Counting statistics for genetic switches based on effective interaction approximation

TL;DR

This paper applies counting statistics to a genetic switch modeled by an infinite-state master equation, using an effective interaction approximation to simplify the problem and reveal non-Poissonian switching behavior.

Contribution

It introduces an effective interaction approximation to analyze counting statistics in infinite-state systems like genetic switches, simplifying the problem to a two-state model.

Findings

Switching obeys non-Poisson statistics

Effective interaction approximation simplifies analysis

Infinite-state problem approximated as two-state model

Abstract

Applicability of counting statistics for a system with an infinite number of states is investigated. The counting statistics has been studied a lot for a system with a finite number of states. While it is possible to use the scheme in order to count specific transitions in a system with an infinite number of states in principle, we have non-closed equations in general. A simple genetic switch can be described by a master equation with an infinite number of states, and we use the counting statistics in order to count the number of transitions from inactive to active states in the gene. To avoid to have the non-closed equations, an effective interaction approximation is employed. As a result, it is shown that the switching problem can be treated as a simple two-state model approximately, which immediately indicates that the switching obeys non-Poisson statistics.