Multiscale Computation of Cytoskeletal Mechanics During Blebbing

Abstract

Cellular blebbing occurs when detachment of the underlying cytoskeleton from a portion of the plasma membrane leads to the formation of protrusions under the influence of cytosol pressure. Blebbing is associated with cellular apoptosis and has been linked to diseased states such as cancer. Multiple phenomena at disparate scales occur during blebbing. At the molecular scale there are biochemical reactions governing actin polymerization, cross-linkage, and formation of membrane adhesion complexes. At the cellular level, forces on the cell membrane lead to deformation of the cytoskeleton and localized mechanical stress. Fluid motion during protrusive activity modifies local concentrations of free actin monomers as well as other molecules that participate in cytoskeleton formation. A computational model of cellular blebbing has to link these disparate scales. In this work a general multiscale interaction procedure is applied to the problem of cellular blebbing. The procedure simultaneously advances in time three models of the cytoskeleton at three different length scales. At the smallest length scale the Langevin dynamics of small actin filament segments is computed by solving stochastic differential equations. At larger scales the cytoskeleton actin network is characterized by probability distribution functions for parameters such as actin filament length and orientation. A Fokker–Planck equation is formulated for the probability distribution functions and advanced in time. At an even larger scale the cytoskeleton is modeled as a continuum, and inhomogeneous elasticity equations are solved. The overall procedure is efficient enough to show cellular level effects produced by changes at the microscopic level, such as biochemical reaction rates.