Cellular polarization: interaction between extrinsic bounded noises and the wave-pinning mechanism

Cell polarization (cued or uncued) is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the onset of cell polarity might arise by means of the well-known phenomenon of wave-pinning [Gamba et al., Proc. Natl. Acad. Sci. USA 102, 16927 (2005)]. A particularly simple and elegant deterministic model of cell polarization based on the wave-pinning mechanism has been proposed by Edelstein-Keshet and coworkers [Biophys. J. 94, 3684 (2008)]. This model consists of a small biomolecular network where an active membrane-bound factor interconverts into its inactive form that freely diffuses in the cell cytosol. However, biomolecular networks do communicate with other networks as well as with the external world. Thus, their dynamics must be considered as perturbed by extrinsic noises. These noises may have both a spatial and a temporal correlation, and in any case they must be bounded to preserve the biological meaningfulness of the perturbed parameters. Here we numerically show that the inclusion of external spatiotemporal bounded parametric perturbations in the above wave-pinning-based model of cellular polarization may sometimes destroy the polarized state. The polarization loss depends on both the extent of temporal and spatial correlations and on the kind of noise employed. For example, an increase of the spatial correlation of the noise induces an increase of the probability of cell polarization. However, if the noise is spatially homogeneous then the polarization is lost in the majority of cases. These phenomena are independent of the type of noise. Conversely, an increase of the temporal autocorrelation of the noise induces an effect that depends on the model of noise.