  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.
