A Computational Model for the Identification of Biochemical Pathways in the Krebs Cycle

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Abstract
We have applied an algorithmic methodology which provably decomposes any complex network into a complete family of principal subcircuits to study the minimal circuits that describe the Krebs cycle. Every operational behavior that the network is capable of exhibiting can be represented by some combination of these principal subcircuits and this computational decomposition is linearly efficient. We have developed a computational model that can be applied to biochemical reaction systems which accurately renders pathways of such reactions via directed hypergraphs (Petri nets). We have applied the model to the citric acid cycle (Krebs cycle). The Krebs cycle, which oxidizes the acetyl group of acetyl CoA to CO2 and reduces NAD and FAD to NADH and FADH2, is a complex interacting set of nine subreaction networks. The Krebs cycle was selected because of its familiarity to the biological community and because it exhibits enough complexity to be interesting in order to introduce this novel analytic approach. This study validates the algorithmic methodology for the identification of significant biochemical signaling subcircuits, based solely upon the mathematical model and not upon prior biological knowledge. The utility of the algebraic-combinatorial model for identifying the complete set of biochemical subcircuits as a data set is demonstrated for this important metabolic process.