STOCHASTIC-MODEL OF RECEPTOR-MEDIATED CYTOMECHANICS AND DYNAMIC MORPHOLOGY OF LEUKOCYTES

The proposed mathematical model investigates the simplified cytomechan ics of cell shape change driven by stochastic stimulation from chemose nsory receptors. The cytomechanical component of our model describes t he dynamical distribution of F-actin and associated forces in an ideal ized cortical actin network around the cell periphery. The chemosensor y component describes the distribution of chemotactic receptors in the cell membrane surrounding the cortex, where bound receptors give rise to an intracellular signal which modulates some property of the corti cal network. As in our earlier models, an account is made for (1) the reactive, contractive properties of cortical actin, but here also for a stress induced by curvature of the cortex-membrane complex which car ries an effective surface tension, and (2) statistical fluctuations in receptor binding, but generalized here to include statistical fluctua tions in the spatial distribution of receptors, entirely determined by the additional prescription of membrane diffusion coefficients along with total receptor number, receptor binding rate constants and the lo cal concentration field of chemotactic factor. We simplify the analysi s by restricting the model to a prototype in which viscous stresses in the cortical network are negligible and the radial extension of the c ell cortex is a prescribed function of the cortical actin concentratio n. We assume in particular that the assembly rate of cortical actin de pends on the local density of bound receptors. These assumptions lead to a 4th-order parabolic differential equation on the unit circle coup led to a system of stochastic differential equations. We characterize via bifurcation analysis, stochastic simulations, and analytical corre lation functions the spatial-temporal pattern of cell morphology under the influence of fluctuations in the bound receptor distribution for the case of a uniform concentration field of chemotactic factor. In ad dition to addressing the biological significance of our model, we rema rk on its relevance to the generic problem of the influence of correla ted stochastic perturbations on spatial patterns in morphogenetic medi a.