Reduction of dynamical biochemical reaction networks in computational biology

TL;DR

This paper explores methods for simplifying complex biochemical reaction networks by leveraging multi-scale properties and tropical geometry, enabling more manageable analysis of biological systems.

Contribution

It introduces a robust framework for model reduction based on dominance and tropical geometry, revisiting classical approaches with new theoretical insights.

Findings

Hierarchical organization of network elements based on dominance.

Practical recipes for reducing linear and nonlinear networks.

Application of reduction techniques to machine learning methods.

Abstract

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to backward pruning machine learning techniques.