BASIC MORPHOGENETIC SYSTEM MODELING SHAPE CHANGES OF MIGRATING CELLS: HOW TO EXPLAIN FLUCTUATING LAMELLIPODIAL DYNAMICS

Abstract

Migration of cells as leukocytes (white blood cells) or keratinocytes (outer epidermic cells) plays an important role in the response of (human) organisms to infections or injuries. When placed on two-dimensional substrata, these cells show extensive protrusions of so-called lamellipods, mostly around the whole cell periphery, inducing characteristic shape changes of the cell outline and subsequent translocation of the cell body. In order to explain the observed lamellipodial dynamics we investigate a "circular" model describing radial extension, L(t, x), of the cell periphery and density, a(t, x), of the underlying cortical polymer layer, consisting of actin and myosin filaments, as well as their contractile activity and their tangential transport velocity v(t, x). The resulting differential equations constitute a system of a non-local hyperbolic transport equation for a on the unit circle combined with a parabolic equation for L. Linear stability analysis as well as numerical simulations provide characteristic "morphogenetic behavior" of this model system, typically showing spatio-temporal patterns with one, two or more protrusions. One important feature of this morphogenetic system on the unit circle is the simple fact that stationary patterns might appear, but are stable only up to rotational shifts. This feature becomes effective, if we introduce stochastic perturbations of the PDE system, e.g. by adding a spatio-temporally correlated Gauss process to the rate term for actin assembly (thought to be induced by fluctuations of bound chemo-receptors which diffuse in the cell membrane). Then, depending on the choice of parameters, typical protrusion patterns transiently appear, or remain but are shifted circumferentially. Characteristic spatio-temporal auto-correlation results for these "model cells" can be compared to corresponding statistical results for "real cells".