Abstract

This paper discusses DNA-based stochastic optimizations under the constraint that the search starts from a given point in a search space. Generally speaking, a stochastic optimization method explores a search space and finds out the optimum or a sub-optimum after many cycles of trials and errors. This search process could be implemented efficiently by ``molecular computing'', which processes DNA molecules by the techniques of molecular biology to generate and evaluate a vast number of solution candidates at a time. We assume the exploration starting from a single point, and propose a method to embody DNA-based optimization under this constraint, because this method has a promising application in the research field of protein engineering. In this application, a string of nucleotide bases encodes a protein possessing a specific activity, which could be given as a value of an objective function. Thus, a problem of obtaining a protein with the optimum or a sub-optimum about the desired activity corresponds to a combinatorial problem of obtaining a base sequence giving the optimum or a sub-optimum in the sequence space. Biologists usually modify a base sequence corresponding to a naturally occurring protein into another sequence giving a desired activity. In other words, they explore the space in the proximity of a natural protein as a start point. We first examined if the optimization methods that involve a single start point, such as simulated annealing, Gibbs sampler, and MH algorithms, can be implemented by DNA-based operations. Then, we proposed an application of genetic algorithm, and examined the performance of this application on a model fitness landscape by computer experiments. These experiments gave helpful guidelines in the embodiments of DNA-based stochastic optimization, including a better design of crossover operator.