Global optimization methods for protein folding problems

Abstract

Abstract. The problem of nding the naturally occurring structure of a protein 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 including 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 reasonablylow local minimizers o f 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 involving all the parameters. In computational tests on the protein polyalanine with up to 58 amino acids (116 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 structure.

High-Performance Numerical Optimization on Multicore Clusters

“…Although many parallel local and global optimization algorithms were proposed in the last decades (e.g. [5,6], only a handful of actual systems exist. One of the most widely used scientific software programs, MATLAB, presented its first parallel optimization solution in 2009 [7].…”

Opportunities for Combinatorial Optimization in Computational Biology

“…One approach to protein structure prediction is to determine the position of a protein's atoms so as to minimize the total free energy (Byrd et al 1996, Neumaier 1997. In practice, accurate energy function calculations cannot be used for protein structure prediction, even for proteins with as few as 50 residues, so approximate models are commonly used.…”

Sourcebook of parallel computing

“…An important reason is that the increasing power of parallel high-performance architectures makes it possible to attack many large, difficult global optimization problems of practical interest. Ten years ago, work in this area was still limited to toy problems of about 10 variables, but now, with the help of parallel computing, advanced algorithms have been developed and applied to problems with hundreds or even thousands of variables in such applications as cluster simulation [159,160,161,162,211,212,858,1007,1008], protein folding [163,214,234,575,576,613,727,764,781,852,853], and molecular docking [270,672].…”

“…, n, where n is the number of the atoms in the protein and usually is in the range of 1000 to 100,000. Recent work to develop special methods for this problem includes Scheraga et al [575,576,764,831], Straub et al [904], Coleman et al [211,212], and Byrd and Schnabel [162,163,234,858].…”