The molecular roots of compositional inheritance.

Non-covalent compositional assemblies, made of monomeric mutually catalytic molecules, constitute an alternative to alphabet-based informational biopolymers as a mechanism of primordial inheritance. Such assemblies appear implicitly in many "Metabolism First" origin of life scenarios, and more explicitly in the Graded Autocatalysis Replication Domain (GARD) model Segréet al. (2000). Proc. Natl Acad. Sci. U.S.A.97, 4112-4117]. In the present work, we provide a detailed analysis of the quantitative molecular roots of such behavior. It is demonstrated that the fidelity of reproduction provided by a newly defined heritability measure eta(*)(s), strongly depends on the values of molecular recognition parameters and on assembly size. We find that if the catalytic rate acceleration coefficients are distributed normally, transfer of compositional information becomes impossible, due to frequent "compositional error catastrophes". In contrast, if the catalytic acceleration rates obey a lognormal distribution, as actually predicted by a statistical formalism for molecular repertoires, high reproduction fidelity is obtained. There is also a clear dependence on assembly size N, whereby maximal eta is seen in a narrow range around N approximately 3.5 N(G)/lambda, where N(G)is the size of the primordial molecular repertoire and lambda is a molecular interaction statistical parameter. Such relationships help define the physicochemical conditions that could underlie the early steps in pre-biotic evolution.