A hybrid approach to protein folding problem integrating constraint programming with local search

Abstract

BackgroundThe protein folding problem remains one of the most challenging open problems in computational biology. Simplified models in terms of lattice structure and energy function have been proposed to ease the computational hardness of this optimization problem. Heuristic search algorithms and constraint programming are two common techniques to approach this problem. The present study introduces a novel hybrid approach to simulate the protein folding problem using constraint programming technique integrated within local search.ResultsUsing the face-centered-cubic lattice model and 20 amino acid pairwise interactions energy function for the protein folding problem, a constraint programming technique has been applied to generate the neighbourhood conformations that are to be used in generic local search procedure. Experiments have been conducted for a few small and medium sized proteins. Results have been compared with both pure constraint programming approach and local search using well-established local move set. Substantial improvements have been observed in terms of final energy values within acceptable runtime using the hybrid approach.ConclusionConstraint programming approaches usually provide optimal results but become slow as the problem size grows. Local search approaches are usually faster but do not guarantee optimal solutions and tend to stuck in local minima. The encouraging results obtained on the small proteins show that these two approaches can be combined efficiently to obtain better quality solutions within acceptable time. It also encourages future researchers on adopting hybrid techniques to solve other hard optimization problems.

Exact methods for lattice protein models

“…The use of HP-optimal structure samples was shown to boost protein structure prediction in more sophisticated models [21,22,48,50]. Here, no exact methods are available and thus local search schemes are applied.…”

“…Nevertheless, it can be extended to HP-related energy models as the HPNX model [46,74,75]. Furthermore, it was shown that the HP model can be used within hierarchical approaches to enhance the prediction of optimal structures in more sophisticated energy models providing 20 × 20-potentials [21,22]. Both directions are discussed in the following.…”

“…This so-called hydrophobic core is present in almost all globular water-solved protein structures. It is central to the CPSP approach and was also used in recent local search methods [22,34]. Beneath the suggested energy potentials by Dill and co-workers [58] (e(S i , S j ) = -1, if S i and S j are hydrophobic; 0, otherwise), other potentials have been applied [47,59].…”

“…Among them are its extension and application to the HPNX model [46], which also takes polar interactions into account [47]. Furthermore, HP-optimal predictions can be used within a hierarchical prediction approach to search for energy-optimal structures within full 20 × 20 pairwise potential models [21,22,48]. The latter requires the identification of HP-optimal conformations that are structurally diverse.…”

“…As exhaustive structure enumeration approaches [20] are restricted to very short sequence lengths, usually heuristic methods are applied. They apply various techniques, e.g., simulated annealing [21,22], quantum annealing [23], ant colonization optimization [24], evolutionary algorithms [25], energy landscape paving [26], large neighborhood search [27,28], constraint programming [29][30][31], or dedicated search heuristics [32][33][34][35]. They enable performance-guaranteed approximations close to the optimum for both backbone-only [36,37] and sidechain models [38,39].…”