Autocatalytic and other general networks for chemical mechanisms,pathways, and cycles: Their systematic and topological generation

Methods to generate a priori all the finite number of possible mechanisms of chemical reactions and/or synthetic pathways or thermodynamic cycles, which we represent by general networks, are given for any number of reaction steps or total number of species (reactants, products, catalysts, and intermediates). General networks do not place limitations on the types of species, e.g. intermediates can be short-lived, thereby participating in at most two elementary reaction steps, or longer-lived, participating in more than one way. Step stoichiometric coefficients can be more than unity. Reactants or products may also act as catalysts or inhibitors. Species vertices and the general networks themselves in which they occur are classified topologically. Topological invariants of the networks with respect to the number of reaction steps are found. Mechanisms with desired features, e.g. containing certain numbers of generalized catalysts, chains, autocatalysts, etc., are generated using the invariants, from the simplest prototypes, for successively larger numbers of reaction steps. Special emphasis is given to autocatalytic networks due to their role in chemical oscillations, dynamical instabilities and in selfreplicating reactions. Examples given include the malic acid cycle, oscillatory cycles in glycolysis, Lotka-Volterra-Prigogine-Glansdorff models, and others. Oscillating and/or self-replicating cycles that have been invoked in various contexts are shown to have a common topological feature. The methods are useful also in the many autocatalytic processes of chemical engineering importance.