Global optimization methods for protein folding problems

The problem of nding the naturally occurring structure of a pro tein is believed to correspond to minimizing the free or potential energy of the protein This is generally a very di cult global optimizationproblem with a large number of parameters and a huge number of local minimizers includ ing many with function values near that of the global minimizer This paper presents a new global optimization method for such problems The method consists of an initial phase that locates some reasonably low local minimizers of the energy function followed by the main phase that progresses from the best current local minimizers to even lower local minimizers The method combines portions that work on small subsets of the parameters including small scale global optimizations using stochastic methods with local minimizations in volving all the parameters In computational tests on the protein polyalanine with up to amino acids internal parameters the method appears to be very successful in nding the lowest energy structures The largest case is particularly signi cant because the lowest energy structures that are found include ones that exhibit interesting tertiary as opposed to just secondary