An Optimization Algorithm for Finding Parameters for Bistability

TL;DR

This paper introduces an optimization algorithm designed to identify parameters in biochemical networks that enable the system to exhibit multiple stable steady states, aiding both understanding and engineering of bistable systems.

Contribution

The authors developed a novel optimization algorithm that finds parameters inducing bistability in dynamical systems based on network topology and trajectory analysis.

Findings

Algorithm successfully identifies parameters for bistability in test systems.

Repeated runs improve the likelihood of finding solutions in narrow parameter spaces.

C code implementation is publicly available for use and further development.

Abstract

Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a network are desirable. In this work, we are particular interested in the question of whether a given pathway can potentially harbor multiple stable steady states. In other words, the challenge is to find the set of parameters such that the dynamical system defined by a set of ordinary differential equations will contain multiple stable steady states. Being able to find parameters that cause a network to be bistable may also be benefitial for engineering synthetic bistable systems where the engineer needs to know a working set of parameters. Result: We have developed an algorithm that optimizes the parameters of a dynamical system so that the system will contain at least one saddle or unstable point. The algorithm then looks at trajectories around this saddle or unstable point to see whether the different trajectories converge to different stable points. The algorithm returns the parameters that causes the system to exhibit multiple stable points. Since this is an optimization algorithm, it is not quaranteed to find a solution. Repeated runs are often required to find a solution for systems where only a narrow set of parameters exhibit bistability. Availability: The C code for the algorithm is available at http://tinkercell.googlecode.com