Multisolitons-like patterns in a one-dimensional MARCKS protein cyclic model

In this paper, we study the nonlinear dynamics of the MARCKS protein between cytosol and cytoplasmic membrane through the modulational instability phenomenon. The reaction-diffusion generic model used here is firstly transformed into a cubic complex Ginzburg-Landau equation. Then, modulational instability (MI) is carried out in order to derive the MI criteria. We find the domains of some parameter space where nonlinear patterns are expected in the model. The analytical results on the MI growth rate predict that phosphorylation and binding rates affect MARCKS dynamics in opposite way: while the phosphorylation rate tends to support highly localized structures of MARCKS, the binding rate in turn tends to slow down such features. On the other hand, self-diffusion process always amplifies the MI phenomenon. These predictions are confirmed by numerical simulations. As a result, the cyclic transport of MARCKS protein from membrane to cytosol may be done by means of multisolitons-like patterns.