Graph-theoretical identification of reaction pathways of chemical and biochemical reaction systems

Abstract

Reaction-pathway determination plays a key role in the study of the kinetics of chemical or biochemical reactions. Candidate pathways or mechanisms of a catalytic or enzymatic complex chemical or biochemical reaction can be identified through the synthesis of networks of plausible elementary reactions constituting such pathways. This thesis provides a rigorous method for executing this synthesis, which is exceedingly convoluted due to its combinatorial complexity. The proposed method for synthesizing networks of chemical or biochemical reaction pathways follows the general framework of a highly exacting combinatorial method established for process-network synthesis. It is based on the unique graph-representation in terms of P-graphs, 2 sets of axioms, and a group of combinatorial algorithms. In the algorithms, the inclusion or exclusion of a either forward or reverse step of each elementary reaction hinges on the general combinatorial properties of feasible reaction networks. Moreover, the decisions are facilitated by solving linear programming (LP) problems comprising a set of mass-balance constraints to determine the existence or absence of any feasible solution. The search is accelerated further by exploiting the inferences of preceding decisions, thereby eliminating redundancy. As a result, all combinatorially independent, feasible chemical or biochemical reaction networks, i.e., pathways, are generated only once; the pathways violating any first principle of either stoichiometry or thermodynamics are eliminated. The proposed method can enumerate all feasible chemical or biochemical reaction pathways or mechanisms which fulfill the principle of microscopic reversibility and satisfy energetic requirement, that is, not only feasible independent pathways, but also feasible, acyclic combined pathways which result from the appropriate combination of other pathways given plausible elementary reactions and the overall reaction. As far as we know, the proposed me...