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

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.