Decomposing the parameter space of biological networks via a numerical discriminant approach

TL;DR

This paper introduces numerical algorithms to decompose high-dimensional parameter spaces of biological networks into regions with consistent steady-state solutions, aiding the analysis of complex nonlinear systems.

Contribution

It develops novel global and local numerical methods to construct discriminant loci and classify parameter landscapes in biological network models.

Findings

Successfully applied algorithms to molecular and cell-network models.

Enabled systematic classification of steady-state behaviors across parameter regions.

Provided tools for analyzing stability and bifurcations in complex systems.

Abstract

Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and characterize the steady-state solutions as the model parameters vary, a technically challenging problem in a high-dimensional parameter landscape. Rather than simply determining the number and stability of steady-states at distinct points in parameter space, we decompose the parameter space into finitely many regions, the steady-state solutions being consistent within each distinct region. From a computational algebraic viewpoint, the boundary of these regions is contained in the discriminant locus. We develop global and local numerical algorithms for constructing the discriminant locus and classifying the parameter landscape. We showcase our numerical approaches by applying them to molecular and cell-network models.