Computational models of chemical systems inspired by Braess’ paradox

Abstract

Systems chemistry is a new discipline which investigates the interactions within a network of chemical reactions. We have studied several computational models of chemical systems inspired by mathematical paradoxes and have found that even simple systems may behave in a counterintuitive, non-linear manner depending upon various conditions. In the present study, we modeled a set of reactions inspired by one such paradox, Braess’ paradox, an interesting phenomenon whereby the introduction of additional capacity (e.g. pathways) in some simple network systems can lead to an unexpected reduction in the overall flow rate of “traffic” through the system. We devised several chemical systems that behaved in this counterintuitive manner; the overall rate of product formation was diminished when an additional pathway was introduced and, conversely, there was an enhancement of product formation when the same interconnecting pathway was removed. We found that, unlike a traffic model, the chemical model needed to include reversible pathways in order to mimic “congestion”—a condition necessary to produce Braess-like behavior. The model was investigated numerically, but a full analytical solution is also included. We propose that this intriguing situation may have interesting implications in chemistry, biochemistry and chemical engineering.