# Minimum Action Path theory reveals the details of stochastic biochemical transitions out of oscillatory cellular states

## TL;DR

This paper introduces a theoretical framework using Minimum Action Path theory to analyze stochastic transitions from oscillatory cellular states, revealing detailed escape paths and timing distributions in biochemical systems.

## Contribution

It develops a method to identify the most probable escape paths and times from oscillatory states in biochemical networks using Freidlin-Wentzell action minimization.

## Key findings

- Derived the stochastic spiral exit path from limit cycles.
- Inferred escape time probability density functions.
- Provided a detailed characterization of noise-driven state transitions.

## Abstract

Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Tran- sitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible multidimensional paths, with probabilities depending non-locally on the noise. Here we characterize the escape from an oscillatory biochemical state by minimizing the Freidlin-Wentzell action, deriving from it the stochastic spiral exit path from the limit cycle. We also use the minimized action to infer the escape time probability density function.