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.     

A heterodimerizing leucine zipper coiled coil system for examining the specificity of a position interactions: amino acids I,V, L,N, A,and K

We use a heterodimerizing leucine zipper system to examine the contribution of the interhelical a-a' interaction to dimer stability for six amino acids (A, V, L, I, K, and N). Circular dichroism (CD) spectroscopy monitored the thermal denaturation of 36 heterodimers that generate six homotypic and 30 heterotypic a-a' interactions. Isoleucine (I-I) is the most stable homotypic a-a' interaction, being 9.2 kcal/mol per dimer more stable than the A-A interaction and 4.0 kcal/mol per dimer more stable than either the L-L or V-V interaction, and 7.0 kcal/mol per dimer more stable than the N-N interaction. Only lysine was less stable than alanine. An alanine-based double-mutant thermodynamic cycle calculated coupling energies between the a and a' positions in the heterodimer. The aliphatic amino acids L, V, and I prefer to form homotypic interactions with coupling energies of -0.6 to -0.9 kcal/mol per dimer, but the heterotypic aliphatic interactions have positive coupling energies of <1.0 kcal/mol per dimer. The asparagine homotypic interaction has a coupling energy of -0.5 kcal/mol per dimer, while heterotypic interactions with the aliphatic amino acids produce coupling energies ranging from 2.6 to 4.9 kcal/mol per dimer. The homotypic K-K interaction is 2.9 kcal/mol per dimer less stable than the A-A interaction, but the coupling energy is only 0.3 kcal/mol per dimer. Heterotypic interactions with lysine and either asparagine or aliphatic amino acids produce similar coupling energies ranging from -0.2 to -0.7 kcal/mol per dimer. Thus, of the amino acids that were examined, asparagine contributes the most to dimerization specificity because of the large positive coupling energies in heterotypic interactions with the aliphatic amino acids which results in the N-N homotypic interaction.     

Strong interaction between disulfide derivatives and aromatic groups in peptides and proteins

The intermolecular interaction energy of complexes of dimethyldisulfide with benzene and cyclohexane, respectively, was computed as function of the relative distance and orientation within each pair of molecules. The energy of the most stable orientation of the dimethyldisulfide-cyclohexane complex is ?2.57 kcal/mol, while that of the most stable orientation of the dimethyldisulfide-benzene complex is ?3.33 kcal/mol. The energy difference of ～0.8 kcal/mol is due to favorable specific nonbonded interactions between the sulfur atoms and the atoms of the aromatic ring. Proper parameterization of empirical interatomic energies, used in computations in this laboratory, accounts for these interactions without the need for a $\text{special}$ sulfur-aromatic potential energy function.     

Quantification of helix-helix binding affinities in micelles and lipid bilayers

A theoretical approach for estimating association free energies of alpha-helices in nonpolar media has been developed. The parameters of energy functions have been derived from DeltaDeltaG values of mutants in water-soluble proteins and partitioning of organic solutes between water and nonpolar solvents. The proposed approach was verified successfully against three sets of published data: (1) dissociation constants of alpha-helical oligomers formed by 27 hydrophobic peptides; (2) stabilities of 22 bacteriorhodopsin mutants, and (3) protein-ligand binding affinities in aqueous solution. It has been found that coalescence of helices is driven exclusively by van der Waals interactions and H-bonds, whereas the principal destabilizing contributions are represented by side-chain conformational entropy and transfer energy of atoms from a detergent or lipid to the protein interior. Electrostatic interactions of alpha-helices were relatively weak but important for reproducing the experimental data. Immobilization free energy, which originates from restricting rotational and translational rigid-body movements of molecules during their association, was found to be less than 1 kcal/mole. The energetics of amino acid substitutions in bacteriorhodopsin was complicated by specific binding of lipid and water molecules to cavities created in certain mutants.     

A consistent set of statistical potentials for quantifying local side-chain and backbone interactions

The frequencies of occurrence of atom arrangements in high-resolution protein structures provide some of the most accurate quantitative measures of interaction energies in proteins. In this report we extend our development of a consistent set of statistical potentials for quantifying local interactions between side-chains and the polypeptide backbone, as well as nearby side-chains. Starting with phi/psi/chi1 propensities that select for optimal interactions of the 20 amino acid side-chains with the 2 flanking peptide bonds, the following 3 new terms are added: (1) a distance-dependent interaction between the side-chain at i and the carbonyl oxygens and amide protons of the peptide units at i +/- 2, i +/- 3, and i +/- 4; (2) a distance-dependent interaction between the side-chain at position i and side-chains at positions i + 1 through i + 4; and (3) an orientation-dependent interaction between the side-chain at position i and side-chains at i + 1 through i + 4. The relative strengths of these 4 pseudo free energy terms are estimated by the average information content of each scoring matrix and by assessing their performance in a simple fragment threading test. They vary from -0.4 - -0.5 kcal/mole per residue for phi/psi/chi1 propensities to a range of -0.15 - -0.6 kcal/mole per residue for each of the other 3 terms. The combined energy function, containing no interactions between atoms more than 4 residues apart, identifies the correct structural fragment for randomly selected 15 mers over 40% of the time, after searching through 232,000 alternative conformations. For 14 out of 20 sets of all-atom Rosetta decoys analyzed, the native structure has a combined score lower than any of the 1700-1900 decoy conformations. The ability of this energy function to detect energetically important details of local structure is demonstrated by its power to distinguish high-resolution crystal structures from NMR solution structures.     

An extended aqueous solvation model based on atom-weighted solvent accessible surface areas: SAWSA v2.0 model

A new method is proposed for calculating aqueous solvation free energy based on atom-weighted solvent accessible surface areas. The method, SAWSA v2.0, gives the aqueous solvation free energy by summing the contributions of component atoms and a correction factor. We applied two different sets of atom typing rules and fitting processes for small organic molecules and proteins, respectively. For small organic molecules, the model classified the atoms in organic molecules into 65 basic types and additionally. For small organic molecules we proposed a correction factor of hydrophobic carbon to account for the aggregation of hydrocarbons and compounds with long hydrophobic aliphatic chains. The contributions for each atom type and correction factor were derived by multivariate regression analysis of 379 neutral molecules and 39 ions with known experimental aqueous solvation free energies. Based on the new atom typing rules, the correlation coefficient (r) for fitting the whole neutral organic molecules is 0.984, and the absolute mean error is 0.40 kcal mol^–1, which is much better than those of the model proposed by Wang et al. and the SAWSA model previously proposed by us. Furthermore, the SAWSA v2.0 model was compared with the simple atom-additive model based on the number of atom types (NA). The calculated results show that for small organic molecules, the predictions from the SAWSA v2.0 model are slightly better than those from the atom-additive model based on NA. However, for macromolecules such as proteins, due to the connection between their molecular conformation and their molecular surface area, the atom-additive model based on the number of atom types has little predictive power. In order to investigate the predictive power of our model, a systematic comparison was performed on seven solvation models including SAWSA v2.0, GB/SA_1, GB/SA_2, PB/SA_1, PB/SA_2, AM1/SM5.2R and SM5.0R. The results showed that for organic molecules the SAWSA v2.0 model is better than the other six solvation models. For proteins, the model classified the atoms into 20 basic types and the predicted aqueous free energies of solvation by PB/SA were used for fitting. The solvation model based on the new parameters was employed to predict the solvation free energies of 38 proteins. The predicted values from our model were in good agreement with those from the PB/SA model and were much better than those given by the other four models developed for proteins.Figure The definition of hydrophobic carbons. Here CA, CB and CD are three carbon atoms; X represents a heteroatom. According to our definition, CB is a hydrophobic carbon, CA is not a hydrophobic carbon because a heteroatom is within four atoms and CD is not a hydrophobic carbon because CD is sp²- hydridized and in a six-member ring.Electronic Supplementary Material Supplementary material is available for this article at     

Aromatic-aromatic interactions and protein stability. Investigation by double-mutant cycles

The side-chains of phenylalanine and tyrosine residues in proteins are frequently found to be involved in pairwise interactions. These occur both within repeating elements of secondary structure and in tertiary and quaternary interactions. It has been suggested that they are important in protein folding and stability, and non-bonded potential energy calculations indicate that a typical aromatic-aromatic interaction has an energy of between -1 and -2 kcal/mol and contributes between -0.6 and -1.3 kcal/mol to protein stability. There is such an aromatic pair on the solvent-exposed face of the first alpha-helix of barnase, the small ribonuclease from Bacillus amyloliquefaciens. The edge of the aromatic ring of Tyr17 interacts with the face of that of Tyr13. The two residues have been mutated both singly and pairwise to alanine, and their free energies of unfolding determined by denaturation with urea. Application of the double-mutant cycle analysis gives an interaction energy of -1.3 kcal/mol for the aromatic pair in the folded protein relative to solvation by water in the unfolded protein. This value is similar to that calculated from the change in surface-accessible area between the rings on the formation of the pair. Analysis of a further double-mutant cycle in which the Tyr residues are mutated to Phe indicates that the aromatic-aromatic interactions of Tyr/Tyr and Phe/Phe make identical contributions to protein stability. However, Tyr is preferred to Phe by 0.3(+/- 0.04) kcal/mol at the solvent-exposed face of the alpha-helix.     

Mapping the energetics of water-protein and water-ligand interactions with the "natural" HINT forcefield: predictive tools for characterizing the roles of water in biomolecules

The energetics and hydrogen bonding pattern of water molecules bound to proteins were mapped by analyzing structural data (resolution better than 2.3A) for sets of uncomplexed and ligand-complexed proteins. Water-protein and water-ligand interactions were evaluated using hydropatic interactions (HINT), a non-Newtonian forcefield based on experimentally determined logP(octanol/water) values. Potential water hydrogen bonding ability was assessed by a new Rank algorithm. The HINT-derived binding energies and Ranks for second shell water molecules were -0.04 kcal mol(-1) and 0.0, respectively, for first shell water molecules -0.38 kcal mol(-1) and 1.6, for active site water molecules -0.45 kcal mol(-1) and 2.3, for cavity water molecules -0.55 kcal mol(-1) and 3.3, and for buried water molecules -0.56 kcal mol(-1) and 4.4. For the last four classes, similar energies indicate that internal and external water molecules interact with protein almost equally, despite different degrees of hydrogen bonding. The binding energies and Ranks for water molecules bridging ligand-protein were -1.13 kcal mol(-1) and 4.5, respectively. This energetic contribution is shared equally between protein and ligand, whereas Rank favors the protein. Lastly, by comparing the uncomplexed and complexed forms of proteins, guidelines were developed for prediction of the roles played by active site water molecules in ligand binding. A water molecule with high Rank and HINT score is unlikely to make further interactions with the ligand and is largely irrelevant to the binding process, while a water molecule with moderate Rank and high HINT score is available for ligand interaction. Water molecule displaced for steric reasons were characterized by lower Rank and HINT score. These guidelines, tested by calculating HINT score and Rank for 50 water molecules bound in the active site of four uncomplexed proteins (for which the structures of the liganded forms were also available), correctly predicted the ultimate roles (in the complex) for 76% of water molecules. Some failures were likely due to ambiguities in the structural data.     

Trypsin specificity as elucidated by LIE calculations, X-ray structures, and association constant measurements

The variation in inhibitor specificity for five different amine inhibitors bound to CST, BT, and the cold-adapted AST has been studied by use of association constant measurements, structural analysis of high-resolution crystal structures, and the LIE method. Experimental data show that AST binds the 1BZA and 2BEA inhibitors 0.8 and 0.5 kcal/mole more strongly than BT. However, structural interactions and orientations of the inhibitors within the S1 site have been found to be virtually identical in the three enzymes studied. For example, the four water molecules in the inhibitor-free structures of AST and BT are channeled into similar positions in the S1 site, and the nitrogen atom(s) of the inhibitors are found in two cationic binding sites denoted Position1 and Position2. The hydrophobic binding contributions for all five inhibitors, estimated by the LIE calculations, are also in the same order (-2.1 +/- 0.2 kcal/mole) for all three enzymes. Our hypothesis is therefore that the observed variation in inhibitor binding arises from different electrostatic interactions originating from residues outside the S1 site. This is well illustrated by AST, in which Asp 150 and Glu 221B, despite some distance from the S1 binding site, lower the electrostatic potential of the S1 site and thus enhance substrate binding. Because the trends in the experimentally determined binding energies were reproduced by the LIE calculations after adding the contribution from long-range interactions, we find this method very suitable for rational studies of protein-substrate interactions.     

Reduced C(beta) statistical potentials can outperform all-atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.     

Ab initio parameterization of YFF1, a universal force field for drug-design applications

The YFF1 is a new universal molecular mechanic force field designed for drug discovery purposes. The electrostatic part of YFF1 has already been parameterized to reproduce ab initio calculated dipole and quadrupole moments. Now we report a parameterization of the van der Waals interactions (vdW) for the same atom types that were previously defined. The 6–12 Lennard-Jones potential terms were parameterized against homodimerization energies calculated at the MP2/6-31 G* level of theory. The Boys-Bernardi counterpoise correction was employed to account for the basis-set superposition error. As a source of structural information we used about 2,400 neutral compounds from the ZINC2007 database. About 6,600 homodimeric configurations were generated from this dataset. A special “closure” procedure was designed to accelerate the parameters fitting. As a result, dimerization energies of small organic compounds are reproduced with an average unsigned error of 1.1 kcal mol^-1. Although the primary goal of this work was to parameterize nonbonded interactions, bonded parameters were also derived, by fitting to PM6 semiempirically optimized geometries of approximately 20,000 compounds.     

Hydrogen-bonding interactions in adrenaline–water complexes: DFT and QTAIM studies of structures, properties, and topologies

ωB97XD/6-311++G(d,p) calculations were carried out to investigate the hydrogen-bonding interactions between adrenaline (Ad) and water. Six Ad-H(2)O complexes possessing various types of hydrogen bonds (H-bonds) were characterized in terms of their geometries, energies, vibrational frequencies, and electron-density topology. Natural bond orbital (NBO) and quantum theory of atoms in molecules (QTAIM) analyses were performed to elucidate the nature of the hydrogen-bonding interactions in these complexes. The intramolecular H-bond between the amino and carboxyl oxygen atom of Ad was retained in most of the complexes, and cooperativity between the intra- and intermolecular H-bonds was present in some of the complexes. H-bonds in which hydroxyls of Ad/water acted as proton donors were stronger than other H-bonds. Both hydrogen-bonding interactions and structural deformation play important roles in the relative stabilities of the complexes. The intramolecular H-bond was broken during the formation of the most stable complex, which indicates that Ad tends to break the intramolecular H-bond and form two new intermolecular H-bonds with the first water molecule.     

Contribution of hydrophobic interactions to protein stability

Our goal was to gain a better understanding of the contribution of hydrophobic interactions to protein stability. We measured the change in conformational stability, Δ(ΔG), for hydrophobic mutants of four proteins: villin headpiece subdomain (VHP) with 36 residues, a surface protein from Borrelia burgdorferi (VlsE) with 341 residues, and two proteins previously studied in our laboratory, ribonucleases Sa and T1. We compared our results with those of previous studies and reached the following conclusions: (1) Hydrophobic interactions contribute less to the stability of a small protein, VHP (0.6 ± 0.3 kcal/mol per -CH₂- group), than to the stability of a large protein, VlsE (1.6 ± 0.3 kcal/mol per -CH₂- group). (2) Hydrophobic interactions make the major contribution to the stability of VHP (40 kcal/mol) and the major contributors are (in kilocalories per mole) Phe18 (3.9), Met13 (3.1), Phe7 (2.9), Phe11 (2.7), and Leu21 (2.7). (3) Based on the Δ(ΔG) values for 148 hydrophobic mutants in 13 proteins, burying a -CH₂- group on folding contributes, on average, 1.1 ± 0.5 kcal/mol to protein stability. (4) The experimental Δ(ΔG) values for aliphatic side chains (Ala, Val, Ile, and Leu) are in good agreement with their ΔG_tr values from water to cyclohexane. (5) For 22 proteins with 36 to 534 residues, hydrophobic interactions contribute 60 ± 4% and hydrogen bonds contribute 40 ± 4% to protein stability. (6) Conformational entropy contributes about 2.4 kcal/mol per residue to protein instability. The globular conformation of proteins is stabilized predominantly by hydrophobic interactions.     

Thermodynamics of interactions between amino acid side chains: experimental differentiation of aromatic-aromatic, aromatic-aliphatic, and aliphatic-aliphatic side-chain interactions in water

A stationary phase for high-pressure liquid chromatography has been prepared by derivatizing microparticulate silica gel with functionality mimicking the side chain of isoleucine. The chromatographic retentions of a series of hydrophobic and amphiphilic amino acid analytes on this stationary phase (Ile MSP) using an aqueous mobile phase were measured as a function of temperature from 273 K to 323 K. Observed temperature dependencies are consistent with a constant change in heat capacity, DeltaC degrees P, upon binding of the analyte to the stationary phase. The curvatures of plots of retention data versus temperature (related to the magnitude of DeltaC degrees P) are distinctly different for retention of aromatic and aliphatic analytes, with retention of aliphatic analytes Val, Ile, and Leu exhibiting the characteristic signature of the hydrophobic effect, i.e., a large negative DeltaC degrees P upon desolvation from water and a maximum of retention around room temperature. Retention of aromatic analytes (Trp, Phe, and Tyr) involves smaller heat capacity changes and pronounced negative enthalpies of interaction with the stationary phase. Estimates of DeltaC degrees P for the interactions of analyte side chains with the Ile side chain were obtained by fitting the temperature dependence of retention to an expression derived from thermodynamic considerations and chromatographic theory. Similar estimates were made for interactions with the Phe side chain, using previously published data for a phenylalanine mimic stationary phase (Phe MSP) (. Protein Sci. 1:786-795). As with the Ile MSP, the retentions of aliphatic analytes show temperature dependencies markedly different from those of aromatic analytes. Data from both phases indicate that a realistic differentiation can be made between the interactions of various types of amino acid side chains tested (i.e., aliphatic/aliphatic, aliphatic/aromatic, and aromatic/aromatic) by comparison of the corresponding thermodynamic functions for pairwise interactions. The retention of leucine on the Phe MSP and that of phenylalanine on the Ile MSP showed similar DeltaC degrees P values, suggesting that the aromatic-aliphatic interaction is reasonably independent of the residue attached to the stationary phase. This result is consistent with a one-to-one interaction and suggests a simple way to estimate the column-dependent phase factor, making it possible to compare entropies and free energies of interaction obtained using different MSPs. The possibilities for using MSP-derived interaction potentials in folding simulations are discussed.     

Strength of CH···π interactions in the C-terminal subdomain of villin headpiece

The relative free energies of the folded structures of the seven model peptides with PLX (X = W, Y, F, H, and A) and ALX (X = W and A) sequences to the corresponding extended structures are calculated using the density functional methods in water to evaluate the relative strengths of CH···π interactions, especially proline···aromatic interactions for the PLX motif of the C-terminal subdomain of villin headpiece. It has been found that the Pro···π contacts for the folded structures of the PLW, PLY, PLF, and PLH peptides have in common a geometric pattern having the edge of the Pro ring interacting with the face of the aromatic ring, as found for functionally important Pro residues in proteins. At the M06-2X/cc-pVTZ//SMD M06-2X/6-31+G(d) level of theory, the relative stabilities of the folded structures to the extended structures are obtained in the order PLW > ALW > PLA > PLH > PLY > ALA > PLF by the conformational Gibbs free energies in water, which is reasonably consistent with the observed results from the CD thermal analysis for wild-type and mutants of the C-terminal subdomains of villin headpieces. Although the interaction energies excluding the solvation free energies play a role in determining the relative stabilities of the PLX and ALX peptides, the solvation and entropic terms are found to be of consequence, too. In particular, it has been known that ～40% of the total interaction energy of the PLW peptide is ascribed to the CH···π interactions of the contacting side chains for Pro and Trp residues, in which the dispersion terms play a role.     

Scanning molecular sieve chromatography of interacting protein systems. IV. The difference profile method as applied to the Gibbs-Duhem expression in the analysis of the dimer-tetramer equilibria of oxyhemoglobin A.

The recently-developed large zone difference profile method in scanning molecular sieve chromatography is applied to the analysis of the Gibbs-Duhem expression in the tetramer-dimer equilibrium of human oxyhemoglobin A. The preferential binding term and solvation parameters of the Hofmeister anion phosphate are examined. Results indicate that as the concentration of phosphate ions increase, a hydrated phosphate is formed which enhances the association by perturbing the solvation layer of the hemoglobin molecules. The standard free energy change at a given Hofmeister anion activity of ln Ax = -3.2476 is 9.4 +/- 0.2 kcal/mole. delta G0 at ln Ax = -1.2711 is 10.90 +/- 0.05 kcal/mole, suggesting that approximately 11 kcal are required to dissociate one mole of tetramer into dimer.     

The geometry and efficacy of cation-pi interactions in a diagonal position of a designed beta-hairpin

Cation-pi interactions are common in proteins, but their contribution to the stability and specificity of protein structure has not been well established. In this study, we examined the impact of cation-pi interactions in a diagonal position of a beta-hairpin peptide through comparison of the interaction of Phe or Trp with Lys or Arg. The diagonal interactions ranged from -0.20 to -0.48 kcal/mole. Our experimental values for the diagonal cation-pi interactions are similar to those found in alpha-helical studies. Upfield shifting of the Lys and Arg side chains indicates that the geometries of cation-pi interactions adopted in the 12-residue beta-hairpin are comparable to those found in protein structures. The Lys was found to interact through the polarized Cepsilon, and the Arg is stacked against the aromatic ring of Phe or Trp. Folding of these peptides was found to be enthalpically favorable (DeltaH degrees equals approximately -3 kcal/mole) and entropically unfavorable (DeltaS degrees equals approximately -8 cal mole(-1) K(-1)).     

Stability of monomeric Cro variants: Isoenergetic transformation of a type I' to a type II' beta-hairpin by single amino acid replacements

The thermodynamic stabilities of three monomeric variants of the bacteriophage lambda Cro repressor that differ only in the sequence of two amino acids at the apex of an engineered beta-hairpin have been determined. The sequences of the turns are EVK-XX-EVK, where the two central residues are DG, GG, and GT, respectively. Standard-state unfolding free energies, determined from circular dichroism measurements as a function of urea concentration, range from 2.4 to 2.7 kcal/mole, while those determined from guanidine hydrochloride range from 2.8 to 3.3 kcal/mole for the three proteins. Thermal denaturation yields van't Hoff unfolding enthalpies of 36 to 40 kcal /mole at midpoint temperatures in the range of 53 to 58 degrees C. Extrapolation of the thermal denaturation free energies with heat capacities of 400 to 600 cal/mole deg gives good agreement with the parameters determined in denaturant titrations. As predicted from statistical surveys of amino acid replacements in beta-hairpins, energetic barriers to transformation from a type I' turn (DG) to a type II' turn (GT) can be quite small.     

AB‐Bind: Antibody binding mutational database for computational affinity predictions

Antibodies (Abs) are a crucial component of the immune system and are often used as diagnostic and therapeutic agents. The need for high‐affinity and high‐specificity antibodies in research and medicine is driving the development of computational tools for accelerating antibody design and discovery. We report a diverse set of antibody binding data with accompanying structures that can be used to evaluate methods for modeling antibody interactions. Our Antibody‐Bind (AB‐Bind) database includes 1101 mutants with experimentally determined changes in binding free energies (ΔΔG) across 32 complexes. Using the AB‐Bind data set, we evaluated the performance of protein scoring potentials in their ability to predict changes in binding free energies upon mutagenesis. Numerical correlations between computed and observed ΔΔG values were low (r = 0.16–0.45), but the potentials exhibited predictive power for classifying variants as improved vs weakened binders. Performance was evaluated using the area under the curve (AUC) for receiver operator characteristic (ROC) curves; the highest AUC values for 527 mutants with |ΔΔG| > 1.0 kcal/mol were 0.81, 0.87, and 0.88 using STATIUM, FoldX, and Discovery Studio scoring potentials, respectively. Some methods could also enrich for variants with improved binding affinity; FoldX and Discovery Studio were able to correctly rank 42% and 30%, respectively, of the 80 most improved binders (those with ΔΔG < −1.0 kcal/mol) in the top 5% of the database. This modest predictive performance has value but demonstrates the continuing need to develop and improve protein energy functions for affinity prediction.     

Contribution of cation-pi interactions to protein stability

Calculations predict that cation- interactions make an important contribution to protein stability. While there have been some attempts to experimentally measure strengths of cation-pi interactions using peptide model systems, much less experimental data are available for globular proteins. We have attempted to determine the magnitude of cation-pi interactions of Lys with aromatic amino acids in four different proteins (LIVBP, MBP, RBP, and Trx). In each case, Lys was replaced with Gln and Met. In a separate series of experiments, the aromatic amino acid in each cation-pi pair was replaced by Leu. Stabilities of wild-type (WT) and mutant proteins were characterized by both thermal and chemical denaturation. Gln and aromatic --> Leu mutants were consistently less stable than corresponding Met mutants, reflecting the nonisosteric nature of these substitutions. The strength of the cation-pi interaction was assessed by the value of the change in the free energy of unfolding [DeltaDeltaG(degrees) = DeltaG(degrees)(Met) - DeltaG(degrees)(WT)]. This ranged from +1.1 to -1.9 kcal/mol (average value -0.4 kcal/mol) at 298 K and +0.7 to -2.6 kcal/mol (average value -1.1 kcal/mol) at the Tm of each WT. It therefore appears that the strength of cation-pi interactions increases with temperature. In addition, the experimentally measured values are appreciably smaller in magnitude than calculated values with an average difference /DeltaG(degrees)expt - DeltaG(degrees)calc/av of 2.9 kcal/mol. At room temperature, the data indicate that cation-pi interactions are at best weakly stabilizing and in some cases are clearly destabilizing. However, at elevated temperatures, close to typical Tm's, cation-pi interactions are generally stabilizing.