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International audience; Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework [1]. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

International audience

International audience; We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs) - one of which associated with the so-called power stroke - and two possible chemical states, i.e. bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model, and (2) to thus account - at the macroscopic scale - for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics, and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight, and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data - taken here for skeletal muscles - and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models.

International audience; Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models however may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models-from the more refined to the more simplified-that are rigorously and systematically related with each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three models families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation.

International audience

Significance We propose a mechanistic description of fusion of a synaptic vesicle with a target membrane executed by a team of zippering SNARE complexes (SNAREpins). In the context of neurotransmitters release, this process naturally decomposes in two steps with rates that depend on the number of SNAREpins N. The first step is synchronized escape from the metastable half-zippered state, which gets exponentially more sluggish as N increases. The second step is fusion of two closely tethered membranes, which is accelerated exponentially by an increase of N. The tradeoff between these two antagonist trends results in a sharply optimal number of SNAREpins N=3−6, which ensures fusion at the physiological submillisecond timescale., SNARE proteins zipper to form complexes (SNAREpins) that power vesicle fusion with target membranes in a variety of biological processes. A single SNAREpin takes about 1 s to fuse two bilayers, yet a handful can ensure release of neurotransmitters from synaptic vesicles much faster: in a 10th of a millisecond. We propose that, similar to the case of muscle myosins, the ultrafast fusion results from cooperative action of many SNAREpins. The coupling originates from mechanical interactions induced by confining scaffolds. Each SNAREpin is known to have enough energy to overcome the fusion barrier of 25–35 kBT; however, the fusion barrier only becomes relevant when the SNAREpins are nearly completely zippered, and from this state, each SNAREpin can deliver only a small fraction of this energy as mechanical work. Therefore, they have to act cooperatively, and we show that at least three of them are needed to ensure fusion in less than a millisecond. However, to reach the prefusion state collectively, starting from the experimentally observed half-zippered metastable state, the SNAREpins have to mechanically synchronize, which takes more time as the number of SNAREpins increases. Incorporating this somewhat counterintuitive idea in a simple coarse-grained model results in the prediction that there should be an optimum number of SNAREpins for submillisecond fusion: three to six over a wide range of parameters. Interestingly, in situ cryoelectron microscope tomography has very recently shown that exactly six SNAREpins participate in the fusion of each synaptic vesicle. This number is in the range predicted by our theory.

International audience; Water diffusion in the vicinity of hydroxyapatite (HAP) crystals is a key issue to describe biomineralization process. In this study, a configuration of parallel HAP platelets mimicking bone nanopores is proposed to characterize the nanoscopic transport properties of water molecules at HAP-water surface and interfaces using various potential models such as combination of the Core-Shell (CS) model, Lennard-Jones (LJ) potentials with SPC or SPC/E water models. When comparing all these potentials models, it appears that the core-shell potential for HAP together with the SPC/E water model more accurately predicts the diffusion properties of water near HAP surface. Moreover, we have been able to put into relief the possibility of observing hydroxyl (OH-) ion dissociation that modifies the water structure near the HAP surface.

International audience; In this paper we report, clarify and broaden various recent efforts to complement the chemistry-centered models of force generation in (skeletal) muscles by mechanics-centered models. The physical mechanisms of interest can be grouped into two classes: passive and active. The main passive effect is the fast force recovery which does not require the detachment of myosin cross-bridges from actin filaments and can operate without a specialized supply of metabolic fuel (ATP). In mechanical terms, it can be viewed as a collective folding-unfolding phenomenon in the system of interacting bi-stable units and modeled by near equilibrium Langevin dynamics. The parallel active force generation mechanism operates at slow time scales, requires detachment and is crucially dependent on ATP hydrolysis. The underlying mechanical processes take place far from equilibrium and are represented by stochastic models with broken time reversal symmetry implying non-potentiality, correlated noise or multiple reservoirs. The modeling approaches reviewed in this paper deal with both active and passive processes and support from the mechanical perspective the biological point of view that phenomena involved in slow (active) and fast (passive) force generation are tightly intertwined. They reveal, however, that biochemical studies in solution, macroscopic physiological measurements and structural analysis do not provide by themselves all the necessary insights into the functioning of the organized contractile system. In particular, the reviewed body of work emphasizes the important role of long-range interactions and criticality in securing the targeted mechanical response in the physiological regime of isometric contractions. The importance of the purely mechanical micro-scale modeling is accentuated at the end of the paper where we address the puzzling issue of the stability of muscle response on the so called “ descending limb” of the isometric tetanus.

Submitted to the Journal of the Mechanics and Physics of Solids (JMPS); International audience; We study a simple micro-mechanical device that does not lose its snap-through behavior in an environment dominated by fluctuations. The main idea is to have several degrees of freedom that can cooperatively resist the de-synchronizing effect of random perturbations. As an inspiration we use the power stroke machinery of skeletal muscles, which ensures at sub-micron scales and finite temperatures a spectacularly swift recovery of an abruptly applied slack. In addition to hypersensitive response at finite temperatures, our prototypical Brownian snap spring also exhibits criticality at special values of parameters which is another potentially interesting property for micro-scale engineering applications.

New insights into the dynamical properties of water in hydroxyapatite (HAP) nanopores, a model sys-\ud 8 tems for the fluid flow within nano-size spaces inside the collagen-apatite structure of bone, were obtained from\ud 9 molecular dynamics simulations of liquid water confined between two parallel HAP surfaces of different sizes\ud 10 (20 Å ≤ H ≤ 240 Å). Calculations were conducted using a core-shell interatomic potential for HAP together with\ud 11 the extended simple point charge model for water. This force field gives an activation energy for water diffusion\ud 12 on the HAP surface that is in excellent agreement with available experimental data. The dynamical properties\ud 13 of water within the HAP nanopores were quantified in terms of the second-order water diffusion tensor. Results\ud 14 indicate that water diffuse anisotropically within the HAP nanopores with the solvent molecules moving parallel\ud 15 to the surface twice as fast as the perpendicular direction. This unusual dynamic behaviour is linked to the strong\ud 16 polarizing effect of calcium ions, and the synergic interactions between the water molecules in the first hydration\ud 17 layer of HAP with the calcium, hydroxyl and phosphate ions, which facilitate the flow of water molecules in the\ud 18 directions parallel to the HAP surface.

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power-stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions., Comment: Physical Review E , American Physical Society (APS), 2016. arXiv admin note: text overlap with arXiv:1510.03011

International audience; Mechanically induced unfolding of passive crosslinkers is a fundamental biological phenomenon encountered across the scales from individual macro-molecules to cytoskeletal actin networks. In this paper we study a conceptual model of athermal load-induced unfolding and use a minimalistic setting allowing one to emphasize the role of long-range interactions while maintaining full analytical transparency. Our model can be viewed as a description of a parallel bundle of N bistable units confined between two shared rigid backbones that are loaded through a series spring. We show that the ground states in this model correspond to synchronized, single phase configurations where all individual units are either folded or unfolded. We then study the fine structure of the wiggly energy landscape along the reaction coordinate linking the two coherent states and describing the optimal mechanism of cooperative unfolding. Quite remarkably, our study shows the fundamental difference in the size and structure of the folding-unfolding energy barriers in the hard (fixed displacements) and soft (fixed forces) loading devices which persists in the continuum limit. We argue that both, the synchronization and the non-equivalence of the mechanical responses in hard and soft devices, have their origin in the dominance of long-range interactions. We then apply our minimal model to skeletal muscles where the power-stroke in acto-myosin crossbridges can be interpreted as passive folding. A quantitative analysis of the muscle model shows that the relative rigidity of myosin backbone provides the long-range interaction mechanism allowing the system to effectively synchronize the power-stroke in individual crossbridges even in the presence of thermal fluctuations. In view of the prototypical nature of the proposed model, our general conclusions pertain to a variety of other biological systems where elastic interactions are mediated by effective backbones.

International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced-dimen\-sional models, in ''0D'' --~typically, to represent a cardiac cavity, or several coupled cavities --~and in ''1D'' --~to model elongated structures such as muscle samples or myocytes. We apply this approach with an earlier-proposed 3D cardiac model designed to capture length-dependence effects in contraction, which we here complement by an additional modeling component devised to represent length-dependent relaxation. We then pre\-sent experimental data produced with rat papillary muscles samples when varying preload and afterload conditions, and we achieve some detailed validations of the 1D model with these data, including for the length-dependence effects that are accurately captured. Finally, when running simulations of the 0D model pre-calibrated with the 1D model parameters, we obtain pressure-volume indicators of the left ventricle in good agreement with some important features of cardiac physiology, including the so-called Frank-Starling mechanism, the End-Systolic Pres\-sure-Volume Relationship (ESPVR), as well as varying elastance properties. This integrated multi-dimensional modeling approach thus sheds new light on the relations between the phenomena observed at different scales and at the local vs. organ levels.

To be published as proceedings in: Functional Imaging and Modeling of the Heart 7th International Conference, FIMH 2013, London, UK, Lecture Notes in Computer Science 7945; International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced- dimensional models, in "0D" - typically, to represent a cardiac cavity, or several coupled cavities - and in "1D" - to model elongated structures such as fibers or myocytes. As illustrations of our approach, we demon- strate model validation based on experiments performed with papillary muscles, and calibration using patient-specific pressure-volume loops.

Passive mechanical response of skeletal muscles at fast time scales is dominated by long range interactions inducing cooperative behavior without breaking the detailed balance. This leads to such unusual "material properties" as negative equilibrium stiffness and different behavior in force and displacement controlled loading conditions. Our fitting of experimental data suggests that "muscle material" is finely tuned to perform close to a critical point which explains large fluctuations observed in muscles close to the stall force., Comment: Accepted for publication in Physical Review Letters

International audience; This work explores experimental procedures for tape-cast proton conducting ceramic fuel cells (PCFC) based on Yttrium-doped Barium Cerate (BCY10). The work is based on several years experience on aqueous tape-casting applied to the shaping of YSZ-based SOFC: however, water-based tape casting of BCY10 appeared to be impracticable for reasons associated with the high basicity of this material that results in rapid hydrolysis when in contact with water. Organic tape casting was therefore developed for BCY10, but only on Electrolyte (BCY10)/Anode (BCY10 + NiO) half cells since up to now no cathode material is available. Planar 20 mm diameter circular half-cells were obtained with the aid of a small load on top of the bi-layer to counterbalance the inevitable warping of the samples. Back-scattered SEM and X-Ray computer-controlled microtomography showed sedimentation of some large grains in the green tapes which are believed to have formed by a mechanism associated with a porosity gradient. The deformation occurring during sintering was modelled taking into account the elastic, thermal, viscoplastic and sintering components of the total deformation. 2D and 3D Finite Element numerical simulations showed that the driving force for deformation is associated with this porosity gradient.

Fibre networks are ubiquitous structures in biological tissues, both at the macroscopic level being the main ingredient in soft tissues and at the microscopic level, as constituents of collagen structures or the cytoskeleton. The goal of this work is to propose a model based on the physical microstructure of fibre networks in order to provide an understanding of the mechanical behaviour of biological fibre networks. The current model starts from fibres sliding with respect to one another and interacting via spring-like cross-bridges. These cross-bridges can attach and detach stochastically with a load-dependent detachment rate. Compared to existing modelling approaches, this work features a dynamic sliding configuration for the interacting fibres and discrete binding sites which permit attachment on localised spaces of the fibre. The detachment of cross-bridges is based on thermal diffusion out of an energy well, following the Kramers rate theory. This theory provides a physical background to the detachment dynamics as well as a natural load dependency in the tilting of the energy landscape by the load force. The model provides two modes by which the depicted system may be driven: an imposed velocity driving, called a hard device and an imposed load driving, called a soft device. The work also provides a way of visualising the behaviour of the model by performing a stochastic simulation. The simulations provided present two algorithms, each tailored to represent the driving of the system, whether in hard or soft device, respecting the causality in each of the driving mode. Simulation results are explored via data visualisation of simulation output. These visualisation serve as an entry point into parametric investigation of the model behaviour and anchor the interpretation of the results into physical systems. In particular, the influence of binding site spacing, one of the key features of the model, is investigated. We also investigate the effects of complex loading paths (transitory, cyclic, etc.) which can be associated to the physiological loadings fibrous tissues.; Les réseaux de fibre sont une structure omniprésente dans les tissus biologiques, aussi bien au niveau macroscopique, où ils sont l'ingrédient principal des tissus mous, qu'au niveau microscopique, en tant que constituants des structures collagèniques ou du cytosquelette. L'objectif de ce travail de thèse est de proposer un modèle basé sur la microstructure physique des réseaux de fibres afin d'obtenir une compréhension du comportement mécanique des réseaux de fibres biologiques. Le modèle est basé sur une description de fibres glissant les unes par rapport aux autres et interagissant via des ponts qui se comportent comme des ressorts. Ces ponts peuvent s'attacher et se détacher de manière stochastique avec un taux de détachement qui dépend de la force subie. Comparé aux modélisations existantes, notre travail met en jeu une configuration en glissement dynamique des fibres, ainsi que des sites d'attachement discrets ne permettant l'attachement qu'à des endroits localisés de la fibre. Le détachement des ponts est basé sur la diffusion thermique hors d'un puit de potentiel suivant la théorie de Kramers. Cette théorie donne un contexte physique à la dynamique du détachement ainsi qu'une dépendance naturelle du détachement au chargement via l'inclinaison du paysage énergétique par la force de chargement. Le modèle donne deux modes de contrôle du système : un contrôle à vitesse imposée, appelé système dur, et un contrôle à force imposée, appelé système mou. Notre travail permet également de visualiser le comportement du système à travers une simulation stochastique. Les simulations offrent deux algorithmes, chacun adapté à la méthode de contrôle du système, en système dur ou mou et respectant la causalité dans chacun des modes. Les résultats de la simulation sont explorés via la visualisation des données sortantes de la simulation, qui servent de support pour l'investigation paramétrique du comportement du modèle et ancrent l'interprétation physique des résultats. En particulier, l'influence de l'espacement des sites d'attachement du système, un point caractéristique du modèle, est examiné. De même, nous explorons l'effet de chargements complexes (transitoires, cycliques, etc.) qui représentent les chargements physiologiques des tissus fibreux.

This PhD thesis deals with the mathematical description of the micro-scale muscle contraction mechanisms with the aim of proposing and integrating our models into a multiscale heart simulation framework.This research effort is made in the context of digital medicine, which proposes to improve the treatment of patients with the use of numerical tools.The first contribution of this thesis is a literature review of the experimental works characterizing the actin-myosin interaction and its regulations to compile information in a useable form for the development of models.This stage is an essential prerequisite to modeling.We then propose a hierarchy of muscle contraction models starting from a previously proposed refined stochastic model, which was only validated for skeletal muscles, and applying successive simplification assumptions.The simplification stages transform the initial stochastic differential equation into a partial differential equation with a model that is part of the Huxley'57 model family.A further simplification then leads to a description governed by a set of ordinary differential equations.The relevance of these models, targeting different time scales, is demonstrated by comparing them with experimental data obtained with cardiac muscles and their range of validity is investigated.To integrate these microscopic descriptions into a heart simulation framework, we extend the models to take into account the force regulation mechanisms that take place in vivo, leading to the derivation of new partial differential equations.Then, we link the microscopic contraction models to the macroscopic organ model.We follow for that an approach based on the thermodynamical principles to deal with the multi-scale nature in time and space of the muscle tissue at the continuous and at the discrete levels.The validity of this simulation framework is demonstrated by showing its ability to reproduce the heart behavior and in particular to capture the essential features of the Frank-Starling effect.; L'objectif de cette thèse est la modélisation mathématique des mécanismes de contraction musculaire à l'échelle microscopique dans le but de proposer et d'intégrer ces modèles dans un environnement de simulation cardiaque multi-échelle.Ce travail est réalisé dans le contexte de la médecine numérique, qui propose d'améliorer le traitement des patients par l'utilisation d'outils numériques.La première contribution de cette thèse est une analyse bibliographique des travaux expérimentaux caractérisant l’interaction actine-myosine et ses régulations afin de compiler les informations sous une forme utilisable pour le développement de modèles.Cette étape est une condition préalable essentielle à la modélisation.Nous proposons ensuite une hiérarchie de modèles de contraction musculaire à partir d'un modèle stochastique raffiné existant, mais validé uniquement pour les muscles squelettiques, en appliquant des hypothèses de simplification successives.Les étapes de simplification transforment l'équation différentielle stochastique initiale en une équation aux dérivées partielles avec une description qui fait partie de la famille de modèles dérivée du modèle Huxley'57.Une simplification supplémentaire conduit ensuite à un modèle décrit par un ensemble d'équations différentielles ordinaires.La pertinence des modèles proposés, qui ciblent différentes échelles de temps, est démontrée en les comparant aux données expérimentales obtenues avec des muscles cardiaques, et leur domaine de validité est étudié.Pour intégrer ces descriptions dans un environnement de simulation cardiaque, nous avons étendu ces modèles afin de prendre en compte les mécanismes de régulation de la force qui se produisent in vivo.Cela conduit à de nouvelles équations aux dérivées partielles.Ensuite, nous lions les modèles de contraction microscopiques à un modèle d’organe macroscopique.Nous suivons pour cela une approche fondée sur les principes thermodynamiques pour traiter la nature multi-échelle en temps et en espace du tissu musculaire aux niveaux continu et discret.La validité de cet environnement de simulation est démontrée en présentant sa capacité à reproduire le comportement du coeur et en particulier les caractéristiques essentielles de l'effet Frank-Starling.

This PhD thesis deals with the mathematical description of the micro-scale muscle contraction mechanisms with the aim of proposing and integrating our models into a multiscale heart simulation framework.This research effort is made in the context of digital medicine, which proposes to improve the treatment of patients with the use of numerical tools.The first contribution of this thesis is a literature review of the experimental works characterizing the actin-myosin interaction and its regulations to compile information in a useable form for the development of models.This stage is an essential prerequisite to modeling.We then propose a hierarchy of muscle contraction models starting from a previously proposed refined stochastic model, which was only validated for skeletal muscles, and applying successive simplification assumptions.The simplification stages transform the initial stochastic differential equation into a partial differential equation with a model that is part of the Huxley'57 model family.A further simplification then leads to a description governed by a set of ordinary differential equations.The relevance of these models, targeting different time scales, is demonstrated by comparing them with experimental data obtained with cardiac muscles and their range of validity is investigated.To integrate these microscopic descriptions into a heart simulation framework, we extend the models to take into account the force regulation mechanisms that take place in vivo, leading to the derivation of new partial differential equations.Then, we link the microscopic contraction models to the macroscopic organ model.We follow for that an approach based on the thermodynamical principles to deal with the multi-scale nature in time and space of the muscle tissue at the continuous and at the discrete levels.The validity of this simulation framework is demonstrated by showing its ability to reproduce the heart behavior and in particular to capture the essential features of the Frank-Starling effect.; L'objectif de cette thèse est la modélisation mathématique des mécanismes de contraction musculaire à l'échelle microscopique dans le but de proposer et d'intégrer ces modèles dans un environnement de simulation cardiaque multi-échelle.Ce travail est réalisé dans le contexte de la médecine numérique, qui propose d'améliorer le traitement des patients par l'utilisation d'outils numériques.La première contribution de cette thèse est une analyse bibliographique des travaux expérimentaux caractérisant l’interaction actine-myosine et ses régulations afin de compiler les informations sous une forme utilisable pour le développement de modèles.Cette étape est une condition préalable essentielle à la modélisation.Nous proposons ensuite une hiérarchie de modèles de contraction musculaire à partir d'un modèle stochastique raffiné existant, mais validé uniquement pour les muscles squelettiques, en appliquant des hypothèses de simplification successives.Les étapes de simplification transforment l'équation différentielle stochastique initiale en une équation aux dérivées partielles avec une description qui fait partie de la famille de modèles dérivée du modèle Huxley'57.Une simplification supplémentaire conduit ensuite à un modèle décrit par un ensemble d'équations différentielles ordinaires.La pertinence des modèles proposés, qui ciblent différentes échelles de temps, est démontrée en les comparant aux données expérimentales obtenues avec des muscles cardiaques, et leur domaine de validité est étudié.Pour intégrer ces descriptions dans un environnement de simulation cardiaque, nous avons étendu ces modèles afin de prendre en compte les mécanismes de régulation de la force qui se produisent in vivo.Cela conduit à de nouvelles équations aux dérivées partielles.Ensuite, nous lions les modèles de contraction microscopiques à un modèle d’organe macroscopique.Nous suivons pour cela une approche fondée sur les principes thermodynamiques pour traiter la nature multi-échelle en temps et en espace du tissu musculaire aux niveaux continu et discret.La validité de cet environnement de simulation est démontrée en présentant sa capacité à reproduire le comportement du coeur et en particulier les caractéristiques essentielles de l'effet Frank-Starling.