Application of Graph Theory and Automata Modeling for the Study of the Evolution of Metabolic Pathways with Glycolysis and Krebs Cycle as Case Studies

Today, graph theory represents one of the most important modeling techniques in biology. One of the most important applications is in the study of metabolic networks. During metabolism, a set of sequential biochemical reactions takes place, which convert one or more molecules into one or more final products. In a biochemical reaction, the transformation of one metabolite into the next requires a class of proteins called enzymes that are responsible for catalyzing the reaction. Whether by applying differential equations or automata theory, it is not easy to explain how the evolution of metabolic networks could have taken place within living organisms. Obviously, in the past, the assembly of biochemical reactions into a metabolic network depended on the independent evolution of the enzymes involved in the isolated biochemical reactions. In this work, a simulation model is presented where enzymes are modeled as automata, and their evolution is simulated with a genetic algorithm. This protocol is applied to the evolution of glycolysis and the Krebs cycle, two of the most important metabolic networks for the survival of organisms. The results obtained show how Darwinian evolution is able to optimize a biological network, such as in the case of glycolysis and Krebs metabolic networks.