Study of protein-protein interaction using conformational space annealing

We apply conformational space annealing (CSA), an efficient global optimization method, to the study of protein-protein interaction. The CSA is incorporated into the Tinker molecular modeling package along with a B-spline method for CAPRI Round 5 experiments. We have used an energy function for the protein-protein interaction that consists of electrostatic interaction, van der Waals interaction, and solvation energy terms represented by the occupancy desolvation method. The parameters of the AMBER94 all-atom empirical force field are used. Each energy term is calculated by precalculated grid potentials and B-spline method approximation. The ligand protein is placed inside a sphere of 50 A radius centered at an appropriate location, and the CSA rigid docking studies are carried out to find stable complexes. Up to 10 complexes are selected using the K-mean clustering method and biological information when available. These complexes are energy-minimized for further refinement by considering the flexibility of interacting proteins. The results show that the CSA method has a potential for the study of protein-protein interaction.     

Solvation thermodynamics of biopolymers. I. Separation of the volume and surface interactions with estimates for proteins

The present paper is a systematic first approach to the problem of solvation thermodynamics of biomolecules. Most previous approaches have been only crude estimates of solvent contributions, and have simply assessed solvation free energy as proportional to surface areas. Here we estimate the various contributions and divide them into (a) hard-core interactions dependent upon the entire volume of solute and (b) the remainder of interactions manifested through surfaces, such as van der Waals, charge-charge, or hydrogen bonds. We have estimated the work to create a cavity with scaled-particle theory (SPT), the van der Waals interactions on the surface, and hydrogen bonds between the surface and the solvent. The conclusion here is that this latter term is the largest component of the solvation free energy of proteins. From estimates on nine diverse proteins, it is clear that the larger the protein, the more dominant is the hydrogen-bond term. In the next paper, we indicate that correlations between hydrogen-bonding groups on the surfaces could increase the magnitude of the hydrogen-bond contribution.     

Protein docking using continuum electrostatics and geometric fit

The computer program DOT quickly finds low-energy docked structures for two proteins by performing a systematic search over six degrees of freedom. A novel feature of DOT is its energy function, which is the sum of both a Poisson-Boltzmann electrostatic energy and a van der Waals energy, each represented as a grid-based correlation function. DOT evaluates the energy of interaction for many orientations of the moving molecule and maintains separate lists scored by either the electrostatic energy, the van der Waals energy or the composite sum of both. The free energy is obtained by summing the Boltzmann factor over all rotations at each grid point. Three important findings are presented. First, for a wide variety of protein-protein interactions, the composite-energy function is shown to produce larger clusters of correct answers than found by scoring with either van der Waals energy (geometric fit) or electrostatic energy alone. Second, free-energy clusters are demonstrated to be indicators of binding sites. Third, the contributions of electrostatic and attractive van der Waals energies to the total energy term appropriately reflect the nature of the various types of protein-protein interactions studied.     

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 refinement of rigid-body protein docking structures with backbone displacement and side-chain optimization

Structures of hitherto unknown protein complexes can be predicted by docking the solved protein monomers. Here, we present a method to refine initial docking estimates of protein complex structures by a Monte Carlo approach including rigid-body moves and side-chain optimization. The energy function used is comprised of van der Waals, Coulomb, and atomic contact energy terms. During the simulation, we gradually shift from a novel smoothed van der Waals potential, which prevents trapping in local energy minima, to the standard Lennard-Jones potential. Following the simulation, the conformations are clustered to obtain the final predictions. Using only the first 100 decoys generated by a fast Fourier transform (FFT)-based rigid-body docking method, our refinement procedure is able to generate near-native structures (interface RMSD <2.5 A) as first model in 14 of 59 cases in a benchmark set. In most cases, clear binding funnels around the native structure can be observed. The results show the potential of Monte Carlo refinement methods and emphasize their applicability for protein-protein docking.     

Stabilization of hen egg white lysozyme by a cavity-filling mutation

Stabilization of a protein using cavity-filling strategy has hardly been successful because of unfavorable van der Waals contacts. We succeeded in stabilizing lysozymes by cavity-filling mutations. The mutations were checked by a simple energy minimization in advance. It was shown clearly that the sum of free energy change caused by the hydrophobicity and the cavity size was correlated very well with protein stability. We also considered the aromatic-aromatic interaction. It is reconfirmed that the cavity-filling mutation in a hydrophobic core is a very useful method to stabilize a protein when the mutation candidate is selected carefully.     

Van der Waals forces. Special characteristics in lipid-water systems and a general method of calculation based on the Lifshitz theory

A practical method for examining and calculating van der Waals forces is derived from Lifshitz'' theory. Rather than treat the total van der Waals energy as a sum of pairwise interactions between atoms, the Lifshitz theory treats component materials as continua in which there are electromagnetic fluctuations at all frequencies over the entire body. It is necessary in principle to use total macroscopic dielectric data from component substances to analyze the permitted fluctuations; in practice it is possible to use only partial information to perform satisfactory calculations. The biologically interesting case of lipid-water systems is considered in detail for illustration. The method gives good agreement with measured van der Waals energy of interaction across a lipid film. It appears that fluctuations at infrared frequencies and microwave frequencies are very important although these are usually ignored in preference to UV contributions. “Retardation effects” are such as to damp out high frequency fluctuation contributions; if interaction specificity is due to UV spectra, this will be revealed only at interactions across <200 angstrom (A). Dependence of van der Waals forces on material electric properties is discussed in terms of illustrative numerical calculations.     

Construction of side-chains in homology modelling. Application to the C-terminal lobe of rhizopuspepsin

A detailed and rule-based side-chain modelling procedure for globular proteins is presented. It uses the conformational information contained in a homologous (template) structure as a starting point and includes recipes for atom placement and for checking and improving the atomic positions. The scheme does not rely on intuitive judgements or visual examination of the model during construction or refinement. It comprises four stages; the first three are relatively simple and the fourth is more complex. In the first stage, initial conformations for as many atoms as possible are transferred from the template structure based on the application of trends reported previously. Second, these trends are used to correct poor van der Waals overlaps. Third, the remaining side-chains atoms (those for which no information is contained in the template) are placed by evaluating their rigid rotation, van der Waals surfaces. The fourth stage consists of a hierarchial series of conformational checks. They involve the evaluation of individual residue energies in the absence and presence of the rest of the protein relative to statistical trends observed in the template structure, the comparison of hydrogen-bonding patterns and side-chain accessibilities in the model and template and brief energy minimization followed by an evaluation of the rigid rotation potential energy surfaces of each side-chain. The checks pinpoint "incorrectly" modelled side-chains, suggest conformational changes and provide a means for determining the portions of the model that are likely to be correct and those likely to be in error. The procedure developed in the paper is tested by modelling the side-chains of the C-terminal lobe of the aspartyl proteinase rhizopuspepsin, using the rhizopuspepsin backbone and the homologous protein, penicillopepsin, as a template for the side-chains. The resultant model was compared to the high-resolution X-ray structure of rhizopuspepsin. Using penicillopepsin data only (stage I), 58% of the chi 1 dihedrals and 44% of the chi 2 dihedrals were modelled correctly. Once poor van der Waals overlaps had been corrected and all of the atoms had been placed (stages II and III), 86% of the chi 1 dihedrals and 75% of the chi 2 dihedrals were correct. After the refinement had been completed (stage IV), 92% of the chi 1 dihedrals and 81% of the chi 2 dihedrals were correctly positioned.(ABSTRACT TRUNCATED AT 400 WORDS)     

PRL-Dock: protein-ligand docking based on hydrogen bond matching and probabilistic relaxation labeling

Protein-ligand docking is widely applied to structure-based virtual screening for drug discovery. This article presents a novel docking technique, PRL-Dock, based on hydrogen bond matching and probabilistic relaxation labeling. It deals with multiple hydrogen bonds and can match many acceptors and donors simultaneously. In the matching process, the initial probability of matching an acceptor with a donor is estimated by an efficient scoring function and the compatibility coefficients are assigned according to the coexisting condition of two hydrogen bonds. After hydrogen bond matching, the geometric complementarity of the interacting donor and acceptor sites is taken into account for displacement of the ligand. It is reduced to an optimization problem to calculate the optimal translation and rotation matrixes that minimize the root mean square deviation between two sets of points, which can be solved using the Kabsch algorithm. In addition to the van der Waals interaction, the contribution of intermolecular hydrogen bonds in a complex is included in the scoring function to evaluate the docking quality. A modified Lennard-Jones 12-6 dispersion-repulsion term is used to estimate the van der Waals interaction to make the scoring function fairly "soft" so that ligands are not heavily penalized for small errors in the binding geometry. The calculation of this scoring function is very convenient. The evaluation is carried out on 278 rigid complexes and 93 flexible ones where there is at least one intermolecular hydrogen bond. The experiment results of docking accuracy and prediction of binding affinity demonstrate that the proposed method is highly effective.     

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.     

Influence of cation-pi interactions in different folding types of membrane proteins

Cation-pi interactions play an important role to the stability of protein structures. In this work, we analyze the influence of cation-pi interactions in three-dimensional structures of membrane proteins. We found that transmembrane strand (TMS) proteins have more number of cation-pi interactions than transmembrane helical (TMH) proteins. In TMH proteins, both the positively charged residues Lys and Arg equally experience favorable cation-pi interactions whereas in TMS proteins, Arg is more likely than Lys to be in such interactions. There is no relationship between number of cation-pi interactions and number of residues in TMH proteins whereas a good correlation was observed in TMS proteins. The average cation-pi interaction energy for TMH proteins is -16 kcal/mol and that for TMS proteins is -27 kcal/mol. The pair-wise cation-pi interaction energy between aromatic and positively charged residues showed that Lys-Trp energy is stronger in TMS proteins than TMH proteins; Arg-Phe, Arg-Tyr and Lys-Phe have higher energy in TMH proteins than TMS proteins. The decomposition of energies into electrostatic and van der Waals revealed that the contribution from electrostatic energy is twice as that from van der Waals energy in both TMH and TMS proteins. The results obtained in the present study would be helpful to understand the contribution of cation-pi interactions to the stability of membrane proteins.     

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.     

Measurement and modification of forces between lecithin bilayers.

We probe in two different ways the competing attractive and repulsive forces that create lamellar arrays of the phospholipid lecithin when in equilibrium with pure water. The first probe involves the addition of low molecular weight solutes, glucose and sucrose, to a system where the phospholipid is immersed in a large excess of water. Small solutes can enter the aqueous region between bilayers. Their effect is first to increase and then to decrease the separation between bilayers as sugar concentration increases. We interpret this waxing and waning of the lattice spacing in terms of the successive weakening and strengthening of the attractive van der Waals forces originally responsible for creation of a stable lattice. The second probe is an "osmotic stress method," in which very high molecular weight neutral polymer is added to the pure water phase but is unable to enter the multilayers. The polymer competes for water with the lamellar lattice, and thereby compresses it. From the resulting spacing (determined by X-ray diffraction) and the directly measured osmotic pressure, we find a force vs. distance curve for compressing the lattice (or, equivalently, the free energy of transfer to bulk water of water between bilayers. This method reveals a very strong, exponentially varying "hydration force" with a decay distance of about 2 A.     

Toward an energy function for the contact map representation of proteins

We analyzed several energy functions for predicting the native state of proteins from an energy minimization procedure. We derived the parameters of a given energy function by imposing the basic requirement that the energy of the native conformation of a protein is lower than that of any conformation chosen from a set of decoys. Our work is motivated by a recent result which proved that the simple pairwise contact approximation of the energy is insufficient to satisfy simultaneously such a basic requirement for all the proteins in a database. Here, we investigate the reasons of such negative results and show how to improve the predictive power of methods based on energy minimization. We generated decoys by gapless threading, and we derive energy parameters by perceptron learning. We first considered hydrophobic contributions to the energy, defined in several ways, and showed that the additional hydrophobic terms enlarge slightly the number of proteins that can be stabilized together. Next, we performed various modifications of the pairwise energy term. We introduced (1) a distinction between inter-residue contacts on the surface and in the core of a protein and (2) a simple distance-dependent pairwise interaction in which a two-tier definition of contact replaces the original (single-tier) one. Our results suggest that a detailed treatment of the pairwise potential is likely to be more relevant than the consideration of other forces.     

Highly accurate method for ligand-binding site prediction in unbound state (apo) protein structures

This article describes a new method for predicting ligand-binding sites of proteins. The method involves calculating the van der Waals interaction energy between a protein and probes placed on the protein surface, and then clustering the probes with attractive interaction to find the energetically most favorable locus. In 80% (28/35) of the test cases, the ligand-binding site was successfully predicted on a ligand-bound protein structure, and in 77% (27/35) was successfully predicted on an unbound structure. Our method was used to successfully predict ligand-binding sites unaffected by induced-fit as long as its scales were not very large, and it contributed to a significant improvement in prediction with unbound state protein structures. This represents a significant advance over conventional methods in detecting ligand-binding sites on uncharacterized proteins. Moreover, our method can predict ligand-binding sites with a narrower locus than those achieved using conventional methods.     

Energy functions for protein design: adjustment with protein-protein complex affinities, models for the unfolded state, and negative design of solubility and specificity

The development of the EGAD program and energy function for protein design is described. In contrast to most protein design methods, which require several empirical parameters or heuristics such as patterning of residues or rotamers, EGAD has a minimalist philosophy; it uses very few empirical factors to account for inaccuracies resulting from the use of fixed backbones and discrete rotamers in protein design calculations, and describes the unfolded state, aggregates, and alternative conformers explicitly with physical models instead of fitted parameters. This approach unveils important issues in protein design that are often camouflaged by heuristic-emphasizing methods. Inter-atom energies are modeled with the OPLS-AA all-atom forcefield, electrostatics with the generalized Born continuum model, and the hydrophobic effect with a solvent-accessible surface area-dependent term. Experimental characterization of proteins designed with an unmodified version of the energy function revealed problems with under-packing, stability, aggregation, and structural specificity. Under-packing was addressed by modifying the van der Waals function. By optimizing only three parameters, the effects of >400 mutations on protein-protein complex formation were predicted to within 1.0 kcal mol(-1). As an independent test, this modified energy function was used to predict the stabilities of >1500 mutants to within 1.0 kcal mol(-1); this required a physical model of the unfolded state that includes more interactions than traditional tripeptide-based models. Solubility and structural specificity were addressed with simple physical approximations of aggregation and conformational equilibria. The complete energy function can design protein sequences that have high levels of identity with their natural counterparts, and have predicted structural properties more consistent with soluble and uniquely folded proteins than the initial designs.     

High quality NMR structures: a new force field with implicit water and membrane solvation for Xplor-NIH

Structure determination of proteins by NMR is unique in its ability to measure restraints, very accurately, in environments and under conditions that closely mimic those encountered in vivo. For example, advances in solid-state NMR methods enable structure determination of membrane proteins in detergent-free lipid bilayers, and of large soluble proteins prepared by sedimentation, while parallel advances in solution NMR methods and optimization of detergent-free lipid nanodiscs are rapidly pushing the envelope of the size limit for both soluble and membrane proteins. These experimental advantages, however, are partially squandered during structure calculation, because the commonly used force fields are purely repulsive and neglect solvation, Van der Waals forces and electrostatic energy. Here we describe a new force field, and updated energy functions, for protein structure calculations with EEFx implicit solvation, electrostatics, and Van der Waals Lennard-Jones forces, in the widely used program Xplor-NIH. The new force field is based primarily on CHARMM22, facilitating calculations with a wider range of biomolecules. The new EEFx energy function has been rewritten to enable OpenMP parallelism, and optimized to enhance computation efficiency. It implements solvation, electrostatics, and Van der Waals energy terms together, thus ensuring more consistent and efficient computation of the complete nonbonded energy lists. Updates in the related python module allow detailed analysis of the interaction energies and associated parameters. The new force field and energy function work with both soluble proteins and membrane proteins, including those with cofactors or engineered tags, and are very effective in situations where there are sparse experimental restraints. Results obtained for NMR-restrained calculations with a set of five soluble proteins and five membrane proteins show that structures calculated with EEFx have significant improvements in accuracy, precision, and conformation, and that structure refinement can be obtained by short relaxation with EEFx to obtain improvements in these key metrics. These developments broaden the range of biomolecular structures that can be calculated with high fidelity from NMR restraints.     

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.     

Fold helical proteins by energy minimization in dihedral space and a DFIRE-based statistical energy function

Statistical energy functions are discrete (or stepwise) energy functions that lack van der Waals repulsion. As a result, they are often applied directly to a given structure (native or decoy) without further energy minimization being performed to the structure. However, the full benefit (or hidden defect) of an energy function cannot be revealed without energy minimization. This paper tests a recently developed, all-atom statistical energy function by energy minimization with a fixed secondary helical structure in dihedral space. This is accomplished by combining the statistical energy function based on a distance-scaled finite ideal-gas reference (DFIRE) state with a simple repulsive interaction and an improper torsion energy function. The energy function was used to minimize 2000 random initial structures of 41 small and medium-sized helical proteins in a dihedral space with a fixed helical region. Results indicate that near-native structures for most studied proteins can be obtained by minimization alone. The average minimum root-mean-squared distance (rmsd) from the native structure for all 41 proteins is 4.1 A. The energy function (together with a simple clustering of similar structures) also makes a reasonable selection of near-native structures from minimized structures. The average rmsd value and the average rank for the best structure in the top five is 6.8 A and 2.4, respectively. The accuracy of the structures sampled and the structure selections can be improved significantly with the removal of flexible terminal regions in rmsd calculations and in minimization and with the increase in the number of minimizations. The minimized structures form an excellent decoy set for testing other energy functions because most structures are well-packed with minimum hard-core overlaps with correct hydrophobic/hydrophilic partitioning. They are available online at http://theory.med.buffalo.edu.