Modeling the Effect of Cell Shape on GTPase Signaling in Neurons

<p>Biological processes such as cell division and synaptic plasticity are regulated by concentration gradients of signaling molecules. A number of biochemical mechanisms can result in intracellular signaling gradients. For example, restriction of diffusional flux of a chemical from one compartment to another will result in a transient gradient. A sustained gradient can be generated by opposite reactions such as phosphorylation and dephosphorylation of a signaling substrate taking place at different locations in the cell. More sophisticated mechanisms for non-uniform spatial signaling profiles include Turing type patterning and wave-pinning. It is becoming apparent that cell shape can regulate concentration gradients and modulate the downstream processes. In Chapter 1 we review how cell geometry can regulate intracellular signaling gradients in the context of the aforementioned gradient-generating mechanisms. The works reviewed make heavy use of mathematical modeling in order to investigate how reaction and diffusion taking place in complex cell geometries can modulate concentration gradients. That is a motivation for Chapter 2 where we implement a computational method to simulate reaction and diffusion on curved surfaces representing the cell membrane coupled with reaction and diffusion in the enclosed volume (representing the cell cytosol). To solve the reaction-diffusion equations on the surface we use the closest point method, a finite-difference technique that embeds the equations in the surrounding space. Such method is coupled with an embedded boundary technique to solve the equations in the enclosed volume with boundary conditions accounting for material exchange between surface and volume. The method is second-order convergent in the grid spacing despite a simple accuracy analysis predicts first-order errors. In Chapter 3 we use mathematical modeling in order to propose mechanisms accounting for the spatiotemporal dynamics of Rho-GTPase signaling at dendritic spines during synaptic plasticity. Dendritic spines are the postsynaptic terminals of most excitatory synapses in the mammalian brain. Learning and memory are associated with long-lasting structural remodeling of dendritic spines (structural plasticity) through an actin-mediated process regulated by the Rho-family GTPases RhoA, Rac, and Cdc42. These GTPases undergo sustained activation following synaptic stimulation, but whereas Rho activity can spread from the stimulated spine, Cdc42 activity remains localized to the stimulated spine. Since Cdc42 itself diffuses rapidly in and out of the spine, the basis for the retention of Cdc42 activity in the stimulated spine long after synaptic stimulation has ceased remains unclear. We model the spread of Cdc42 activation at dendritic spines by means of reaction-diffusion equations solved on spine-like geometries. Excitable behavior arising from positive feedback in Cdc42 activation leads to spreading waves of Cdc42 activity. However, because of the very narrow neck of the dendritic spine, wave propagation is halted through a phenomenon we term geometrical wave-pinning. We show that this can account for the localization of Cdc42 activity in the stimulated spine and interestingly, retention is enhanced by high diffusivity of Cdc42. These findings are broadly applicable to other instances of signaling in extreme geometries, including filopodia and primary cilia.</p>Dissertatio