Open chemical reaction networks, steady-state loads and Braess-like paradox

TL;DR

This paper investigates how adding extra reaction pathways in open chemical networks can unexpectedly increase steady-state concentrations, revealing Braess-like paradoxes and their implications for biochemical reaction mechanisms.

Contribution

It demonstrates the existence of Braess-like paradoxes in chemical reaction networks and explores their effects on steady-state load, including in biological systems like uric acid degradation.

Findings

Extra reaction pathways can increase steady-state load unexpectedly.

Braess-like paradoxes are observed across networks of varying complexity.

Decomposition steps can reduce load, influencing reaction evolution.

Abstract

Open chemical reaction systems involve matter-exchange with the surroundings. As a result, species can accumulate inside a system during the course of the reaction. We study the role of network topology in governing the concentration build-up inside a fixed reaction volume at steady state, particularly focusing on the effect of additional paths. The problem is akin to that in traffic networks where an extra route, surprisingly, can increase the overall travel time. This is known as the Braess' paradox. Here, we report chemical analogues of such a paradox in suitably chosen reaction networks, where extra reaction step(s) can inflate the total concentration, denoted as `load', at steady state. It is shown that, such counter-intuitive behavior emerges in a qualitatively similar pattern in networks of varying complexities. We then explore how such extra routes affect the load in a biochemical scheme of uric acid degradation. From a thorough analysis of this network, we propose a functional role of some decomposition steps that can trim the load, indicating the importance of the latter in the evolution of reaction mechanisms in living matter.