A novel empirical free energy function that explains and predicts protein-protein binding affinities

A free energy function can be defined as a mathematical expression that relates macroscopic free energy changes to microscopic or molecular properties. Free energy functions can be used to explain and predict the affinity of a ligand for a protein and to score and discriminate between native and non-native binding modes. However, there is a natural tension between developing a function fast enough to solve the scoring problem but rigorous enough to explain and predict binding affinities. Here, we present a novel, physics-based free energy function that is computationally inexpensive, yet explanatory and predictive. The function results from a derivation that assumes the cost of polar desolvation can be ignored and that includes a unique and implicit treatment of interfacial water-bridged interactions. The function was parameterized on an internally consistent, high quality training set giving R2=0.97 and Q2=0.91. We used the function to blindly and successfully predict binding affinities for a diverse test set of 31 wild-type protein-protein and protein-peptide complexes (R2=0.79, rmsd=1.2 kcal mol(-1)). The function performed very well in direct comparison with a recently described knowledge-based potential and the function appears to be transferable. Our results indicate that our function is well suited for solving a wide range of protein/peptide design and discovery problems.     

Ab initio folding of proteins with all-atom discrete molecular dynamics

Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. We performed folding simulations of six small proteins (20-60 residues) with distinct native structures by the replica exchange method. In all cases, native or near-native states were reached in simulations. For three small proteins, multiple folding transitions are observed, and the computationally characterized thermodynamics are in qualitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes and applied to protein engineering and design of protein-protein interactions.     

Comparison of sequence-based and structure-based phylogenetic trees of homologous proteins: Inferences on protein evolution

Several studies based on the known three-dimensional (3-D) structures of proteins show that two homologous proteins with insignificant sequence similarity could adopt a common fold and may perform same or similar biochemical functions. Hence, it is appropriate to use similarities in 3-D structure of proteins rather than the amino acid sequence similarities in modelling evolution of distantly related proteins. Here we present an assessment of using 3-D structures in modelling evolution of homologous proteins. Using a dataset of 108 protein domain families of known structures with at least 10 members per family we present a comparison of extent of structural and sequence dissimilarities among pairs of proteins which are inputs into the construction of phylogenetic trees. We find that correlation between the structure-based dissimilarity measures and the sequence-based dissimilarity measures is usually good if the sequence similarity among the homologues is about 30% or more. For protein families with low sequence similarity among the members, the correlation coefficient between the sequence-based and the structure-based dissimilarities are poor. In these cases the structure-based dendrogram clusters proteins with most similar biochemical functional properties better than the sequence-similarity based dendrogram. In multi-domain protein families and disulphide-rich protein families the correlation coefficient for the match of sequence-based and structure-based dissimilarity (SDM) measures can be poor though the sequence identity could be higher than 30%. Hence it is suggested that protein evolution is best modelled using 3-D structures if the sequence similarities (SSM) of the homologues are very low.     

Effective knowledge‐based potentials

Empirical or knowledge‐based potentials have many applications in structural biology such as the prediction of protein structure, protein–protein, and protein–ligand interactions and in the evaluation of stability for mutant proteins, the assessment of errors in experimentally solved structures, and the design of new proteins. Here, we describe a simple procedure to derive and use pairwise distance‐dependent potentials that rely on the definition of effective atomic interactions, which attempt to capture interactions that are more likely to be physically relevant. Based on a difficult benchmark test composed of proteins with different secondary structure composition and representing many different folds, we show that the use of effective atomic interactions significantly improves the performance of potentials at discriminating between native and near‐native conformations. We also found that, in agreement with previous reports, the potentials derived from the observed effective atomic interactions in native protein structures contain a larger amount of mutual information. A detailed analysis of the effective energy functions shows that atom connectivity effects, which mostly arise when deriving the potential by the incorporation of those indirect atomic interactions occurring beyond the first atomic shell, are clearly filtered out. The shape of the energy functions for direct atomic interactions representing hydrogen bonding and disulfide and salt bridges formation is almost unaffected when effective interactions are taken into account. On the contrary, the shape of the energy functions for indirect atom interactions (i.e., those describing the interaction between two atoms bound to a direct interacting pair) is clearly different when effective interactions are considered. Effective energy functions for indirect interacting atom pairs are not influenced by the shape or the energy minimum observed for the corresponding direct interacting atom pair. Our results suggest that the dependency between the signals in different energy functions is a key aspect that need to be addressed when empirical energy functions are derived and used, and also highlight the importance of additivity assumptions in the use of potential energy functions.     

HLA mismatches and hematopoietic cell transplantation: Structural simulations assess the impact of changes in peptide binding specificity on transplant outcome

The success of hematopoietic cell transplantation from an unrelated donor depends in part on the degree of Human Histocompatibility Leukocyte Antigen (HLA) matching between donor and patient. We present a structure-based analysis of HLA mismatching, focusing on individual amino acid mismatches and their effect on peptide binding specificity. Using molecular modeling simulations of HLA-peptide interactions, we find evidence that amino acid mismatches predicted to perturb peptide binding specificity are associated with higher risk of mortality in a large and diverse dataset of patient-donor pairs assembled by the International Histocompatibility Working Group in Hematopoietic Cell Transplantation consortium. This analysis may represent a first step toward sequence-based prediction of relative risk for HLA allele mismatches.     

Towards universal structure-based prediction of class II MHC epitopes for diverse allotypes

The binding of peptide fragments of antigens to class II MHC proteins is a crucial step in initiating a helper T cell immune response. The discovery of these peptide epitopes is important for understanding the normal immune response and its misregulation in autoimmunity and allergies and also for vaccine design. In spite of their biomedical importance, the high diversity of class II MHC proteins combined with the large number of possible peptide sequences make comprehensive experimental determination of epitopes for all MHC allotypes infeasible. Computational methods can address this need by predicting epitopes for a particular MHC allotype. We present a structure-based method for predicting class II epitopes that combines molecular mechanics docking of a fully flexible peptide into the MHC binding cleft followed by binding affinity prediction using a machine learning classifier trained on interaction energy components calculated from the docking solution. Although the primary advantage of structure-based prediction methods over the commonly employed sequence-based methods is their applicability to essentially any MHC allotype, this has not yet been convincingly demonstrated. In order to test the transferability of the prediction method to different MHC proteins, we trained the scoring method on binding data for DRB1*0101 and used it to make predictions for multiple MHC allotypes with distinct peptide binding specificities including representatives from the other human class II MHC loci, HLA-DP and HLA-DQ, as well as for two murine allotypes. The results showed that the prediction method was able to achieve significant discrimination between epitope and non-epitope peptides for all MHC allotypes examined, based on AUC values in the range 0.632-0.821. We also discuss how accounting for peptide binding in multiple registers to class II MHC largely explains the systematically worse performance of prediction methods for class II MHC compared with those for class I MHC based on quantitative prediction performance estimates for peptide binding to class II MHC in a fixed register.     

Genome-Wide Prediction and Validation of Peptides That Bind Human Prosurvival Bcl-2 Proteins

Programmed cell death is regulated by interactions between pro-apoptotic and prosurvival members of the Bcl-2 family. Pro-apoptotic family members contain a weakly conserved BH3 motif that can adopt an alpha-helical structure and bind to a groove on prosurvival partners Bcl-x_L, Bcl-w, Bcl-2, Mcl-1 and Bfl-1. Peptides corresponding to roughly 13 reported BH3 motifs have been verified to bind in this manner. Due to their short lengths and low sequence conservation, BH3 motifs are not detected using standard sequence-based bioinformatics approaches. Thus, it is possible that many additional proteins harbor BH3-like sequences that can mediate interactions with the Bcl-2 family. In this work, we used structure-based and data-based Bcl-2 interaction models to find new BH3-like peptides in the human proteome. We used peptide SPOT arrays to test candidate peptides for interaction with one or more of the prosurvival proteins Bcl-x_L, Bcl-w, Bcl-2, Mcl-1 and Bfl-1. For the 36 most promising array candidates, we quantified binding to all five human receptors using direct and competition binding assays in solution. All 36 peptides showed evidence of interaction with at least one prosurvival protein, and 22 peptides bound at least one prosurvival protein with a dissociation constant between 1 and 500 nM; many peptides had specificity profiles not previously observed. We also screened the full-length parent proteins of a subset of array-tested peptides for binding to Bcl-x_L and Mcl-1. Finally, we used the peptide binding data, in conjunction with previously reported interactions, to assess the affinity and specificity prediction performance of different models.     

Accurate sequence-based prediction of catalytic residues

MOTIVATION: Prediction of catalytic residues provides useful information for the research on function of enzymes. Most of the existing prediction methods are based on structural information, which limits their use. We propose a sequence-based catalytic residue predictor that provides predictions with quality comparable to modern structure-based methods and that exceeds quality of state-of-the-art sequence-based methods. RESULTS: Our method (CRpred) uses sequence-based features and the sequence-derived PSI-BLAST profile. We used feature selection to reduce the dimensionality of the input (and explain the input) to support vector machine (SVM) classifier that provides predictions. Tests on eight datasets and side-by-side comparison with six modern structure- and sequence-based predictors show that CRpred provides predictions with quality comparable to current structure-based methods and better than sequence-based methods. The proposed method obtains 15-19% precision and 48-58% TP (true positive) rate, depending on the dataset used. CRpred also provides confidence values that allow selecting a subset of predictions with higher precision. The improved quality is due to newly designed features and careful parameterization of the SVM. The features incorporate amino acids characterized by the highest and the lowest propensities to constitute catalytic residues, Gly that provides flexibility for catalytic sites and sequence motifs characteristic to certain catalytic reactions. Our features indicate that catalytic residues are on average more conserved when compared with the general population of residues and that highly conserved amino acids characterized by high catalytic propensity are likely to form catalytic sites. We also show that local (with respect to the sequence) hydrophobicity contributes towards the prediction.     

On the role of structural information in remote homology detection and sequence alignment: new methods using hybrid sequence profiles

Structural alignments often reveal relationships between proteins that cannot be detected using sequence alignment alone. However, profile search methods based entirely on structural alignments alone have not been found to be effective in finding remote homologs. Here, we explore the role of structural information in remote homolog detection and sequence alignment. To this end, we develop a series of hybrid multidimensional alignment profiles that combine sequence, secondary and tertiary structure information into hybrid profiles. Sequence-based profiles are profiles whose position-specific scoring matrix is derived from sequence alignment alone; structure-based profiles are those derived from multiple structure alignments. We compare pure sequence-based profiles to pure structure-based profiles, as well as to hybrid profiles that use combined sequence-and-structure-based profiles, where sequence-based profiles are used in loop/motif regions and structural information is used in core structural regions. All of the hybrid methods offer significant improvement over simple profile-to-profile alignment. We demonstrate that both sequence-based and structure-based profiles contribute to remote homology detection and alignment accuracy, and that each contains some unique information. We discuss the implications of these results for further improvements in amino acid sequence and structural analysis.     

Identifying Cytochrome P450 Functional Networks and Their Allosteric Regulatory Elements

Cytochrome P450 (CYP) enzymes play key roles in drug metabolism and adverse drug-drug interactions. Despite tremendous efforts in the past decades, essential questions regarding the function and activity of CYPs remain unanswered. Here, we used a combination of sequence-based co-evolutionary analysis and structure-based anisotropic thermal diffusion (ATD) molecular dynamics simulations to detect allosteric networks of amino acid residues and characterize their biological and molecular functions. We investigated four CYP subfamilies (CYP1A, CYP2D, CYP2C, and CYP3A) that are involved in 90% of all metabolic drug transformations and identified four amino acid interaction networks associated with specific CYP functionalities, i.e., membrane binding, heme binding, catalytic activity, and dimerization. Interestingly, we did not detect any co-evolved substrate-binding network, suggesting that substrate recognition is specific for each subfamily. Analysis of the membrane binding networks revealed that different CYP proteins adopt different membrane-bound orientations, consistent with the differing substrate preference for each isoform. The catalytic networks were associated with conservation of catalytic function among CYP isoforms, whereas the dimerization network was specific to different CYP isoforms. We further applied low-temperature ATD simulations to verify proposed allosteric sites associated with the heme-binding network and their role in regulating metabolic fate. Our approach allowed for a broad characterization of CYP properties, such as membrane interactions, catalytic mechanisms, dimerization, and linking these to groups of residues that can serve as allosteric regulators. The presented combined co-evolutionary analysis and ATD simulation approach is also generally applicable to other biological systems where allostery plays a role.     

Side chain substitution benchmark for peptide/MHC interaction

The prediction of T-cell epitopes is an essential part in virtual immunology. Apart from sequence-based techniques, which achieve good results but fail to give insight into the binding behavior of a certain peptide binding to a major histocompatibility complex, structure-based approaches are another important technique. An essential step is the correct placement of the side chains for a given peptide in cases where no experimental data for the structure are available. To our knowledge, no benchmark for side chain substitution in the area of HLA has been reported in the literature. Here, we present a comparison of five different tools (SCWRL, SCATD, SPDBV, SCit, IRECS) applicable for side chain substitution. Each tool is tested on 29 different HLA-A2 structures with experimentally known side chain positions. Parts of the benchmark are correctness, reliability, runtime, and usability. For validation, the root mean square deviations between X-ray structures and predicted structures are used. All tools show different strengths and weaknesses.     

Folding thermodynamics of three beta-sheet peptides: a model study

We study the folding thermodynamics of a beta-hairpin and two three-stranded beta-sheet peptides using a simplified sequence-based all-atom model, in which folding is driven mainly by backbone hydrogen bonding and effective hydrophobic attraction. The native populations obtained for these three sequences are in good agreement with experimental data. We also show that the apparent native population depends on which observable is studied; the hydrophobicity energy and the number of native hydrogen bonds give different results. The magnitude of this dependence matches well with the results obtained in two different experiments on the beta-hairpin.     

Energy barriers, cooperativity, and hidden intermediates in the folding of small proteins

Current theoretical views of the folding process of small proteins (< approximately 100 amino acids) postulate that the landscape of potential mean force (PMF) for the formation of the native state has a funnel shape and that the free energy barrier to folding arises from the chain configurational entropy only. However, recent theoretical studies on the formation of hydrophobic clusters with explicit water suggest that a barrier should exist on the PMF of folding, consistent with the fact that protein folding generally involves a large positive activation enthalpy at room temperature. In addition, high-resolution structural studies of the hidden partially unfolded intermediates have revealed the existence of non-native interactions, suggesting that the correction of the non-native interactions during folding should also lead to barriers on PMF. To explore the effect of a PMF barrier on the folding behavior of proteins, we modified Zwanzig's model for protein folding with an uphill landscape of PMF for the formation of transition states. We found that the modified model for short peptide segments can satisfy the thermodynamic and kinetic criteria for an apparently two-state folding. Since the Levinthal paradox can be solved by a stepwise folding of short peptide segments, a landscape of PMF with a locally uphill search for the transition state and cooperative stabilization of folding intermediates/native state is able to explain the available experimental results for small proteins. We speculate that the existence of cooperative hidden folding intermediates in small proteins could be the consequence of the highly specific structures of the native state, which are selected by evolution to perform specific functions and fold in a biologically meaningful time scale.     

DynaPred: a structure and sequence based method for the prediction of MHC class I binding peptide sequences and conformations

MOTIVATION: The binding of endogenous antigenic peptides to MHC class I molecules is an important step during the immunologic response of a host against a pathogen. Thus, various sequence- and structure-based prediction methods have been proposed for this purpose. The sequence-based methods are computationally efficient, but are hampered by the need of sufficient experimental data and do not provide a structural interpretation of their results. The structural methods are data-independent, but are quite time-consuming and thus not suited for screening of whole genomes. Here, we present a new method, which performs sequence-based prediction by incorporating information obtained from molecular modeling. This allows us to perform large databases screening and to provide structural information of the results. RESULTS: We developed a SVM-trained, quantitative matrix-based method for the prediction of MHC class I binding peptides, in which the features of the scoring matrix are energy terms retrieved from molecular dynamics simulations. At the same time we used the equilibrated structures obtained from the same simulations in a simple and efficient docking procedure. Our method consists of two steps: First, we predict potential binders from sequence data alone and second, we construct protein-peptide complexes for the predicted binders. So far, we tested our approach on the HLA-A0201 allele. We constructed two prediction models, using local, position-dependent (DynaPred(POS)) and global, position-independent (DynaPred) features. The former model outperformed the two sequence-based methods used in our evaluation; the latter shows a much higher generalizability towards other alleles than the position-dependent models. The constructed peptide structures can be refined within seconds to structures with an average backbone RMSD of 1.53 A from the corresponding experimental structures.     

T-Cell Receptors Binding Orientation over Peptide/MHC Class I Is Driven by Long-Range Interactions

Crystallographic data about T-Cell Receptor – peptide – major histocompatibility complex class I (TCRpMHC) interaction have revealed extremely diverse TCR binding modes triggering antigen recognition. Understanding the molecular basis that governs TCR orientation over pMHC is still a considerable challenge. We present a simplified rigid approach applied on all non-redundant TCRpMHC crystal structures available. The CHARMM force field in combination with the FACTS implicit solvation model is used to study the role of long-distance interactions between the TCR and pMHC. We demonstrate that the sum of the coulomb interactions and the electrostatic solvation energies is sufficient to identify two orientations corresponding to energetic minima at 0° and 180° from the native orientation. Interestingly, these results are shown to be robust upon small structural variations of the TCR such as changes induced by Molecular Dynamics simulations, suggesting that shape complementarity is not required to obtain a reliable signal. Accurate energy minima are also identified by confronting unbound TCR crystal structures to pMHC. Furthermore, we decompose the electrostatic energy into residue contributions to estimate their role in the overall orientation. Results show that most of the driving force leading to the formation of the complex is defined by CDR1,2/MHC interactions. This long-distance contribution appears to be independent from the binding process itself, since it is reliably identified without considering neither short-range energy terms nor CDR induced fit upon binding. Ultimately, we present an attempt to predict the TCR/pMHC binding mode for a TCR structure obtained by homology modeling. The simplicity of the approach and the absence of any fitted parameters make it also easily applicable to other types of macromolecular protein complexes.     

Convergent evolution in structural elements of proteins investigated using cross profile analysis

Background  

Evolutionary relations of similar segments shared by different protein folds remain controversial, even though many examples of such segments have been found. To date, several methods such as those based on the results of structure comparisons, sequence-based classifications, and sequence-based profile-profile comparisons have been applied to identify such protein segments that possess local similarities in both sequence and structure across protein folds. However, to capture more precise sequence-structure relations, no method reported to date combines structure-based profiles, and sequence-based profiles based on evolutionary information. The former are generally regarded as representing the amino acid preferences at each position of a specific conformation of protein segment. They might reflect the nature of ancient short peptide ancestors, using the results of structural classifications of protein segments.     

Quantitative understanding of the energy transfer between fluorescent proteins connected via flexible peptide linkers

The fusion of different protein domains via peptide linkers is a powerful, modular approach to obtain proteins with new functions. A detailed understanding of the conformational behavior of peptide linkers is important for applications such as fluorescence resonance energy transfer (FRET)-based sensor proteins and multidomain proteins involved in multivalent interactions. To investigate the conformational behavior of flexible glycine- and serine-containing peptide linkers, we constructed a series of fusion proteins of enhanced cyan and yellow fluorescent proteins (ECFP-linker-EYFP) in which the linker length was systematically varied by incorporating between 1 and 9 GGSGGS repeats. As expected, both steady-state and time-resolved fluorescence measurements showed a decrease in energy transfer with increasing linker length. The amount of energy transfer observed in these fusion proteins can be quantitatively understood by simple models that describe the flexible linker as a worm-like chain with a persistence length of 4.5 A or a Gaussian chain with a characteristic ratio of 2.3. The implications of our results for understanding the properties of FRET-based sensors and other fusion proteins with Gly/Ser linkers are discussed.     

Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.