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

Cued and un-cued cell polarization is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the cell polarity might onset by means of the well-known phenomenon of wave-pinning (Gamba et al, PNAS, 2005). A particularly simple and elegant model of wave-pinning has been proposed by Edelstein-Keshet and coworkers (Biop. J., 2008). However, biomolecular networks do communicate with other networks as well as with the external world. As such, their dynamics has to be considered as perturbed by extrinsic noises. These noises may have both a spatial and a temporal correlation, but any case they must be bounded to preserve the biological meaningfulness of the perturbed parameters. Here we numerically show that the inclusion of external spatio-temporal bounded perturbations may sometime destroy the polarized state. The polarization loss depends on both the extent of temporal and spatial correlations, and on the kind of adopted noise. Namely, independently of the specific model of noise, an increase of the spatial correlation induces an increase of the probability of polarization. However, if the noise is spatially homogeneous then the polarization is lost in the majority of cases. On the contrary, an increase of the temporal autocorrelation of the noise induces an effect that depends on the noise model.