Protein docking and complementarity

Predicting the structures of protein-protein complexes is a difficult problem owing to the topographical and thermodynamic complexity of these structures. Past efforts in this area have focussed on fitting the interacting proteins together using rigid body searches, usually with the conformations of the proteins as they occur in crystal structure complexes. Here we present work which uses a rigid body docking method to generate the structures of three known protein complexes, using both the bound and unbound conformations of the interacting molecules. In all cases we can regenerate the geometry of the crystal complexes to high accuracy. We also are able to find geometries that do not resemble the crystal structure but nevertheless are surprisingly reasonable both mechanistically and by some simple physical criteria. In contrast to previous work in this area, we find that simple methods for evaluating the complementarity at the protein-protein interface cannot distinguish between the configurations that resemble the crystal structure complex and those that do not. Methods that could not distinguish between such similar and dissimilar configurations include surface area burial, solvation free energy, packing and mechanism-based filtering. Evaluations of the total interaction energy and the electrostatic interaction energy of the complexes were somewhat better. Of the techniques that we tried, energy minimization distinguished most clearly between the "true" and "false" positives, though even here the energy differences were surprisingly small. We found the lowest total interaction energy from amongst all of the putative complexes generated by docking was always within 5 A root-mean-square of the crystallographic structure. There were, however, several putative complexes that were very dissimilar to the crystallographic structure but had energies that were close to that of the low energy structure. The magnitude of the error in energy calculations has not been established in macromolecular systems, and thus the reliability of the small differences in energy remains to be determined. The ability of this docking method to regenerate the crystallographic configurations of the interacting proteins using their unbound conformations suggests that it will be a useful tool in predicting the structures of unsolved complexes.     

Protein structure prediction based on fragment assembly and parameter optimization

We propose a novel method for ab-initio prediction of protein tertiary structures based on the fragment assembly and global optimization. Fifteen residue long fragment libraries are constructed using the secondary structure prediction method PREDICT, and fragments in these libraries are assembled to generate full-length chains of a query protein. Tertiary structures of 50 to 100 conformations are obtained by minimizing an energy function for proteins, using the conformational space annealing method that enables one to sample diverse low-lying local minima of the energy. Then in order to enhance the performance of the prediction method, we optimize the linear parameters of the energy function, so that the native-like conformations become energetically more favorable than the non-native ones for proteins with known structures. We test the feasibility of the parameter optimization procedure by applying it to the training set consisting of three proteins: the 10-55 residue fragment of staphylococcal protein A (PDB ID 1bdd), a designed protein betanova, and 1fsd.     

Native atomic burials, supplemented by physically motivated hydrogen bond constraints, contain sufficient information to determine the tertiary structure of small globular proteins

We investigate the possibility that atomic burials, as measured by their distances from the structural geometrical center, contain sufficient information to determine the tertiary structure of globular proteins. We report Monte Carlo simulated annealing results of all-atom hard-sphere models in continuous space for four small proteins: the all-beta WW-domain 1E0L, the alpha/beta protein-G 1IGD, the all-alpha engrailed homeo-domain 1ENH, and the alpha + beta engineered monomeric form of the Cro protein 1ORC. We used as energy function the sum over all atoms, labeled by i, of |R(i) - R(i) (*)|, where R(i) is the atomic distance from the center of coordinates, or central distance, and R(i) (*) is the "ideal" central distance obtained from the native structure. Hydrogen bonds were taken into consideration by the assignment of two ideal distances for backbone atoms forming hydrogen bonds in the native structure depending on the formation of a geometrically defined bond, independently of bond partner. Lowest energy final conformations turned out to be very similar to the native structure for the four proteins under investigation and a strong correlation was observed between energy and distance root mean square deviation (DRMS) from the native in the case of all-beta 1E0L and alpha/beta 1IGD. For all alpha 1ENH and alpha + beta 1ORC the overall correlation between energy and DRMS among final conformations was not as high because some trajectories resulted in high DRMS but low energy final conformations in which alpha-helices adopted a non-native mutual orientation. Comparison between central distances and actual accessible surface areas corroborated the implicit assumption of correlation between these two quantities. The Z-score obtained with this native-centric potential in the discrimination of native 1ORC from a set of random compact structures confirmed that it contains a much smaller amount of native information when compared to a traditional contact Go potential but indicated that simple sequence-dependent burial potentials still need some improvement in order to attain a similar discriminability. Taken together, our results suggest that central distances, in conjunction to physically motivated hydrogen bond constraints, contain sufficient information to determine the native conformation of these small proteins and that a solution to the folding problem for globular proteins could arise from sufficiently accurate burial predictions from sequence followed by minimization of a burial-dependent energy function.     

HOPE: a homotopy optimization method for protein structure prediction.

We use a homotopy optimization method, HOPE, to minimize the potential energy associated with a protein model. The method uses the minimum energy conformation of one protein as a template to predict the lowest energy structure of a query sequence. This objective is achieved by following a path of conformations determined by a homotopy between the potential energy functions for the two proteins. Ensembles of solutions are produced by perturbing conformations along the path, increasing the likelihood of predicting correct structures. Successful results are presented for pairs of homologous proteins, where HOPE is compared to a variant of Newton's method and to simulated annealing.     

Influence of solvent molecules on the stereochemical code of glycyl residues in proteins

The Ramachandran steric map and energy diagrams of the glycyl residue are symmetric. A plot of (phi,psi) angles of glycyl residues in 250 nonhomologous and high-resolution protein structures is also largely symmetric. However, there is a clear aberration in the symmetry. Although there is a cluster of points corresponding to the right-handed alpha-helical region, the "equivalent" cluster is clearly shifted to in and around the (phi,psi) values of (90 degrees, 0 degrees ) instead of being centered at the left-handed alpha-helical region of (60 degrees, 40 degrees ). This lack of symmetry exists even in the (phi,psi) distribution of residues from non-alpha-helical regions in proteins. Here we provide an explanation for this observation. An analysis of glycyl conformations in small peptide structures and in "coil" proteins, which are largely devoid of helical and sheet regions, shows that glycyl residues prefer to adopt conformations around (+/-90 degrees, 0 degrees ) instead of right- and left-handed alpha-helical regions. By using theoretical calculations, such conformations are shown to have highest solvent accessibility in a system of two-linked peptide units with glycyl residue at the central C(alpha) atom. This finding is consistent with the observations from 250 nonhomologous protein structures where glycyl residues with conformations close to (+/-90 degrees, 0 degrees ) are seen to have high solvent accessibility. Analysis of a subset of nonhomologous structures with very high resolution (1.5 A or better) shows that water molecules are indeed present at distances suitable for hydrogen bond interaction with glycyl residues possessing conformations close to (+/-90 degrees, 0 degrees ). It is suggested that water molecules play a key role in determining and stabilizing these conformations of glycyl residues and explain the aberration in the symmetry of glycyl conformations in proteins.     

Progress in protein-protein docking: atomic resolution predictions in the CAPRI experiment using RosettaDock with an improved treatment of side-chain flexibility

RosettaDock uses real-space Monte Carlo minimization (MCM) on both rigid-body and side-chain degrees of freedom to identify the lowest free energy docked arrangement of 2 protein structures. An improved version of the method that uses gradient-based minimization for off-rotamer side-chain optimization and includes information from unbound structures was used to create predictions for Rounds 4 and 5 of CAPRI. First, large numbers of independent MCM trajectories were carried out and the lowest free energy docked configurations identified. Second, new trajectories were started from these lowest energy structures to thoroughly sample the surrounding conformation space, and the lowest energy configurations were submitted as predictions. For all cases in which there were no significant backbone conformational changes, a small number of very low-energy configurations were identified in the first, global search and subsequently found to be close to the center of the basin of attraction in the free energy landscape in the second, local search. Following the release of the experimental coordinates, it was found that the centers of these free energy minima were remarkably close to the native structures in not only the rigid-body orientation but also the detailed conformations of the side-chains. Out of 8 targets, the lowest energy models had interface root-mean-square deviations (RMSDs) less than 1.1 A from the correct structures for 6 targets, and interface RMSDs less than 0.4 A for 3 targets. The predictions were top submissions to CAPRI for Targets 11, 12, 14, 15, and 19. The close correspondence of the lowest free energy structures found in our searches to the experimental structures suggests that our free energy function is a reasonable representation of the physical chemistry, and that the real space search with full side-chain flexibility to some extent solves the protein-protein docking problem in the absence of significant backbone conformational changes. On the other hand, the approach fails when there are significant backbone conformational changes as the steric complementarity of the 2 proteins cannot be modeled without incorporating backbone flexibility, and this is the major goal of our current work.     

Discrimination of native loop conformations in membrane proteins: decoy library design and evaluation of effective energy scoring functions

The recent determination of crystal structures for several important membrane proteins opens the way for comparative modeling of their membrane-spanning regions. However, the ability to predict correctly the structures of loop regions, which may be critical, for example, in ligand binding, remains a considerable challenge. To meet this challenge, accurate scoring methods have to discriminate between candidate conformations of an unknown loop structure. Some success in loop prediction has been reported for globular proteins; however, the proximity of membrane protein loops to the lipid bilayer casts doubt on the applicability of the same scoring methods to this problem. In this work, we develop "decoy libraries" of non-native folds generated, using the structures of two membrane proteins, with molecular dynamics and Monte Carlo techniques over a range of temperatures. We introduce a new approach for decoy library generation by constructing a flat distribution of conformations covering a wide range of Calpha-root-mean-square deviation (RMSD) from the native structure; this removes possible bias in subsequent scoring stages. We then score these decoy conformations with effective energy functions, using increasingly more cpu-intensive implicit solvent models, including (1) simple Coulombic electrostatics with constant or distance-dependent dielectrics; (2) atomic solvation parameters; (3) the effective energy function (EEF1) of Lazaridis and Karplus; (4) generalized Born/Analytical Continuum Solvent; and (5) finite-difference Poisson-Boltzmann energy functions. We show that distinction of native-like membrane protein loops may be achieved using effective energies with the assumption of a homogenous environment; thus, the absence of the adjacent lipid bilayer does not affect the scoring ability. In particular, the Analytical Continuum Solvent and finite-difference Poisson-Boltzmann energy functions are seen to be the most powerful scoring functions. Interestingly, the use of the uncharged states of ionizable sidechains is shown to aid prediction, particularly for the simplest energy functions.     

An investigation of the pyranose ring interconversion path of alpha-L-idose calculated using density functional theory

The interconversion pathways of the pyranose ring conformation of alpha-L-idose from a (4)C1 chair to other conformations were investigated using density functional calculations. From these calculations, four different ring interconversion paths and their transition state structures from the (4)C1 chair to other conformations, such as B(3,O), and (1)S3, were obtained. These four transition-state conformations cover four possible combinations of the network patterns of the hydroxyl group hydrogen bonds (clockwise and counterclockwise) and the conformations of the primary alcohol group (tg and gg). The optimized conformations, transition states, and their intrinsic reaction coordinates (IRC) were all calculated at the B3LYP/6-31G** level. The energy differences among the structures obtained were evaluated at the B3LYP/6-311++G** level. The optimized conformations indicate that the conformers of (4)C1, (2)S(O), and B(3,O) have similar energies, while (1)S3 has a higher energy than the others. The comparison of the four transition states and their ring interconversion paths, which were confirmed using the IRC calculation, suggests that the most plausible ring interconversion of the alpha-L-idopyranose ring occurs between (4)C1 and B(3,O) through the E3 envelope, which involves a 5.21 kcal/mol energy barrier.     

Probabilistic sampling of protein conformations: New hope for brute force?

Protein structure prediction from sequence alone by "brute force" random methods is a computationally expensive problem. Estimates have suggested that it could take all the computers in the world longer than the age of the universe to compute the structure of a single 200-residue protein. Here we investigate the use of a faster version of our FOLDTRAJ probabilistic all-atom protein-structure-sampling algorithm. We have improved the method so that it is now over twenty times faster than originally reported, and capable of rapidly sampling conformational space without lattices. It uses geometrical constraints and a Leonard-Jones type potential for self-avoidance. We have also implemented a novel method to add secondary structure-prediction information to make protein-like amounts of secondary structure in sampled structures. In a set of 100,000 probabilistic conformers of 1VII, 1ENH, and 1PMC generated, the structures with smallest Calpha RMSD from native are 3.95, 5.12, and 5.95A, respectively. Expanding this test to a set of 17 distinct protein folds, we find that all-helical structures are "hit" by brute force more frequently than beta or mixed structures. For small helical proteins or very small non-helical ones, this approach should have a "hit" close enough to detect with a good scoring function in a pool of several million conformers. By fitting the distribution of RMSDs from the native state of each of the 17 sets of conformers to the extreme value distribution, we are able to estimate the size of conformational space for each. With a 0.5A RMSD cutoff, the number of conformers is roughly 2N where N is the number of residues in the protein. This is smaller than previous estimates, indicating an average of only two possible conformations per residue when sterics are accounted for. Our method reduces the effective number of conformations available at each residue by probabilistic bias, without requiring any particular discretization of residue conformational space, and is the fastest method of its kind. With computer speeds doubling every 18 months and parallel and distributed computing becoming more practical, the brute force approach to protein structure prediction may yet have some hope in the near future.     

The opening of the SPP1 bacteriophage tail, a prevalent mechanism in Gram-positive-infecting siphophages

The SPP1 siphophage uses its long non-contractile tail and tail tip to recognize and infect the Gram-positive bacterium Bacillus subtilis. The tail-end cap and its attached tip are the critical components for host recognition and opening of the tail tube for genome exit. In the present work, we determined the cryo-electron microscopic (cryo-EM) structure of a complex formed by the cap protein gp19.1 (Dit) and the N terminus of the downstream protein of gp19.1 in the SPP1 genome, gp21(1-552) (Tal). This complex assembles two back-to-back stacked gp19.1 ring hexamers, interacting loosely, and two gp21(1-552) trimers interacting with gp19.1 at both ends of the stack. Remarkably, one gp21(1-552) trimer displays a "closed" conformation, whereas the second is "open" delineating a central channel. The two conformational states dock nicely into the EM map of the SPP1 cap domain, respectively, before and after DNA release. Moreover, the open/closed conformations of gp19.1-gp21(1-552) are consistent with the structures of the corresponding proteins in the siphophage p2 baseplate, where the Tal protein (ORF16) attached to the ring of Dit (ORF15) was also found to adopt these two conformations. Therefore, the present contribution allowed us to revisit the SPP1 tail distal-end architectural organization. Considering the sequence conservation among Dit and the N-terminal region of Tal-like proteins in Gram-positive-infecting Siphoviridae, it also reveals the Tal opening mechanism as a hallmark of siphophages probably involved in the generation of the firing signal initiating the cascade of events that lead to phage DNA release in vivo.     

A new computational model for protein folding based on atomic solvation.

A new model for calculating the solvation energy of proteins is developed and tested for its ability to identify the native conformation as the global energy minimum among a group of thousands of computationally generated compact non-native conformations for a series of globular proteins. In the model (called the WZS model), solvation preferences for a set of 17 chemically derived molecular fragments of the 20 amino acids are learned by a training algorithm based on maximizing the solvation energy difference between native and non-native conformations for a training set of proteins. The performance of the WZS model confirms the success of this learning approach; the WZS model misrecognizes (as more stable than native) only 7 of 8,200 non-native structures. Possible applications of this model to the prediction of protein structure from sequence are discussed.     

A Nonstatistical Approach to the Prediction of Regular Structures in Proteins by the Example of α Helices

A new approach to the analysis of regular structures in proteins that is based on the method of molecular mechanics is proposed. The method uses only the information about the amino acid sequence. The -helical conformation was simulated using the ICM program of molecular mechanics. Energy profiles of the sequences in the -helical conformation, spanning the entire polypeptide chain, were plotted for eight proteins from the Protein Data Bank. The regions of each profile that exhibit energy minima were found to correspond to the -helical regions of the real spatial structure of the protein. Twenty-four out of 25 helices were distinctly pronounced, which indicates a rather high accuracy of the prediction. The energy profiles also help reveal the short regions that correspond to 3/10-helices and the turns that include local -helical conformations. Unlike the known statistical methods of prediction, this method makes it possible to establish the physical principles of the formation of -helical conformations.     

On the role of the crystal environment in determining protein side-chain conformations

The role of crystal packing in determining the observed conformations of amino acid side-chains in protein crystals is investigated by (1) analysis of a database of proteins that have been crystallized in different unit cells (space group or unit cell dimensions) and (2) theoretical predictions of side-chain conformations with the crystal environment explicitly represented. Both of these approaches indicate that the crystal environment plays an important role in determining the conformations of polar side-chains on the surfaces of proteins. Inclusion of the crystal environment permits a more sensitive measurement of the achievable accuracy of side-chain prediction programs, when validating against structures obtained by X-ray crystallography. Our side-chain prediction program uses an all-atom force field and a Generalized Born model of solvation and is thus capable of modeling simple packing effects (i.e. van der Waals interactions), electrostatic effects, and desolvation, which are all important mechanisms by which the crystal environment impacts observed side-chain conformations. Our results are also relevant to the understanding of changes in side-chain conformation that may result from ligand docking and protein-protein association, insofar as the results reveal how side-chain conformations change in response to their local environment.     

Variable-target-function and build-up procedures for the calculation of protein conformation. Application to bovine pancreatic trypsin inhibitor using limited simulated nuclear magnetic resonance data

An implementation of the variable-target-function procedure, first introduced by Braun and Go [W. Braun and N. Go, J. Mol. Biol. 186, 611-626 (1985)], has been used to generate conformations of the small protein bovine pancreatic trypsin inhibitor (BPTI), given a limited set of simulated data that could be obtained by nuclear magnetic resonance (NMR) techniques. A hybrid strategy was also used to calculate conformations of BPTI, given the same information. In the hybrid strategy, low-energy structures of medium-size fragments (decapeptides) of BPTI were generated using the variable-target-function method, followed by restrained energy optimization. The low-energy conformations were used as a basis to build up the complete fifty-eight-residue BPTI molecule. By using the variable-target-function approach, in which energy considerations were not introduced until full conformations of the entire BPTI molecule had been generated, it was not possible to obtain calculated structures with rms deviations from the X-ray conformation of less than 1.6 A for the alpha-carbons. On the other hand, with the hybrid strategy, which involved the consideration of realistic energy terms in the early stages of the calculations, it was possible to calculate low-energy conformations of BPTI with rms deviations from the X-ray structure of 1.06 to 1.50 A for the alpha-carbons. When the rms deviations were computed along the amino acid sequence, it was found that there was a good correlation between deviations among the calculated structures and deviations from the X-ray structure.     

A novel energy-based stochastic method for positioning polar protons in protein structures from X-rays

A novel automated method for the optimal placement of polar hydrogens in a protein structure is presented. The algorithm adds initially, to a protein data bank file of the protein, nonrotatable hydrogens such as peptide backbone hydrogens according to geometric considerations. Then, water protons and polar side chain protons of lysine, serine, threonine, tyrosine, aspartic acid, glutamic acid, and the C and N termini of a protein are added according to energy considerations. A unique stochastic approach has been developed to overcome a combinatorial explosion in the search for the lowest energy structure. First, the system is divided into ensembles. Each ensemble is treated separately: N conformations are sampled at random, their energies computed, whereas common components of high-energy combinations are gathered on one hand, and low-energy combinations on the other. Components that yield only high-energy conformations and do not contribute to any low energies are excluded. This is reiterated while the total amount of combinations is decreased along the iterative process. When the total number of combinations is lower than a user defined threshold, all remaining combinations are evaluated by exhaustive search. Energy evaluations use nonbonding energy expressions alone. The program was tested on five high-resolution crystal structures: bovine pancreatic trypsin inhibitor (Brookhaven Protein Data Bank file 5PTI), RNase-A (5RSA), trypsin (1NTP), and carbon monoxymyoglobin (2MB5), for which neutron diffraction structures are available, as well as phosphate binding protein (1IXH) for which very high resolution X-ray crystallography was used. The low RMS values prove the efficiency of this algorithm as a tool for positioning protons in proteins. It may be used for other biological structures.     

A non-statistical approach to the prediction of regular structures in proteins by the example of alpha-helices

A new approach to the analysis of regular structures in proteins that is based on the method of molecular mechanics is proposed. The method uses only the information about the amino acid sequence. The alpha-helical conformation was simulated using the ICM program of molecular mechanics. Energy profiles of the sequences in the alpha-helical conformation, spanning the entire polypeptide chain, were plotted for eight proteins from the Protein Data Bank. The regions of each profile that exhibit energy minima were found to correspond to the alpha-helical regions of the real spatial structure of the protein. Twenty-four out of 25 helices were distinctly pronounced, which indicates a rather high accuracy of the prediction. The energy profiles also help reveal the short regions that correspond to 3/10-helices and the turns that include local alpha-helical conformations. Unlike the known statistical methods of prediction, this method makes it possible to establish the physical principles of the formation of alpha-helical conformations. The English version of the paper: Russian Journal of Bioorganic Chemistry, 2002, vol. 28, no. 6; see also http://www.maik.ru.     

Correspondence of homologies in amino acid sequence and tertiary structure of protein molecules

According to the method developed previously (Kubota, Y., Takahashi, S., Nishikawa, K. and Ooi, T. (1981) J. Theor, Biol. 91, 347-361), homology among proteins may be estimated quantitatively. We extended the method to investigate the relationship of an amino acid sequence to its teritary structure and identify homologous segments which have homologous native conformations in proteins. First, we selected proper indices for the computation of correlation coefficients from 32 properties inherent to amino acids, such as hydrophobicity. The arithmetic average of correlation coefficients using six indices gave rise to a good correlation for the CD- and EF-hand regions (Ca2+ binding sites) in carp parvalbumin, but poor ones for other segments. We then applied the method to homologous proteins, the three-dimensional structures of which are known: horse hemoglobin alpha-chain and beta-chain; cytochrome c and c2; serine proteases, chymotrypsinogen and elastase; alpha-lytic protease and protease A from prokaryotic organisms. The results show that the sequence homology estimated by the present method has a good correspondence to the homology in three-dimensional structures and therefore the method is promising for the identification of important sites in sequences which have similar native conformations. For an example of the application of the method, two sequences of human interferon, one from fibroblast and the other from leukocyte, are compared, suggesting functional sites in the molecule.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.