Dynamic Morphology of Leukocytes: Statistical Analysis and a Stochastic Model for Receptor-Mediated Cell Motion and Orientation

Summary

Motility of leukocytes, like that of many other similar blood and tissue cells, can be stimulated by external chemicals which are either diffusing (chemotactic polypeptides, for example) or fixed to a substratum (adhesion proteins like fibronectin, for example). Depending on their adhesive strength, cells respond by more or less spreading, irregular protrusion of lamellipods around the cell periphery and eventually changing polarity and translocation of the cell body. Moreover, in a spatial gradient of a chemoattractant (CA) the direction of these motile activities is biased; however, cells tend to meander rather than migrate directly up-gradient, and occasionally even transiently migrate down-gradient. Thus, the inherent randomness of locomotion exhibited in a homogenous environment seems to be manifested during chemotaxis and, therefore, it should play a central role in modeling and explaining the underlying mechanisms of cell locomotion and orientation.

To this aim, we first describe a statistical approach for quantifying “dynamic shape changes” using spatial-temporal auto-correlation functions. Then we briefly describe the simplest prototype of a “stochastically perturbed morphogenetic dynamical system”. It considers the (deterministic) cytomechanics of an idealized cortical actin network around the cell periphery under the influence of local signals induced by the (stochastic) distribution of bound chemotactic receptors in the cell membrane surrounding the cortex. As in earlier models, an account is made for statistical fluctuations in receptor binding, entirely determined by binding rate constants and the local CA concentration field, but generalized here to include statistical fluctuations in the spatial distribution of receptors, entirely determined by membrane diffusion coefficients. Then, as one particular case study, we assume the local density of bound receptors to determine the local F-actin assembly rate in cortical cytoplasma. Using this simple model we characterize via bifurcation analysis, stochastic simulations, and correlation functions the morphogenetic dynamics of a cortical F-actin layer and the resulting dynamic cell morphology. Animation of the simulations reveal various modes of changes in cell polarity as well as orientation in a CA gradient, whereby the degree of directional turning depends on the strength of lateral forces exerted between contracting actin network and adhesion receptors as well as the gradient steepness.