Reconstruction of Surface Diffusion from Projected Data

Abstract

The planar projections of short fragments of trajectories of particles (e.g., neuronal receptors) diffusing in the surface of a cell membrane are acquired by a confocal microscope to form a large data set. This and the next sections show how the data can be used to reconstruct the shape of the membrane surface and the physical properties of the receptor motion. A general method for the reconstruction of a two-dimensional surface from the statistics of planar projections of many independent trajectories of a diffusion process on the surface begins with determining the drift field and diffusion tensor of the stochastic dynamics from the projections. The latter represent physical interactions in the surface.