Energy Landscape of Met-Enkephalin and Leu-Enkephalin Drawn Using Mutually Orthogonal Latin Squares Sampling

Protein-small molecule docking with receptor flexibility in iMOLSDOCK

We have earlier reported the iMOLSDOCK technique to perform 'induced-fit' peptide-protein docking. iMOLSDOCK uses the mutually orthogonal Latin squares (MOLSs) technique to sample the conformation and the docking pose of the small molecule ligand and also the flexible residues of the receptor protein, and arrive at the optimum pose and conformation. In this paper we report the extension carried out in iMOLSDOCK to dock nonpeptide small molecule ligands to receptor proteins. We have benchmarked and validated iMOLSDOCK with a dataset of 34 protein-ligand complexes as well as with Astex Diverse dataset, with nonpeptide small molecules as ligands. We have also compared iMOLSDOCK with other flexible receptor docking tools GOLD v5.2.1 and AutoDock Vina. The results obtained show that the method works better than these two algorithms, though it consumes more computer time. The source code and binary of MOLS 2.0 (under a GNU Lesser General Public License) are freely available for download at https://sourceforge.net/projects/mols2-0/files/ .

Thermodynamics of Protein Folding Studied by Umbrella Sampling along a Reaction Coordinate of Native Contacts

Spontaneous transitions between the native and non-native protein conformations are normally rare events that hardly take place in typical unbiased molecular dynamics simulations. It was recently demonstrated that such transitions can be well described by a reaction coordinate, Q, that represents the collective fraction of the native contacts between the protein atoms. Here we attempt to use this reaction coordinate to enhance the conformational sampling. We perform umbrella sampling simulations with biasing potentials on Q for two model proteins, Trp-Cage and BBA, using the CHARMM force field. Hamiltonian replica exchange is implemented in these simulations to further facilitate the sampling. The simulations appear to have reached satisfactory convergence, resulting in unbiased free energies as a function of Q. In addition to the native structure, multiple folded conformations are identified in the reconstructed equilibrium ensemble. Some conformations without any native contacts nonetheless have rather compact geometries and are stabilized by hydrogen bonds not present in the native structure. Whereas the enhanced sampling along Q reasonably reproduces the equilibrium conformational space, we also find that the folding of an α-helix in Trp-Cage is a slow degree of freedom orthogonal to Q and therefore cannot be accelerated by biasing the reaction coordinate. Overall, we conclude that whereas Q is an excellent parameter to analyze the simulations, it is not necessarily a perfect reaction coordinate for enhanced sampling, and better incorporation of other slow degrees of freedom may further improve this reaction coordinate.

iMOLSDOCK: Induced-fit docking using mutually orthogonal Latin squares (MOLS)

We have earlier reported the MOLSDOCK technique to perform rigid receptor/flexible ligand docking. The method uses the MOLS method, developed in our laboratory. In this paper we report iMOLSDOCK, the 'flexible receptor' extension we have carried out to the algorithm MOLSDOCK. iMOLSDOCK uses mutually orthogonal Latin squares (MOLS) to sample the conformation and the docking pose of the ligand and also the flexible residues of the receptor protein. The method then uses a variant of the mean field technique to analyze the sample to arrive at the optimum. We have benchmarked and validated iMOLSDOCK with a dataset of 44 peptide-protein complexes with peptides. We have also compared iMOLSDOCK with other flexible receptor docking tools GOLD v5.2.1 and AutoDock Vina. The results obtained show that the method works better than these two algorithms, though it consumes more computer time.

MOLS 2.0: software package for peptide modeling and protein-ligand docking

We previously developed an algorithm to perform conformational searches of proteins and peptides, and to perform the docking of ligands to protein receptors. In order to identify optimal conformations and docked poses, this algorithm uses mutually orthogonal Latin squares (MOLS) to rationally sample the vast conformational (or docking) space, and then analyzes this relatively small sample using a variant of mean field theory. The conformational search part of the algorithm was denoted MOLS 1.0. The docking portion of the algorithm, which allows only "flexible ligand/rigid receptor" docking, was denoted MOLSDOCK. Both are FORTRAN-based command-line-only molecular docking computer programs, though a GUI was developed later for MOLS 1.0. Both the conformational search and the rigid receptor docking parts of the algorithm have been extensively validated. We have now further enhanced the capabilities of the program by incorporating "induced fit" side-chain receptor flexibility for docking peptide ligands. Benchmarking and extensive testing is now being carried out for the flexible receptor portion of the docking. Additionally, to make both the peptide conformational search and docking algorithms (the latter including both flexible ligand/rigid receptor and flexible ligand/flexible receptor techniques) more accessible to the research community, we have developed MOLS 2.0, which incorporates a new Java-based graphical user interface (GUI). Here, we give a detailed description of MOLS 2.0. The source code and binary for MOLS 2.0 are distributed free (under a GNU Lesser General Public License) to the scientific community. They are freely available for download at https://sourceforge.net/projects/mols2-0/files/ .

MOLS sampling and its applications in structural biophysics

This review describes the MOLS method and its applications. This computational method has been developed in our laboratory primarily to explore the conformational space of small peptides and identify features of interest, particularly the minima, i.e., the low energy conformations. A systematic "brute-force" search through the vast conformational space for such features faces the insurmountable problem of combinatorial explosion, whilst other techniques, e.g., Monte Carlo searches, are somewhat limited in their region of exploration and may be considered inexhaustive. The MOLS method, on the other hand, uses a sampling technique commonly employed in experimental design theory to identify a small sample of the conformational space that nevertheless retains information about the entire space. The information is extracted using a technique that is a variant of the self-consistent mean field technique, which has been used to identify, for example, the optimal set of side-chain conformations in a protein. Applications of the MOLS method to understand peptide structure, predict the structures of loops in proteins, predict three-dimensional structures of small proteins, and arrive at the best conformation, orientation, and positions of a small molecule ligand in a protein receptor site have all yielded satisfactory results.

On potential energy models for EA-based ab initio protein structure prediction

Ab initio protein structure prediction involves determination of the three-dimensional (3D) conformation of proteins on the basis of their amino acid sequence, a potential energy (PE) model that captures the physics of the interatomic interactions, and a method to search for and identify the global minimum in the PE (or free energy) surface such as an evolutionary algorithm (EA). Many PE models have been proposed over the past three decades and more. There is currently no understanding of how the behavior of an EA is affected by the PE model used. The study reported here shows that the EA behavior can be profoundly affected: the EA performance obtained when using the ECEPP PE model is significantly worse than that obtained when using the Amber, OPLS, and CVFF PE models, and the optimal EA control parameter values for the ECEPP model also differ significantly from those associated with the other models.

The SAAP force field: development of the single amino acid potentials for 20 proteinogenic amino acids and Monte Carlo molecular simulation for short peptides

Molecular simulation by using force field parameters has been widely applied in the fields of peptide and protein research for various purposes. We recently proposed a new all-atom protein force field, called the SAAP force field, which utilizes single amino acid potentials (SAAPs) as the fundamental elements. In this article, whole sets of the SAAP force field parameters in vacuo, in ether, and in water have been developed by ab initio calculation for all 20 proteinogenic amino acids and applied to Monte Carlo molecular simulation for two short peptides. The side-chain separation approximation method was employed to obtain the SAAP parameters for the amino acids with a long side chain. Monte Carlo simulation for Met-enkephalin (CHO-Tyr-Gly-Gly-Phe-Met-NH2) by using the SAAP force field revealed that the conformation in vacuo is mainly controlled by strong electrostatic interactions between the amino acid residues, while the SAAPs and the interamino acid Lennard-Jones potentials are predominant in water. In ether, the conformation would be determined by the combination of the three components. On the other hand, the SAAP simulation for chignolin (H-Gly-Tyr-Asp-Pro-Glu-Thr-Gly-Thr-Trp-Gly-OH) reasonably reproduced a native-like beta-hairpin structure in water although the C-terminal and side-chain conformations were different from the native ones. It was suggested that the SAAP force field is a useful tool for analyzing conformations of polypeptides in terms of intrinsic conformational propensities of the single amino acid units.

An estimate of the numbers and density of low-energy structures (or decoys) in the conformational landscape of proteins

BACKGROUND

The conformational energy landscape of a protein, as calculated by known potential energy functions, has several minima, and one of these corresponds to its native structure. It is however difficult to comprehensively estimate the actual numbers of low energy structures (or decoys), the relationships between them, and how the numbers scale with the size of the protein.

METHODOLOGY

We have developed an algorithm to rapidly and efficiently identify the low energy conformers of oligo peptides by using mutually orthogonal Latin squares to sample the potential energy hyper surface. Using this algorithm, and the ECEPP/3 potential function, we have made an exhaustive enumeration of the low-energy structures of peptides of different lengths, and have extrapolated these results to larger polypeptides.

CONCLUSIONS AND SIGNIFICANCE

We show that the number of native-like structures for a polypeptide is, in general, an exponential function of its sequence length. The density of these structures in conformational space remains more or less constant and all the increase appears to come from an expansion in the volume of the space. These results are consistent with earlier reports that were based on other models and techniques.

Exploring conformational space using a mean field technique with MOLS sampling

The computational identification of all the low energy structures of a peptide given only its sequence is not an easy task even for small peptides,due to the multiple-minima problem and combinatorial explosion. We have developed an algorithm, called the MOLS technique,that addresses this problem, and have applied it to a number of different aspects of the study of peptide and protein structure. Conformational studies of oligopeptides, including loop sequences in proteins have been carried out using this technique. In general the calculations identified all the folds determined by previous studies,and in addition picked up other energetically favorable structures. The method was also used to map the energy surface of the peptides. In another application, we have combined the MOLS technique, using it to generate a library of low energy structures of an oligopeptide, with a genetic algorithm to predict protein structures. The method has also been applied to explore the conformational space of loops in protein structures.Further, it has been applied to the problem of docking a ligand in its receptor site, with encouraging results.

Exploring the conformational space of protein loops using a mean field technique with MOLS sampling

We have recently developed a computational technique that uses mutually orthogonal Latin square sampling to explore the conformational space of oligopeptides in an exhaustive manner. In this article, we report its use to analyze the conformational spaces of 120 protein loop sequences in proteins, culled from the PDB, having the length ranging from 5 to 10 residues. The force field used did not have any information regarding the sequences or structures that flanked the loop. The results of the analyses show that the native structure of the loop, as found in the PDB falls at one of the low energy points in the conformational landscape of the sequences. Thus, a large portion of the structural determinants of the loop may be considered intrinsic to the sequence, regardless of either adjacent sequences or structures, or the interactions that the atoms of the loop make with other residues in the protein or in neighboring proteins.