Shortest Hyperpaths in Directed Hypergraphs for Reaction Pathway Inference

Free-energy diagrams, or reaction coordinate diagrams, are graphs showing the energy changes that occur during a chemical reaction. The reaction coordinate represented on the horizontal axis shows how far the reaction has progressed structurally. Positions along the x-axis close to the reactants have structures resembling the reactants, while positions close to the products resemble the products.  Peaks on the energy diagram represent stable structures with measurable lifetimes, while...

Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...

Amino acid biosynthesis is essential for cell growth, protein synthesis, and metabolic regulation. Cells generate essential and non-essential amino acids from metabolic intermediates to sustain vital biological functions. These intermediates originate from key metabolic pathways: glycolysis, the tricarboxylic acid (TCA) cycle, and the pentose phosphate pathway. Important precursors include α-ketoglutarate, pyruvate, oxaloacetate, phosphoenolpyruvate, and erythrose-4-phosphate, which...

The pentose phosphate pathway (PPP) operates in parallel with glycolysis, facilitating the metabolism of both pentoses and glucose. This pathway consists of two distinct phases: the oxidative and non-oxidative phases. While it does not directly generate ATP, the intermediates formed during the process can integrate into glycolysis, contributing to cellular energy metabolism when required.Oxidative Phase: NADPH ProductionThe oxidative phase of the pentose phosphate pathway is primarily...

Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k and the reaction orders are determined experimentally by observing how the rate of reaction changes as the concentrations of the reactants are changed. A common experimental approach to the determination of rate laws is the method of initial rates. This method involves measuring reaction rates for multiple experimental trials carried out using...