Monte Carlo loop refinement and virtual screening of the thyroid-stimulating hormone receptor transmembrane domain

Metropolis Monte Carlo (MMC) loop refinement has been performed on the three extracellular loops (ECLs) of rhodopsin and opsin-based homology models of the thyroid-stimulating hormone receptor transmembrane domain, a class A type G protein-coupled receptor. The Monte Carlo sampling technique, employing torsion angles of amino acid side chains and local moves for the six consecutive backbone torsion angles, has previously reproduced the conformation of several loops with known crystal structures with accuracy consistently less than 2?Å. A grid-based potential map, which includes van der Waals, electrostatics, hydrophobic as well as hydrogen-bond potentials for bulk protein environment and the solvation effect, has been used to significantly reduce the computational cost of energy evaluation. A modified sigmoidal distance-dependent dielectric function has been implemented in conjunction with the desolvation and hydrogen-bonding terms. A long high-temperature simulation with 2?kcal/mol repulsion potential resulted in extensive sampling of the conformational space. The slow annealing leading to the low-energy structures predicted secondary structure by the MMC technique. Molecular docking with the reported agonist reproduced the binding site within 1.5?Å. Virtual screening performed on the three lowest structures showed that the ligand-binding mode in the inter-helical region is dependent on the ECL conformations.     

Protein-protein docking with simultaneous optimization of rigid-body displacement and side-chain conformations

Protein-protein docking algorithms provide a means to elucidate structural details for presently unknown complexes. Here, we present and evaluate a new method to predict protein-protein complexes from the coordinates of the unbound monomer components. The method employs a low-resolution, rigid-body, Monte Carlo search followed by simultaneous optimization of backbone displacement and side-chain conformations using Monte Carlo minimization. Up to 10(5) independent simulations are carried out, and the resulting "decoys" are ranked using an energy function dominated by van der Waals interactions, an implicit solvation model, and an orientation-dependent hydrogen bonding potential. Top-ranking decoys are clustered to select the final predictions. Small-perturbation studies reveal the formation of binding funnels in 42 of 54 cases using coordinates derived from the bound complexes and in 32 of 54 cases using independently determined coordinates of one or both monomers. Experimental binding affinities correlate with the calculated score function and explain the predictive success or failure of many targets. Global searches using one or both unbound components predict at least 25% of the native residue-residue contacts in 28 of the 32 cases where binding funnels exist. The results suggest that the method may soon be useful for generating models of biologically important complexes from the structures of the isolated components, but they also highlight the challenges that must be met to achieve consistent and accurate prediction of protein-protein interactions.     

ROSETTALIGAND: protein-small molecule docking with full side-chain flexibility

Protein-small molecule docking algorithms provide a means to model the structure of protein-small molecule complexes in structural detail and play an important role in drug development. In recent years the necessity of simulating protein side-chain flexibility for an accurate prediction of the protein-small molecule interfaces has become apparent, and an increasing number of docking algorithms probe different approaches to include protein flexibility. Here we describe a new method for docking small molecules into protein binding sites employing a Monte Carlo minimization procedure in which the rigid body position and orientation of the small molecule and the protein side-chain conformations are optimized simultaneously. The energy function comprises van der Waals (VDW) interactions, an implicit solvation model, an explicit orientation hydrogen bonding potential, and an electrostatics model. In an evaluation of the scoring function the computed energy correlated with experimental small molecule binding energy with a correlation coefficient of 0.63 across a diverse set of 229 protein- small molecule complexes. The docking method produced lowest energy models with a root mean square deviation (RMSD) smaller than 2 A in 71 out of 100 protein-small molecule crystal structure complexes (self-docking). In cross-docking calculations in which both protein side-chain and small molecule internal degrees of freedom were varied the lowest energy predictions had RMSDs less than 2 A in 14 of 20 test cases.     

Scoring docked conformations generated by rigid-body protein-protein docking

Rigid-body methods, particularly Fourier correlation techniques, are very efficient for docking bound (co-crystallized) protein conformations using measures of surface complementarity as the target function. However, when docking unbound (separately crystallized) conformations, the method generally yields hundreds of false positive structures with good scores but high root mean square deviations (RMSDs). This paper describes a two-step scoring algorithm that can discriminate near-native conformations (with less than 5 A RMSD) from other structures. The first step includes two rigid-body filters that use the desolvation free energy and the electrostatic energy to select a manageable number of conformations for further processing, but are unable to eliminate all false positives. Complete discrimination is achieved in the second step that minimizes the molecular mechanics energy of the retained structures, and re-ranks them with a combined free-energy function which includes electrostatic, solvation, and van der Waals energy terms. After minimization, the improved fit in near-native complex conformations provides the free-energy gap required for discrimination. The algorithm has been developed and tested using docking decoys, i.e., docked conformations generated by Fourier correlation techniques. The decoy sets are available on the web for testing other discrimination procedures. Proteins 2000;40:525-537.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

Combination of scoring functions improves discrimination in protein-protein docking

Two structure-based potentials are used for both filtering (i.e., selecting a subset of conformations generated by rigid-body docking), and rescoring and ranking the selected conformations. ACP (atomic contact potential) is an atom-level extension of the Miyazawa-Jernigan potential parameterized on protein structures, whereas RPScore (residue pair potential score) is a residue-level potential, based on interactions in protein-protein complexes. These potentials are combined with other energy terms and applied to 13 sets of protein decoys, as well as to the results of docking 10 pairs of unbound proteins. For both potentials, the ability to discriminate between near-native and non-native docked structures is substantially improved by refining the structures and by adding a van der Waals energy term. It is observed that ACP and RPScore complement each other in a number of ways (e.g., although RPScore yields more hits than ACP, mainly as a result of its better performance for charged complexes, ACP usually ranks the near-native complexes better). As a general solution to the protein-docking problem, we have found that the best discrimination strategies combine either an RPScore filter with an ACP-based scoring function, or an ACP-based filter with an RPScore-based scoring function. Thus, ACP and RPScore capture complementary structural information, and combining them in a multistage postprocessing protocol provides substantially better discrimination than the use of the same potential for both filtering and ranking the docked conformations.     

Many-atom van der Waals interactions lead to direction-sensitive interactions of covalent bonds

Strict physical theory and numerical calculations show that a specific coupling of many-atom van der Waals interactions with covalent bonding can significantly (half as much) increase the strength of attractive dispersion interactions when the direction of interaction coincides with the direction of the covalent bond, and decrease this strength when the direction of interaction is perpendicular to the direction of the covalent bond. The energy effect is comparable to that caused by the replacement of atoms (e.g. N by C or O) in conventional pairwise van der Waals interactions. Analysis of protein structures shows that they bear an imprint of this effect. This means that many-atom van der Waals interactions cannot be ignored in refinement of protein structures, in simulations of their folding, and in prediction of their binding affinities.     

A combination of rescoring and refinement significantly improves protein docking performance

To determine the structures of protein-protein interactions, protein docking is a valuable tool that complements experimental methods to characterize protein complexes. Although protein docking can often produce a near-native solution within a set of global docking predictions, there are sometimes predictions that require refinement to elucidate correct contacts and conformation. Previously, we developed the ZRANK algorithm to rerank initial docking predictions from ZDOCK, a docking program developed by our lab. In this study, we have applied the ZRANK algorithm toward refinement of protein docking models in conjunction with the protein docking program RosettaDock. This was performed by reranking global docking predictions from ZDOCK, performing local side chain and rigid-body refinement using RosettaDock, and selecting the refined model based on ZRANK score. For comparison, we examined using RosettaDock score instead of ZRANK score, and a larger perturbation size for the RosettaDock search, and determined that the larger RosettaDock perturbation size with ZRANK scoring was optimal. This method was validated on a protein-protein docking benchmark. For refining docking benchmark predictions from the newest ZDOCK version, this led to improved structures of top-ranked hits in 20 of 27 cases, and an increase from 23 to 27 cases with hits in the top 20 predictions. Finally, we optimized the ZRANK energy function using refined models, which provides a significant improvement over the original ZRANK energy function. Using this optimized function and the refinement protocol, the numbers of cases with hits ranked at number one increased from 12 to 19 and from 7 to 15 for two different ZDOCK versions. This shows the effective combination of independently developed docking protocols (ZDOCK/ZRANK, and RosettaDock), indicating that using diverse search and scoring functions can improve protein docking results.     

Low-resolution structure refinement in electron microscopy

A real-space structure refinement method, originally developed for macromolecular X-ray crystallography, has been applied to protein structure analysis by electron microscopy (EM). This method simultaneously optimizes the fit of an atomic model to a density map and the stereo-chemical properties of the model by minimizing an energy function. The performance of this method is characterized at different resolution and signal-to-noise ratio conditions typical for EM electron density maps. A multi-resolution scheme is devised to improve the convergence of the refinement on the global energy minimum. Applications of the method to various model systems are demonstrated here. The first case is the arrangement of FlgE molecules in the helical filament of flagellar hook, in which refinement with segmented rigid bodies improves the density correlation and reduces severe van der Waals contacts among the symmetry-related subunits. The second case is a conformational analysis of the NSF AAA ATPase in which a multi-conformer model is used in the refinement to investigate the arrangement of the two ATPase domains in the molecule. The third case is a docking simulation in which the crystal structure of actin and the NOE data from NMR experiments on the dematin headpiece are combined with a low-resolution EM density map to generate an atomic model of the F-actin-dematin headpiece structure.     

Free energy landscapes of two model peptides: α-helical and β-hairpin peptides explored with Brownian dynamics simulation

We applied an atomistic Brownian dynamics (BD) simulation with multiple time step method for the folding simulation of a 13-mer α-helical peptide and a 12-mer β-hairpin peptide, giving successful folding simulations. In this model, the driving energy contribution towards folding came from both electrostatic and van der Waals interactions for the α-helical peptide and from van der Waals interactions for the β-hairpin peptide. Although, many non-native structures having the same or lower energy than that of native structure were observed, the folded states formed the most populated cluster when the structures obtained by the BD simulations were subjected to the cluster analysis based on distance-based root mean square deviation of side-chains between different structures. This result indicates that we can predict the native structures from conformations sampled by BD simulation.     

Torsional relaxation for biopolymers.

We describe a method for making natural, physical movements in a chained polymer by sequentially adjusting a few neighboring torsion angles in the polymer backbone. In addition to being very fast and easy to implement, the method is also very general. It applies equally well to proteins and nucleic acids. This method is then used to design a local refinement procedure. We test the refinement procedure on the minimization of a simple energy function for proteins. The energy function has a simplified potential for hydrophobic interaction, a hydrogen-bond term, and a term for van der Waals interaction. There is considerable current interest in such simple energy functions for protein folding. When applied to refine structures found by a global search method, the refinement is able to produce large reduction in the hydrogen-bond term and the van der Waal term of the energy. We conclude that the method is particularly effective in finding good "packing" of residues in an initially compact conformation.     

On the Role of Density Fluctuations in the Equation of State of a Simple Fluid

Abstract

We address the wellknown problems intorduced into the theory of fluids by density fluctuations in the form of van der Waals loops and nonclassical critical phenomena. A clean separation of long and short range density fluctuations is achieved by use of cell-constrained models which display well-defined van der Waals loops and classical behaviour around the critical point. For a pure Lennard-Jones fluid with occupancy restricted to 1 or 8 particles per cell, the phase diagram is determined by Monte Carlo simulation. By considering the deviations from the normal simulations without cell constraint, the effects of longer range density fluctuations are exposed. The system size dependence of the van der Waals loops present in all simulations of fluids is analyzed in terms of the GvdW free energy density functional theory, which is formuiated on the basis of the cell concept. The loops are found to gradually disappear either with greater cel occupancy or increasing total particle number in the simulation box.     

De novo protein design. I. In search of stability and specificity.

We have developed a fully automated protein design strategy that works on the entire sequence of the protein and uses a full atom representation. At each step of the procedure, an all-atom model of the protein is built using the template protein structure and the current designed sequence. The energy of the model is used to drive a Monte Carlo optimization in sequence space: random moves are either accepted or rejected based on the Metropolis criterion. We rely on the physical forces that stabilize native protein structures to choose the optimum sequence. Our energy function includes van der Waals interactions, electrostatics and an environment free energy. Successful protein design should be specific and generate a sequence compatible with the template fold and incompatible with competing folds. We impose specificity by maintaining the amino acid composition constant, based on the random energy model. The specificity of the optimized sequence is tested by fold recognition techniques. Successful sequence designs for the B1 domain of protein G, for the lambda repressor and for sperm whale myoglobin are presented. We show that each additional term of the energy function improves the performance of our design procedure: the van der Waals term ensures correct packing, the electrostatics term increases the specificity for the correct native fold, and the environment solvation term ensures a correct pattern of buried hydrophobic and exposed hydrophilic residues. For the globin family, we show that we can design a protein sequence that is stable in the myoglobin fold, yet incompatible with the very similar hemoglobin fold.     

Monte Carlo Study of the Buckingham Exponential-six Fluid

Abstract

In this paper we report the results of extensive Monte Carlo simulations of a pure fluid of Buckingham modified exponential-six molecules. Data are presented for the configurational energy and pressure covering a wide range of temperatures and densities. These data are interpreted using the generalized van der Waals partition function with a novel separation into free volume and mean potential terms. We find, surprisingly, that the Buckingham fluid is described by a simple van der Waals-like equation of state provided that the b parameter is temperature dependent and chosen in a theoretically correct manner.     

pyDock: electrostatics and desolvation for effective scoring of rigid-body protein-protein docking

The accurate scoring of rigid-body docking orientations represents one of the major difficulties in protein-protein docking prediction. Other challenges are the development of faster and more efficient sampling methods and the introduction of receptor and ligand flexibility during simulations. Overall, good discrimination of near-native docking poses from the very early stages of rigid-body protein docking is essential step before applying more costly interface refinement to the correct docking solutions. Here we explore a simple approach to scoring of rigid-body docking poses, which has been implemented in a program called pyDock. The scheme is based on Coulombic electrostatics with distance dependent dielectric constant, and implicit desolvation energy with atomic solvation parameters previously adjusted for rigid-body protein-protein docking. This scoring function is not highly dependent on specific geometry of the docking poses and therefore can be used in rigid-body docking sets generated by a variety of methods. We have tested the procedure in a large benchmark set of 80 unbound docking cases. The method is able to detect a near-native solution from 12,000 docking poses and place it within the 100 lowest-energy docking solutions in 56% of the cases, in a completely unrestricted manner and without any other additional information. More specifically, a near-native solution will lie within the top 20 solutions in 37% of the cases. The simplicity of the approach allows for a better understanding of the physical principles behind protein-protein association, and provides a fast tool for the evaluation of large sets of rigid-body docking poses in search of the near-native orientation.     

Probing the electronic structures and properties of neutral and anionic ScSi n (0,−1) (n = 1–6) clusters using ccCA-TM and G4 theory

We apply molecular docking, molecular dynamics (MD) simulation, and binding free energy calculation to investigate and reveal the binding mechanism between five xanthine inhibitors and DPP-4. The electrostatic and van der Waals interactions of the five inhibitors with DPP-4 are analyzed and discussed. The computed binding free energies using MM-PBSA method are in qualitatively agreement with experimental inhibitory potency of five inhibitors. The hydrogen bonds of inhibitors with Ser630 and Asp663 can stabilize the inhibitors in binding sites. The van der Waals interactions, especially the key contacts with His740, Asn710, Trp629, and Tyr666 have larger contributions to the binding free energy and play important roles in distinguishing the variant bioactivity of five inhibitors.     

Numerical Analysis of the Adhesive Forces in Nano-Scale Structure

Nanohairs, which can be found on the epidermis of Tokay gecko＇s toes, contribute to the adhesion by means of van der Waals force, capillary force, etc. This structure has inspired many researchers to fabricate the attachable nano-scale structures. However, the efficiency of artificial nano-scale structures is not reliable sufficiently. Moreover, the mechanical parameters related to the nano-hair attachment are not yet revealed qualitatively. The mechanical parameters which have influence on the ability of adhesive nano-hairs were investigated through numerical simulation in which only van der Waals force was considered. For the numerical analysis, finite element method was utilized and van der Waals force, assumed as 12-6 Lennard-Jones potential, was implemented as the body force term in the finite element formulation.