Kinetic Theory of the Evolution of Molecules

Almost simultaneously with Spiegelman's review, Manfred Eigen published a kinetic theory of molecular evolution that combined chemical reaction kinetics with knowledge from molecular biology (Eigen, 1971). The kinetic model treats evolution at the population level and can be seen as a generalization of population genetics by a straightforward account for molecular data: Correct replication and mutation are modeled as parallel chemical reactions and accordingly low and high mutation frequency cases can be handled in the same way. The model is likewise applicable to in vitro RNA optimization, evolution of viruses, bacteria, and, in principle, higher organisms. Further developments of the theory led to the concepts of molecular quasi-species and error thresholds (Eigen and Schuster, 1977; Swetina and Schuster, 1982): The quasi-species is a stationary mutant distribution centered around a most efficiently replicating master sequence. In formal terms the quasi-species is the largest eigenvector of the replication-mutation matrix (Eigen et al., 1989). The frequencies of individual mutants in this distribution are determined by the mutation rates and by the differences in replication parameters between master sequence and mutant. An increase in the error rate per site and replication, p, leads to broadening of the quasi-species in the sense that the frequencies of the mutants become higher. At a defined and computable error threshold, pcr o ln o/n,1'. the mutant distribution changes abruptly and becomes uniform: All mutants have the same probability of occurrence and inheritance or conservation of sequences over generations breaks down. Error thresholds were found to set limitations to the genome lengths of organisms (Drake et al., 1998). The error thresholds for RNA viruses of chain length n lie in the range of 1/n per site and replication event, which implies that error rates up to 1/n can be tolerated. In other words, the maximal error frequency is one per genome and replication (implying ln o o 1).

The kinetic theory of molecular evolution provides insight into the replication-mutation dynamics in large populations. Like population genetics it focuses on processing genotypes through correct and error prone copying and does not account explicitly for the phenotype. Indeed, the phenotype enters the model exclusively as a set of rate and equilibrium parameters. In the 1980s the first attempts were made to incorporate RNA structures or phenotypes as explicit entities into the evolutionary process. Unfolding the phenotype from the genotype then becomes tantamount to the formation of RNA minimum free energy structures and the relation between genotypes and phenotypes boils down to a mapping from a space of sequences onto a space of structures (for review see Schuster, 2003).

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