Evolution in vitro - From Kinetic Equations to Magic Molecules

Evolution in vitro - From Kinetic Equations to Magic Molecules  

In his seminal paper on the evolution of molecules, Manfred Eigen [16] combined the knowledge of molecular biology and chemical reaction kinetics and formulated a 

which are the building blocks for polynucleotide synthesis. The rate of RNA synthesis (lower part) is measured through incorporation of radioactive GTP into the newly produced RNA molecules. The rate of replication shows stepwise increase. An early decrease is observed, because first a quasi-species is formed by the master sequence through production of mutants of lower fitness. The figure is redrawn from the data in [12]. 

1) Often it is very difficult to find out whether or not an experimentally observed distribution of genotypes is stationary. The notion of virus quasi-species has been coined to characterize a distribution of variants around a fittest genotype irrespectively of its closeness to a steady state. 

An important feature of the replication-mutation kinetics of Eq. (2) is its straightforward accessibility to justifiable model assumptions. As an example we discuss the uniform error model [18,19] This refers to a molecule which is reproduced sequentially, i.e. digit by digit from one end of the (linear) polymer to the other. The basic assumption is that the accuracy of replication is independent of the particular site and the nature of the monomer at this position. Then, the frequency of mutation depends exclusively on the number of monomers that have to be exchanged in order to mutate from 4 to Ij, which are counted by the Hamming distance of the two strings, d(Ij,Ik)  

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