High-resolution structural and thermodynamic analysis of extreme stabilization of human procarboxypeptidase by computational protein design

Recent efforts to design de novo or redesign the sequence and structure of proteins using computational techniques have met with significant success. Most, if not all, of these computational methodologies attempt to model atomic-level interactions, and hence high-resolution structural characterization of the designed proteins is critical for evaluating the atomic-level accuracy of the underlying design force-fields. We previously used our computational protein design protocol RosettaDesign to completely redesign the sequence of the activation domain of human procarboxypeptidase A2. With 68% of the wild-type sequence changed, the designed protein, AYEdesign, is over 10 kcal/mol more stable than the wild-type protein. Here, we describe the high-resolution crystal structure and solution NMR structure of AYEdesign, which show that the experimentally determined backbone and side-chains conformations are effectively superimposable with the computational model at atomic resolution. To isolate the origins of the remarkable stabilization, we have designed and characterized a new series of procarboxypeptidase mutants that gain significant thermodynamic stability with a minimal number of mutations; one mutant gains more than 5 kcal/mol of stability over the wild-type protein with only four amino acid changes. We explore the relationship between force-field smoothing and conformational sampling by comparing the experimentally determined free energies of the overall design and these focused subsets of mutations to those predicted using modified force-fields, and both fixed and flexible backbone sampling protocols.     

Electrostatic control of charge separation in bacterial photosynthesis

Electrostatic interaction energies of the electron carriers with their surroundings in a photosynthetic bacterial reaction center are calculated. The calculations are based on the detailed crystal structure of reaction centers from Rhodopseu-domonas viridis, and use an iterative, self-consistent procedure to evaluate the effects of induced dipoles in the protein and the surrounding membrane. To obtain the free energies of radical-pair states, the calculated electrostatic interaction energies are combined with the experimentally measured midpoint redox potentials of the electron carriers and of bacteriochlorophyll (BChl) and bacteriopheophytin (BPh) in vitro. The P+HL- radical-pair, in which an electron has moved from the primary electron donor (P) to a BPh on the 'L' side of the reaction center (HL), is found to lie approx. 2.0 kcal/mol below the lowest excited singlet state (P*), when the radical-pair is formed in the static crystallographic structure. The reorganization energy for the subsequent relaxation of P+HL- is calculated to be 5.0 kcal/mol, so that the relaxed radical-pair lies about 7 kcal/mol below P*. The unrelaxed P+BL- radical-pair, in which the electron acceptor is the accessory BChl located between P and HL, appears to be essentially isoenergetic with P*.P+BM-, in which an electron moves to the BChl on the 'M' side, is calculated to lie about 5.5 kcal/mol above P*. These results have an estimated error range of +/- 2.5 kcal/mol. They are shown to be relatively insensitive to various details of the model, including the charge distribution in P+, the atomic charges used for the amino acid residues, the boundaries of the structural region that is considered microscopically and the treatments of the histidyl ligands of P and of potentially ionizable amino acids. The calculated free energies are consistent with rapid electron transfer from P* to HL by way of BL, and with a much slower electron transfer to the pigments on the M side. Tyrosine M208 appears to play a particularly important role in lowering the energy of P+BL-. Electrostatic interactions with the protein favor localization of the positive charge of P+ on PM, one of the two BChl molecules that make up the electron donor.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.     

Crystal structure and ligand-binding studies of a screened peptide complexed with streptavidin.

The thermodynamic binding parameters and crystal structure for streptavidin-peptide complexes where the peptide sequences were obtained by random screening methods are reported. The affinities between streptavidin and two heptapeptides were determined by titrating calorimetric methods [Phe-Ser-His-Pro-Gln-Asn-Thr, Ka = 7944 (+/- 224) M-1, delta G degrees = -5.32 (+/- 0.01) kcal/mol, and delta H degrees = -19.34 (+/- 0.48) kcal/mol; His-Asp-His-Pro-Gln-Asn-Leu, Ka = 3542 (+/- 146) M-1, delta G degrees = -4.84 (+/- 0.03) kcal/mol, and delta H degrees = -19.00 (+/- 0.64) kcal/mol]. The crystal structure of streptavidin complexed with one of these peptides has been determined at 2.0-A resolution. The peptide (Phe-Ser-His-Pro-Gln-Asn-Thr) binds in a turn conformation with the histidine, proline, and glutamine side chains oriented inward at the biotin-binding site. A water molecule is immobilized between the histidine and glutamine side chains of the peptide and an aspartic acid side chain of the protein. Although some of the residues that participate in binding biotin also interact with the screened peptide, the peptide adopts an alternate method of utilizing binding determinants in the biotin-binding site of streptavidin.     

pKa predictions with a coupled finite difference Poisson-Boltzmann and Debye-Hückel method

Modeling charge interactions is important for understanding many aspects of biological structure and function, and continuum methods such as Finite Difference Poisson-Boltzmann (FDPB) are commonly employed. Calculations of pH-dependence have identified separate populations; surface groups that can be modeled with a simple Debye-Hückel (DH) model, and buried groups, with stronger resultant interactions that are dependent on detailed conformation. This observation led to the development of a combined FDPB and DH method for pK(a) prediction (termed FD/DH). This study reports application of this method to ionizable groups, including engineered buried charges, in staphylococcal nuclease. The data had been made available to interested research groups before publication of mutant structures and/or pK(a) values. Overall, FD/DH calculations perform as intended with low ΔpK(a) values for surface groups (RMSD between predicted and experimental pK(a) values of 0.74), and much larger ΔpK(a) values for the engineered internal groups, with RMSD = 1.64, where mutant structures were known and RMSD = 1.80, where they were modeled. The weaker resultant interactions of the surface groups are determined mostly by charge-charge interactions. For the buried groups, R(2) for correlation between predicted and measured ΔpK(a) values is 0.74, despite the high RMSDs. Charge-charge interactions are much less important, with the R(2) value for buried group ΔpK(a) values increasing to 0.80 when the term describing charge desolvation alone is used. Engineered charge burial delivers a relatively uniform, nonspecific effect, in terms of pK(a) . How the protein environment adapts in atomic detail to deliver this resultant effect is still an open question.     

Protein surface roughness accounts for binding free energy of Plasmepsin II‐ligand complexes

The calculation of absolute binding affinities for protein‐inhibitor complexes remains as one of the main challenges in computational structure‐based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high‐resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x‐ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20 ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave‐one‐out cross‐validation showed that our model reproduced accurately the absolute binding free energies for our training set (R² = 0.76; <|error|> =0.55 kcal/mol; SD_error = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article.     

Crystal structures and increased stabilization of the protein G variants with switched folding pathways NuG1 and NuG2

We recently described two protein G variants (NuG1 and NuG2) with redesigned first hairpins that were almost twice as stable, folded 100-fold faster, and had a switched folding mechanism relative to the wild-type protein. To test the structural accuracy of our design algorithm and to provide insights to the dramatic changes in the kinetics and thermodynamics of folding, we have now determined the crystal structures of NuG1 and NuG2 to 1.8 A and 1.85 A, respectively. We find that they adopt hairpin structures that are closer to the computational models than to wild-type protein G; the RMSD of the NuG1 hairpin to the design model and the wild-type structure are 1.7 A and 5.1 A, respectively. The crystallographic B factor in the redesigned first hairpin of NuG1 is systematically higher than the second hairpin, suggesting that the redesigned region is somewhat less rigid. A second round of structure-based design yielded new variants of NuG1 and NuG2, which are further stabilized by 0.5 kcal/mole and 0.9 kcal/mole.     

Theoretical calculation of the binding free energies for pyruvate dehydrogenase E1 binding with ligands

We have tested a computational protocol based on molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free-energy calculations to examine the detailed microscopic structures and binding free energies for the pyruvate dehydrogenase multienzyme complex (PDHc) E1 binding with its ligands (cofactor and inhibitors). The calculated binding free energies are all in good agreement with available experimental data, with an average absolute deviation of approximately 0.7 kcal/mol, suggesting that the computational protocol tested may be valuable in future rational design of new, more potent inhibitors of PDHc E1.     

Empirical calculation of the relative free energies of peptide binding to the molecular chaperone DnaK

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.     

Reaction pathway and free energy profiles for butyrylcholinesterase-catalyzed hydrolysis of acetylthiocholine

The catalytic mechanism for butyrylcholineserase (BChE)-catalyzed hydrolysis of acetylthiocholine (ATCh) has been studied by performing pseudobond first-principles quantum mechanical/molecular mechanical-free energy (QM/MM-FE) calculations on both acylation and deacylation of BChE. Additional quantum mechanical (QM) calculations have been carried out, along with the QM/MM-FE calculations, to understand the known substrate activation effect on the enzymatic hydrolysis of ATCh. It has been shown that the acylation of BChE with ATCh consists of two reaction steps including the nucleophilic attack on the carbonyl carbon of ATCh and the dissociation of thiocholine ester. The deacylation stage includes nucleophilic attack of a water molecule on the carboxyl carbon of substrate and dissociation between the carboxyl carbon of substrate and hydroxyl oxygen of Ser198 side chain. QM/MM-FE calculation results reveal that the acylation of BChE is rate-determining. It has also been demonstrated that an additional substrate molecule binding to the peripheral anionic site (PAS) of BChE is responsible for the substrate activation effect. In the presence of this additional substrate molecule at PAS, the calculated free energy barrier for the acylation stage (rate-determining step) is decreased by ~1.7 kcal/mol. All of our computational predictions are consistent with available experimental kinetic data. The overall free energy barriers calculated for BChE-catalyzed hydrolysis of ATCh at regular hydrolysis phase and substrate activation phase are ~13.6 and ~11.9 kcal/mol, respectively, which are in reasonable agreement with the corresponding experimentally derived activation free energies of 14.0 kcal/mol (for regular hydrolysis phase) and 13.5 kcal/mol (for substrate activation phase).     

Noncontact dipole effects on channel permeation. II. Trp conformations and dipole potentials in gramicidin A

The four Trp dipoles in the gramicidin A (gA) channel modulate channel conductance, and their side chain conformations should therefore be important, but the energies of different conformations are unknown. A conformational search for the right-handed helix based on molecular mechanics in vacuo yielded 46 conformations within 20 kcal/mol of the lowest energy conformation. The two lowest energy conformations correspond to the solid-state and solution-state NMR conformations, suggesting that interactions within the peptide determine the conformation. For representative conformations, the electrostatic potential of the Trp side chains on the channel axis was computed. A novel application of the image-series method of. Biophys. J. 9:1160-1170) was introduced to simulate the polarization of bulk water by the Trp side chains. For the experimentally observed structures, the CHARm toph19 potential energy (PE) of a cation in the channel center is -1.65 kcal/mol without images. With images, the PE is -1.9 kcal/mol, demonstrating that the images further enhance the direct dipole effect. Nonstandard conformations yielded less favorable PEs by 0.4-1.1 kcal/mol.     

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. Copyright © 1999 John Wiley & Sons, Ltd.     

Drug targeted virtual screening and molecular dynamics of LipU protein of Mycobacterium tuberculosis and Mycobacterium leprae

The lipolytic protein LipU was conserved in mycobacterium sp. including M. tuberculosis (MTB LipU) and M. leprae (MLP LipU). The MTB LipU was identified in extracellular fraction and was reported to be essential for the survival of mycobacterium. Therefore to address the problem of drug resistance in pathogen, LipU was selected as a drug target and the viability of finding out some FDA approved drugs as LipU inhibitors in both the cases was explored. Three-dimensional (3D) model structures of MTB LipU and MLP LipU were generated and stabilized through molecular dynamics (MD). FDA approved drugs were screened against these proteins. The result showed that the top-scoring compounds for MTB LipU were Diosmin, Acarbose and Ouabain with the Glide XP score of ?12.8, ?11.9 and ?11.7 kcal/mol, respectively, whereas for MLP LipU protein, Digoxin (?9.2 kcal/mol), Indinavir (?8.2 kcal/mol) and Travoprost (?8.2 kcal/mol) showed highest affinity. These drugs remained bound in the active site pocket of MTB LipU and MLP LipU structure and interaction grew stronger after dynamics. RMSD, RMSF and Rg were found to be persistent throughout the simulation period. Hydrogen bonds along with large number of hydrophobic interactions stabilized the complex structures. Binding free energies obtained through Prime/MM-GBSA were found in the significant range from ?63.85 kcal/mol to ?34.57 kcal/mol for MTB LipU and ?71.33 kcal/mol to ?23.91 kcal/mol for MLP LipU. The report suggested high probability of these drugs to demolish the LipU activity and could be probable drug candidates to combat TB and leprosy disease.     

Position-dependence of stabilizing polar interactions of asparagine in transmembrane helical bundles

Recent studies with model peptides and statistical analyses of the crystal structures of membrane proteins have shown that buried polar interactions contribute significantly to the stabilization of the three-dimensional structures of membrane proteins. Here, we probe how the location of these polar groups along the transmembrane helices affect their free energies of interaction. Asn residues were placed singly and in pairs at three positions within a model transmembrane helix, which had previously been shown to support the formation of trimers in micelles. The model helix was designed to form a transmembrane coiled coil, with Val side chains at the "a" positions of the heptad repeat. Variants of this peptide were prepared in which an Asn residue was introduced at one or more of the "a" positions, and their free energies of association were determined by analytical ultracentrifugation. When placed near the middle of the transmembrane helix, the formation of trimers was stabilized by at least -2.0 kcal/mol per Asn side chain. When the Asn was placed at the interface between the hydrophobic and polar regions of the peptide, the substitution was neither stabilizing nor destabilizing (0.0 +/- 0.5 kcal/mol of monomer). Finally, it has previously been shown that a Val-for-Asn mutation in a water-soluble coiled coil destabilizes the structure by approximately 1.5 kcal/mol of monomer [Acharya, A., et al. (2002) Biochemistry 41, 14122-14131]. Thus, the headgroup region of a micelle appears to have a conformational impact intermediate between that of bulk water and the apolar region of micelle. A similarly large dependence on the location of the polar residues was found in a statistical survey of helical transmembrane proteins. The tendency of different types of residues to be buried in the interiors versus being exposed to lipids was analyzed. Asn and Gln show a very strong tendency to be buried when they are located near the middle of a transmembrane helix. However, when placed near the ends of transmembrane helices, they show little preference for the surface versus the interior of the protein. These data show that Asn side chains within the apolar region of the transmembrane helix provide a significantly larger driving force for association than Asn residues near the apolar/polar interface. Thus, although polar interactions are able to strongly stabilize the folding of membrane proteins, the energetics of association depend on their location within the hydrophobic region of a transmembrane helix.     

Calculations of electrostatic energies in proteins. The energetics of ionized groups in bovine pancreatic trypsin inhibitor

The importance of including different energy contributions in calculations of electrostatic energies in proteins is examined by calculating the intrinsic pKa values of the acidic groups of bovine pancreatic trypsin inhibitor. It appears that such calculations provide a powerful and revealing test; the relevant solvation energies of the ionized acids are of the order of -70 kcal/mol (1 cal = 4.184 J), and microscopic calculations that do not attempt to simulate the complete protein dielectric effect (including the surrounding solvent) can underestimate the solvation energy by as much as 50 kcal/mol. Reproducing correctly, by the same set of parameters, the solvation energies of ionized acids in different sites of a protein cannot be accomplished by including only part of the key energy contributions. The problems associated with macroscopic calculations are also considered and illustrated by the specific case of bovine pancreatic trypsin inhibitor. A promising approach is shown to be provided by a refinement of the previously developed Protein Dipoles Langevin Dipoles model. This model seems to represent consistently the microscopic dielectric of the protein and the surrounding water molecules. The model overcomes the problems associated with the macroscopic models (by treating explicitly the solvent molecules) and avoids the convergence problems associated with all-atom solvent models (by treating the average solvent polarization rather than averaging the actual polarization energy). This paper describes in detail the actual implementation of the model and examines its performance in evaluating intrinsic pKa values. Preliminary microscopic considerations of charge-charge interactions are presented.     

Ultra-fast evaluation of protein energies directly from sequence

The structure, function, stability, and many other properties of a protein in a fixed environment are fully specified by its sequence, but in a manner that is difficult to discern. We present a general approach for rapidly mapping sequences directly to their energies on a pre-specified rigid backbone, an important sub-problem in computational protein design and in some methods for protein structure prediction. The cluster expansion (CE) method that we employ can, in principle, be extended to model any computable or measurable protein property directly as a function of sequence. Here we show how CE can be applied to the problem of computational protein design, and use it to derive excellent approximations of physical potentials. The approach provides several attractive advantages. First, following a one-time derivation of a CE expansion, the amount of time necessary to evaluate the energy of a sequence adopting a specified backbone conformation is reduced by a factor of 10(7) compared to standard full-atom methods for the same task. Second, the agreement between two full-atom methods that we tested and their CE sequence-based expressions is very high (root mean square deviation 1.1-4.7 kcal/mol, R2 = 0.7-1.0). Third, the functional form of the CE energy expression is such that individual terms of the expansion have clear physical interpretations. We derived expressions for the energies of three classic protein design targets-a coiled coil, a zinc finger, and a WW domain-as functions of sequence, and examined the most significant terms. Single-residue and residue-pair interactions are sufficient to accurately capture the energetics of the dimeric coiled coil, whereas higher-order contributions are important for the two more globular folds. For the task of designing novel zinc-finger sequences, a CE-derived energy function provides significantly better solutions than a standard design protocol, in comparable computation time. Given these advantages, CE is likely to find many uses in computational structural modeling.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

Predicting Ligand Binding Affinity with Alchemical Free Energy Methods in a Polar Model Binding Site

We present a combined experimental and modeling study of organic ligand molecules binding to a slightly polar engineered cavity site in T4 lysozyme (L99A/M102Q). For modeling, we computed alchemical absolute binding free energies. These were blind tests performed prospectively on 13 diverse, previously untested candidate ligand molecules. We predicted that eight compounds would bind to the cavity and five would not; 11 of 13 predictions were correct at this level. The RMS error to the measurable absolute binding energies was 1.8 kcal/mol. In addition, we computed “relative” binding free energies for six phenol derivatives starting from two known ligands: phenol and catechol. The average RMS error in the relative free energy prediction was 2.5 kcal/mol (phenol) and 1.1 kcal/mol (catechol). To understand these results at atomic resolution, we obtained x-ray co-complex structures for nine of the diverse ligands and for all six phenol analogs. The average RMSD of the predicted pose to the experiment was 2.0 Å (diverse set), 1.8 Å (phenol-derived predictions), and 1.2 Å (catechol-derived predictions). We found that predicting accurate affinities and rank-orderings required near-native starting orientations of the ligand in the binding site. Unanticipated binding modes, multiple ligand binding, and protein conformational change all proved challenging for the free energy methods. We believe that these results can help guide future improvements in physics-based absolute binding free energy 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.