Exact solution of a stochastic protein dynamics model with delayed degradation

TL;DR

This paper provides an exact solution to a stochastic protein dynamics model with delayed degradation, clarifying how delay affects stochastic behavior and mean values, and showing oscillations are not possible.

Contribution

The authors derive an exact solution for a stochastic model with delay, revealing differences from previous approximations and analyzing correlation functions.

Findings

Mean value equations differ from intuitive models

Oscillatory behavior is not observed in the system

Exact correlation functions highlight delay effects

Abstract

We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained differ from others intuitively proposed and that oscillatory behavior is not possible in this system. We discuss the calculation of correlation functions in stochastic systems with delay, stressing the differences with Markovian processes. The exact results allow to clarify the interplay between stochasticity and delay.