A mathematical model considering system size expansion for describing neuronal symmetry breaking

SILVIA A. MENCHÓN

Congreso; LAWNP 2013; 2013

Neurons can spontaneously establish and maintain asymmetric distributions of signalling molecules on the plasma membrane, even in a homogeneous environment, suggesting the existence of an internal polarity-generating mechanism. This spatial self-organization involves an autocat- alytic process and small random uctuations. In this work we propose a stochastic model and study neuronal polarity via the system size expansion. The mean-eld equations are derived and shown to lead to organized Turing patterns within a specic parameters region. Withthis approach we also consider the cross-diusive terms, often neglected in the derivation of reaction-diusion schemes, and analyze the power spectra of the uctuations.