Design as a Simulation of Evolutionary Process

The concept of evolution of primary sequences of biopolymers has attracted great interest from biologists, chemists and physicists for a long time [65-68]. As has been discussed, it is natural to expect that the content of information in the sequences of biopolymers (proteins, DNA, RNA) is relatively high in comparison with random sequences where it should be almost zero [69]. Presumably, the information complexity of early ancestors of present-day biopolymers has been increased in the course of molecular evolution when the 

It is worthwhile to note that since the information content of a sequence can be represented as a mathematically defined quantity, the whole process of evolution of biopolymer sequences can be specified in exact mathematical terms. The formulated fundamental problem is extremely difficult because of the absence of direct information on the early prebiological evolution. Therefore, of particular interest are toy models of evolution of sequences that show different possibilities for appearance of statistical complexity and of long-range correlations in the sequences. 

It is clear that information complexity cannot emerge just as a result of random mutations. Some coupling of mutations to other factors is necessary. It is most straightforward and natural to introduce the interrelation of mutations and conformations, i.e., to consider conformation-dependent sequence design in the context of evolution. 

Evolutionary computation approaches are optimization methods. They are conveniently presented using the metaphor of natural evolution a randomly initialized population of individuals evolves following a crude parody of the Darwinian principle of the survival of the fittest. New individuals are generated using simulated evolutionary operations such as mutations. The probability of survival of the newly generated solutions depends on their fitness (how well they perform with respect to the optimization problem at hand) the best are kept with a high probability, the worst are rapidly discarded. 

In the literature, some computer models describing the evolution of copolymer sequences have been proposed [26,28]. Most of them are based on a stochastic Monte Carlo optimization principle (Metropolis scheme) and aimed at the problems of protein physics. Such optimization algorithms start with arbitrary sequences and proceed by making random substitutions biased to minimize relative potential energy of the initial sequence and/or to maximize the folding rate of the target structure. 

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