A linear elimination framework

TL;DR

This paper introduces a linear elimination framework that unifies various analytical methods in molecular biology and systems biology, enabling systematic calculation of steady states in nonlinear biochemical systems.

Contribution

It presents a unified linear graph-based framework that simplifies the analysis of complex biochemical networks and reveals connections between previously distinct methods.

Findings

Unified analysis of enzyme kinetics and gene regulation.

Algorithmic calculation of steady states in nonlinear systems.

Revealed connections between different biological analysis methods.

Abstract

Key insights in molecular biology, such as enzyme kinetics, protein allostery and gene regulation emerged from quantitative analysis based on time-scale separation, allowing internal complexity to be eliminated and resulting in the well-known formulas of Michaelis-Menten, Monod-Wyman-Changeux and Ackers-Johnson-Shea. In systems biology, steady-state analysis has yielded eliminations that reveal emergent properties of multi-component networks. Here we show that these analyses of nonlinear biochemical systems are consequences of the same linear framework, consisting of a labelled, directed graph on which a Laplacian dynamics is defined, whose steady states can be algorithmically calculated. Analyses previously considered distinct are revealed as identical, while new methods of analysis become feasible.