Signal propagation across layered biochemical networks

Abstract

Biochemical reaction networks typically consist of a complicated structure with many interacting species and components. Techniques for the analysis of such complex systems commonly use decompositions into simpler subsystems. These decompositions are often modular, representing the state vector as a concatenation of component vectors. Without transformation, modular decompositions may lead to system parameters directly influencing the dynamics of many subsystems at once. When parameters are the control inputs, this complicates analysis and design. This paper investigates an alternative decomposition, termed layering, which partitions parameters between layers. This allows for hierarchical analysis, where the steady state response of the integrated system to the perturbation of a parameter is calculated in stages. The first stage is to calculate the local response of the steady state of a layer, considered in isolation from other layers; the second is to calculate the perturbed layer's effect on the others when connected back into the full system. This analysis results in a strategy for detecting the layered structure of a biochemical network based on preserving cycles of mass flow within layers. Additionally, by expressing how the local response propagates through the system we uncover the paths by which the direct control of a certain layer may indirectly control others, giving insights into how to exploit their dependencies.