Joining and decomposing reaction networks

TL;DR

This paper develops a theoretical framework using algebraic geometry to analyze how joining or decomposing reaction networks impacts key properties like identifiability, invariants, and multistationarity, aiding systems biology research.

Contribution

It provides novel mathematical results that relate properties of combined or separated networks to those of their components, advancing the understanding of complex reaction systems.

Findings

Proves how network joining affects identifiability and invariants.

Establishes conditions under which properties of smaller networks imply those of larger networks.

Uses algebraic geometry techniques to analyze reaction network properties.

Abstract

In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how cross-talk (coupling two or more pathways) or inhibiting molecular function (isolating one part of the pathway) affects systems-level behavior. However, the theory for tackling these larger systems in general has lagged behind. Here, we analyze how joining networks (e.g., cross-talk) or decomposing networks (e.g., inhibition or knock-outs) affects three properties that reaction networks may possess---identifiability (recoverability of parameter values from data), steady-state invariants (relationships among species concentrations at steady state, used in model selection), and multistationarity (capacity for multiple steady states, which correspond to multiple cell decisions). Specifically, we prove results that clarify, for a network obtained by joining two smaller networks, how properties of the smaller networks can be inferred from or can imply similar properties of the original network. Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.