Autocatalysis is a fundamental concept, used in a wide range of domains. From its most general definition, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. The notion of autocatalysis covers a large variety of mechanistic realizations with very similar behaviors; it is proposed that its key signature is its kinetic pattern expressed in a mathematical form. This notion, while describing dynamic behaviors at the most fundamental level, is at the basis for developing higher-level concepts towards life: autocatalytic sets, and autopoietic systems.

A coevolutionary model is discussed that incorporates the logical structure of constitutional chemistry and its kinetics on the one hand and the topological evolution of the chemical reaction network on the other hand. The motivation for designing this model is twofold. First, experiments that are to provide insight into chemical problems should be expressed in a syntax that remains as close as possible to real chemistry. Second, the study of physical properties of the complex chemical reaction networks requires growing models that incorporate features realistic from a biochemical perspective. In this article the theory and algorithms underlying the coevolutionary model are explained, and two illustrative examples are provided. These examples show that one needs to be careful in making general claims concerning the structure of chemical reaction networks.