Role of delay in the stochastic creation process

TL;DR

This paper introduces an approximate theoretical approach to analyze how delay times influence fluctuations in stochastic birth-death models, including applications to protein dynamics with transcription and translation delays.

Contribution

It presents a novel method for studying the impact of delay in stochastic processes, enhancing understanding of stochasticity and delay interplay in biological systems.

Findings

Delay can qualitatively change fluctuation behavior.

Distributed delay effects are analyzed.

Application to protein dynamics models with delays.

Abstract

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter them. We also study the effect of distributed delay. We apply the method to a protein-dynamics model that explicitly includes transcription and translation delays. The theoretical model allows us to understand in a general way the interplay between stochasticity and delay.