF] Dichter | Autism is characterized by dorsal anterior cingulate hyperactivation during social target detection[END_REF][START_REF] Ochsner | Emerging perspectives on emotion-cognition interactions[END_REF].

Cognitive control refers to the ability to maintain a task, suppress inappropriate behavior and flexibly adjust behavior according to changing environmental demands [START_REF] Geurts | The paradox of cognitive flexibility in autism[END_REF]. Here we investigate the interplay between emotion and cognition, by studying the cognitive control of social and non-social information in ASD with an fMRI (functional Magnetic Resonance Imaging ) version of the emotional Wisconsin Card Sorting Test (WCST; [START_REF] Henaff | Cortical dynamics of a self driven choice: a MEG study during a card sorting task[END_REF].

Although the processes underlying RRB are not well understood, a potential explanation is cognitive inflexibility, e.g., a reduced ability to switch between mental processes in order to generate appropriate behavioral responses. Cognitive (in)flexibility is a component of Latinus -5 executive functioning, that has been a particularly active topic of investigation in ASD (Elisabeth L. [START_REF] Hill | Executive dysfunction in autism☆[END_REF][START_REF] Ozonoff | Executive function deficits in highfunctioning autistic individuals: relationship to theory of mind[END_REF][START_REF] Rumsey | Conceptual problem-solving in highly verbal, nonretarded autistic men[END_REF][START_REF] Russell | Two intact executive capacities in children with autism: implications for the core executive dysfunctions in the disorder[END_REF] . Individuals with ASD generally experience difficulties in cognitive flexibility [START_REF] Ozonoff | Brief report: specific executive function profiles in three neurodevelopmental disorders[END_REF]. Yet, laboratory studies of cognitive flexibility in ASD have provided conflicting results at odds with day-to-day behavior [START_REF] Geurts | The paradox of cognitive flexibility in autism[END_REF][START_REF] Lopez | Examining the relationship between executive functions and restricted, repetitive symptoms of Autistic Disorder[END_REF][START_REF] Van Eylen | Cognitive flexibility in autism spectrum disorder: Explaining the inconsistencies?[END_REF]. Inconsistencies have repeatedly been described using a range of cognitive flexibility tasks with studies reporting either deficient [START_REF] Lopez | Examining the relationship between executive functions and restricted, repetitive symptoms of Autistic Disorder[END_REF][START_REF] Pellicano | Multiple cognitive capabilities/deficits in children with an autism spectrum disorder: "weak" central coherence and its relationship to theory of mind and executive control[END_REF] or intact performance (E. L. [START_REF] Hill | Executive processes in Asperger syndrome: patterns of performance in a multiple case series[END_REF][START_REF] Minshew | Neuropsychological functioning in nonmentally retarded autistic individuals[END_REF] in ASD.

Cognitive flexibility refers to the ability to switch between different task demands, and requires monitoring the environment to realize that an ongoing rule is no longer valid, inhibiting previous responses, finding and shifting toward a new rule, and finally maintaining the new ongoing rule. The Wisconsin Card Sorting Test (WCST; [START_REF] Grant | A behavioral analysis of degree of reinforcement and ease of shifting to new responses in a Weigl-type card-sorting problem[END_REF]) is a neuropsychological task-shifting test used test to assess cognitive flexibility; it provides reliable behavioral indices of these successive processing steps. This task involves the implementation of cognitive flexibility to unexpected changes, which typically challenges ASD and causes significant daily difficulties (de Vries [START_REF] De Vries | Cognitive flexibility in ASD; task switching with emotional faces[END_REF][START_REF] Yerys | Set-shifting in children with autism spectrum disorders: reversal shifting deficits on the Intradimensional/Extradimensional Shift Test correlate with repetitive behaviors[END_REF].

The WCST is the neuropsychological test of flexibility which presents the highest discriminative power between controls and ASD [START_REF] Geurts | The paradox of cognitive flexibility in autism[END_REF], although modified version of the WCST making the change more explicit suppresses group differences [START_REF] Van Eylen | Cognitive flexibility in autism spectrum disorder: Explaining the inconsistencies?[END_REF]. Briefly, participants have to switch attention between relevant dimensions of a picture, by finding the correct sorting criterion that changes at random, by a trial-anderror approach with the help of feedback. Succeeding at the WCST rests on abilities in multiple cognitive domains: learning, memory, perception, attention and executive control.

Different subcomponents of the WCST involve, in healthy participants, a distributed neural Latinus -6 network including bilateral prefrontal cortex (PFC), both dorsolateral (dlPFC) and ventrolateral (vlPFC), posterior superior frontal sulcus (SFS), inferior parietal sulci (IPS), anterior cingulate cortex (ACC), temporo-parietal association cortex, and primary and secondary visual cortices as well as a range of subcortical structures such as basal ganglia, and cerebellum (e.g., [START_REF] Buchsbaum | Meta-analysis of neuroimaging studies of the Wisconsin card-sorting task and component processes[END_REF] for review; [START_REF] Konishi | Contribution of working memory to transient activation in human inferior prefrontal cortex during performance of the Wisconsin Card Sorting Test[END_REF][START_REF] Monchi | Wisconsin Card Sorting revisited: distinct neural circuits participating in different stages of the task identified by event-related functional magnetic resonance imaging[END_REF]. The parietal cortex is involved in the prioritization of behaviorally relevant attributes, both spatial and non-spatial, among multi-attributes representations [START_REF] Egner | Neural integration of top-down spatial and feature-based information in visual search[END_REF][START_REF] Ptak | The frontoparietal attention network of the human brain: action, saliency, and a priority map of the environment[END_REF][START_REF] Wager | Neuroimaging studies of shifting attention: a meta-analysis[END_REF], through the updating of "priority maps" [START_REF] Ptak | The frontoparietal attention network of the human brain: action, saliency, and a priority map of the environment[END_REF], that are topographically organized representations of the environment which encode feature-based expectancies [START_REF] Egner | Neural integration of top-down spatial and feature-based information in visual search[END_REF]. The PFC, and in particular the vlPFC [START_REF] Wager | Toward a taxonomy of attention shifting: individual differences in fMRI during multiple shift types[END_REF], has an important role in cognitive control; it is involved in representing the rule underlying a task that allow guiding the selection of appropriate behavior [START_REF] Miller | An integrative theory of prefrontal cortex function[END_REF][START_REF] Wager | Neuroimaging studies of shifting attention: a meta-analysis[END_REF].

The behavioral performance of individuals with ASD on the WSCT has generally been reported as impaired, with more perseverative errors and fewer categories completed than matched controls (CTRL) [START_REF] Ozonoff | Brief report: specific executive function profiles in three neurodevelopmental disorders[END_REF][START_REF] Tsuchiya | Computerized version of the Wisconsin card sorting test in children with high-functioning autistic disorder or attentiondeficit/hyperactivity disorder[END_REF][START_REF] Yasuda | Cognitive inflexibility in Japanese adolescents and adults with autism spectrum disorders[END_REF], although some studies report intact performance on some parameters [START_REF] Kaland | Brief report: cognitive flexibility and focused attention in children and adolescents with Asperger syndrome or high-functioning autism as measured on the computerized version of the Wisconsin Card Sorting Test[END_REF][START_REF] Liss | Executive functioning in high-functioning children with autism[END_REF][START_REF] Minshew | Neuropsychological functioning in nonmentally retarded autistic individuals[END_REF]. These discrepancies have been attributed to participants characteristics and/or task explicitness [START_REF] Van Eylen | Cognitive flexibility in autism spectrum disorder: Explaining the inconsistencies?[END_REF]. A recent meta-analysis including thirty-one WCST studies in children or adult participants with ASD confirmed poorer performance for four measures: number of categories completed, perseveration, failure-to-maintain-set and non-perseverative errors [START_REF] Landry | A Meta-analysis of the Wisconsin Card Sort Task in Autism[END_REF]. The neural substrates of cognitive flexibility in ASD have rarely been studied [START_REF] Schmitz | Neural correlates of executive function in autistic spectrum disorders[END_REF][START_REF] Shafritz | The neural circuitry mediating shifts in behavioral response and cognitive set in autism[END_REF]Yeung, Han, Latinus -7 Sze, & Chan, 2016), and yielded contradictory findings. Schmitz and collaborators (2006) reported increased activity in bilateral IPS in participants with ASD when comparing switch to repeat trials, while Shafritz and collaborators (2008) reported a larger activity for controls than participants with ASD in the IPS, among other regions, for both target-maintain and target-shift trials.

Marked abnormalities in affective behaviors constitute a prominent feature of ASD, including limited sharing of affect and difficulties in the perception and recognition of emotional expressions [START_REF] Hobson | What is autism?[END_REF]. Accordingly, brain functions involved in the processing of social information have been found altered in ASD [START_REF] Batty | Early processing of emotional faces in children with autism: An event-related potential study[END_REF][START_REF] Guillon | Both dog and human faces are explored abnormally by young children with autism spectrum disorders[END_REF][START_REF] Kaiser | Disrupted action perception in autism: behavioral evidence, neuroendophenotypes, and diagnostic utility[END_REF][START_REF] Nomi | Face processing in autism spectrum disorders: From brain regions to brain networks[END_REF][START_REF] Sperdin | Aberrant Development of Speech Processing in Young Children with Autism: New Insights from Neuroimaging Biomarkers[END_REF]. Accurate processing of socio-emotional stimuli, which are complex, multisensory and rapidly changing, requires fast tracking of salient features and rapid adaption to subtle changes. They typically challenge the impaired skills of individuals with ASD and questions remain as to whether socio-emotional impairments in ASD are specific to emotional information processing or if they are rooted in a more general cognitive dysfunction.

Nevertheless, few studies have addressed the interactive effects of cognitive and socioemotional deficits in ASD (e.g., [START_REF] Dichter | Social stimuli interfere with cognitive control in autism[END_REF][START_REF] Dichter | Autism is characterized by dorsal anterior cingulate hyperactivation during social target detection[END_REF][START_REF] Dicriscio | Brief Report: Cognitive Control of Social and Nonsocial Visual Attention in Autism[END_REF][START_REF] Gaigg | The Interplay between Emotion and Cognition in Autism Spectrum Disorder: Implications for Developmental Theory[END_REF][START_REF] Shafritz | Neural systems mediating decision-making and response inhibition for social and nonsocial stimuli in autism[END_REF]. Emotional stimuli tend to have ''priority processing'' as they have been found to evoke earlier and stronger responses in limbic areas, in visual recognition areas [START_REF] Batty | Early neurophysiological effects in the explicit and implicit processing of facial emotions[END_REF][START_REF] Vuilleumier | Distributed and interactive brain mechanisms during emotion face perception: evidence from functional neuroimaging[END_REF], as well as in subcortical structures associated with gating attention and eye movements [START_REF] Vuilleumier | Neural response to emotional faces with and without awareness: event-related fMRI in a parietal patient with visual extinction and spatial neglect[END_REF]. While in typical individuals, attentional blink is partly overcome when the target stimuli are emotionally charged, this emotional modulation is reduced in ASD (e.g., [START_REF] Corden | Emotional modulation of perception in Asperger's syndrome[END_REF][START_REF] Gaigg | Brief report: Attenuated emotional suppression of the attentional blink in Autism Spectrum Disorder: another non-social abnormality?[END_REF]. In the same Latinus -8 line, while typically developing children showed a higher precision in detecting faces than butterflies in a social visual search task, this was not observed in ASD [START_REF] Kovarski | Faster eye movements in children with autism spectrum disorder[END_REF]. In fMRI, social, but not non-social, stimulation were shown to induce a decrease of activity in a network (including bilateral IPS, dlPFC, ACC and right insula) mediating inhibition interference from irrelevant visual information in ASD [START_REF] Dichter | Social stimuli interfere with cognitive control in autism[END_REF]. According to these findings, the influence of emotional processing on cognitive functions could be reduced in ASD.

The aim of the current study was to explore the interplay between socio-emotional information processing and cognitive flexibility in autism. To this aim we used a computerized version of a modified WCST: the emotional WCST [START_REF] Henaff | Cortical dynamics of a self driven choice: a MEG study during a card sorting task[END_REF], which is a highly sensitive indicator of mental flexibility and set maintenance applied to socioemotional information. Although our work was mainly exploratory, under the hypothesis of a reduced influence of emotional processing on cognitive functions in ASD, at the behavioral level, we expected an interaction between sorting criteria and group on perseverative errors and failure-to-maintain set. In the fMRI analysis, we analyzed brain activity involved in different task-shifting steps as a function of sorting criteria; we expected an interaction between group, sorting criteria and task-shifting step.

Methods

Participants

Twelve participants with a diagnosis of Autism Spectrum Disorders partook in the experiment (1 female; mean age ± standard deviation (std) = 29.25 years±7.21; mean Intellectual Quotient=117.42±22.59; ADOS score=10.08±(std)4.25; see supplementary material). They were recruited among patients attending units specialized in autism diagnosis and evaluation (Centre de Ressource Autisme) or were referred by Psychiatrists all over France. Adults with Latinus -9 ASD were matched with eleven healthy participants (1 female, 29.36 years±7.15; recruited through an e-mail list and flyers at the University of Lyon), with no history of neurological and/or psychiatric disorders. All participants had normal or corrected-to-normal vision. The study was approved by the local ethics committee (CPP n°2006-20). All subjects gave written informed consent in accordance with the Declaration of Helsinki.

Stimuli

Face stimuli were chosen from the NimStim Face Stimulus Set [START_REF] Tottenham | The NimStim set of facial expressions: judgments from untrained research participants[END_REF] http://www.macbrain.org/resources.htm). Stimuli were surrounded by a colored frame (4 colors) and represented faces of four different individuals (2 males), displaying four different emotions (anger, happiness, fear, disgust). Stimuli were chosen to allow an easy identification of emotions and identities. Basic emotions were presented to ensure that known emotion recognition difficulties in ASD would not influence the findings (de Vries [START_REF] De Vries | Cognitive flexibility in ASD; task switching with emotional faces[END_REF].

Experimental design and procedure

Participants, lying in a supine position in the scanner, viewed the stimuli, rear-projected on a screen at the back of the scanner, through a mirror attached to the antenna. A modified version of the emotional WCST was presented to participants using the Presentation Software.

Participants were presented with 5 cards (Figure 1A): 1 central card and 4 surrounding cards.

They were asked to match the central card with one of the four surrounding cards according to one of three criteria: frame color, facial identity or expression. The experiment lasted 20.8min; participants performed as many trials as possible during the allocated time. Before the start of the experiment, participants were informed of the three sorting rules, and that they will change at random; they also knew that the first sorting rule was a frame color matching.

The rule subsequently changed randomly, without warning, after 3-to-8 correct trials. At each trial (Figure 1), the current sorting criterion was only met by one card.

Latinus -10 fMRI acquisition

Magnetic resonance data were acquired on a 1.5T Siemens Magnetom (Siemens AG, Erlangen, Germany) scanner at the CERMEP (Imagerie du Vivant, Bron, F-69677, France) imaging facilities. Structural image acquisition consisted in a 3D anatomical T1-weighted sequence (TR=1970ms; TE=3.9ms; inversion time=1100ms; FOV=256mm; matrix size: 256 2 voxel size: 1mm 3 ). Functional images were collected using a T2*-weighted gradient-echo planar imaging sequence (TR=2.5s; TE=50ms; flip angle=90°; FOV=220mm; Matrix=64x64; in-plane resolution=3.4x3.4mm 2 ). The acquisition volume consisted of 29 interleaved axial slices with a 4mm slice thickness (no interslice gap); 500 volumes were acquired per participant.

Data analysis

Behavioural data: WCST scores

Classical indexes (e.g., perseverative errors, maintenance trials etc.) scored in a WCST were measured as percentage relative to the total number of trials (Jarvinen-Pasley & Heaton, 2007; see supplementary material). In addition, we propose a new score for evaluating the WCST, termed the "bias error". The 'bias error' is the percentage of rule changes that required more than two trials (including the first negative feedback) to correctly identify the next rule. Indeed, while two incorrect responses following a rule change may be expected by chance, more than two errors may reflect a bias toward more automatic and comfortable responses. Therefore. , the bias error may reflect the willingness to avoid the realization of a specific criteria.

A mixed ANOVA with group as a between-subject factor and sorting criteria as withinsubject factor was used to analyze bias error. [START_REF] Henaff | Cortical dynamics of a self driven choice: a MEG study during a card sorting task[END_REF]. To better understand brain activity related to several aspects of taskshifting and their interaction with sorting criteria, six types of feedback events were modelled (Figure 1B). Change events, i.e., negative feedbacks indicating a need to change rule, were modelled according to the preceding rule (the rule that was correct in the previous trial):

Latinus

change-color, change-identity, and change-emotion. They reflect the processes involved in error monitoring, and the need to shift to the new rule and inhibit the preceding rule. Switch events, i.e., the first positive feedback following a change of rule, were modelled according to the current ongoing rule: switch-color, switch-identity, and switch-emotion. Switch events informed participants that they have found the correct rule, and have to start maintaining the new rule. Maintenance events, which reflects processes involved in maintaining task-sets, regroup all other positive feedbacks; they were also modelled according to the ongoing rule (maintenance-color, maintenance-identity, and maintenance-emotion). All other feedback events (e.g., failures) were modelled in a ninth regressor of no interest. Therefore, the design matrix included 10 regressors (3 event types x 3 sorting criteria, plus one regressor of no interest), which contained finite impulse responses representing the onset of feedback events convolved with a canonical hemodynamic response function. The design matrix also included realignment parameters as nuisance covariates to account for residual motion artefacts. Betas estimates were calculated for each of the 10 regressors. These betas images were then used to create three contrast images per sorting criteria in order to identify regions involved in Latinus -12 different task-shifting steps per sorting criteria: 1) change vs. maintenance events; 2) change vs. switch events; 3) switch vs. maintenance events.

These contrast images were taken into a three-way mixed ANOVA (group x task-shifting step

x sorting criteria), performed with GLMFlex (Version June 1st, 2014; http://mrtools.mgh.harvard.edu/index.php/GLM_Flex_Fast2). Results are reported at an FWE-corrected cluster (FWEc) threshold with a cluster-defining threshold of p<0.001.

Results

Behavioural data: WCST scores

The total number of trials performed by the participants varied between groups (T(21)=-3.05; p=0.006) with participants with ASD completing less trials (312± (standard error of mean, s.e.m.) 10.34) than control participants (356.9±9.99). However there was no difference in the global percentage of errors between groups (T(21)=0.99; p=0.33).

The percentage of rule changes occurring during the course of the experiment is indicative of overall success rate, with a higher number of changes reflecting a greater amount of category completed and thus overall better performance. Participants with ASD had a significantly smaller percentage of rule changes than control participants (T(21)=-2.12; p=0.046). Yet, participants with ASD were presented with the same proportion of changes in each possible direction (N=6: color-emotion, color-identity, identity-color, identity-emotion, emotion-color, emotion-identity) than CTRL participants (abs(T(21))<1.8; all p>0.085).

Percentages of PE (Figure 2A), non-perseverative errors and maintenance trials were not modulated by groups and showed no rule-by-group interaction. A 2-way mixed ANOVA (group x sorting criteria) on the percentage of failures-to-maintain-set (Figure 2C) revealed a main effect of group (F(1,21)=5.76; p = 0.026), showing that participants with ASD failed more than control participants. A main effect of sorting criteria (F(1.31,27.43)=9.32; p=0.003)

Latinus -13 revealed that participants failed more in the maintenance of the emotion rule than in the identity (p = 0.005) and color (p = 0.0004) rules. Noteworthy there was no group by sorting criteria interaction (F(1.31,27.43)=2.68; p=0.1).

A 2-way mixed ANOVA (group x to-be-found sorting criteria) on "bias error" (Figure 2B) revealed a main effect of sorting criteria (F(1.58,33.14)=8.56; p=0.002) and a significant interaction between group and sorting criteria (F(1.58,33.14)=4.157; p=0.033). Student Ttests between groups ran on each sorting criteria revealed that participants with ASD committed more errors than control participants when they had to find the emotion rule (p=0.024), while there was no significant group differences for the color or identity criteria.

Notably there was no group difference for the number of maintenance errors during the emotion matching rule.

fMRI data

At the chosen statistical threshold, there was neither a main effect of group, nor a sorting criteria by group interaction, and no three way interaction (e.g., task-shifting step by sorting criteria by group). As per our interest, below we report the main effects of task-shifting step and the task-shifting step by group interaction (other significant effects are presented in supplementary material).

(

1) Main effect of Task-shifting step

A main effect of Task-shifting step was observed (cluster-defining threshold:

F(2,42)=8.18, p=0.001; FWEc=42) in nine clusters. Overall task-shifting step modulated a large bilateral network overlapping both ventral and dorsal fronto-parietal networks (FPN), visual cortices and a range of subcortical structures (see Figure 3A; Table 1). More precisely, the first cluster overlapped bilateral insulae, putamen, posterior cingulate gyrus (pCG), bilateral superior and inferior parietal lobule (SPL, IPL), including IPS and extending to the Latinus -14 supramarginal and angular gyri, middle frontal gyrus (MFG) of the right hemisphere and left hippocampus. A second cluster overlapped the cerebellum, extending to bilateral inferior occipital gyrus and left fusiform gyrus. Task-shifting step also modulated activity in posterior and anterior medial superior frontal gyrus (SFG), the calcarine fissure extending to the lingual gyrus of both hemispheres, superior occipital gyrus, bilateral inferior frontal sulci (IFS), and left MFG.

To better interpret main effects of task-shifting step, statistical maps were evaluated for each task-shifting step independently, that is, we look at the modulation of activity in the above-mentioned clusters for the three contrasts of interest (Figure 3B, C): change vs.

maintenance events, change vs. switch events, and switch vs. maintenance events.

Change vs. maintenance events

A larger activity to change events was observed in the medial SFG, bilateral anterior insulae, right MFG, bilateral IFS, middle-to-posterior Cingulate Gyrus (pCG), calcarine fissure extending to bilateral lingual gyri and precuneus, and around the IPS, extending to SPL and IPL(Figure 3B; blue).

A larger activity to maintenance than change events was observed in bilateral rolandic operculum, left hippocampus and in the medial anterior SFG.

Change vs. switch events

Change events yielded significantly different activity than switch events in medial SFG, and bilaterally in posterior IFS, anterior insulae, and in the medial occipital cortex overlapping the calcarine fissure and extending to the lingual gyrus and precuneus (Figure 3B; red).

A larger activity to switch than change events (Figure 3C; cyan) was observed in bilateral rolandic operculum, left hippocampus, medial anterior SFG; regions that were also Latinus -15 more activated by maintenance than change events. In addition, a larger activity to switch events was observed in bilateral putamen extending to posterior insulae, and bilateral SPL.

Switch vs. maintenance events

Among the regions showing a modulation of their activity by task-shifting step, none showed a larger activity to maintenance than switch events.

A larger activity to switch than maintenance events (Figure 3C; yellow) was observed in the cerebellum cluster, bilateral parietal cortex including IPS, SPL and IPL, right MFG, bilateral putamen and pCG.

(2) Group by task-shifting step interaction

Activity in the IPL of both hemispheres was further characterized by a group by task-shifting step interaction (cluster-defining threshold: F(2,42)=8.18, p=0.001; FWEc = 35; Figure 4A).

In the IPS, there was no group difference for the change vs. maintenance contrast. However, in the ASD group, the IPS was strongly activated by switch events while it was mostly activated by change events in the control group.

In addition, interaction between task-shifting step and group were found in the left inferior temporal gyrus, bilateral posterior superior frontal sulcus (SFS), right inferior frontal gyrus, and right anteriorMFG (Figure 4A; Table 2). In all clusters, this interaction was driven by an atypical response to switch events in the ASD group: switch events yielded larger activity than change and maintenance events, while in the CTRL group a larger activity was observed for change events. In summary, the interaction between group and task-shifting step mainly revealed that CTRL participants tended to process switch events as maintenance events, while ASD participants processed switch events similarly to change events.

Intersubject variability in each cluster is illustrated on Figure 4B using threshold-weighted overlap maps for each task-shifting step collapsed per sorting criteria [START_REF] Seghier | Visualising inter-subject variability in fMRI using threshold-weighted overlap maps[END_REF].

Latinus -16

Overlap map revealed a consistent activation of bilateral IPS and right SFS for switch events relative to maintenance events in the ASD group; consistency reached a maximum value of 0.62 in the right IPS. All ASD participants, but one, presented a significantly (p<.001, uncorrected) larger activation for switch than maintenance events in the IPS, one participant presented a near threshold difference. Therefore, despite relatively small sample sizes, the group by task-shifting step observed in bilateral IPS, in particular, appears to reflect a genuine difference between ASD and control participants.

Discussion

We used an emotional Wisconsin Card Sorting Test [START_REF] Henaff | Cortical dynamics of a self driven choice: a MEG study during a card sorting task[END_REF] in fMRI to explore the interplay between cognitive and emotional dimensions of ASD. Behavioral data highlighted a significant interaction between group and sorting criteria for "bias error", a measure of the unwillingness to switch towards a specific sorting rule, but no group effect or interaction was observed on parameters measuring pure cognitive flexibility (e.g., perseverative errors). Accordingly, at the fMRI level, we found no group differences in the processing of change events relative to other events. However, the processing of switch events yielded a larger activation in bilateral IPS in ASD participants suggesting an atypical processing of the confirming cue.

Behavioral results are only partially consistent with previous studies as we found no group difference for perseverative and non-perseverative errors [START_REF] Landry | A Meta-analysis of the Wisconsin Card Sort Task in Autism[END_REF]. This lack of difference could be attributed to task explicitness [START_REF] Van Eylen | Cognitive flexibility in autism spectrum disorder: Explaining the inconsistencies?[END_REF]: in our study task was relatively explicit as participants were aware of the general principle of the test and of the sorting rules. An interaction between group and sorting criteria was found on the "bias error" which reflects a bias away from the realization of a specific task. Participants with autism had Latinus -17 a larger "bias error" than control participants but only when switching to the emotion sorting rule, which was equally maintained by both groups, highlighting no specific difficulties in performing socio-emotional matching. These results differ from those of de Vries and Geurts (2012), who reported a trend reflecting difficulty in disengaging from emotional faces during task switching in ASD. Nonetheless, taken together these findings highlight difficulties in the engagement/disengagement linked to socio-emotional stimulation. Our exploratory findings indicate that inflexible behaviors in ASD are mostly characterized by the avoidance of switching toward processing of emotional information. This is of great importance for understanding the functional role of RRBs, as it suggests that patients with ASD may be displaying routines or repetitive behaviors not because of a 'true' lack of cognitive flexibility, but rather to avoid some specific (emotional) situations [START_REF] Geurts | The paradox of cognitive flexibility in autism[END_REF]. This observation, if further confirmed, would suggest to tightly associate socio-emotional and cognitive rehabilitation programs.

At the fMRI level, we found modulations of brain activity by task-shifting step, and sorting criteria as well as an interaction between these two factors. Therefore, these data provide evidence that the processing of social information interact with cognitive task, as previously reported (e.g., [START_REF] Corden | Emotional modulation of perception in Asperger's syndrome[END_REF][START_REF] Gaigg | Brief report: Attenuated emotional suppression of the attentional blink in Autism Spectrum Disorder: another non-social abnormality?[END_REF]. However, and contrarily to behavioral observations there was neither further interaction with group, nor any sorting criteria by group interaction. Despite a small sample size, strong interactions were observed between task-shifting step and group, highlighting different cognitive strategies. In both groups, change events induced a larger activity than maintenance or switch events in a large bilateral neural network including both the dorsal and ventral FPN [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF], the medial SFG and visual cortices. On the contrary, ASD participants presented a larger activity to switch than maintenance events in bilateral posterior IPS, and right posterior SFS, consistent with Schmitz and collaborators (2006).

Latinus -18

Change events are the only negative feedback events as such they act not only as an error feedback, but also as a start-cue indicating the need to find a new rule and start a new task-set.

It makes sense to find activity related to processing a negative feedback in both ventral and dorsal FPN [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF][START_REF] Dosenbach | A dual-networks architecture of top-down control[END_REF][START_REF] Dosenbach | Distinct brain networks for adaptive and stable task control in humans[END_REF]. Within the dorsal FPN, bilateral IPS and posterior SFS show cue-driven activity when participants prepare to shift their attention to a specific feature or attribute, suggesting that dorsal FPN also mediates non-spatial orienting of attention [START_REF] Egner | Neural integration of top-down spatial and feature-based information in visual search[END_REF][START_REF] Ptak | The frontoparietal attention network of the human brain: action, saliency, and a priority map of the environment[END_REF][START_REF] Wager | Neuroimaging studies of shifting attention: a meta-analysis[END_REF]. Task-set instantiation corresponds to the prioritization of new behaviorally-relevant attributes among multi-attributes representations [START_REF] Wager | Neuroimaging studies of shifting attention: a meta-analysis[END_REF], and may occur through the updating of "priority maps" [START_REF] Ptak | The frontoparietal attention network of the human brain: action, saliency, and a priority map of the environment[END_REF].

Priority maps are topographically organized representations of the environment and encode feature-based expectancies, which confer a competitive processing advantage for the selection of task-related features [START_REF] Egner | Neural integration of top-down spatial and feature-based information in visual search[END_REF].

For control participants, the IPS was only activated in the reception of a negative feedback (e.g., change events), suggesting that change events are the only cues indicating the need to start a new task-set, and to prioritize new attributes (e.g., update priority maps). When switch events occurs, control participants have performed all tasks needed for the switch, and are set in a stable processing stage. However, IPS was consistently activated (across ASD subjects) by switch events suggesting that they also act as start-cue in our sample of participants with ASD. Therefore, priority maps may be stabilized only after autistic participants received a confirmatory positive feedback. A larger IPS and SFS activation in people with ASD to switch events could reflect the need to adapt cognitive strategies until certainty regarding the task to-be-performed is achieved. Accordingly, while control participants flexibly modulate cortical activity according to level of certainty, autistic participants cannot do so (Thillay et Latinus -19 al., 2016). This observation suggests that people with ASD stabilized their priority maps only when reaching a high level of certainty.

We did not find any interaction between group, sorting criteria and cognitive flexibility at the cerebral level. Note that the observed behavioral effects could not be tested as bias error corresponds to an insufficient number of trials for an fMRI analysis. Nonetheless, fMRI and behavioral data are consistent in that they show 1) no real deficit in cognitive flexibility per se, and 2) no interaction on traditional measures of cognitive flexibility and socio-emotional processing. fMRI data highlighted that a higher level of certainty was needed before switchrelated brain activity decreases in ASD, while behavioral findings suggest that this high need for certainty might yield different behavioral outcomes depending on the task to-beperformed. Priority maps incorporate prior knowledge, acquired through experience, regarding the information relevant to the task to-be-performed [START_REF] Fair | Development of distinct control networks through segregation and integration[END_REF][START_REF] Zelinsky | The what, where, and why of priority maps and their interactions with visual working memory[END_REF]. We hypothesize that the observed behavioral outcomes of the need for certainty is linked to prior knowledge of the task to-be-performed. For control participants, the existence of prior knowledge for the realization of the sorting tasks facilitates the selection of relevant information leading to smaller bias errors. A larger bias error in the emotion sorting task for the ASD group is expected to reflect the weakness of prior knowledge or of top-down influence for the realization of that particular task [START_REF] Gomot | A challenging, unpredictable world for people with autism spectrum disorder[END_REF][START_REF] Pellicano | When the world becomes 'too real': a Bayesian explanation of autistic perception[END_REF][START_REF] Pellicano | Abnormal adaptive face-coding mechanisms in children with autism spectrum disorder[END_REF]. Moreover, this allows refining these theories by showing that these difficulties are particularly evident for socio-emotional information.

The need for a high-level of certainty before setting in a stable task-set, combined with the weakness of prior knowledge in socio-emotional tasks may produce a greater avoidance of socio-emotional rules leading to a larger bias error in the social sorting tasks. It remains to be determined whether the prior knowledge-related difficulties drives the need for certainty or Latinus -20 whether the high need for certainty, which is rarely matched in socio-emotional contexts, prevents the generation of priors.

Conclusions

Using an emotional WCST with fMRI we showed that participants with ASD present a bias toward avoiding socio-emotional sorting tasks, and present an increased activity in IPS for switch events that may reflect a continuous updating of priority maps until a high level of certainty is reached. This need for certainty would be more detrimental for the realization of cognitive tasks, which rely on emotion-related prior knowledge.

An unusual processing of confirmatory events combined with atypical prior knowledge of socio-emotional information would thus constitute a hallmark of brain functioning in ASD.

These findings provide new insights for the understanding of ASD and suggest that these brain dysfunctions tightly interact and should be considered conjointly in future research aiming at better understanding the interplay between the two clinical dimensions characteristic of ASD and their underlying mechanisms. voxel of maximum consistency in each subject (i.e., each bar). Note that bilateral IPS and right SFS showed a high consistency of activation in our sample of ASD participants.

Figure legends

Latinus -28

Table 1: Main effects of task-shifting step. For the large cluster only one peak per brain regions is Latinus -30

Figure 1 :

 1 Figure 1: Experimental design. A. Trial overview. A trial was designed as follows: the five

Figure 2 :

 2 Figure 2: Behavioral results in the emotional WCST. A. Perseverative errors per sorting

Figure 3 :

 3 Figure 3: Main effect of task-shifting step. A. Cluster-wise thresholded images of the main

Figure 4 :

 4 Figure 4: Task-shifting step by group interaction. A. Cluster-wise thresholded (FWEc)

-11 fMRI data: Image preprocessing and analysis

	Image preprocessing and analysis were performed with SPM12b (Statistical Parametric
	Mapping,	Wellcome	Department	of	Cognitive	Neurology,	London,
	http://www.fil.ion.ucl.ac.uk/spm), following classical guidelines (see supplementary
	material). Functional data of the experimental block were analyzed in a two-level random-
	effects design. At the first level, onsets were defined as the presentation of the feedback

Table 2 :

 2 Group by task-shifting step interaction. Orientation: R: right hemisphere; L: left hemisphere; M: medial; P: posterior; A: anterior. F-values greater than 18.89 corresponds to a FWE-corrected voxel threshold.

			Cluster
	Region	Orientation		T	Z	x	y	z
			size
	Inferior Parietal Sulcus	R	279	19.02	4.7	27	-67	50
		L	255	13.32	3.99	-24	-59	48
	Superior Frontal sulcus	R	58	10.93	3.61	21	-4	58
		L	35	15.09	4.23	-21	11	66
	Inferior Temporal Gyrus	L	58	21.8	4.98	-45	-49	-10
	Middle Frontal sulcus	A, M	82	16.37	4.4	18	50	6
	Inferior Frontal Gyrus	R	67	10.06	3.46	45	27	16

reported. SFG: superior frontal gyrus; SMA: supplementary motor area; Orientation: R: right

We are thankful to Alix Thillay for helpful comments on prior version of this manuscript. Development of the MacBrain Face Stimulus Set was overseen by Nim Tottenham and supported by the John D. and Catherine T. MacArthur Foundation Research Network on Early Experience and Brain Development. Please contact Nim Tottenham at tott0006for more information concerning the stimulus set.

This research was supported by grants from the Agence Nationale de la Recherche (ANR-12-JSH2-0001), the "Fondation Orange" and by the Ministère des affaires sociales et de la santé, CHRU Bretonneau, Tours (PHRR05-FBB EPCA).

Lay Summary

List of abbreviations

Ethics approval and consent to participate

The study was approved by the Ethics Committee of the University Hospital of Tours; all participants provided written informed consent. Adults with autism included in the study were all legally adults, had no legal guardianship; they were thus allowed to approve research and/or medical programs that concern them.

Consent for publication

Stimuli displayed in Figure 1 were extracted from the NimStim database (http://www.macbrain.org/resources.htm) and correspond to models that provided consent for publications of their data.

Conflict of Interest

The authors declare no biomedical financial interests or potential conflicts of interest.

Authors' contributions

The study presented here results from teamwork.