The myristoylated alanine-rich C-kinase substrate (MARCKS) have a wide range of functions, ranging from roles in embryonic development to adult brain plasticity and the inflammatory response. Recently, this protein has also been identified as important players in regeneration. MARCKS is expressed at the highest levels in the brain during embryonic development and ubiquitous expression persists throughout adulthood. In neurons, MARCKS is heterogeneously distributed and enriched in axons and dendrites. During early development, MARCKS is broadly expressed in the cells surrounding the neural tube, and later, throughout the forebrain with particular enrichment at the apical membranes of ventricular zone neural progenitor cells. Alonso and Bär proposed a model which describes the patio-temporal evolution of the concentration of the MARCKS protein at the bio membrane involving: binding, phosphorylation and dephosphorylation of the MARCKS protein. The pioneers have shown by using numerical simulations that the model presents two qualitatively different mechanisms of protein domain formation. Base on this result, we performed the modulational instability (MI) phenomenon. 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.
Chenceline Fouedji (Sun,) studied this question.