The role of cooperativity in a p53-miR34 dynamical mathematical model

•Cooperativity is the change of the rate constant describing each successive stage of a multi-step binding reaction.•p53-miR34 dynamics.•qualitative analysis.•numerical analysis. The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal math...

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Bibliographic Details
Published in:Journal of theoretical biology 2020-06, Vol.495, p.110252-110252, Article 110252
Main Authors: Nikolov, Svetoslav, Wolkenhauer, Olaf, Vera, Julio, Nenov, Momchil
Format: Article
Language:English
Subjects:
Cooperativity
Numerical analysis
p53-miR34 dynamics
Qualitative analysis
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Summary:•Cooperativity is the change of the rate constant describing each successive stage of a multi-step binding reaction.•p53-miR34 dynamics.•qualitative analysis.•numerical analysis. The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal mathematical model describing the interactions between p53 and miR-34a. The model equations are analyzed for negative, none and normal cooperativity using a specific version of bifurcation theory and they are solved numerically. Special attention is paid to the sign of so-called first Lyapunov value. Interpretations of the results are given, both according to dynamic theory and in biological terms. In terms of cell signaling, we propose the hypothesis that when the outgoing signal of a system spends a physiologically significant amount of time outside of its equilibrium state, then the value of that signal can be sampled at any point along the trajectory towards that equilibrium and indeed, at multiple points. Coupled with non-linear behavior, such as that caused by cooperativity, this feature can account for a complex and varied response, which p53 is known for. From dynamical point of view, we found that when cooperativity is negative, the system has only one stable equilibrium point. In the absence of cooperativity, there is a single unstable equilibrium point with a critical boundary of stability. In the case with normal cooperativity, the system can have one, two, or three steady states with both, bi-stability and bi-instability occurring.
ISSN:0022-5193
1095-8541
DOI:10.1016/j.jtbi.2020.110252