Impact of morphology on diffusive dynamics on curved surfaces

Abstract

Diffusive processes on nonplanar substrates are deeply relevant for cellular function and transport and increasingly used to probe and characterize the behavior of proteins in membranes. We present analytical and numerical analyses of in-plane diffusion of discrete particles on curved geometries reflecting various generic motifs in biology and explore, in particular, the effect that the shape of the substrate has on the characteristic time scales of diffusive processes. To this end, we consider both collective measures (the relaxation of concentration profiles towards equilibrium) and single-particle measures (escape rates and first passage times of individual diffusing molecules): the first relevant for the correct interpretation of FRAP experiments in curved environments; the second, for single-particle tracking probes. Each of these measures is sensitively affected by the morphology of the substrate, and we find that the exit rate out of a domain is not uniquely set by the size of its boundary, illustrating the general principle we reveal: By varying the shape of a substrate, Nature can control the diffusive time scales in a microenvironment without changing the bare substrate properties.

Analysis of diffusion in curved surfaces and its application to tubular membranes

“…, 2011; Holcman and Schuss, 2011; Singh et al. , 2012; Kusters and Storm, 2014; Kusters et al. , 2014).…”

“…The predicted slowdown also confirms other theoretical works by groups who have investigated diffusion in curved surfaces. For instance, Kusters and Storm (2014), using random-walk simulations of single particles diffusing on tubes, have shown that curved surfaces retain molecules for an increased period of time before the molecules escape. The predicted slowing down of diffusion due to curvature effects was shown to influence receptor egress from the dendritic spine (Kusters et al.…”

A Method for Molecular Dynamics on Curved Surfaces

“…Many experimental (6,7,8,9) and theoretical (5,10,11,12) efforts have been made to understand how membrane shape and composition regulates protein diffusion on highly curved membrane structures. Most theoretical models are based on solving the diffusion equation on the curved surface (10,11,12,13). This method, however, is not always tractable, especially when complex particle-particle interactions, which are of great importance in these systems, are involved (2).…”

Barriers in the brain: resolving dendritic spine morphology and compartmentalization

“…Mushroom shaped spines were found to retain AMPA receptors in the vicinity of the synapse for an increased period of time (Ashby et al, 2006 ; Ehlers et al, 2007 ; Opazo and Choquet, 2011 , see Figure 3A ). These observations have been rationalized by several modeling studies, which showed that the typical mushroom-like morphology of dendritic spines strongly alters the lateral diffusion of AMPA receptors, demonstrating a pronounced suppression of the receptor exit rate out of spines with decreasing neck radius as well as increasing neck length (Holcman and Schuss, 2011 ; Kusters et al, 2013 ; Kusters and Storm, 2014 ). More specifically, the characteristic timescale for retention, the mean escape time of receptors through the neck of a typical mushroom-shaped spines follows a power-law dependence on neck radius r , …”

“…where λ and η are positive constants, whose numerical value depends on the actual shape of the spine (Kusters et al, 2013 ; Kusters and Storm, 2014 ).…”