Computing equilibrium concentrations for large heterodimerization networks

TL;DR

This paper introduces a fast iterative algorithm to compute equilibrium concentrations in large heterodimerization networks governed by mass action kinetics, demonstrating rapid convergence even with millions of species.

Contribution

A novel, efficient iterative method with guaranteed convergence for large-scale heterodimerization networks, applicable to biological data analysis.

Findings

Rapid convergence for most species in large networks

Effective handling of networks with up to a million species

Insights into slow convergence in specific subnetworks

Abstract

We consider a chemical reaction network governed by mass action kinetics and composed of N different species which can reversibly form heterodimers. A fast iterative algorithm is introduced to compute the equilibrium concentrations of such networks. We show that the convergence is guaranteed by the Banach fixed point theorem. As a practical example, of relevance for a quantitative analysis of microarray data, we consider a reaction network formed by N~10^6 mutually hybridizing different mRNA sequences. We show that, despite the large number of species involved, the convergence to equilibrium is very rapid for most species. The origin of slow convergence for some specific subnetworks is discussed. This provides some insights for improving the performance of the algorithm.