Absolute transition rates for rare events from dynamical decoupling of reaction variables

Interpretation of amperometric kinetics of content release during contacts of vesicles with a lipid membrane

The exocytotic pathway of secretion of molecules from cells includes transport by vesicles, tether-mediated fusion of vesicles with the plasma membrane accompanied by pore formation, and diffusion-mediated release of their contents via a pore to the outside. In related basic biophysical studies, vesicle-content release is tracked by measuring corresponding amperometric spikes. Although experiments of this type have a long history, the understanding of the underlying physics is still elusive. The present study elucidates the likely contribution of line energy, membrane tension and bending, osmotic pressure, hydration forces, and tethers to the potential energy for fusion-related pore formation and evolution. The overdamped Langevin equation is used to describe the pore dynamics, which are in turn employed to calculate the kinetics of content release and to interpret the shape of amperometric spikes.

Summing over trajectories of stochastic dynamics with multiplicative noise

We demonstrate that previous path integral formulations for the general stochastic interpretation generate incomplete results exemplified by the geometric Brownian motion. We thus develop a novel path integral formulation for the overdamped Langevin equation with multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally generates a normalized transition probability in examples. Our result solves the inconsistency of the previous path integral formulations for the general stochastic interpretation, and can have wide applications in chemical and physical stochastic processes.