Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell
Anotida Madzvamuse

Last modified: 2014-06-09


In this talk I will present a model for cell deformation and cell movement that

couples the mechanical and biochemical properties of the cortical network of

actin _laments with its concentration. Actin is a polymer that can exist either

in _lamentous form (F-actin) or in monometric form (G-actin) (Chen et al., in

Trends Biochem Sci 25:19-23, 2000) and the _lamentous form is arranged in a

paired helix of two proto_laments (Ananthakrishnan et al., in Recent Res Devel

Biophys 5:39-69, 2006). By assuming that cell deformations are a result of the

cortical actin dynamics in the cell cytoskeleton, we consider a continuum math-

ematical model that couples the mechanics of the network of actin _laments

with its biochemical dynamics. Numerical treatment of the model is carried out

using the moving grid _nite element method (Madzvamuse et al., in J Com-

put Phys 190:478-500, 2003). Furthermore, by assuming slow deformations of

the cell, we use linear stability theory to validate the numerical simulation re-

sults close to bifurcation points. Far from bifurcation points, we show that the

mathematical model is able to describe the complex cell deformations typically

observed in experimental results. Our numerical results illustrate cell expansion,

cell contraction, cell translation and cell relocation as well as cell protrusions

in agreement with experimental observations. In all these results, the contrac-

tile tonicity formed by the association of actin _laments to the myosin II motor

proteins is identi_ed as a key bifurcation parameter. Cell migration plays a crit-

ical and pivotal role in a variety of biological and biomedical disease processes

and is important for emerging areas of biotechnology which focus on cellular

transplantation and the manufacture of arti_cial tissues and surfaces, as well as

for the development of new therapeutic strategies for controlling invasive tumor