arXiv subjects

Yoichiro Mori

Publications and source records attributed to Yoichiro Mori.

39 records · Page 3Linked to original sources

arXiv2011

A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.

q-bio.CB↗

arXiv2010

Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization

We describe and analyze a bistable reaction-diffusion (RD) model for two interconverting chemical species that exhibits a phenomenon of wave-pinning: a wave of activation of one of the species is initiated at one end of the domain, moves into the domain, decelerates, and eventually stops inside the domain, forming a stationary front. The second ("inactive") species is depleted in this process. This behavior arises in a model for chemical polarization of a cell by Rho GTPases in response to stimulation. The initially spatially homogeneous concentration profile (representative of a resting cell) develops into an asymmetric stationary front profile (typical of a polarized cell). Wave-pinning here is based on three properties: (1) mass conservation in a finite domain, (2) nonlinear reaction kinetics allowing for multiple stable steady states, and (3) a sufficiently large difference in diffusion of the two species. Using matched asymptotic analysis, we explain the mathematical basis of wave-pinning, and predict the speed and pinned position of the wave. An analysis of the bifurcation of the pinned front solution reveals how the wave-pinning regime depends on parameters such as rates of diffusion and total mass of the species. We describe two ways in which the pinned solution can be lost depending on the details of the reaction kinetics: a saddle-node or a pitchfork bifurcation.

q-bio.CB↗

arXiv2009

From Three-Dimensional Electrophysiology to the Cable Model: an Asymptotic Study

Cellular electrophysiology is often modeled using the cable equations. The cable model can only be used when ionic concentration effects and three dimensional geometry effects are negligible. The Poisson model, in which the electrostatic potential satisfies the Poisson equation and the ionic concentrations satisfy the drift-diffusion equation, is a system of equations that can incorporate such effects. The Poisson model is unfortunately prohibitively expensive for numerical computation because of the presence of thin space charge layers at internal membrane boundaries. As a computationally efficient and biophysically natural alternative, we introduce the electroneutral model in which the Poisson equation is replaced by the electroneutrality condition and the presence of the space charge layer is incorporated in boundary conditions at the membrane interfaces. We use matched asymptotics and numerical computations to show that the electroneutral model provides an excellent approximation to the Poisson model. Further asymptotic calculations illuminate the relationship of the electroneutral or Poisson models with the cable model, and reveal the presence of a hierarchy of electrophysiology models.

q-bio.NC↗