Mechanistic Distinctions

The notion of autocatalysis actually covers a large variety of mechanistic realisations of chemical systems. From the most general definition of autocatalysis, 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 proposed that the key signature of autocatalysis is its kinetic pattern expressed in a mathematical form. It will be shown how such a pattern can be generated by different systems of chemical reactions. Introduction The notion of “autocatalysis” was introduced by Ostwald in 1890 for describing reactions showing a rate acceleration as a function of time. It is for example the case of esters hydrolysis, that is at the same time acid catalyzed and producing an organic acid (Laidler, 1986). Defined as a chemical reaction that is catalyzed by its own products, it has quickly been described on the basis of a characteristic differential equation (Ostwald, 1902, 1912). Typically used to describe complex behaviors of chemical systems, like oscillatory patterns (Lotka, 1910), it has immediately appeared to be essential for the description of biological systems: growth of individual living beings (Robertson, 1908), population evolution (Lotka, 1920) or gene evolution (Muller, 1922). Extending this concept from a chemical description to a more open context was initially carefully described as an analogy, sometime qualified by the more general notion of “autocatakinesis” (Lotka, 1925; Witzemann, 1933). However, this eventually leads to an overgeneralization of the term of autocatalysis, tending to be assimilated to the notion of “positive feedback”, for example in economy (Malcai et al., 2002). The notion of autocatalysis is now actively being used for describing self-organizing systems, namely in the field of emergence of life and artificial life. Autocatalytic processes are the core of the mechanisms leading to the symmetry breaking of chemical compounds towards homochirality (Frank, 1953; Plasson et al., 2007), and could be identified in several experimental systems (Kondepudi et al., 1990; Soai et al., 1995). However, how such autocatalytic processes shall manifest is still under heavy debate (Plasson, 2008; Blackmond, 2009). The purpose of this article is thus to clarify the meaning of chemical autocatalysis and this effort will be undertaken by covering these following points: • What is autocatalysis for a chemical system? On the basis of the general description of a process allowing a chemical compound to enhance the rate of its own formation, autocatalysis is defined by a kinetic signature, expressed in a mathematical form. • How can an autocatalytic process be realized? As many mechanisms can reduce to the same macroscopic kinetic laws exhibiting autocatalysis, the focus is put on several mechanistic realisations of autocatalytic processes, based on simple models further illustrated by concrete chemical examples. • How can autocatalysis be observed and characterized? The focus is put on the dynamic properties, showing that this observable is the direct consequence of the kinetic pattern, rather than the underlying mechanism. • What is the role of autocatalysis? Embedded in nonequilibrium reaction network, the competition between autocatalytic processes allows the onset of chemical selection, that is the existence of bifurcation phenomena allowing the extinction of some compounds in favor of others. Autocatalysis: a Practical Definition A Kinetic Signature From its origin, the notion of autocatalysis has focused on the kinetic pattern of the chemical evolution (Ostwald, 1902). The general definition of autocatalysis as a chemical process in which one of the products catalyzes its own formation can be mathematically generalized as: dxi dt = k(X) ·xi +f(X), k > 0; n > 0; |k| |f | (1) ar X iv :1 00 6. 26 34 v1 [ qbi o. B M ] 1 4 Ju n 20 10