This paper presents a two-level protein folding optimization on a three-dimensional AB off-lattice model. The first level is responsible for forming conformations with a good hydrophobic core or a set of compact hydrophobic amino acid positions. These conformations are forwarded to the second level, where an accurate search is performed with the aim of locating conformations with the best energy value. The optimization process switches between these two levels until the stopping condition is satisfied. An auxiliary fitness function was designed for the first level, while the original fitness function is used in the second level. The auxiliary fitness function includes expression about the quality of the hydrophobic core. This expression is crucial for leading the search process to the promising solutions that have a good hydrophobic core and, consequently, improves the efficiency of the whole optimization process. Our differential evolution algorithm was used for demonstrating the efficiency of the two-level optimization. It was analyzed on well-known amino acid sequences that are used frequently in the literature. The obtained experimental results show that the employed two-level optimization improves the efficiency of our algorithm significantly, and that the proposed algorithm is superior to other state-of-the-art algorithms.
Information about a hydrophobic core, or a set of positions of the hydrophobic amino acids, is very useful for structure prediction in different methods. The authors in @cite_11 presented a constraint-based method. The key concept of this method is the ability to compute maximally compact hydrophobic cores. Information about hydrophobic core was also used within stochastic algorithms for PFO. In @cite_27 @cite_31 a macro-mutation operator is incorporated into the genetic algorithm and applied to the three-dimensional face-centered cubic lattice. This operator compresses the conformation and quickly forms the hydrophobic-core. The obtained results show that the macro-mutation operator improves the efficiency of the algorithm significantly.
@cite_27 @cite_31 @cite_11
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In-vitro methods for protein structure determination are time-consuming, cost-intensive, and failure-prone. Because of these expenses, alternative computer-based predictive methods have emerged. Predicting a protein’s 3-D structure from only its amino acid sequence—also known as ab initio protein structure prediction (PSP)—is computationally demanding because the search space is astronomically large and energy models are extremely complex. Some successes have been achieved in predictive methods but these are limited to small sized proteins (around 100 amino acids); thus, developing efficient algorithms, reducing the search space, and designing effective search guidance heuristics are necessary to study large sized proteins. An on-lattice model can be a better ground for rapidly developing and measuring the performance of a new algorithm, and hence we consider this model for larger proteins (>150 amino acids) to enhance the genetic algorithms (GAs) framework. In this paper, we formulate PSP as a combinatorial optimization problem that uses 3-D face-centered-cubic lattice coordinates to reduce the search space and hydrophobic-polar energy model to guide the search. The whole optimization process is controlled by an enhanced GA framework with four enhanced features: 1) an exhaustive generation approach to diversify the search; 2) a novel hydrophobic core-directed macro-mutation operator to intensify the search; 3) a per-generation duplication elimination strategy to prevent early convergence; and 4) a random-walk technique to recover from stagnation. On a set of standard benchmark proteins, our algorithm significantly outperforms state-of-the-art algorithms. We also experimentally show that our algorithm is robust enough to produce very similar results regardless of different parameter settings. Graphical abstractDisplay Omitted HighlightsGraded energy-model strategically mixes the 20×20 MJ potential matrix with 2×2 HP energy model.HP guided macro-mutation operator within GA provides efficient sampling.Proposed Algorithm outperformed other state-of-the-art approaches.Splits the energy function related complexities into two less complex functions through macro-mutation operator. Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited scopes to exercise and evaluate the algorithmic developments due to its astronomically large set of data-points. In contrast, an on-lattice model widens the scopes and permits studying the relatively larger proteins because of its finite set of data-points. In this work, we took the full advantage of an on-lattice model by using a face-centered-cube lattice that has the highest packing density with the maximum degree of freedom. We proposed a graded energy-strategically mixes the Miyazawa-Jernigan (MJ) energy with the hydrophobic-polar (HP) energy-based genetic algorithm (GA) for conformational search. In our application, we introduced a 2×2 HP energy guided macro-mutation operator within the GA to explore the best possible local changes exhaustively. Conversely, the 20×20 MJ energy model-the ultimate objective function of our GA that needs to be minimized-considers the impacts amongst the 20 different amino acids and allow searching the globally acceptable conformations. On a set of benchmark proteins, our proposed approach outperformed state-of-the-art approaches in terms of the free energy levels and the root-mean-square deviations. Protein structure prediction remains one of the significant challenges in computational biology. We have previously shown that our kinetostatic compliance method can overcome some of the key difficulties faced by other de novo structural prediction methods, such as the very small time steps required by the molecular dynamics approaches, or the very large number of samples required by the sampling based techniques. In this paper we extend the previous free energy formulation by adding the solvent effects, which contribute predominantly to the folding phenomena. We show that the addition of the solvation effects, which complement the existing Coulombic and van der Waals interactions, lead to a physically effective energy function. Furthermore, we achieve significant computational speed-up by employing efficient algorithms and data structures that effectively reduce the time complexity from O(n2) to O(n), n being the number of atoms. Our simulations are consistent with the general behavior observed in protein folding, and show that the hydrophobic atoms tend to pack inside the core of the molecule in an aqueous solvent, while a vacuum environment produces no such effect.Copyright © 2013 by ASME Abstract Two major components are required for a successful prediction of the three-dimensional structure of peptides and proteins: an efficient global optimization procedure which is capable of finding an appropriate local minimum for the strongly anisotropic function of hundreds of variables, and a set of free energy components for a protein molecule in solution which are computationally inexpensive enough to be used in the search procedure, yet sufficiently accurate to ensure the uniqueness of the native conformation. We here found an efficient way to make a random step in a Monte Carlo procedure given knowledge of the energy or statistical properties of conformational subspaces (e.g. φ-ψ zones or side-chain torsion angles). This biased probability Monte Carlo (BPMC) procedure randomly selects the subspace first, then makes a step to a new random position independent of the previous position, but according to the predefined continuous probability distribution. The random step is followed by a local minimization in torsion angle space. The positions, sizes and preferences for high-probability zones on φ-ψ maps and χ-angle maps were calculated for different residue types from the representative set of 191 and 161 protein 3D-structures, respectively. A fast and precise method to evaluate the electrostatic energy of a protein in solution is developed and combined with the BPMC procedure. The method is based on the modified spherical image charge approximation, efficiently projected onto a molecule of arbitrary shape. Comparison with the finite-difference solutions of the Poisson-Boltzmann equation shows high accuracy for our approach. The BPMC procedure is applied successfully to the structure prediction of 12- and 16-residue synthetic peptides and the determination of protein structure from NMR data, with the immunoglobulin binding domain of streptococcal protein G as an example. The BPMC runs display much better convergence properties than the non-biased simulations. The advantage of a true global optimization procedure for NMR structure determination is its ability to cope with local minima originating from data errors and ambiguities in NMR data.