MES may be one such approach but there is no proof that it does include natural selection mechanisms or `punctuated evolution mechanisms' ?
I'm not sure I quite understand the question. MES is a multidisciplinary approach to the understanding of biological evolution, while "directed molecular evolution" is an experimental method to produce novel proteins. The way we are using "directed molecular evolution" is not as a method to analyze the processes of natural evolution, but as a protein engineering strategy to improve the biophysical and functional properties of a particular protein.
Starting from a gene library (fully synthetic, including nucleotide or trinucleotide mixtures to introduce variability in specific position or produced from natural genes through error-prone replication and in-vitro recombination of families of related genes), improved variants of the protein encoded by the gene are selected by techniques such as ribosome display, phage display or bacterial and yeast surface display in alternating rounds of selection and randomization. Depending on the gene randomization procedures used, types and location of mutations as well as the mutational load can be under experimental control, as well as the selection stringency applied to the selection. A mathematical description of a "directed molecular evolution" experiment would have to take into account the initial library design and randomization scheme (global mutagenesis or focussed diversification), theoretical library diversity of the initial library and actual library size, mutational tolerance of the particular protein analyzed, the stringency and resolving power of the particular selection procedures used, mutational load in subsequent randomization steps.
My question did not include ,,molecular" in directed evolution. MES in my question referred to Memory Evolutive Systems introduced recently and mathematically by Andree Ehresmann.
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