Movement on Uneven Surfaces Displays Characteristic Features of Hop Diffusion

Abstract

Diffusion in cell plasma membranes is reported to be appreciably slower than diffusion in artificial membranes. We suspect that this is largely an artifact resulting from 2D interpretation of 3D movement over an uneven surface, which leads to the consequent underestimation of the net movement (1). Transient anchorage and/or confinement in domains can easily be explained by topographical trapping. The most serious flaw in the current methods of diffusion measurement is the assumption that the membrane is smooth. When the membrane is uneven, the straight-line-distance between two points requires that the particle leaves the surface, which underestimates the distance travelled. Clearly this is an illegitimate move since both lipids and proteins are restricted to movement within the plane of the membrane. We have therefore developed a new method for analyzing tracks that confines the path to the surface - the shortest within surface distance (SWSD). Simple diffusion was simulated over smooth and uneven surfaces created on a 3D orthogonal grid using an array of connected voxels starting a conditional dilation at the first location that spreads over the surface for a defined number of steps. Notably, after a few steps the diffusion coefficient was higher than after more steps - a characteristic feature of the hop diffusion. We conclude that the minimum requirement for accurate diffusion measurements on the plasma membrane is high resolution topographical images that can be used to assess the effect of local topography on simple diffusion. Only if there is a discrepancy between the measured diffusion coefficient and that expected from Brownian motion within the plane of the membrane after accounting for cell topography is it relevant to invoke anomalous diffusion.1. Adler et al. (2010) Nat. Methods 7, 170-171