Diffusion with Moving Boundary on Spherical Surfaces

Abstract

In this work, we illustrate two approaches to the simulation of surface diffusion over a sphere coupled with the formation of a cluster by reactive particles as a paradigm of a wide variety of problems occurring in many areas of nanosciences and biology. The problem is treated using a Brownian motion approach and a numerical solution of the corresponding continuous Fick's laws of diffusion. While being computationally more expensive, the Brownian motion approach allows one to consider a wider range of situations, particularly those corresponding to relatively high concentrations of diffusing particles and the ensuing problem of particle overlap when they are ascribed finite sizes.

Reconstruction of Aperture Functions during Full Fusion in Vesicular Exocytosis of Neurotransmitters

“…In a former contribution concerning diffusion from a partially masked spherical body [10] we considered that the fraction of the surface area permeable to diffusion was opened instantly, that is, that a op ðtÞ=a max op was a Heaviside time function VðtÞ, while now we wish to consider that this may be a rapid but smooth time function as it ought to be in a biological phenomenon such as vesicular exocytosis.…”

“…One of the purposes of this work is then to take advantage of our present increased understanding about diffusion from within a spherical body [10] to examine whether the fusion rate may be extracted from experimental individual vesicular exocytotic events monitored by amperometry. Up to now, this method has proven to afford the best kinetic and quantitative resolution in investigating such fusion events occurring at a wide variety of cells.…”

“…[10]. This allows accurate but time-consuming simulations so we will then establish on its basis and test an approximate but considerably faster method rooted on semi-analytical formulations of jðtÞ developed in our former work (see Equation (27) in ref.…”

“…[4,6] One process reflects the time variation of the aperture angle a op ðtÞ, since this controls the surface area of the boundary permeable to diffusing species so that an increased a op value is tantamount of an increased released flux. The other represents the diffusion of the species inside the vesicle matrix so as to reach the permeable area of its surface [10] and ultimately escape into the extracellular fluid to be comparatively quickly and quantitatively collected by the electrode. Hence, it is expected that deconvoluting the diffusional contribution from an actual current spike may allow unraveling the aperture angle function a op ðtÞ.…”

Theory of Long‐Range Diffusion of Proteins on a Spherical Biological Membrane: Application to Protein Cluster Formation and Actin‐Comet Tail Growth

“…However, though the random walk approach requires larger computation times it allowed a facile incorporation of size effects of the moving particles. [10] Since in the present work the proteins sizes are not at all negligible compared to the distances they have to travel on the 2D-spherical membrane and their concentration is high, size-exclusion effects are expected to play a significant role. Hence, the random walk numerical approach which can easily implement such effects seemed to us to fit perfectly the biological constraints.…”