When tissue cells are plated on a flexible substrate, durotaxis, the directed migration of cells towards mechanically stiff regions, has been observed. Environmental mechanical signals are not only important in cell migration, but also seem to influence all aspects of cell differentiation and development, including the metastatic process in cancer cells. Based on a theoretical model suggesting that this mechanosensation has a mechanical basis, we introduce a simple model of a cell by considering the contraction of F-actin bundles containing myosin motors (stress fibers) mediated by the movement of adhesions. We show that, when presented with a linear stiffness gradient, this simple model exhibits durotaxis. Interestingly, since stress fibers do not form on soft surfaces and since adhesion sliding becomes stiffness independent on stiff surfaces, the model predicts that the average cell velocity reaches a maximum at an intermediate stiffness. This prediction can be experimentally tested. We therefore argue that stiffness-dependent cellular adaptations (mechanosensation) and durotaxis are intimately related, and may share a mechanical basis. We therefore identify the essential physical ingredients, which combined with additional biochemical mechanisms, can explain durotaxis and mechanosensation in cells.

Markovian models based on the stochastic master equation are often encountered in single molecule dynamics, reaction networks, and nonequilibrium problems in chemistry, physics, and biology. An efficient and convenient method to simulate these systems is the kinetic Monte Carlo algorithm which generates continuous-time stochastic trajectories. We discuss an alternative simulation method based on sampling of stochastic paths. Utilizing known probabilities of stochastic paths, it is possible to apply Metropolis Monte Carlo in path space to generate a desired ensemble of stochastic paths. The method is a generalization of the path sampling idea to stochastic dynamics, and is especially suited for the analysis of rare paths which are not often produced in the standard kinetic Monte Carlo procedure. Two generic examples are presented to illustrate the methodology.

The electrical properties of the cellular membrane are important for ion transport across cells and electrophysiology. Plasma membranes also resist bending and stretching, and mechanical properties of the membrane influence cell shape and forces in membrane tethers pulled from cells. There exists a coupling between the electrical and mechanical properties of the membrane. Previous work has shown that applied voltages can induce forces and movements in the lipid bilayer. We present a theory that computes membrane bending deformations and forces as the applied voltage is changed. We discover that electromechanical coupling in lipid bilayers depends on the voltage-dependent adsorption of ions into the region occupied by the phospholipid head groups. A simple model of counter-ion absorption is investigated. We show that electromechanical coupling can be measured using membrane tethers and we use our model to predict the membrane tether tension as a function of applied voltage. We also discuss how electromechanical coupling in membranes may influence transmembrane protein function.

Outer hair cell electromechanics, critically important to mammalian active hearing, is driven by the cell membrane potential. The membrane protein prestin is a crucial component of the active outer hair cell’s motor. The focus of the paper is the analysis of the local membrane potential and electric field resulting from the interaction of electric charges involved. Here the relevant charges are the ions inside and outside the cell, lipid bilayer charges, and prestin-associated charges (mobile-transferred by the protein under the action of the applied field and stationary-relatively unmoved by the field). The electric potentials across and along the membrane are computed for the case of an applied DC-field. The local amplitudes and phases of the potential under different frequencies are analyzed for the case of a DC+AC-field. We found that the effect of the system of charges alters the electric potential and internal field, which deviate significantly from their traditional linear and constant distributions. Under DC+AC conditions, the strong frequency dependence of the prestin mobile charge has a relatively small effect on the amplitude and phase of the resulting potential. The obtained results can help in a better understanding and experimental verification of the mechanism of prestin performance.

When tissue cells are plated on a flexible substrate, durotaxis, the directed migration of cells towards mechanically stiff regions, has been observed. Environmental mechanical signals are not only important in cell migration, but also seem to influence all aspects of cell differentiation and development, including the metastatic process in cancer cells. Based on a theoretical model suggesting that this mechanosensation has a mechanical basis, we introduce a simple model of a cell by considering the contraction of F-actin bundles containing myosin motors (stress fibers) mediated by the movement of adhesions. We show that, when presented with a linear stiffness gradient, this simple model exhibits durotaxis. Interestingly, since stress fibers do not form on soft surfaces and since adhesion sliding becomes stiffness independent on stiff surfaces, the model predicts that the average cell velocity reaches a maximum at an intermediate stiffness. This prediction can be experimentally tested. We therefore argue that stiffness-dependent cellular adaptations (mechanosensation) and durotaxis are intimately related, and may share a mechanical basis. We therefore identify the essential physical ingredients, which combined with additional biochemical mechanisms, can explain durotaxis and mechanosensation in cells.