Turing Instabilities in a Mathematical Model for Signaling Networks
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Date
2011-07-11
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Abstract
GTPase molecules are important regulators in cells that continuously run through
an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated
GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops
contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic
processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for
this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion
system in the inner volume to a reaction-diffusion system on the membrane via a
flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler nonlocal
reaction-diffusion model and perform a stability analysis and numerical simulations for this
reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion
of inactivated GTPase is much faster than the diffusion of activated GTPase.