mathematical model to study the nonlinear influence of dyrk1a in actin polymerization

Dyrk1A is a member of the dual-specificity tyrosine phosphorylation-regulated kinase (DYRK) family. It is believed that Dyrk1A plays a significant role in signaling pathways regulating cell proliferation and may be involved in neuron development. On the one hand, it has been reported that overexpression of Dyrk1A is sufficient to produce the dendritic alterations, in particular, it was shown that changes in Dyrk1A gene dosage strongly alter the dendritic arborization processes characterized by a reduction of neurite outgrowth [Martinez de Legran et al., 2012]. On the other hand, it was found that cells in Dyrk1A+/- mouse, a model lacking one copy of Dyrk1A, were less branched and less spinous than WT. This results suggest that Dyrk1A is affecting cellular pathways involved in neural development in a way that dosage changes lead to similar alteration regardless the direction of this change [Benavides-Piccione et al., 2005]. Here, we present a simple mathematical model that may explain both alterations observed in Dyrk1A+/- and Ts65Dn. It is based on a model proposed by Park et al., which describes a regulatory mechanism for Neural Wiskott–Aldrich syndrome protein (N-WASP) activity through Dyrk1A phosphorylation and how it regulates the actin filament assembly [Park et al., 2011]. In this work, we present a full characterization of the behavior of the system as a function of different set of parameters. We study how Dyrk1A may affect the dynamics of the system and how Dyrk1A dosage may regulate the actin polymerization. We believe that these findings may shed same light on how Dyrk1A affects cellular processes such as morphogenesis and neuronal differentiation.