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Time-delayed model of RNA interference

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posted on 2023-06-09, 04:21 authored by G Neofytou, Yuliya KyrychkoYuliya Kyrychko, Konstantin BlyussKonstantin Blyuss
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Ecological Complexity

ISSN

1476-945X

Publisher

Elsevier

Volume

30

Page range

11-25

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Mathematics Applied to Biology Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-06

First Open Access (FOA) Date

2018-01-06

First Compliant Deposit (FCD) Date

2017-01-06

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