Time-delayed model of RNA interference

TL;DR

This paper develops a mathematical model of RNA interference incorporating time delays, revealing how delays can induce oscillations and alter stability, which enhances understanding of gene silencing dynamics.

Contribution

It introduces a novel time-delayed RNAi model and analyzes how delays affect stability and bifurcations, expanding current understanding of RNAi regulation.

Findings

Time delays can cause loss of stability via Hopf bifurcation.

Delays lead to coexistence of stable steady states and periodic orbits.

Original bi-stability is affected by the inclusion of time delays.

Abstract

RNA interference (RNAi) is a fundamental cellular process that inhibits gene expression through cleavage and destruction of target mRNA. It is responsible for a number of important intracellular functions, from being the first line of immune defence against pathogens to regulating development and morphogenesis. In this paper we consider a mathematical model of RNAi with particular emphasis on time delays associated with two aspects of primed amplification: binding of siRNA to aberrant RNA, and binding of siRNA to mRNA, both of which result in the expanded production of dsRNA responsible for RNA silencing. Analytical and numerical stability analyses are performed to identify regions of stability of different steady states and to determine conditions on parameters that lead to instability. Our results suggest that while the original model without time delays exhibits a bi-stability due to the presence of a hysteresis loop, under the influence of time delays, one of the two steady states with the high (default) or small (silenced) concentration of mRNA can actually lose its stability via a Hopf bifurcation. This leads to the co-existence of a stable steady state and a stable periodic orbit, which has a profound effect on the dynamics of the system.