Equilibrium switching in nonlinear interaction networks with concurrent antagonism

1 Institute of Mathematical Sciences and Physics, University of the Philippines Los Banos, Laguna, Philippines
2 Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines
DOI
10.7287/peerj.preprints.382v1
Published
Accepted
Subject Areas
Bioinformatics, Biophysics, Computational Biology, Mathematical Biology, Computational Science
Keywords
biological switch, regulatory network, species competition, sigmoid kinetics, multi-stability, repressilator
Copyright
© 2014 Rabajante
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
Rabajante J. 2014. Equilibrium switching in nonlinear interaction networks with concurrent antagonism. PeerJ PrePrints 2:e382v1

Abstract

In this paper, we examine a nonlinear concurrent decision-making model (CDM) of interaction networks that involve more than two antagonistic components (e.g., proteins, species, communities, mental choices). The model assumes sigmoid kinetics where every component stimulates itself but represses all others. We are able to prove general dynamical properties of the CDM (e.g., location and stability of steady states) for any dimension of the state space even if the reciprocal antagonism between two components is asymmetric. There are cases where asymmetric interaction generates oscillatory behavior. Some parameters can serve as biological regulators for inducing steady state switching by leading a temporal state to escape an undesired equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state with the desired component having the dominant value. We further show that perpetually adding an external stimulus can shutdown multi-stability of the system that increases the robustness of the system against stochastic noise.

Author Comment

This is an early preprint version only.