Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation
- Published
- Accepted
- Subject Areas
- Bioinformatics, Biophysics, Computational Biology, Mathematical Biology, Computational Science
- Keywords
- biological switch, regulatory network, species competition, sigmoid kinetics, multi-stability, repressilator, perception, mental cognition, oscillations, relative dominance regime
- Copyright
- © 2015 Rabajante et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ PrePrints) and either DOI or URL of the article must be cited.
- Cite this article
- 2015. Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation. PeerJ PrePrints 3:e382v3 https://doi.org/10.7287/peerj.preprints.382v3
Abstract
Concurrent decision-making model (CDM) of interaction networks with more than two antagonistic components represents various biological systems, such as gene interaction, species competition and mental cognition. The CDM model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove generic mathematical properties (e.g., location and stability of steady states) of n-dimensional CDM with either symmetric or asymmetric reciprocal antagonism between components. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by driving a temporal state to escape an undesirable equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state that contains the desired dominant component. Perpetually adding an external stimulus could shut down multi-stability of the system which increases the robustness of the system against stochastic noise. We further show that asymmetric interaction forming a repressilator-type network generates oscillatory behavior.
Author Comment
This is an updated version of the preprint. The final version of the manuscript is accepted for publication in Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena. DOI of the peer-reviewed manuscript is 10.1016/j.chaos.2015.01.018
Supplemental Information
Supplementary Text
Supplementary Text (includes mathematical proofs of the theorems/properties)