Speaker
Description
Protein aggregation plays a key role in the formation of many subcellular structures, ranging from lipid raft formation to protein cluster formation in postsynaptic domains. In many cases the underlying mechanism of protein aggregation involves diffusing particles being assimilated into protein clusters in the presence of a recycling process that exchanges particles with the cytosol. The resulting models support non-equilibrium stationary states (NESS) due to the dynamical balance between particle recycling, diffusion and absorption at cluster interfaces. We investigate protein aggregation models from the wider perspective of moving boundary problems. Given the complexity of the spectral problem underlying the stability of stationary protein clusters, we develop the theory in terms of a single one-dimensional (1D) cluster. This also allows us to exploit certain analogies with a model of tubulin-based neurite elongation, in which the tip of the neurite is treated as a moving boundary subject to polymerization/depolymeriztion. We derive conditions for the existence and stability of a stationary cluster and compare the predictions of the spectral theory with direct numerical simulations of the full reaction-diffusion equations. One of our main results is that a low density cluster in a sea of higher density diffusing proteins can become unstable via a Hopf-like instability. Finally, we show that analogous results hold for a circularly symmetric cluster in $\mathbb R^2$.
