Stochastic Chemical Reactions in Micro-domains

TL;DR

This paper develops stochastic models to describe chemical reactions in micro-domains where molecule numbers are small, capturing fluctuations and noise in biological systems like ionic channels and sensory cells.

Contribution

It introduces a master-diffusion equation and a Markov model to analyze stochastic chemical dynamics in confined micro-domains, extending traditional kinetics.

Findings

Derived a master-diffusion equation for joint probability density.

Calculated fluctuations in substrate binding as a function of initial conditions.

Presented a Markov model based on mean first passage time for boundary interactions.

Abstract

Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a master-diffusion equation for the joint probability density of a mobile reactant and the number of bound substrate in a confined domain. We use the equation to calculate the fluctuations in the number of bound substrate molecules as a function of initial reactant distribution. A second model is presented based on a Markov description of the binding and unbinding and on the mean first passage time of a molecule to a small portion of the boundary. These models can be used for the description of noise due to gating of ionic channels by random binding and unbinding of ligands in biological sensor cells, such as olfactory cilia, photo-receptors, hair cells in the cochlea.