Optimality-preserving Reduction of Chemical Reaction Networks

TL;DR

This paper introduces a polynomial-time reduction algorithm for chemical reaction networks that simplifies optimal control problems while preserving their solutions, enabling efficient control of large-scale biological systems.

Contribution

The paper presents a novel optimality-preserving reduction method for CRNs that reduces problem complexity without losing solution accuracy, applicable to large biological networks.

Findings

Reduction algorithm runs in polynomial time.

Enables control of large-scale protein-interaction networks.

Successfully applied to vaccination models with hundreds of thousands of variables.

Abstract

Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology, CRN parameters such as the kinetic reaction rates can be used as control inputs to steer the system toward a given target. Unfortunately, the resulting optimal control problem is nonlinear, therefore, computationally very challenging. We address this issue by introducing an optimality-preserving reduction algorithm for CRNs. The algorithm partitions the original state variables into a reduced set of macro-variables for which one can define a reduced optimal control problem from which one can exactly recover the solution of the original control problem. Notably, the reduction algorithm runs with polynomial time complexity in the size of the CRN. We use this result to reduce reachability and control problems of large-scale protein-interaction networks and vaccination models with hundreds of thousands of state variables.