Finding Thermodynamically Favorable Pathways in Chemical Reaction Networks Using Flows in Hypergraphs and Mixed-Integer Linear Programming

TL;DR

This paper introduces a mixed-integer linear programming approach to identify thermodynamically favorable pathways in chemical reaction networks modeled as hypergraphs, enabling better pathway ranking and enumeration.

Contribution

It develops a novel ILP formulation that incorporates thermodynamic constraints into pathway search in hypergraph-represented reaction networks.

Findings

Successfully applied to HCN-formamide chemistry network.

Identified alternative pathways with better thermodynamic scores.

Enabled ranking of pathways based on thermodynamic favorability.

Abstract

The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as hypergraphs, modeling that facilitates the search for pathways by computational means. We propose to enrich an existing search method for pathways by including thermodynamic principles. In more detail, we give a mixed-integer linear programming (mixed ILP) formulation of the search problem into which we integrate chemical potentials and concentrations for individual molecules, enabling us to constrain the search to return pathways containing only thermodynamically favorable reactions. Moreover, if multiple possible pathways are found, we can rank these by objective functions based on thermodynamics. As an example of use, we apply the framework to a reaction network representing the HCN-formamide chemistry. Alternative pathways to the one currently hypothesized in the literature are queried and enumerated, including some that score better according to our chosen objective function.