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Abstract Cardiovascular disease continues to be the leading cause of death in the United States. A major contributing factor is cardiac arrhythmia, which results from irregular electrical activity in the heart. On a tissue level, cardiac conduction involves the spread of action potentials (AP) across the heart, enabling coordinated contraction of the myocardium. On a cellular level, the transmission of signals between cells is facilitated by low-resistance pathways formed by gap junctions (GJs). Recent experimental studies have sparked discussion on whether GJs play a dominant role in cell communication. Interestingly, research has revealed that GJ knockout mice can still demonstrate signal propagation in the heart, albeit more slowly and discontinuously, indicating the presence of an alternative mechanism for cardiac conduction. Unlike GJ-mediated propagation, ephaptic coupling (EpC) has emerged as a distinct form of electrical transmission, characterized by contactless electrochemical signaling across the narrow intercalated discs (IDs) between cardiomyocytes. Advancements in cardiac research have highlighted the crucial role of EpC in restoring conduction by increasing conduction velocity (CV), reducing conduction block (CB), and terminating reentry arrhythmias, particularly when GJs are impaired. However, most EpC studies are either numerical or experimental, while analytical studies on ephaptic conduction–an equally important aspect of understanding EpC–remain extremely limited. In this paper, we applied asymptotic theory to calculate the CV in the presence of weak EpC. To achieve this, we developed both continuous and discrete models to describe ephaptic conduction along a strand of cells. Ionic dynamics were modeled using the piecewise linear and cubic functions. The resulting system represents a bistable system with weak EpC. We calculated an expression for CV in the presence of weak EpC for both models, and validated our analytical results with numerical simulations. Additionally, we showed that under weak EpC, CV can increase if the distribution of INa is more prominent on the end membrane. 

This paper introduces the 3D Peskin problem: a two-dimensional elastic membrane immersed in a three-dimensional steady Stokes flow. We obtain the equations that model this free boundary problem and show that they admit a boundary integral reduction, providing an evolution equation for the elastic interface. We consider general nonlinear elastic laws, i.e. the fully nonlinear Peskin problem, and prove that the problem is well-posed in low-regularity Hölder spaces. Moreover, we prove that the elastic membrane becomes smooth instantly in time. 

Mammalian cell migration in open spaces requires F-actin polymerization and myosin contraction. While many studies have focused on myosin’s coupling to focal adhesion and stress fibers, the indirect effect of myosin contraction on cell migration through actin depolymerization is not well studied. In this work, we quantified how cell velocity and effective power output are influenced by the rate of actin depolymerization, which is affected by myosin contraction. In addition, we derived scaling laws to provide physical insights into cell migration. Model analysis shows that the cell migration velocity displays a biphasic dependence on the rate of actin depolymerization and myosin contraction. Our model further predicts that the effective cell energy output depends not only on the cell velocity but also on myosin contractility. The work has implications on in vivo processes such as immune response and cancer metastasis, where cells overcome barriers imposed by the physical environment. 

Abstract We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in ${\mathbb{R}}^3$. The hydrodynamics are described by resistive force theory, and the fibre elasticity is governed by Euler–Bernoulli beam theory. Our aim is twofold: (1) Serve as a starting point for developing the mathematical analysis of filament elastohydrodynamics, particularly the analytical treatment of an inextensibility constraint, and (2) As an application, prove conditions on internal fibre forcing that allow a free-ended filament to swim. Our analysis of fibre swimming speed is supplemented with a numerical optimization of the internal fibre forcing, as well as a novel numerical method for simulating an inextensible swimmer.