Effect of stochasticity on the dynamics of a lac operon model with multiple delays

Asma ben Halim; Sergiy Shelyag; Krishna Busawon; Tania Pencheva; Maia Angelova

doi:10.1098/rsfs.2025.0072

Effect of stochasticity on the dynamics of a lac operon model with multiple delays

Asma ben Halim
, Sergiy Shelyag
, Krishna Busawon
, Tania Pencheva
, Maia Angelova^*

^*Corresponding author for this work

The Sir Peter Rigby Digital Futures Institute

University of Northumbria Newcastle
Flinders University of South Australia
Deakin University
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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Abstract

We have investigated the stability of a mathematical model of the lac operon with multiple time delays, enhanced with stochastic perturbations. Sufficient conditions for exponential mean square stability have been used to determine analytical threshold values. Numerical exploration of the bistability with respect to lactose concentration and noise has been performed. The effect of noise, represented by a stochastic perturbation, was investigated with respect to lactose production in the lac operon system. We have demonstrated that noise can induce changes in the bistable region, including transitions/switching between states owing to the lactose concentration. This article is part of the theme issue ‘Data driven modelling for living systems’.

Original language	English
Article number	20250072
Number of pages	14
Journal	Interface Focus
Volume	16
Issue number	3
Early online date	28 Aug 2026
DOIs	https://doi.org/10.1098/rsfs.2025.0072
Publication status	Published - 28 Aug 2026

Bibliographical note

Copyright © 2026 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/ , which permits unrestricted use, provided the original author and source are credited.

Data Access Statement

This paper presents a new model using data published in another paper, cited in our paper [2 ]. It does not present new data.

Funding

This work was partly supported by European FP7 project 247541 MATSIQEL, Marie Curie Actions-IRSES.

Access to Document

10.1098/rsfs.2025.0072Licence: CC BY 4.0

Effect of stochasticity on the dynamics of a lac operon model with multiple delays
Copyright © 2026 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/ , which permits unrestricted use, provided the original author and source are credited.
Final published version, 3.12 MBLicence: CC BY 4.0

Cite this

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title = "Effect of stochasticity on the dynamics of a lac operon model with multiple delays",

abstract = "We have investigated the stability of a mathematical model of the lac operon with multiple time delays, enhanced with stochastic perturbations. Sufficient conditions for exponential mean square stability have been used to determine analytical threshold values. Numerical exploration of the bistability with respect to lactose concentration and noise has been performed. The effect of noise, represented by a stochastic perturbation, was investigated with respect to lactose production in the lac operon system. We have demonstrated that noise can induce changes in the bistable region, including transitions/switching between states owing to the lactose concentration. This article is part of the theme issue {\textquoteleft}Data driven modelling for living systems{\textquoteright}.",

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AU - ben Halim, Asma

AU - Shelyag, Sergiy

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AU - Pencheva, Tania

AU - Angelova, Maia

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PY - 2026/8/28

Y1 - 2026/8/28

N2 - We have investigated the stability of a mathematical model of the lac operon with multiple time delays, enhanced with stochastic perturbations. Sufficient conditions for exponential mean square stability have been used to determine analytical threshold values. Numerical exploration of the bistability with respect to lactose concentration and noise has been performed. The effect of noise, represented by a stochastic perturbation, was investigated with respect to lactose production in the lac operon system. We have demonstrated that noise can induce changes in the bistable region, including transitions/switching between states owing to the lactose concentration. This article is part of the theme issue ‘Data driven modelling for living systems’.

AB - We have investigated the stability of a mathematical model of the lac operon with multiple time delays, enhanced with stochastic perturbations. Sufficient conditions for exponential mean square stability have been used to determine analytical threshold values. Numerical exploration of the bistability with respect to lactose concentration and noise has been performed. The effect of noise, represented by a stochastic perturbation, was investigated with respect to lactose production in the lac operon system. We have demonstrated that noise can induce changes in the bistable region, including transitions/switching between states owing to the lactose concentration. This article is part of the theme issue ‘Data driven modelling for living systems’.

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Effect of stochasticity on the dynamics of a lac operon model with multiple delays

Abstract

Bibliographical note

Data Access Statement

Funding

Access to Document

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