Empirical free energy calculation: comparison to calorimetric data

Experimental Binding Energies in Supramolecular Complexes

On the basis of many literature measurements, a critical overview is given on essential noncovalent interactions in synthetic supramolecular complexes, accompanied by analyses with selected proteins. The methods, which can be applied to derive binding increments for single noncovalent interactions, start with the evaluation of consistency and additivity with a sufficiently large number of different host-guest complexes by applying linear free energy relations. Other strategies involve the use of double mutant cycles, of molecular balances, of dynamic combinatorial libraries, and of crystal structures. Promises and limitations of these strategies are discussed. Most of the analyses stem from solution studies, but a few also from gas phase. The empirically derived interactions are then presented on the basis of selected complexes with respect to ion pairing, hydrogen bonding, electrostatic contributions, halogen bonding, π-π-stacking, dispersive forces, cation-π and anion-π interactions, and contributions from the hydrophobic effect. Cooperativity in host-guest complexes as well as in self-assembly, and entropy factors are briefly highlighted. Tables with typical values for single noncovalent free energies and polarity parameters are in the Supporting Information.

The cis conformation of proline leads to weaker binding of a p53 peptide to MDM2 compared to trans

The cis and trans conformations of the Xaa-Pro (Xaa: any amino acid) peptide bond are thermodynamically stable while other peptide bonds strongly prefer trans. The effect of proline cis-trans isomerization on protein binding has not been thoroughly investigated. In this study, computer simulations were used to calculate the absolute binding affinity for a p53 peptide (residues 17-29) to MDM2 for both cis and trans isomers of the p53 proline in position 27. Results show that the cis isomer of p53(17-29) binds more weakly to MDM2 than the trans isomer, and that this is primarily due to the difference in the free energy cost associated with the loss of conformational entropy of p53(17-29) when it binds to MDM2. The population of cis p53(17-29) was estimated to be 0.8% of the total population in the bound state. The stronger binding of trans p53(17-29) to MDM2 compared to cis may leave a minimal level of p53 available to respond to cellular stress. This study demonstrates that it is feasible to estimate the absolute binding affinity for an intrinsically disordered protein fragment binding to an ordered protein that are in good agreement with experimental results.

Functional and dysfunctional conformers of human neuroserpin characterized by optical spectroscopies and Molecular Dynamics

Neuroserpin (NS) is a serine protease inhibitor (SERPIN) involved in different neurological pathologies, including the Familial Encephalopathy with Neuroserpin Inclusion Bodies (FENIB), related to the aberrant polymerization of NS mutants. Here we present an in vitro and in silico characterization of native neuroserpin and its dysfunctional conformation isoforms: the proteolytically cleaved conformer, the inactive latent conformer, and the polymeric species. Based on circular dichroism and fluorescence spectroscopy, we present an experimental validation of the latent model and highlight the main structural features of the different conformers. In particular, emission spectra of aromatic residues yield distinct conformational fingerprints, that provide a novel and simple spectroscopic tool for selecting serpin conformers in vitro. Based on the structural relationship between cleaved and latent serpins, we propose a structural model for latent NS, for which an experimental crystallographic structure is lacking. Molecular Dynamics simulations suggest that NS conformational stability and flexibility arise from a spatial distribution of intramolecular salt-bridges and hydrogen bonds.

Protein-protein binding affinity prediction on a diverse set of structures

MOTIVATION

Accurate binding free energy functions for protein-protein interactions are imperative for a wide range of purposes. Their construction is predicated upon ascertaining the factors that influence binding and their relative importance. A recent benchmark of binding affinities has allowed, for the first time, the evaluation and construction of binding free energy models using a diverse set of complexes, and a systematic assessment of our ability to model the energetics of conformational changes.

RESULTS

We construct a large set of molecular descriptors using commonly available tools, introducing the use of energetic factors associated with conformational changes and disorder to order transitions, as well as features calculated on structural ensembles. The descriptors are used to train and test a binding free energy model using a consensus of four machine learning algorithms, whose performance constitutes a significant improvement over the other state of the art empirical free energy functions tested. The internal workings of the learners show how the descriptors are used, illuminating the determinants of protein-protein binding.

AVAILABILITY

The molecular descriptor set and descriptor values for all complexes are available in the Supplementary Material. A web server for the learners and coordinates for the bound and unbound structures can be accessed from the website: http://bmm.cancerresearchuk.org/~Affinity.

CONTACT

paul.bates@cancer.org.uk.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Salt bridges: geometrically specific, designable interactions

Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms.

CUSA and CUDE: GPU-accelerated methods for estimating solvent accessible surface area and desolvation

It is well-established that a linear correlation exists between accessible surface areas and experimentally measured solvation energies. Combining this knowledge with an analytic formula for calculation of solvent accessible surfaces, we derive a simple model of desolvation energy as a differentiable function of atomic positions. Additionally, we find that this algorithm is particularly well suited for hardware acceleration on graphics processing units (GPUs), outperforming the CPU by up to two orders of magnitude. We explore the scaling of this desolvation algorithm and provide implementation details applicable to general pairwise algorithms.

Development and validation of an empirical free energy function for calculating protein-protein binding free energy surfaces

In a previous paper, we described a novel empirical free energy function that was used to accurately predict experimental binding free energies for a diverse test set of 31 protein-protein complexes to within approximately 1.0 kcal. Here, we extend that work and show that an updated version of the function can be used to (1) accurately predict native binding free energies and (2) rank crystallographic, native-like and non-native binding modes in a physically realistic manner. The modified function includes terms designed to capture some of the unfavorable interactions that characterize non-native interfaces. The function was used to calculate one-dimensional binding free energy surfaces for 21 protein complexes. In roughly 90% of the cases tested, the function was used to place native-like and crystallographic binding modes in global free energy minima. Our analysis further suggests that buried hydrogen bonds might provide the key to distinguishing native from non-native interactions. To the best of our knowledge our function is the only one of its kind, a single expression that can be used to accurately calculate native and non-native binding free energies for a large number of proteins. Given the encouraging results presented in this paper, future work will focus on improving the function and applying it to the protein-protein docking problem.

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.

Invariant amino acids essential for decoding function of polypeptide release factor eRF1

In eukaryotic ribosome, the N domain of polypeptide release factor eRF1 is involved in decoding stop signals in mRNAs. However, structure of the decoding site remains obscure. Here, we specifically altered the stop codon recognition pattern of human eRF1 by point mutagenesis of the invariant Glu55 and Tyr125 residues in the N domain. The 3D structure of generated eRF1 mutants was not destabilized as demonstrated by calorimetric measurements and calculated free energy perturbations. In mutants, the UAG response was most profoundly and selectively affected. Surprisingly, Glu55Arg mutant completely retained its release activity. Substitution of the aromatic ring in position 125 reduced response toward all stop codons. This result demonstrates the critical importance of Tyr125 for maintenance of the intact structure of the eRF1 decoding site. The results also suggest that Tyr125 is implicated in recognition of the 3d stop codon position and probably forms an H-bond with Glu55. The data point to a pivotal role played by the YxCxxxF motif (positions 125-131) in purine discrimination of the stop codons. We speculate that eRF1 decoding site is formed by a 3D network of amino acids side chains.

Probing Fragment Complementation by Rigid-Body Docking: in Silico Reconstitution of Calbindin D9k

Fragment complementation is gaining an increasing impact as a nonperturbing method to probe noncovalent interactions within protein supersecondary structures. In this study, the fast Fourier transform rigid-body docking algorithm ZDOCK has been employed for in silico reconstitution of the calcium binding protein calbindin D9k, from its two EF-hands subdomains, namely, EF1 (residues 1-43) and EF2 (residues 44-75). The EF1 fragment has been used both in its wild type and in nine mutant forms, in line with in vitro experiments. Consistent with in vitro data, ZDOCK reconstituted the proper fold of wild-type and mutated calbindin, locating the nativelike structures (i.e., holding a root-mean-square deviation < 1 A with respect to the X-ray structure) among the first 10 top-scored solutions out of 4000. Moreover, the three independent in silico reconstitutions of wild-type calbindin ranked a nativelike structure at the top of the output list, that is, the best scored one. The algorithm has been also successfully challenged in reconstituting the EF2 homodimer from two identical copies of the monomer. Furthermore, quantitative models consisting of linear correlations between thermodynamic data and ZDOCK scores were built, providing a tested tool for very fast in silico predictions of the free energy of association of protein-protein complexes solved at the atomic level and known to not undergo significant conformational changes upon binding.

Novel knowledge-based potentials for ligand docking: variational approach to the old problem

The variational approach of evaluation for knowledge-based potentials is considered for the first time. In this approach, the problem to derive knowledge-based potentials is solved as the optimization task in the multiparametric model of atom types, reference states and interaction cutoff radii. Using analogy to liquid state theory we offered four new reference states and derived corresponding knowledge-based potentials. The cutoff radii and atom types are optimized to minimize averaged root-mean square deviations (RMSD) of the ligand docked positions regarding to the experimentally determined poses. The number of atom types is varied on the developed atom type tree with 6 root (C, N, O, S, P and the halogen type) and 49 apical atom types. We showed a pronounced effect of atom type choice on docking accuracy and proved that splitting of elements C, N and O of the periodic system up to the 18 optimal atom types essentially improves docking accuracy.

A double-deletion method to quantifying incremental binding energies in proteins from experiment: example of a destabilizing hydrogen bonding pair

The contribution of a specific hydrogen bond in apoflavodoxin to protein stability is investigated by combining theory, experiment and simulation. Although hydrogen bonds are major determinants of protein structure and function, their contribution to protein stability is still unclear and widely debated. The best method so far devised to estimate the contribution of side-chain interactions to protein stability is double mutant cycle analysis, but the interaction energies so derived are not identical to incremental binding energies (the energies quantifying net contributions of two interacting groups to protein stability). Here we introduce double-deletion analysis of 'isolated' residue pairs as a means to precisely quantify incremental binding. The method is exemplified by studying a surface-exposed hydrogen bond in a model protein (Asp96/Asn128 in apoflavodoxin). Combined substitution of these residues by alanines slightly destabilizes the protein due to a decrease in hydrophobic surface burial. Subtraction of this effect, however, clearly indicates that the hydrogen-bonded groups in fact destabilize the native conformation. In addition, molecular dynamics simulations and classic double mutant cycle analysis explain quantitatively that, due to frustration, the hydrogen bond must form in the native structure because when the two groups get approximated upon folding their binding becomes favorable. We would like to remark that 1), this is the first time the contribution of a specific hydrogen bond to protein stability has been measured by experiment; and 2), more hydrogen bonds need to be analyzed to draw general conclusions on protein hydrogen bond energetics. To that end, the double-deletion method should be of help.

A fast empirical approach to binding free energy calculations based on protein interface information

Three useful variables from the interfaces of 20 protein-protein complexes were investigated. These variables are the side-chain accessible number (N(b)), the number of hydrophilic pairs (N(pair)) and buried a polar solvent accessible surface areas (DeltaDeltaASA(apol)). An empirical model based on the three variables was developed to describe the free energy of protein associations. As the results show, the side-chain accessible numbers characterize the loss of side-chain conformational entropy of protein interactions and the effective empirical function presented here has great capability for estimating the binding free energy. It was found that the variables of interface information capture most of the significant features of protein-protein association. Also, we applied the model based on the variables as a rescoring function to docking simulations and found that it has the potential to distinguish the 'true' binding mode. It is clear that the simple and empirical scale developed here is an attractive target function for calculating binding free energy for various biological processes to rational protein design.

Energetic and entropic contributions to the interactions between like-charged groups in cationic peptides: A molecular dynamics simulation study

The interaction between like-charged amino acid residues has been proposed to stabilize the folded state of peptides and proteins, and to modulate the substrate binding and the action mechanism of enzymes. We have used an alanine- and lysine-based peptide as a model system to study the interaction between like charges, and we have performed a 16-nsec molecular dynamics simulation in solution. The calculated potential of mean force for the approach of the lysine's Nzeta atoms showed a minimum at a distance of 0.7 nm, in agreement with the separation probabilities obtained from analysis of protein crystal structures. The analysis of the individual energy components showed that the solvent polarization pays for the approach of the like charges and that the van der Waals energies do not contribute significantly. The entropic contributions have been divided in conformational and desolvation terms. Both terms favor the formation of the charge pair. A 10-fold increase in counterion concentration was observed-with respect to its bulk concentration-next to the peptide charges, which helps to stabilize the peptide charges at a close distance.

Hierarchy of simulation models in predicting structure and energetics of the Src SH2 domain binding to tyrosyl phosphopeptides

Structure and energetics of the Src Src Homology 2 (SH2) domain binding with the recognition phosphopeptide pYEEI and its mutants are studied by a hierarchical computational approach. The proposed structure prediction strategy includes equilibrium sampling of the peptide conformational space by simulated tempering dynamics with the simplified, knowledge-based energy function, followed by structural clustering of the resulting conformations and binding free energy evaluation of a single representative from each cluster, a cluster center. This protocol is robust in rapid screening of low-energy conformations and recovers the crystal structure of the pYEEI peptide. Thermodynamics of the peptide-SH2 domain binding is analyzed by computing the average energy contributions over conformations from the clusters, structurally similar to the predicted peptide bound structure. Using this approach, the binding thermodynamics for a panel of studied peptides is predicted in a better agreement with the experiment than previously suggested models. However, the overall correlation between computed and experimental binding affinity remains rather modest. The results of this study show that small differences in binding free energies between the Ala and Gly mutants of the pYEEI peptide are considerably more difficult to predict than the structure of the bound peptides, indicating that accurate computational prediction of binding affinities still remains a major methodological and technical challenge.

Free energy decomposition of protein-protein interactions

A free energy decomposition scheme has been developed and tested on antibody-antigen and protease-inhibitor binding for which accurate experimental structures were available for both free and bound proteins. Using the x-ray coordinates of the free and bound proteins, the absolute binding free energy was computed assuming additivity of three well-defined, physical processes: desolvation of the x-ray structures, isomerization of the x-ray conformation to a nearby local minimum in the gas-phase, and subsequent noncovalent complex formation in the gas phase. This free energy scheme, together with the Generalized Born model for computing the electrostatic solvation free energy, yielded binding free energies in remarkable agreement with experimental data. Two assumptions commonly used in theoretical treatments; viz., the rigid-binding approximation (which assumes no conformational change upon complexation) and the neglect of vdW interactions, were found to yield large errors in the binding free energy. Protein-protein vdW and electrostatic interactions between complementary surfaces over a relatively large area (1400--1700 A(2)) were found to drive antibody-antigen and protease-inhibitor binding.

Towards understanding the mechanisms of molecular recognition by computer simulations of ligand-protein interactions

The thermodynamic and kinetic aspects of molecular recognition for the methotrexate (MTX)-dihydrofolate reductase (DHFR) ligand-protein system are investigated by the binding energy landscape approach. The impact of 'hot' and 'cold' errors in ligand mutations on the thermodynamic stability of the native MTX-DHFR complex is analyzed, and relationships between the molecular recognition mechanism and the degree of ligand optimization are discussed. The nature and relative stability of intermediates and thermodynamic phases on the ligand-protein association pathway are studied, providing new insights into connections between protein folding and molecular recognition mechanisms, and cooperativity of ligand-protein binding. The results of kinetic docking simulations are rationalized based on the thermodynamic properties determined from equilibrium simulations and the shape of the underlying binding energy landscape. We show how evolutionary ligand selection for a receptor active site can produce well-optimized ligand-protein systems such as MTX-DHFR complex with the thermodynamically stable native structure and a direct transition mechanism of binding from unbound conformations to the unique native structure.

Solvation energy and thermal stability of hydrophilization-modified alpha-chymotrypsin

As reported in the literature [Mozhaev et al. (1988), Eur. J. Biochem. 173, 147-154], when a series of modifiers, especially the cyclic anhydrides of pyromellitic and mellitic acids, are introduced into each lysine located in the alpha-chymotrypsin (CT) surface, a substantial hydrophilization of the enzyme surface can occur and remarkable stabilization effects of modified enzymes can be obtained. In this paper, four models are applied to calculate the solvation energy of native and the modified CT based on their tertiary structures, which can be built by the CVFF force field. Analyzing the relationship between the solvation energy and the thermal stability in detail, we find that the results of three solvation energy models (Ooi model, WE-1 model, and WE-2 model) can be used to illustrate the relative stability among these enzymes qualitatively. The present study should be of practical value as well as of some theoretical interest.

Prediction of the binding energy for small molecules, peptides and proteins

A fast and reliable evaluation of the binding energy from a single conformation of a molecular complex is an important practical task. Knowledge-based scoring schemes may not be sufficiently general and transferable, while molecular dynamics or Monte Carlo calculations with explicit solvent are too computationally expensive for many applications. Recently, several empirical schemes using finite difference Poisson-Boltzmann electrostatics to predict energies for particular types of complexes were proposed. Here, an improved empirical binding energy function has been derived and validated on three different types of complexes: protein-small ligand, protein-peptide and protein-protein. The function uses the boundary element algorithm to evaluate the electrostatic solvation energy. We show that a single set of parameters can predict the relative binding energies of the heterogeneous validation set of complexes with 2.5 kcal/mol accuracy. We also demonstrate that global optimization of the ligand and of the flexible side-chains of the receptor improves the accuracy of the evaluation.

Free energy landscapes of encounter complexes in protein-protein association

We report the computer generation of a high-density map of the thermodynamic properties of the diffusion-accessible encounter conformations of four receptor-ligand protein pairs, and use it to study the electrostatic and desolvation components of the free energy of association. Encounter complex conformations are generated by sampling the translational/rotational space of the ligand around the receptor, both at 5-A and zero surface-to-surface separations. We find that partial desolvation is always an important effect, and it becomes dominant for complexes in which one of the reactants is neutral or weakly charged. The interaction provides a slowly varying attractive force over a small but significant region of the molecular surface. In complexes with no strong charge complementarity this region surrounds the binding site, and the orientation of the ligand in the encounter conformation with the lowest desolvation free energy is similar to the one observed in the fully formed complex. Complexes with strong opposite charges exhibit two types of behavior. In the first group, represented by barnase/barstar, electrostatics exerts strong orientational steering toward the binding site, and desolvation provides some added adhesion within the local region of low electrostatic energy. In the second group, represented by the complex of kallikrein and pancreatic trypsin inhibitor, the overall stability results from the rather nonspecific electrostatic attraction, whereas the affinity toward the binding region is determined by desolvation interactions.

A streptavidin mutant with altered ligand-binding specificity

The biotin-binding site of streptavidin was modified to alter its ligand-binding specificity. In natural streptavidin, the side chains of N23 and S27 make two of the three hydrogen bonds with the ureido oxygen of biotin. These two residues were mutated to severely weaken biotin binding while attempting to maintain the affinity for two biotin analogs, 2-iminobiotin and diaminobiotin. Redesigning of the biotin-binding site used the difference in local electrostatic charge distribution between biotin and these biotin analogs. Free energy calculations predicted that the introduction of a negative charge at the position of S27 plus the mutation N23A should disrupt two of the three hydrogen bonds between natural streptavidin and the ureido oxygen of biotin. In contrast, the imino hydrogen of 2-iminobiotin should form a hydrogen bond with the side chain of an acidic amino acid at position 27. This should reduce the biotin-binding affinity by approximately eight orders of magnitude, while leaving the affinities for these biotin analogs virtually unaffected. In good agreement with these predictions, a streptavidin mutant with the N23A and S27D substitutions binds 2-iminobiotin with an affinity (Ka) of 1 x 10(6) M-1, two orders of magnitude higher than that for biotin (1 x 10(4) M-1). In contrast, the binding affinity of this streptavidin mutant for diaminobiotin (2.7 x 10(4) M-1) was lower than predicted (2.9 x 10(5) M-1), suggesting the position of the diaminobiotin in the biotin-binding site was not accurately determined by modeling.

Protein folding via binding and vice versa

The terms intermolecular and intramolecular recognition are often used when referring to binding and folding, highlighting the common ground between the two processes. Most studies, however, are aimed at either one process or the other. Here, we show how knowledge from binding can aid in understanding folding and vice versa.

Selecting near-native conformations in homology modeling: the role of molecular mechanics and solvation terms

A free energy function, combining molecular mechanics energy with empirical solvation and entropic terms, is used for ranking near-native conformations that occur in the conformational search steps of homology modeling, i.e., side-chain search and loop closure calculations. Correlations between the free energy and RMS deviation from the X-ray structure are established. It is shown that generally both molecular mechanics and solvation/entropic terms should be included in the potential. The identification of near-native backbone conformations is accomplished primarily by the molecular mechanics term that becomes the dominant contribution to the free energy if the backbone is even slightly strained, as frequently occurs in loop closure calculations. Both terms become equally important if a sufficiently accurate backbone conformation is found. Finally, the selection of the best side-chain positions for a fixed backbone is almost completely governed by the solvation term. The discriminatory power of the combined potential is demonstrated by evaluating the free energies of protein models submitted to the first meeting on Critical Assessment of techniques for protein Structure Prediction (CASP1), and comparing them to the free energies of the native conformations.