  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.
