A mathematical model for the dynamics of large membrane deformations of isolated fibroblasts

In this paper we develop and extend a previous model of cell deformations, initially proposed to describe the dynamical behaviour of round-shaped cells such as keratinocytes or leukocytes, in order to take into account cell pseudopodial dynamics with large amplitude membrane deformations such as those observed in fibroblasts. Beyond the simulation (from a quantitative, parametrized model) of the experimentally observed oscillatory cell deformations, a final goal of this work is to underline that a set of common assumptions regarding intracellular actin dynamics and associated cell membrane local motion allows us to describe a wide variety of cell morphologies and protrusive activity. The model proposed describes cell membrane deformations as a consequence of the endogenous cortical actin dynamics where the driving force for large-amplitude cell protrusion is provided by the coupling between F-actin polymerization and contractility of the cortical actomyosin network. Cell membrane movements then result of two competing forces acting on the membrane, namely an intracellular hydrostatic protrusive force counterbalanced by a retraction force exerted by the actin filaments of the cell cortex. Protrusion and retraction forces are moreover modulated by an additional membrane curvature stress. As a first approximation, we start by considering a heterogeneous but stationary distribution of actin along the cell periphery in order to evaluate the possible morphologies that an individual cell might adopt. Then non-stationary actin distributions are considered. The simulated dynamic behaviour of this cytomechanical model not only reproduces the small amplitude rotating waves of deformations of round-shaped cells such as keratinocytes [as proposed in the original model of Alt and Tranquillo (1995, J. Biol. Syst. 3, 905-916)] but is furthermore in very good agreement with the protrusive activity of cells such as fibroblasts, where large amplitude contracting/retracting pseudopods are more or less periodically extended in opposite directions. In addition, the biophysical and biochemical processes taken into account by the cytomechanical model are characterized by well-defined parameters which (for the majority) can be discussed with regard to experimental data obtained in various experimental situations.