A stochastic model for topographically influenced cell migration.

Migrating cells traverse a range of topographic configurations presented by the native extracellular environment to conduct their physiologic functions. It is well documented cells can modulate their behaviour in response to different topographic features, finding promising applications in biomaterial and bioimplant design. It is useful, in these areas of research, to be able to predict which topographic arrangements could be used to promote certain patterns of migration prior to laboratory experimentation. Despite a profusion of study and interest shown in these fields by experimentalists, the related modelling literature is as yet relatively sparse and tend to focus more on either cell-matrix interaction or morphological responses of cells. We propose a mathematical model for individual cell migration based on an Ornstein-Uhlenbeck process, and set out to see if the model can be used to predict migration patterns on 2-d isotropic and anisotropic topographies, whose characteristics can be broadly described as either uniform flat, uniform linear with variable ridge density or non-uniform disordered with variable feature density. Results suggest the model is capable of producing realistic patterns of migration for flat and linear topographic patterns, with calibrated output closely approximating NIH3T3 fibroblast migration behaviour derived from an experimental dataset, in which migration linearity increased with ridge density and average speed was highest at intermediate ridge densities. Exploratory results for non-uniform disordered topographies suggest cell migration patterns may adopt disorderedness present in the topography and that 'distortion' introduced to linear topographic patterns may not impede linear guidance of migration, given it's magnitude is bounded within certain limits. We conclude that an Ornstein-Uhlenbeck based model for topographically influenced migration may be useful to predict patterns of migration behaviour for certain isotropic (flat) and anisotropic (linear) topographies in the NIH3T3 fibroblast cell line, but additional investigation is required to predict with confidence migration patterns for non-uniform disordered topographic arrangements.