Protein structure prediction using mutually orthogonal Latin squares and a genetic algorithm

We combine a new, extremely fast technique to generate a library of low energy structures of an oligopeptide (by using mutually orthogonal Latin squares to sample its conformational space) with a genetic algorithm to predict protein structures. The protein sequence is divided into oligopeptides, and a structure library is generated for each. These libraries are used in a newly defined mutation operator that, together with variation, crossover, and diversity operators, is used in a modified genetic algorithm to make the prediction. Application to five small proteins has yielded near native structures.     

Enhanced sampling of the molecular potential energy surface using mutually orthogonal latin squares: application to peptide structures

The computational identification of the optimal three-dimensional fold of even a small peptide chain from its sequence, without reference to other known structures, is a complex problem. There have been several attempts at solving this by sampling the potential energy surface of the molecule in a systematic manner. Here we present a new method to carry out the sampling, and to identify low energy conformers of the molecule. The method uses mutually orthogonal Latin squares to select (of the order of) n(2) points from the multidimensional conformation space of size m(n), where n is the number of dimensions (i.e., the number of conformational variables), and m specifies the fineness of the search grid. The sampling is accomplished by first calculating the value of the potential energy function at each one of the selected points. This is followed by analysis of these values of the potential energy to obtain the optimal value for each of the n-variables separately. We show that the set of the n-optimal values obtained in this manner specifies a low energy conformation of the molecule. Repeated application of the method identifies other low energy structures. The computational complexity of this algorithm scales as the fourth power of the size of the molecule. We applied this method to several small peptides, such as the neuropeptide enkephalin, and could identify a set of low energy conformations for each. Many of the structures identified by this method have also been previously identified and characterized by experiment and theory. We also compared the best structures obtained for the tripeptide (Ala)(3) by the present method, with those obtained by an exhaustive grid search, and showed that the algorithm is successful in identifying all the low energy conformers of this molecule.     

Conformations of cysteine disulfides of peptide toxins: Advantage of differentiating forward and reverse asymmetric disulfide conformers

Conformations of cysteine disulfides were analyzed in X-ray, nuclear magnetic resonance (NMR), and co-crystal structures of peptide toxins retrieved from Protein Data Bank. The parameters side chain torsional angles, disulfide strain energy, interatomic Cα/Cβ distances, and Ramachandran angles were used as probes to derive conformational features of cysteine disulfides. Schmidt, Ho, and Hogg (2006 Schmidt, B., Ho, L., &; Hogg, P. J. (2006). Allosteric disulfide bonds. Biochemistry, 45, 7429–7433.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) Allosteric disulfide bonds. Biochemistry, 45, 7429–7433 scheme was adapted to classify the disulfide conformations of peptide toxins. Anomalies were observed while treating “forward” and “reverse” asymmetric disulfide conformers as same disulfide conformation in peptide toxins. Thus, new scheme was proposed to classify “forward” and “reverse” asymmetric disulfide conformers separately. Total available conformers space for classification of toxins disulfides is 32. Interestingly, all 32 disulfide conformations are observed in peptide toxins. –LHSpiral is predominant disulfide conformation of peptide toxins. Significant variations were observed in population of occurrence of disulfide conformers, disulfide strain energy, and distribution of D_Cα-Cα and D_Cβ-Cβ values between X-ray, NMR, and co-crystal structures of peptide toxins. The observed differences in conformations of disulfides of same peptide toxins between different states were used as platform to demonstrate advantage of differentiating forward and reverse asymmetric disulfide conformers. Newly proposed scheme allows accurate representation of true conformational diversity of disulfides between X-ray and NMR structures of same peptide toxins. Newly proposed scheme also permits to derive additional structural information from nomenclature which was illustrated by comparing conformations of disulfides between unbound and bound form of toxin with channel/receptor. The results will be of interest for growing field of structural venomics and conformational analysis of peptide/protein disulfides.

Communicated by Ramaswamy H. Sarma     

Enhanced sampling of peptide and protein conformations using replica exchange simulations with a peptide backbone biasing-potential

During replica exchange molecular dynamics (RexMD) simulations, several replicas of a system are simulated at different temperatures in parallel allowing for exchange between replicas at frequent intervals. This technique allows significantly improved sampling of conformational space and is increasingly being used for structure prediction of peptides and proteins. A drawback of the standard temperature RexMD is the rapid increase of the replica number with increasing system size to cover a desired temperature range. In an effort to limit the number of replicas, a new Hamiltonian-RexMD method has been developed that is specifically designed to enhance the sampling of peptide and protein conformations by applying various levels of a backbone biasing potential for each replica run. The biasing potential lowers the barrier for backbone dihedral transitions and promotes enhanced peptide backbone transitions along the replica coordinate. The application on several peptide cases including in all cases explicit solvent indicates significantly improved conformational sampling when compared with standard MD simulations. This was achieved with a very modest number of 5-7 replicas for each simulation system making it ideally suited for peptide and protein folding simulations as well as refinement of protein model structures in the presence of explicit solvent.     

An application of experimental design using mutually orthogonal Latin squares in conformational studies of peptides

We address the question-can we use experimental design methods to investigate peptide conformation and identify conformational parameters that may contribute more significantly to the potential energy than others? We used mutually orthogonal Latin square design to sample the conformational space of peptides and analysed the samples using analysis of variance. We examined the equality of the effect of the torsion angles on the conformational potential energy. The results showed that different torsion angles contributed differently to the conformational energy. We are able to identify those parameters that may have to be more carefully considered in conformational studies of peptides.     

基于联合残基力场的蛋白质能量优化

简述了蛋白质结构预测中存在的问题,主要介绍了蛋白质分子力场的一种模型即联合残基力场,然后利用这种模型对一种多肽和葡萄球菌蛋白的部分段进行试验,使它们的能量不同程度的得到了最小化,其中前者的初始能量为-71.50461kcal/mol,最小化后为-73.32767kcal/mol.     

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as “the protein folding problem,” has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.