Title: A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

Abstract

Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of themore » objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.« less

Authors:

Reyes, Brandon C. ^[1]; Otero-Muras, Irene ^[2]; Petyuk, Vladislav A.  ^[1]

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• Search DOE PAGES for ORCID "0000-0003-4076-151X"

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+ Show Author Affiliations

1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2. Consejo Superior de Investigaciones Cientificas (CSIC), Vigo (Spain)

Publication Date:

Tue Jan 04 00:00:00 EST 2022

Research Org.:

Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Sponsoring Org.:

USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:

1841972

Report Number(s):

PNNL-SA-167099
Journal ID: ISSN 1471-2105

Grant/Contract Number:  

AC05-76RL01830

Resource Type:

Accepted Manuscript

Journal Name:

BMC Bioinformatics

Additional Journal Information:

Journal Volume: 23; Journal Issue: 1; Journal ID: ISSN 1471-2105

Publisher:

BioMed Central

Country of Publication:

United States

Language:

English

Subject:

59 BASIC BIOLOGICAL SCIENCES; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; systems biology; signaling pathways; chemical reaction network theory; mass action kinetics; bistability; switch-like behavior