arXiv subjects

Marino Arroyo

Publications and source records attributed to Marino Arroyo.

At least 19 recordsLinked to original sources

arXiv2025

Theory of active self-organization of dense nematic structures in the actin cytoskeleton

The actin cytoskeleton is remarkably adaptable and multifunctional. It often organizes into nematic bundles such as contractile rings or stress fibers. However, how a uniform and isotropic actin gel self-organizes into dense nematic bundles is not fully understood. Here, using an active gel model accounting for nematic order and density variations, we identify an active patterning mechanism leading to localized dense nematic structures. Linear stability analysis and nonlinear finite element simulations establish the conditions for nematic bundle self-assembly and how active gel parameters control the architecture, orientation, connectivity and dynamics of self-organized patterns. Finally, we substantiate with discrete network simulations the main requirements for nematic bundle formation according to our theory, namely increased active tension perpendicular to the nematic direction and generalized active forces conjugate to nematic order. Our work portrays actin gels a reconfigurable active materials with a spontaneous tendency to develop patterns of dense nematic bundles.

physics.bio-ph↗

arXiv2024

Variational formulation of active nematics: theory and simulation

The structure and dynamics of important biological quasi-two-dimensional systems, ranging from cytoskeletal gels to tissues, are controlled by nematic order, flow, defects and activity. Continuum hydrodynamic descriptions combined with numerical simulations have been used to understand such complex systems. The development of thermodynamically consistent theories and numerical methods to model active nemato-hydrodynamics is eased by mathematical formalisms enabling systematic derivations and structured-preserving algorithms. Alternative to classical nonequilibrium thermodynamics and bracket formalisms, here we develop a theoretical and computational framework for active nematics based on Onsager's variational formalism to irreversible thermodynamics, according to which the dynamics result from the minimization of a Rayleighian functional capturing the competition between free-energy release, dissipation and activity. We show that two standard incompressible models of active nemato-hydrodynamics can be framed in the variational formalism, and develop a new compressible model for density-dependent active nemato-hydrodynamics relevant to model actomyosin gels. We show that the variational principle enables a direct and transparent derivation not only of the governing equations, but also of the finite element numerical scheme. We exercise this model in two representative examples of active nemato-hydrodynamics relevant to the actin cytoskeleton during wound healing and to the dynamics of confined colonies of elongated cells.

physics.bio-ph↗

arXiv2024

Mechanisms enabling efficient fountain-flow supracellular migration

In a prototypical mode of single-cell migration, retrograde cytoskeletal flow is mechanically coupled to the environment, propels the cell, and is sustained by an anterograde cytosolic flow of disassembled cytoskeletal components. Supracellular collectives also develop fountain-flows to migrate, but the opposing cellular streams interact with the environment producing conflicting forces. To understand the biophysical constraints of fountain-flow supracellular migration, we develop an active gel model of a cell cluster driven by a polarized peripheral contractile cable. While the model develops fountain-flows and directed migration, efficiency and cluster velocity are extremely small compared to observations. We find that patterned friction or cluster-polarized single-cell directed migration, both suggested by contact inhibition of locomotion, rescue robust and efficient supracellular migration.

physics.bio-ph↗

arXiv2023

Estimation of anisotropic bending rigidities and spontaneous curvatures of crescent curvature-inducing proteins from tethered-vesicle experimental data

The Bin/amphiphysin/Rvs (BAR) superfamily proteins have a crescent binding domain and bend biomembranes along the domain axis. However, their anisotropic bending rigidities and spontaneous curvatures have not been experimentally determined. Here, we estimated these values from the bound protein densities on tethered vesicles using a mean-field theory of anisotropic bending energy and orientation-dependent excluded volume. The dependence curves of the protein density on the membrane curvature are fitted to the experimental data for the I-BAR and N-BAR domains reported by C. Prevost et al. Nat. Commun. 6, 8529 (2015) and F.-C. Tsai et al. Soft Matter 17, 4254 (2021), respectively. For the I-BAR domain, all three density curves of different chemical potentials exhibit excellent fits with a single parameter set of anisotropic bending energy. When the classical isotropic bending energy is used instead, one of the curves can be fitted well, but the others exhibit large deviations. In contrast, for the N-BAR domain, two curves are not well-fitted simultaneously using the anisotropic model, although it is significantly improved compared to the isotropic model. This deviation likely suggests a cluster formation of the N-BAR domains.

cond-mat.soft↗

arXiv2022

A theory for the flow of chemically-responsive polymer solutions: equilibrium and shear-induced phase separation

Chemically-responsive polymers are macromolecules that respond to local variations of the chemical composition of the solution by changing their conformation, with notable examples including polyelectrolytes, proteins and DNA. The polymer conformation changes can occur in response to changes to the pH, the ionic strength or to the concentration of a generic solute that interacts with the polymer. These chemical stimuli can lead to drastic variations of the polymer flexibility and even trigger a transition from a coil to a globule polymer conformation. In many situations the spatial distribution of the chemical stimuli can be highly inhomogeneous, which can lead to large spatial variations of polymer conformation and of the rheological properties of the mixture. In this paper, we develop a theory for the flow of a mixture of a solute and chemically-responsive polymers. The approach is valid for generic flows and inhomogeneous distributions of polymers and solutes. To model the polymer conformation changes introduced by the interactions with the solute, we consider the polymers as linear elastic dumbbells whose spring stiffness depends on the solute concentration. We use the Onsager's variational formalism to derive the equations governing the evolution of the variables, which unveils novel couplings between the distribution of dumbbells and that of the solute. Finally, we use a linear stability analysis to show that the governing equations predict an equilibrium phase separation and a distinct shear-induced phase separation whereby a homogeneous distribution of solute and dumbbells spontaneously demix. Similar phase transitions have been observed in previous experiments using stimuli-responsive polymers and may play an important role in living systems.

cond-mat.soft↗

arXiv2022

Binding of anisotropic curvature-inducing proteins onto membrane tubes

Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembrane. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered using mean-field theory including an orientation-dependent excluded volume. The proteins exhibit a second-order or first-order nematic transition with increasing protein density depending on the radius of the membrane tube. The tube curvatures for the maximum protein binding and orientational order are different and varied by the protein density and rigidity. As the external force along the tube axis increases, a first-order transition from a large tube radius with low protein density to a small radius with high density occurs once, and subsequently, the protein orientation tilts to the tube-axis direction. When an isotropic bending energy is used for the proteins with an elliptic shape, the force-dependence curves become symmetric and the first-order transition occurs twice. This theory quantitatively reproduces the results of meshless membrane simulation for short proteins, whereas deviations are seen for long proteins owing to the formation of protein clusters.

cond-mat.soft↗

arXiv2022

Peeling dynamics of fluid membranes bridged by molecular bonds: moving or breaking

Biological adhesion is a critical mechanical function of complex organisms operating at multiple scales. At the cellular scale, cell-cell adhesion is remarkably tunable to enable both cohesion and malleability during development, homeostasis and disease. Such adaptable adhesion is physically supported by transient bonds between laterally mobile molecules embedded in fluid membranes. Thus, unlike specific adhesion at solid-solid or solid-fluid interfaces, peeling at fluid-fluid interfaces can proceed by breaking bonds, by moving bonds, or by a combination of both. How the additional degree of freedom provided by bond mobility changes the mechanics of peeling is not understood. To address this, we develop a theoretical model coupling self-consistently diffusion, reactions and mechanics. Lateral mobility and reaction rates determine distinct peeling regimes. In a diffusion-dominated Stefan-like regime, bond motion establishes self-stabilizing dynamics that increase the effective adhesion fracture energy. A reaction-dominated regime exhibits traveling peeling solutions where small-scale diffusion and marginal unbinding control peeling speed. In a mixed reaction-diffusion regime, strengthening by bond motion competes with weakening by bond breaking in a force-dependent manner, defining the strength of the adhesion patch. In turn, patch strength depends on molecular properties such as bond stiffness, force sensitivity, or crowding. We thus establish the physical rules enabling tunable cohesion in cellular tissues and in engineered biomimetic systems.

cond-mat.soft↗

arXiv2020

A theory of ordering of elongated and curved proteins on membranes driven by density and curvature

Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the work of [Nascimento et. al, Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientational order and evaluate the free-energy of ensembles of elongated and curved objects on curved membranes. This theory depends on the microscopic properties of the particles and explains how a density-dependent isotropic-to-nematic transition is modified by anisotropic curvature. We also examine the coexistence of isotropic and nematic phases. This theory lays the ground to understand the interplay between membrane reshaping by BAR proteins and molecular order, examined in [Le Roux et. al, Submitted, 2020].

cond-mat.soft↗

arXiv2020

Spontaneous polarization and locomotion of an active particle with surface-mobile enzymes

We examine a mechanism of locomotion of active particles whose surface is uniformly coated with mobile enzymes. The enzymes catalyze a reaction that drives phoretic flows but their homogeneous distribution forbids locomotion by symmetry. We find that the ability of the enzymes to migrate over the surface combined with self-phoresis can lead to a spontaneous symmetry breaking instability whereby the homogeneous distribution of enzymes polarizes and the particle propels. The instability is driven by the advection of enzymes by the phoretic flows and occurs above a critical Péclet number. The transition to polarized motile states occurs via a supercritical or subcritical pitchfork bifurcations, the latter of which enables hysteresis and coexistence of uniform and polarized states.

cond-mat.soft↗

arXiv2020

Swimming Euglena respond to confinement with a behavioural change enabling effective crawling

Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modelling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells.

cond-mat.soft↗

arXiv2020

Smart helical structures inspired by the pellicle of euglenids

This paper deals with a concept for a reconfigurable structure bio-inspired by the cell wall architecture of euglenids, a family of unicellular protists, and based on the relative sliding of adjacent strips. Uniform sliding turns a cylinder resulting from the assembly of straight and parallel strips into a cylinder of smaller height and larger radius, in which the strips are deformed into a family of parallel helices. We examine the mechanics of this cylindrical assembly, in which the interlocking strips are allowed to slide freely at their junctions, and compute the external forces (axial force and axial torque at the two ends, or pressure on the lateral surface) necessary to drive and control the shape changes of the composite structure. Despite the simplicity of the structure, we find a remarkably complex mechanical behaviour that can be tuned by the spontaneous curvature or twist of the strips.

cond-mat.soft↗

arXiv2020

Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations

We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g.~as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDE) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE). The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.

physics.comp-ph↗

arXiv2019

The 2019 Motile Active Matter Roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of active matter in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines.

cond-mat.soft↗

arXiv2018

Modelling fluid deformable surfaces with an emphasis on biological interfaces

Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex, or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry, and geometry, and govern important biological processes such as cellular traffic, division, migration, or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics and computational framework for fluid deformable surfaces. The dual solid-fluid nature of fluid deformable surfaces challenges classical Lagrangian or Eulerian descriptions of deforming bodies. Here, we extend the notion of Arbitrarily Lagrangian-Eulerian (ALE) formulations, well-established for bulk media, to deforming surfaces. To systematically develop models for fluid deformable surfaces, which consistently treat all couplings between fields and geometry, we follow a nonlinear Onsager formalism according to which the dynamics minimize a Rayleighian functional where dissipation, power input and energy release rate compete. Finally, we propose new computational methods, which build on Onsager's formalism and our ALE formulation, to deal with the resulting stiff system of higher-order of partial differential equations. We apply our theoretical and computational methodology to classical models for lipid bilayers and the cell cortex. The methods developed here allow us to formulate/simulate these models for the first time in their full three-dimensional generality, accounting for finite curvatures and finite shape changes.

physics.flu-dyn↗

arXiv2017

Towards understanding the geometry effects on fracture in thin elastic shells

We examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and eventually develop new concepts for optimizing the design of thin shell structures, we derive the configurational force conjugate to crack extension for Koiter's linear thin shell theory. We identify the conservative contribution to this force through an Eshelby tensor, as well as non-conservative contributions arising from curvature.

cond-mat.soft↗

arXiv2014

Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant

In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is due to direct phospholipid packing modification in the outer leaflet that is promoted by protonation of cardiolipin headgroups. Here we compare the case of cardiolipin-containing giant unilamellar vesicles with that of phosphatidylglycerol-containing giant unilamellar vesicles. Local acidification also promotes formation of tubules in the latter. However, compared to cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH-gradient. Simulations using a fully non-linear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondrial activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondrial function.

cond-mat.soft↗

arXiv2011

Thin-shell theory based analysis of radially pressurized multiwall carbon nanotubes

Elastic radial deformation of multiwall carbon nanotubes (MWNTs) under hydrostatic pressure is investigated within the continuum elastic approximation. The thin-shell theory, with accurate elastic constants and interwall couplings, allows us to estimate the critical pressure $p_c$ above which the original circular cross-section transforms into radially corrugated ones. Emphasis is placed on the rigorous formulation of the van der Waals interaction between adjacent walls, which we analyze using two different approaches. Possible consequences of the radial corrugation in the physical properties of pressurized MWNTs are also discussed.

cond-mat.mes-hall↗

arXiv2010

The role of membrane viscosity in the dynamics of fluid membranes

Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.

math.NA↗