Barriers in the Brain: Morphology and Confinement as Barrier for Lateral Diffusion in Dendritic Spines

Abstract

Dendritic spines are the small-scale neuronal protrusions where the signal transmission between dendrites and axons is localized. The strength of such connections is regulated, among others, by a controlled concentration of AMPA receptors which are effectively confined to the spine's membrane.The spine is able to retain these receptors in its functional domain for long times, but how does it do this? We show that the shape and curvature of the spine's membrane strongly influence the diffusive motion of receptor proteins on the spine's surface. These geometrical effects, together with crowding effects, hinder the lateral diffusion of particles on a membrane. We consider the lateral motion of receptors in the dendritic spine membrane, and find that geometrical confinement and crowding help sustain gradients in concentrations of receptors for very long times, in support of recent experiments. This suggests a deep relationship between shape and physiological function.We present numerical and analytical results showing that the diffusion of receptors is increasingly hindered for decreasing neck sizes of the spine. Besides these geometrical effects, our simulations provide novel insights in crowding effects for interacting particles on curved surfaces. Both geometry and crowding dramatically increase the characteristic time scale for lateral diffusion, thus greatly suppressing the escape rate. This facilitates the confinement of receptors to their functional domain for very long times. These insights help to rationalize Fluorescence after Photobleaching (FRAP) and Single Particle Tracking (SPT) experiments - not only in dendritic spines, but also on bacteria, mitochondria, and other biological structures in which curved membranes feature.