Open Access

ARTICLE

Optimal Resource Allocation in a Bacterial Growth Model Under Cold Stress and Temperature

Saira Batool^*, Muhammad Imran^*, Brett McKinney^*

Tandy School of Computer Science, University of Tulsa, Tulsa, OK, USA

* Corresponding Authors: Saira Batool. Email: ; Muhammad Imran. Email: ; Brett McKinney. Email:

(This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)

Computer Modeling in Engineering & Sciences 2026, 146(3), 30 https://doi.org/10.32604/cmes.2026.079067

Received 14 January 2026; Accepted 03 March 2026; Issue published 30 March 2026

Abstract

Bacterial growth requires strategic allocation of limited intracellular resources, especially under cold stress, where stabilized messenger ribonucleic acid (mRNA) secondary structures slow translation by impairing ribosome binding. Escherichia coli (E. coli) counters this bottleneck by inducing the cold-shock protein A (CspA), an RNA chaperone that remodels inhibitory structures. However, synthesizing CspA diverts biosynthetic capacity from ribosome production and metabolism, creating a fundamental resource-allocation trade-off. In this work, we develop a dynamical model capturing the interplay between metabolic precursors, ribosomes, and CspA, and use it to examine how growth and allocation patterns shift with temperature. Steady-state analysis shows that each temperature produces a distinct, locally stable equilibrium, illustrating how cold environments reshape cellular priorities. We then formulate growth maximization as an optimal control problem, solved using Pontryagin’s Maximum Principle, to identify allocation strategies that balance translation maintenance and biomass production. The resulting optimal strategies exhibit bang-bang and singular structures, highlighting periods of extreme and intermediate allocation that reflect how bacteria might dynamically prioritize competing cellular functions. These control patterns converge to their corresponding steady state allocations and provide quantitative insight into optimal resource management under cold stress. These results provide a quantitative optimal-control framework linking RNA-level cold-shock adaptation to proteome allocation and growth, yielding testable predictions for how bacteria balance translational maintenance and biomass production at suboptimal temperatures.

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Keywords

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