Interaction cutoff effect on ruggedness of protein-protein energy landscape

Decoding Protein-protein Interactions: An Overview

Drug discovery has focused on the paradigm "one drug, one target" for a long time. However, small molecules can act at multiple macromolecular targets, which serves as the basis for drug repurposing. In an effort to expand the target space, and given advances in X-ray crystallography, protein-protein interactions have become an emerging focus area of drug discovery enterprises. Proteins interact with other biomolecules and it is this intricate network of interactions that determines the behavior of the system and its biological processes. In this review, we briefly discuss networks in disease, followed by computational methods for protein-protein complex prediction. Computational methodologies and techniques employed towards objectives such as protein-protein docking, protein-protein interactions, and interface predictions are described extensively. Docking aims at producing a complex between proteins, while interface predictions identify a subset of residues on one protein that could interact with a partner, and protein-protein interaction sites address whether two proteins interact. In addition, approaches to predict hot spots and binding sites are presented along with a representative example of our internal project on the chemokine CXC receptor 3 B-isoform and predictive modeling with IP10 and PF4.

ROTAS: a rotamer-dependent, atomic statistical potential for assessment and prediction of protein structures

Background

Multibody potentials accounting for cooperative effects of molecular interactions have shown better accuracy than typical pairwise potentials. The main challenge in the development of such potentials is to find relevant structural features that characterize the tightly folded proteins. Also, the side-chains of residues adopt several specific, staggered conformations, known as rotamers within protein structures. Different molecular conformations result in different dipole moments and induce charge reorientations. However, until now modeling of the rotameric state of residues had not been incorporated into the development of multibody potentials for modeling non-bonded interactions in protein structures.

Results

In this study, we develop a new multibody statistical potential which can account for the influence of rotameric states on the specificity of atomic interactions. In this potential, named “rotamer-dependent atomic statistical potential” (ROTAS), the interaction between two atoms is specified by not only the distance and relative orientation but also by two state parameters concerning the rotameric state of the residues to which the interacting atoms belong. It was clearly found that the rotameric state is correlated to the specificity of atomic interactions. Such rotamer-dependencies are not limited to specific type or certain range of interactions. The performance of ROTAS was tested using 13 sets of decoys and was compared to those of existing atomic-level statistical potentials which incorporate orientation-dependent energy terms. The results show that ROTAS performs better than other competing potentials not only in native structure recognition, but also in best model selection and correlation coefficients between energy and model quality.

Conclusions

A new multibody statistical potential, ROTAS accounting for the influence of rotameric states on the specificity of atomic interactions was developed and tested on decoy sets. The results show that ROTAS has improved ability to recognize native structure from decoy models compared to other potentials. The effectiveness of ROTAS may provide insightful information for the development of many applications which require accurate side-chain modeling such as protein design, mutation analysis, and docking simulation.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-307) contains supplementary material, which is available to authorized users.

Multi-dimensional characterization of electrostatic surface potential computation on graphics processors

BACKGROUND

Calculating the electrostatic surface potential (ESP) of a biomolecule is critical towards understanding biomolecular function. Because of its quadratic computational complexity (as a function of the number of atoms in a molecule), there have been continual efforts to reduce its complexity either by improving the algorithm or the underlying hardware on which the calculations are performed.

RESULTS

We present the combined effect of (i) a multi-scale approximation algorithm, known as hierarchical charge partitioning (HCP), when applied to the calculation of ESP and (ii) its mapping onto a graphics processing unit (GPU). To date, most molecular modeling algorithms perform an artificial partitioning of biomolecules into a grid/lattice on the GPU. In contrast, HCP takes advantage of the natural partitioning in biomolecules, which in turn, better facilitates its mapping onto the GPU. Specifically, we characterize the effect of known GPU optimization techniques like use of shared memory. In addition, we demonstrate how the cost of divergent branching on a GPU can be amortized across algorithms like HCP in order to deliver a massive performance boon.

CONCLUSIONS

We accelerated the calculation of ESP by 25-fold solely by parallelization on the GPU. Combining GPU and HCP, resulted in a speedup of at most 1,860-fold for our largest molecular structure. The baseline for these speedups is an implementation that has been hand-tuned SSE-optimized and parallelized across 16 cores on the CPU. The use of GPU does not deteriorate the accuracy of our results.

DECK: Distance and environment-dependent, coarse-grained, knowledge-based potentials for protein-protein docking

Background

Computational approaches to protein-protein docking typically include scoring aimed at improving the rank of the near-native structure relative to the false-positive matches. Knowledge-based potentials improve modeling of protein complexes by taking advantage of the rapidly increasing amount of experimentally derived information on protein-protein association. An essential element of knowledge-based potentials is defining the reference state for an optimal description of the residue-residue (or atom-atom) pairs in the non-interaction state.

Results

The study presents a new Distance- and Environment-dependent, Coarse-grained, Knowledge-based (DECK) potential for scoring of protein-protein docking predictions. Training sets of protein-protein matches were generated based on bound and unbound forms of proteins taken from the DOCKGROUND resource. Each residue was represented by a pseudo-atom in the geometric center of the side chain. To capture the long-range and the multi-body interactions, residues in different secondary structure elements at protein-protein interfaces were considered as different residue types. Five reference states for the potentials were defined and tested. The optimal reference state was selected and the cutoff effect on the distance-dependent potentials investigated. The potentials were validated on the docking decoys sets, showing better performance than the existing potentials used in scoring of protein-protein docking results.

Conclusions

A novel residue-based statistical potential for protein-protein docking was developed and validated on docking decoy sets. The results show that the scoring function DECK can successfully identify near-native protein-protein matches and thus is useful in protein docking. In addition to the practical application of the potentials, the study provides insights into the relative utility of the reference states, the scope of the distance dependence, and the coarse-graining of the potentials.

Sequence composition and environment effects on residue fluctuations in protein structures

Structure fluctuations in proteins affect a broad range of cell phenomena, including stability of proteins and their fragments, allosteric transitions, and energy transfer. This study presents a statistical-thermodynamic analysis of relationship between the sequence composition and the distribution of residue fluctuations in protein-protein complexes. A one-node-per-residue elastic network model accounting for the nonhomogeneous protein mass distribution and the interatomic interactions through the renormalized inter-residue potential is developed. Two factors, a protein mass distribution and a residue environment, were found to determine the scale of residue fluctuations. Surface residues undergo larger fluctuations than core residues in agreement with experimental observations. Ranking residues over the normalized scale of fluctuations yields a distinct classification of amino acids into three groups: (i) highly fluctuating-Gly, Ala, Ser, Pro, and Asp, (ii) moderately fluctuating-Thr, Asn, Gln, Lys, Glu, Arg, Val, and Cys, and (iii) weakly fluctuating-Ile, Leu, Met, Phe, Tyr, Trp, and His. The structural instability in proteins possibly relates to the high content of the highly fluctuating residues and a deficiency of the weakly fluctuating residues in irregular secondary structure elements (loops), chameleon sequences, and disordered proteins. Strong correlation between residue fluctuations and the sequence composition of protein loops supports this hypothesis. Comparing fluctuations of binding site residues (interface residues) with other surface residues shows that, on average, the interface is more rigid than the rest of the protein surface and Gly, Ala, Ser, Cys, Leu, and Trp have a propensity to form more stable docking patches on the interface. The findings have broad implications for understanding mechanisms of protein association and stability of protein structures.

An n log n Generalized Born Approximation

Molecular dynamics (MD) simulations based on the generalized Born (GB) model of implicit solvation offer a number of important advantages over the traditional explicit solvent based simulations. Yet, in MD simulations, the GB model has not been able to reach its full potential partly due to its computational cost, which scales as ∼n(2), where n is the number of solute atoms. We present here an ∼n log n approximation for the generalized Born (GB) implicit solvent model. The approximation is based on the hierarchical charge partitioning (HCP) method (Anandakrishnan and Onufriev J. Comput. Chem. 2010 , 31 , 691 - 706 ) previously developed and tested for electrostatic computations in gas-phase and distant dependent dielectric models. The HCP uses the natural organization of biomolecular structures to partition the structures into multiple hierarchical levels of components. The charge distribution for each of these components is approximated by a much smaller number of charges. The approximate charges are then used for computing electrostatic interactions with distant components, while the full set of atomic charges are used for nearby components. To apply the HCP concept to the GB model, we define the equivalent of the effective Born radius for components. The component effective Born radius is then used in GB computations for points that are distant from the component. This HCP approximation for GB (HCP-GB) is implemented in the open source MD software, NAB in AmberTools, and tested on a set of representative biomolecular structures ranging in size from 632 atoms to ∼3 million atoms. For this set of test structures, the HCP-GB method is 1.1-390 times faster than the GB computation without additional approximations (the reference GB computation), depending on the size of the structure. Similar to the spherical cutoff method with GB (cutoff-GB), which also scales as ∼n log n, the HCP-GB is relatively simple. However, for the structures considered here, we show that the HCP-GB method is more accurate than the cutoff-GB method as measured by relative RMS error in electrostatic force compared to the reference (no cutoff) GB computation. MD simulations of four biomolecular structures on 50 ns time scales show that the backbone RMS deviation for the HCP-GB method is in reasonable agreement with the reference GB simulation. A critical difference between the cutoff-GB and HCP-GB methods is that the cutoff-GB method completely ignores interactions due to atoms beyond the cutoff distance, whereas the HCP-GB method uses an approximation for interactions due to distant atoms. Our testing suggests that completely ignoring distant interactions, as the cutoff-GB does, can lead to qualitatively incorrect results. In general, we found that the HCP-GB method reproduces key characteristics of dynamics, such as residue fluctuation, χ1/χ2 flips, and DNA flexibility, more accurately than the cutoff-GB method. As a practical demonstration, the HCP-GB simulation of a 348 000 atom chromatin fiber was used to refine the starting structure. Our findings suggest that the HCP-GB method is preferable to the cutoff-GB method for molecular dynamics based on pairwise implicit solvent GB models.

Computational modeling of the potential interactions of the proteasome beta5 subunit and catechol-O-methyltransferase-resistant EGCG analogs

(-)-Epigallocatechin gallate [(-)-EGCG] has been implicated in cancer chemoprevention and has been shown as an inhibitor of tumor proteasomal chymotrypsin-like activity in vitro and in vivo. However, EGCG is subjected to rapid biotransforming modifications such as methylation by catechol-Omicron-methyltransferase (COMT) that limits its action. We recently reported that structure 7, an EGCG analog which should be resistant to COMT-mediated methylation and inactivation in cells, was able to inhibit the activity of purified 20S proteasome and cellular 26S proteasome. However, the involved molecular mechanism is unknown. Herein, we applied computational solution to understand the possible interaction between EGCG analogs including structure 7 and the proteasome beta5 subunit which is responsible for the chymotrypsin-like activity. We report that the ester carbonyls at C2 and C3 carbon atoms may be the active sites for nucleophilic attack in structure 7 and 5. Equally spaced carbon atoms in COMT-resistant structure 7 give more stable conformation and lower docked free energy than other EGCG analogs. The absence of a second gallate group in structure 16 and 21 significantly decreases the ability to inhibit the proteasome.

Accelerating electrostatic surface potential calculation with multi-scale approximation on graphics processing units

Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed-up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson-Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multi-scale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone.

An N log N approximation based on the natural organization of biomolecules for speeding up the computation of long range interactions

Presented here is a method, the hierarchical charge partitioning (HCP) approximation, for speeding up computation of pairwise electrostatic interactions in biomolecular systems. The approximation is based on multiple levels of natural partitioning of biomolecular structures into a hierarchical set of its constituent structural components. The charge distribution in each component is systematically approximated by a small number of point charges, which, for the highest level component, are much fewer than the number of atoms in the component. For short distances from the point of interest, the HCP uses the full set of atomic charges available. For long-distance interactions, the approximate charge distributions with smaller sets of charges are used instead. For a structure consisting of N charges, the computational cost of computing the pairwise interactions via the HCP scales as O(N log N), under assumptions about the structural organization of biomolecular structures generally consistent with reality. A proof-of-concept implementation of the HCP shows that for large structures it can lead to speed-up factors of up to several orders of magnitude relative to the exact pairwise O(N(2)) all-atom computation used as a reference. For structures with more than 2000-3000 atoms the relative accuracy of the HCP (relative root-mean-square force error per atom), approaches the accuracy of the particle mesh Ewald (PME) method with parameter settings typical for biomolecular simulations. When averaged over a set of 600 representative biomolecular structures, the relative accuracies of the two methods are roughly equal. The HCP is also significantly more accurate than the spherical cutoff method. The HCP has been implemented in the freely available nucleic acids builder (NAB) molecular dynamics (MD) package in Amber tools. A 10 ns simulation of a small protein indicates that the HCP based MD simulation is stable, and that it can be faster than the spherical cutoff method. A critical benefit of the HCP approximation is that it is algorithmically very simple, and unlike the PME, the HCP is straightforward to use with implicit solvent models.

Homology modeling and docking analysis of the interaction between polyphenols and mammalian 20S proteasomes

Molecular docking of small ligands to biologically active macromolecules has become a valuable strategy to predict the stability of complexes between potential partners and their binding modes. In this perspective, we applied this computational procedure to rationalize the reported role of polyphenols as inhibitors of the mammalian 20S proteasomes. In particular, polyphenols were shown to modulate each proteasomal activity at different extents both in the constitutive and the inducible enzyme. We performed a flexible molecular docking analysis between a set of polyphenols previously demonstrated to have the highest binding affinity and both the constitutive (from deposited PDB structures) and homology modeled active subunits of the IFN-gamma inducible proteasome, to provide insight into the possible mechanism of interaction. Among the tested polyphenols, (-)-epigallocatechin-3-gallate showed the highest affinity for the proteasome subunits, both in terms of intermolecular energy and predicted equilibrium constants, in particular for beta5 and beta5i subunits (E(total) = -66 kcal/mol, Ki = 81.3 microM and E(Total) = -83.9 kcal/mol, Ki = 0.29 microM, respectively), known to be related to the chymotrypsin-like and BrAAP activities. Collectively, polyphenols showed a higher affinity for the inducible subunits, in agreement with previous in vitro studies. Additionally, different contributions to the interaction energy (van der Waals, electrostatic, H-bond) of proteasome-polyphenols complexes were dissected.

Principles of flexible protein-protein docking

Treating flexibility in molecular docking is a major challenge in cell biology research. Here we describe the background and the principles of existing flexible protein-protein docking methods, focusing on the algorithms and their rational. We describe how protein flexibility is treated in different stages of the docking process: in the preprocessing stage, rigid and flexible parts are identified and their possible conformations are modeled. This preprocessing provides information for the subsequent docking and refinement stages. In the docking stage, an ensemble of pre-generated conformations or the identified rigid domains may be docked separately. In the refinement stage, small-scale movements of the backbone and side-chains are modeled and the binding orientation is improved by rigid-body adjustments. For clarity of presentation, we divide the different methods into categories. This should allow the reader to focus on the most suitable method for a particular docking problem.

The ruggedness of protein-protein energy landscape and the cutoff for 1/r(n) potentials

MOTIVATION

Computational studies of the energetics of protein association are important for revealing the underlying fundamental principles and for designing better tools to model protein complexes. The interaction cutoff contribution to the ruggedness of protein-protein energy landscape is studied in terms of relative energy fluctuations for 1/r(n) potentials based on a simplistic model of a protein complex. This artificial ruggedness exists for short cutoffs and gradually disappears with the cutoff increase.

RESULTS

The critical values of the cutoff were calculated for each of 11 popular power-type potentials with n=0/9, 12 and for two thresholds of 5% and 10%. The artificial ruggedness decreases to tolerable thresholds for cutoffs larger than the critical ones. The results showed that for both thresholds the critical cutoff is a non-monotonic function of the potential power n. The functions reach the maximum at n=3/4 and then decrease with the increase of the potential power. The difference between two cutoffs for 5% and 10% artificial ruggedness becomes negligible for potentials decreasing faster than 1/r(12). The analytical results obtained for the simple model of protein complexes agree with the analysis of artificial ruggedness in a dataset of 62 protein-protein complexes, with different parameterizations of soft Lennard-Jones potential and two types of protein representations: all-atom and coarse-grained. The results suggest that cutoffs larger than the critical ones can be recommended for protein-protein potentials.

Chasing funnels on protein-protein energy landscapes at different resolutions

Studies of intermolecular energy landscapes are important for understanding protein association and adequate modeling of protein interactions. Landscape representation at different resolutions can be used for the refinement of docking predictions and detection of macro characteristics, like the binding funnel. A representative set of protein-protein complexes was used to systematically map the intermolecular landscape by grid-based docking. The change of the resolution was achieved by varying the range of the potential, according to the variable resolution GRAMM methodology. A formalism was developed to consistently parameterize the potential and describe essential characteristics of the landscape. The results of gradual landscape smoothing, from high to low resolution, indicate that i), the number of energy basins, the landscape ruggedness, and the slope decrease accordingly; ii), the number of near-native matches, defined as those inside the funnel, increases until the trend breaks down at critical resolution; the rate of the increase and the critical resolution are specific to the type of a complex (enzyme inhibitor, antigen-antibody, and other), reflect known underlying recognition factors, and correlate with earlier determined estimates of the funnel size; iii), the native/nonnative energy gap, a major characteristic of the energy minima hierarchy, remains constant; and iv), the putative funnel (defined as the deepest basin) has the largest average depth-related ruggedness and slope, at all resolutions. The results facilitate better understanding of the binding landscapes and suggest directions for implementation in practical docking protocols.