arXiv subjects

Marc Durand

Publications and source records attributed to Marc Durand.

At least 19 recordsLinked to original sources

arXiv2026

Interface dynamics in tissue invasion

We rely on a hydrodynamic description of living tissues to describe the interface separating two of them with distinct constitutive properties. Using the difference in their homeostatic pressures as a control parameter, we show that the interface generates an emergent capillary surface tension that depends on the hydrodynamic scale, and that makes it very stable to large wavelengths perturbations. Using the difference of active forces the two tissues experience as a control parameter, we not only find that the front propagation mechanism shifts from the pushed wave to the Burgers wave, but we also find that the emergent surface tension is not sufficient to stabilize the interface at large enough drive and low enough viscosity.

cond-mat.soft↗

arXiv2026

Continuous limit of a discrete stochastic model of cell migration

We analytically derive the continuous limit of the Cellular Potts Model (CPM) for a one-dimensional cell subjected to constant and run-and-tumble driving forces. By coarse-graining the discrete lattice dynamics, we obtain the Fokker-Planck equations governing the cell's size and center-of-mass position. We show that in the low-force regime, the cell dynamics are accurately described by an overdamped Langevin equation. Beyond this regime, we expose intrinsic algorithmic artifacts, including a force-dependent diffusion coefficient, a non-linear force-velocity relationship, and the breakdown of the Einstein relation. We demonstrate that replacing the conventional Metropolis update rule with Glauber dynamics significantly mitigates these artifacts, broadening the physically valid parameter space. Our exact results bridge the gap between lattice-based simulations and continuous active matter models.

cond-mat.soft↗

arXiv2026

Multiscale order, flocking and phenotypic hysteresis in the cellular Potts model of epithelia

In epithelia, how do collective cell migration and tissue spatial organization feedback on each other? We address this question through large-scale numerical simulations of the cellular Potts model. By accounting for both cell morphology and cytoskeletal activity, we uncover a remarkably rich phase diagram featuring multiple types of orientational order, either as distinct phases or coexisting across length scales. We identify a specific pathway in parameter space along which a gradual increase in the actin polymerization rate drives a phase transition into a long-range flocking state. Simultaneously, quasi-long-range nematic order emerges at length scales much larger than the cell size due to the combined effects of directed motion and lateral cell-cell interactions. At length scales comparible to cell size, however, cells adopt an approximatively hexagonal morphology, resulting in hexanematic order, similar to that observed in reconstituted Madin-Darby Canine Kidney (MDCK) cell monolayers. With further increases in actin polymerization, nematic order becomes fully long-range, while hexatic order remains quasi-long-range and confined to short length scales, but independent of cytoskeletal activity. When noise is sufficiently low to allow crystallization at finite actin polymerization rate, cycling the cell-monolayer across the melting transition yields an example of phenotypical hysteresis, reminiscent of that observed across the epithelial-mesenchymal transition.

cond-mat.soft↗

arXiv2025

Slow modulation of the contraction patterns in Physarum polycephalum

The slime mould Physarum polycephalum has emerged as a model for self-organisation and coordination of contractile activity at large spatial scales. This self-organisation largely results from cytoplasmic flows generated by propagating contractile waves of the actomyosin cortex. In addition to these relatively fast travelling waves, complex slow modulations of the contractile activity have been observed on timescales much longer than the primary oscillation period; these slow dynamics are however scarcely characterised. Here we characterise these slow modulations by confining organisms inside annular geometries. We quantify contractile activity simultaneously across the entire organism on long time scales, exhibiting correlations between contractile wave direction, amplitude modulation, and the moving mean vein diameter. We observe travelling and alternating wave patterns: travelling wave periods scale clearly with system size, while alternating wave periods remain broadly distributed and probe larger values as the system size increases. Strikingly, the measured periods align with integer multiples of an intrinsic modulation time scale obtained independently from statistical analysis. These observations support the hypothesis that transport of a slowly advected chemical agent, which locally modifies membrane/cortex mechanical properties, underpins the observed slow modulation dynamics, accounting for the coordination across the organism on long time scales.

cond-mat.soft↗

arXiv2024

Temporal instability of the frontier between mechanically regulated tissues

The stability of the boundary between regenerating tissues is essential to the maintenance of their integrity and biological function. Stress is known to play an important role in the regulation of cell division, cell growth and cell death, and it is thought that stress balance ensures the stability of tissue boundaries. Using a multicellular numerical model, we investigate the stability of the frontier between two confluent cell monolayers whose cell renewal is mechanically regulated. We show that even for two tissues having similar mechanical and biological properties, the location of their common frontier is subject to strong fluctuations until the complete disappearance of one of the tissues. Using a population dynamics model, we show that this temporal instability is inherent to the stochasticity of cell division and cell death events, and derive an analytical expression for the mean disappearance time of a tissue. These results call for a rethinking of the regulating mechanism of tissue renewal.

physics.bio-ph↗

arXiv2023

Deflection and oscillations of an anchored elastic fiber embedded in a quasistatic two-dimensional foam flow

We study the deflection and fluctuations of a clamped elastic fiber embedded in 2D foam under quasistatic flow. At all times, the fiber conformation results from the elasto-capillary interactions with the foam. We independently measure the action of capillary and pressure forces on the fiber, and show that the fiber deformation is adequately described assuming a uniform continuous normal force acting on it. When bending energy exceeds a threshold value, the fiber relaxes to a less deflected shape, generating a cascade of plastic rearrangements within the foam, and the process repeats periodically. We analyze the statistical distributions of stored and released energy, and estimate the yield stress and shear modulus of the foam, as well as the number of elementary plastic events involved in a cascade.

cond-mat.soft↗

arXiv2023

Nematic Torques in Scalar Active Matter: when Fluctuations Favor Polar Order and Persistence

We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles.

cond-mat.stat-mech↗

arXiv2022

Network emergence and reorganization in confined slime moulds

A fundamental question regarding biological transport networks is the interplay between the network development or reorganization and the flows it carries. We use Physarum polycephalum, a true slime mould with a transport network which adapts quickly to change of external conditions, as a biological model to make progress in this question. We explore the network emergence and reorganization in specimens suddenly confined in chambers with ring geometry. Using an image analysis method based on the structure tensor, we quantify the emergence and directionality of the network. We show that confinement induces a reorganization of the network with a typical $10^{4}$s timescale, during which veins align orthoradially along the ring. We show that this network evolution relies on local dynamics.

physics.bio-ph↗

arXiv2022

Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime

Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be a possible driving source for cell sorting, no clear consensus has emerged on the kinetic law of cell sorting driven by differential adhesion. Using a modified Cellular Potts Model algorithm that allows for efficient simulations while preserving the connectivity of cells, we numerically explore cell-sorting dynamics over very large scales in space and time. For a binary mixture of cells surrounded by a medium, increase of domain size follows a power-law with exponent $n=1/4$ independently of the mixture ratio, revealing that the kinetics is dominated by the diffusion and coalescence of rounded domains. We compare these results with recent numerical studies on cell sorting, and discuss the importance of algorithmic differences as well as boundary conditions on the observed scaling.

cond-mat.soft↗

arXiv2021

Frame tension governs the thermal fluctuations of a fluid membrane: new evidence

Two different tensions can be defined for a fluid membrane: the internal tension, $\gamma$, conjugated to the real membrane area in the Hamiltonian, and the frame tension, $\tau$, conjugated to the projected (or frame) area. According to the standard statistical description of a membrane, the fluctuation spectrum is governed by $\gamma$. However, using rotational invariance arguments, several studies argued that fluctuation spectrum must be governed by the frame tension $\tau$ instead. These studies disagree on the origin of the result obtained with the standard description yet: either a miscounting of configurations, quantified with the integration measure, or the use of a quadratic approximation of the Helfrich Hamiltonian. Analyzing the simplest case of a one-dimensional membrane, for which arc length offers a natural parametrization, we give a new proof that the fluctuations are driven by $\tau$, and show that the origin of the issue with the standard description is a miscounting of membrane configurations. The origin itself of this miscounting depends on the thermodynamic ensemble in which calculations are made.

cond-mat.soft↗

arXiv2021

Quasistatic rheology of soft cellular systems using Cellular Potts Model

Soft cellular systems, such as foams or biological tissues, exhibit highly complex rheological properties, even in the quasistatic regime, that numerical modeling can help to apprehend. We present a numerical implementation of quasistatic strain within the widely used cellular Potts model. The accuracy of the method is tested by simulating the quasistatic strain 2D dry foams, both ordered and disordered. The implementation of quasistatic strain in CPM allows the investigation of sophisticated interplays between stress-strain relationship and structural changes that take place in cellular systems.

cond-mat.soft↗

arXiv2020

Mechanical approach to surface tension and capillary phenomena

Many textbooks dealing with surface tension favor the thermodynamic approach (minimization of some thermodynamic potential such as free energy) over the mechanical approach (balance of forces) to describe capillary phenomena, stating that the latter is flawed and misleading. Yet, mechanical approach is more intuitive for students than free energy minimization, and does not require any knowledge of thermodynamics. In this paper we show that capillary phenomena can be unmistakably described using the mechanical approach, as long as the system on which the forces act is properly defined. After reminding the microscopic origin of a tangential tensile force at the interface, we derive the Young-Dupr{\'e} equation, emphasizing that this relation should be interpreted as an interface condition at the contact line, rather than a force balance equation. This correct interpretation avoids misidentification of capillary forces acting on a given system. Moreover, we show that a reliable method to correctly identify the acting forces is to define a control volume that does not embed any contact line on its surface. Finally, as an illustration of this method, we apply the mechanical approach in a variety of ways on a classic example: the derivation of the equilibrium height of capillary rise (Jurin's law).

cond-mat.soft↗

arXiv2019

Thermally driven order-disorder transition in two-dimensional soft cellular systems

Many systems, including biological tissues and foams, are made of highly packed units having high deformability but low compressibility. At two dimensions, these systems offer natural tesselations of plane with fixed density, in which transitions from ordered to disordered patterns are often observed, in both directions. Using a modified Cellular Potts Model algorithm that allows rapid thermalization of extensive systems, we numerically explore the order-disorder transition of monodisperse, two-dimensional cellular systems driven by thermal agitation. We show that the transition follows most of the predictions of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory developed for melting of 2D solids, extending the validity of this theory to systems with many-body interactions. In particular, we show the existence of an intermediate hexatic phase, which preserves the orientational order of the regular hexagonal tiling, but looses its positional order. In addition to shedding light on the structural changes observed in experimental systems, our study shows that soft cellular systems offer macroscopic systems in which KTHNY melting scenario can be explored, in the continuation of Bragg's experiments on bubble rafts.

cond-mat.soft↗

arXiv2016

Hydrodynamics of bilayer membranes with diffusing transmembrane proteins

We consider the hydrodynamics of lipid bilayers containing transmembrane proteins of arbitrary shape. This biologically-motivated problem is relevant to the cell membrane, whose fluctuating dynamics play a key role in phenomena ranging from cell migration, intercellular transport, and cell communication. Using Onsager's variational principle, we derive the equations that govern the relaxation dynamics of the membrane shape, of the mass densities of the bilayer leaflets, and of the diffusing proteins' concentration. With our generic formalism, we obtain several results on membrane dynamics. We find that proteins that span the bilayer increase the intermonolayer friction coefficient. The renormalization, which can be significant, is in inverse proportion to the protein's mobility. Second, we find that asymmetric proteins couple to the membrane curvature and to the difference in monolayer densities. For practically all accessible membrane tensions ($σ> 10^{-8}$ N/m) we show that the protein density is the slowest relaxing variable. Furthermore, its relaxation rate decreases at small wavelengths due to the coupling to curvature. We apply our formalism to the large-scale diffusion of a concentrated protein patch. We find that the diffusion profile is not self-similar, owing to the wavevector dependence of the effective diffusion coefficient.

cond-mat.soft↗

arXiv2016

Structural Properties of Stiff Elastic Networks

Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on the relationship between microscopic geometry and macroscopic mechanics, we characterize the structural features of networks which deform uniformly, through the stretching of the beams only. We provide a convenient set of geometrical criteria to identify such networks, and derive the values of their effective elastic moduli. The analysis of these criteria elucidates the variability of mechanical response of elastic networks. In particular, our study rationalizes the difference in mechanical behavior of cellular and fiber networks.

cond-mat.soft↗

arXiv2016

An efficient Cellular Potts Model algorithm that forbids cell fragmentation

The Cellular Potts Model (CPM) is a lattice based modeling technique which is widely used for simulating cellular patterns such as foams or biological tissues. Despite its realism and generality, the standard Monte Carlo algorithm used in the scientific literature to evolve this model preserves connectivity of cells on a limited range of simulation temperature only. We present a new algorithm in which cell fragmentation is forbidden for all simulation temperatures. This allows to significantly enhance realism of the simulated patterns. It also increases the computational efficiency compared with the standard CPM algorithm even at same simulation temperature, thanks to the time spared in not doing unrealistic moves. Moreover, our algorithm restores the detailed balance equation, ensuring that the long-term stage is independent of the chosen acceptance rate and chosen path in the temperature space.

cond-mat.soft↗

arXiv2016

Statistical mechanics of two-dimensional foams: Physical foundations of the model

In a recent series of papers [1--3], a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data. Here, the various assumptions on which the model is based are exposed and justified: the equiprobability hypothesis of the foam configurations is argued. The range of correlations between bubbles is discussed, and the mean field approximation that is used in the model is detailed. The two self-consistency equations associated with this mean field description can be interpreted as the conservation laws of number of sides and bubble curvature, respectively. Finally, the use of a '' Grand-Canonical '' description, in which the foam constitutes a reservoir of sides and curvature, is justified.

cond-mat.soft↗

arXiv2013

Stiffest Elastic Networks

The rigidity of a network of elastic beams crucially depends on the specific details of its structure. We show both numerically and theoretically that there is a class of isotropic networks which are stiffer than any other isotropic network with same density. The elastic moduli of these \textit{stiffest elastic networks} are explicitly given. They constitute upper-bounds which compete or improve the well-known Hashin-Shtrikman bounds. We provide a convenient set of criteria (necessary and sufficient conditions) to identify these networks, and show that their displacement field under uniform loading conditions is affine down to the microscopic scale. Finally, examples of such networks with periodic arrangement are presented, in both two and three dimensions.

cond-mat.soft↗