A hybrid genetic algorithm with pattern search for finding heavy atoms in protein crystals

Abstract

One approach for determining the molecular structure of proteins is a technique called iso-morphous replacement, in which crystallographers dope protein crystals with heavy atoms, such as mercury or platinum. By comparing measured amplitudes of diffracted x-rays through protein crystals with and without the heavy atoms, the locations of the heavy atoms can be estimated. Once the locations of the heavy atoms are known, the phases of the diffracted x-rays through the protein crystal can be estimated, which in turn enables the structure of the protein to be estimated. Unfortunately, the key step in this process is the estimation of the locations of the heavy atoms, and this is a multi-modal, non-linear inverse problem. We report results of a pilot study that show that a 2-stage hybrid algorithm, using a stochastic genetic algorithm for stage 1 followed by a deterministic pattern search algorithm for stage 2, can successfully locate up to 5 heavy atoms in computer simulated crystals using noise free data. We conclude that the method may be a viable approach for finding heavy atoms in protein crystals, and suggest ways in which the approach can be scaled up to larger problems.

Randomly distributed unit sources to enhance optimization in tsunami waveform inversion

“…The hybrid technique is preferred because global optimization methods, such as GA, are capable of exploring broader search space, but not as good in fine tuning the approximation of the expected solution. Therefore, PS is employed as a local search algorithm to locate other nearby solutions that could possibly be better than the result of the previous search by GA (Payne and Eppstein, 2005;Costa et al, 2010).…”

Asynchronous parallel hybrid optimization combining DIRECT and GSS

“…Recently, metaheuristics have been combined with deterministic methods such as pattern search to form hybrids that perform global and local search [2,6,13,25,51,59,61,64,66]. As mentioned in Section 1, the new approach described in this paper generalizes Gray et al [25]; see also closely related work in [26,58].…”

“…In [61], a few iterations of DIRECT are followed by a few iterations of generalized pattern search (a special case of GSS). Other examples of integrating GSS into a sequential hybrid algorithm may be found in [51,59,66]. In our strategy, the executions are interleaved, though it is not the case that the iterations of the individual solvers are necessarily interleaved.…”

Energy-efficient resource allocation and provisioning for in-memory database clusters

“…We are further interested in the performance of pattern search (PS), a standard direct search method whose mechanics can be found in [32]. While this method does not perform a global search, it can be beneficial for refining existing solutions found in an exploratory search phase [33]. Hence in our case, we want to investigate if PS is able to improve solutions found by BFD.…”