On the Statistical Mechanics of Active Membranes: Some Selected Results

arXiv (Cornell University) · 2026-02-22

Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical mechanics and linear elasticity have yielded deep insights into membrane morphology and the role of thermal fluctuations on cellular function. However, real biological membranes operate far from equilibrium, continuously driven by active processes powered by energy consuming proteins. In this work, we employ a nonequilibrium statistical mechanics framework to model active membranes and derive analytical expressions for four fundamental properties that characterize their mechanical behavior: (a) the tension area relation, (b) the mean square amplitude of fluctuations, (c) correlation of normal vectors, and (d) the persistence length. These results collectively highlight the utility of fluctuation spectra as a starting point for elucidating membrane mechanics in both passive and active settings. Moreover, these results provide a theoretical basis for analyzing and interpreting fluctuation based assays of active membrane behavior.

Gravity driven collapse of fibrous gels

European Journal of Mechanics - A/Solids · 2026-02-03

Instabilities and phase transitions in architected metamaterials: a gradient-enhanced continuum approach

Computer Methods in Applied Mechanics and Engineering · 2026-01-15

On the Statistical Mechanics of Active Membranes: Some Selected Results

Journal of Applied Mechanics · 2026-04-27

Abstract Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical mechanics and linear elasticity have yielded deep insights into membrane morphology and the role of thermal fluctuations on cellular function. However, real biological membranes operate far from equilibrium, continuously driven by active processes powered by energy-consuming proteins. In this work, we employ a non-equilibrium statistical mechanics framework to model active membranes and derive analytical expressions for four fundamental properties that characterize their mechanical behavior: (a) the tension–area relation, (b) the mean square amplitude of fluctuations, (c) correlation of normal vectors, and (d) the persistence length. These results collectively highlight the utility of fluctuation spectra as a starting point for elucidating membrane mechanics in both passive and active settings. Moreover, these results provide a theoretical basis for analyzing and interpreting fluctuation-based assays of active membrane behavior.

A Tutorial on the Statistical Mechanics of Soft Active Matter

Applied Mechanics Reviews · 2026-02-26

Abstract Physical modeling of biological matter has conventionally treated them as engineering or physical materials that subscribe to laws of equilibrium physics and are considered “passive” or ”nonliving”. However, biological systems are “active” or “alive” with their own energy source, capable of circumventing equilibrium considerations. In fact, active biological matter including self-propelled particles, filaments, and membranes, is the hallmark of living matter and drives life?s most dynamic processes. Unlike passive soft materials that exhibit only equilibrium thermal fluctuations at the microscopic scales, active systems consume energy to generate unique mechanical behavior. Examples of such behavior include persistent dynamics, stress generation, and large deformations that violate fluctuation?dissipation relations from equilibrium statistical mechanics, placing active matter far from equilibrium. This tutorial introduces a unified approach that combines continuum theory with non-equilibrium statistical mechanics to study soft active biological matter. The discussion is organized by dimensionality: we begin with zero-dimensional active Brownian particles, proceed to one-dimensional active filaments modeled as elastic rods, and conclude with two-dimensional active membranes described using linear curvature elasticity. For each class of active matter, we review equilibrium and non-equilibrium models, illustrate key concepts through simple examples, and provide a concise survey of the literature. Our aim is to emphasize physical interpretation and practical modeling tools, equipping readers with a coherent framework for understanding the existing body of work and pursuing research in non-equilibrium statistical mechanics of living systems.

Numerical experiments with a poro-viscoelastic continuum model for gels

Journal of the Mechanics and Physics of Solids · 2026-03-24

On the Statistical Mechanics of Active Membranes: Some Selected Results

ArXiv.org · 2026-01-01

Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical mechanics and linear elasticity have yielded deep insights into membrane morphology and the role of thermal fluctuations on cellular function. However, real biological membranes operate far from equilibrium, continuously driven by active processes powered by energy consuming proteins. In this work, we employ a nonequilibrium statistical mechanics framework to model active membranes and derive analytical expressions for four fundamental properties that characterize their mechanical behavior: (a) the tension area relation, (b) the mean square amplitude of fluctuations, (c) correlation of normal vectors, and (d) the persistence length. These results collectively highlight the utility of fluctuation spectra as a starting point for elucidating membrane mechanics in both passive and active settings. Moreover, these results provide a theoretical basis for analyzing and interpreting fluctuation based assays of active membrane behavior.

Exploring effects of platelet contractility on the kinetics, thermodynamics, and mechanisms of fibrin clot contraction

npj Biological Physics and Mechanics. · 2025-02-24 · 8 citations

Mechanisms of blood clot contraction – platelet-driven fibrin network remodeling, are not fully understood. We developed a detailed computational ClotDynaMo model of fibrin network with activated platelets, whose clot contraction rate for normal 450,000/µl human platelets depends on serum viscosity η, platelet filopodia length l, and weakly depends on filopodia traction force f and filopodia extension-retraction speed v. Final clot volume is independent of η, but depends on v, f and l. Analysis of ClotDynaMo output revealed a 2.24 TJ/mol clot contraction free energy change, with ~67% entropy and ~33% internal energy changes. The results illuminate the “optimal contraction principle” that maximizes volume change while minimizing energy cost. An 8-chain continuum model of polymer elasticity containing platelet forces, captures clot contractility as a function of platelet count, η and l. The ClotDynaMo and continuum models can be extended to include red blood cells, variable platelet properties, and mechanics of fibrin network.

Modeling tumor transport and growth with poroelastic biopolymer networks

bioRxiv (Cold Spring Harbor Laboratory) · 2025-09-25 · 1 citations

The mechanical properties of the extracellular matrix (ECM) regulate tumor growth and invasion in the tumor microenvironment. Models of biopolymer networks have been used to investigate the impact of elasticity and viscoelasticity of ECM on tumor behavior. Under tumor compression, these networks also show poroelastic behavior that is governed by the resistance to water flow through their pores. This work investigates the hypothesis that poroelastic properties regulate tumor growth. Here, alginate hydrogels with tunable ionic and hybrid ionic/covalent crosslinking are used as a model biopolymer system. Hydrogel stiffness, viscoelasticity, and stress relaxation behavior were characterized using stepwise axial compression. Among these properties, we find poroelastic fluid outflow dominates ECM stress relaxation, as the measured water flux was significantly affected under compression. Continuum mechanics-based modeling was developed to formulate and calculate the chemical potential gradients of water (solvent) in the hydrogels under compression. This framework was extended into an advection-diffusion framework to quantify growth factor (solute) distribution under varying strengths of stress and diffusion indexed by the relative strength of convective to diffusive transport, characterized by the Péclet number. An agent-based computational simulation showed that tumor growth was affected by Péclet number. Together, these results highlight the role of the poroelastic properties of ECM on water flux and transport in the tumor microenvironment.

Analysis of disordered trusses using network Laplacians

Soft Matter · 2025-01-01

a network Laplacian; a matrix object which couples the motions of the structure joints. We show that this method is equivalent to the continuum limit of linear finite element methods as well as capable of reproducing natural frequencies and modes determined by more complex and computationally costlier methods. Our results show that balls-and-springs models inadequately describe dynamics, especially at short times relative to wave propagation time through rods. Furthermore, we illustrate the method's utility in optimizing target joint displacements using impedance matching and resonance-based schemes, offering a computationally efficient approach for analyzing large, complex truss structures.