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J Theor Biol. 2020 Mar 18:110252. doi: 10.1016/j.jtbi.2020.110252. [Epub ahead of print]

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

Author information

1
Department of Systems Biology and Bioinformatics, University of Rostock, 18051 Rostock; Institute of Mechanics and Biomechanics-Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria; University of Transport, Geo Milev Str., 158, 1574 Sofia, Bulgaria; Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen, Erlangen, Germany. Electronic address: s.nikolov@imbm.bas.bg.
2
Department of Systems Biology and Bioinformatics, University of Rostock, 18051 Rostock; Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, Stellenbosch, South Africa.
3
Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen, Erlangen, Germany.
4
Institute of Mechanics and Biomechanics-Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria.

Abstract

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.

KEYWORDS:

Cooperativity, p53-miR34 dynamics; Numerical analysis; Qualitative analysis

PMID:
32199858
DOI:
10.1016/j.jtbi.2020.110252

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