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Time-correlated forces and biological variability in cell motility

Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal forces but also the biological variability which is inherent of the intra-cellular biochemical processes. Such model allow us to derive exact expressions for the mean-squared displacement and the effective time-dependent diffusion coefficient which are compared to numerical results obtained from non-markovian stochastic simulations. In addition, we show that the heterogeneity of persistence times lead to non-gaussian distributions which can be obtained analytically and that were validated by the numerical simulations. Our results indicate that such model might be used to describe the behaviour observed in experimental results obtained for isolated cells without external signaling.