Electrostatic contributions to protein-protein binding affinities: application to Rap/Raf interaction

On the origin of the electrostatic barrier for proton transport in aquaporin

The nature of the electrostatic barrier for proton transport in aquaporins is analyzed by semimacroscopic and microscopic models. It is found that the barrier is associated with the loss of the generalized solvation energy upon moving from the bulk solvent to the center of the channel. It is clarified that our solvation concept includes the effect of the protein polar groups and ionized residues. The nature of the contributions to the solvation barrier is examined by using the linear response approximation. It is found that the residues in the NPA region contribute much less than what would be deduced from calculations that do not consider the protein reorganization. It is clarified that the contributions of different structural or electrostatic elements to the solvation barrier can be established by removing these elements and examining the corresponding effect on the barrier height. Using this definition and "mutating" the NPA residues to their non-polar analogues establishes that these residues do not provide the major contribution to the solvation barrier.

Change in protein flexibility upon complex formation: Analysis of Ras-Raf using molecular dynamics and a molecular framework approach

Changes in flexibility upon protein-protein complex formation of H-Ras and the Ras-binding domain of C-Raf1 have been investigated using the molecular framework approach FIRST (Floppy Inclusion and Rigid Substructure Topology) and molecular dynamics simulations (MD) of in total approximately 35 ns length. In a computational time of about one second, FIRST identifies flexible and rigid regions in a single, static three-dimensional molecular framework, whose vertices represent protein atoms and whose edges represent covalent and non-covalent (hydrogen bond and hydrophobic) constraints and fixed bond angles within the protein. The two methods show a very good agreement with respect to the identification of changes in flexibility in both binding partners on a local scale. This implies that flexibility can be successfully predicted by identifying which bonds limit motion within a molecule and how they are coupled. In particular, as identified by MD, the beta-sheet in Raf shows considerably more pronounced orientational correlations in the bound state compared to the unbound state. Similarly, FIRST assigns the beta-sheet to the largest rigid cluster of the complex. Interestingly, FIRST allows us to identify that interactions across the interface (but not conformational changes upon complex formation) result in the observed rigidification. Since regions of the beta-sheet of Raf that do not interact directly with Ras become rigidified, this also demonstrates the long-range aspect to rigidity percolation. Possible implications of the change of flexibility of the Ras-binding domain of Raf on the activation of Raf upon complex formation are discussed. Finally, the sensitivity of FIRST results with respect to the representation of non-covalent interactions used as constraints is probed.

Calculating proton uptake/release and binding free energy taking into account ionization and conformation changes induced by protein-inhibitor association: Application to plasmepsin, cathepsin D and endothiapepsin-pepstatin complexes

The protein-inhibitor binding energies of enzymes are often pH dependent, and binding induces either proton uptake or proton release. The proton uptake/release and the binding energy for three complexes with available experimental data were numerically studied: pepstatin-cathepsin D, pepstatin-plasmepsin II and pepstatin-endothiapepsin. Very good agreement with the experimental data was achieved when conformational changes were taken into account. The role of the desolvation energy and the conformational changes was revealed by modeling the complex, the separated molecules in the complex conformation and the free molecules. It was shown that the conformational changes induced by the complex formation are as important for the proton transfer as the loss of solvation energy caused by the burial of interface residues. The residues responsible for the proton transfer were identified and their contribution to the proton uptake/release calculated. These residues were found to be scattered along the whole protein rather than being localized only at the active site. In the case of cathepsin D, these residues were found to be highly conserved among the cathepsin D sequences of other species. It was shown that conformation and ionization changes induced by the complex formation are critical for the correct calculation of the binding energy. Taking into account the electrostatics and the van der Waals (vdW) energies within the Boltzmann distribution of energies and allowing ionization and conformation changes to occur makes the calculated binding energy more realistic and closer to the experimental value. The interplay between electrostatic and vdW forces makes the pH dependence of the binding energy smoother, because the vdW force acts in reaction to the changes of the electrostatic energy. It was found that a small fraction of the ionizable groups remain uncharged in both the free and complexed molecules. The sequence and structural position of these groups aligns well within the three proteases, suggesting that these may have specific role.

Experimental and numerical study of the poplar plastocyanin isoforms using Tyr as a probe for electrostatic similarity and dissimilarity

A detailed study of the tyrosine spectral characteristics was carried out in a broad range of pHs for both isoforms of plastocyanin from poplar. It was found that Tyr 80 is always protonated while Tyr 83 can form a tirosinate at high pHs. The pK(a) of Tyr 83 is practically identical in plastocyanin a and b, but the quenching of its spectrum is different in the isoforms. This provides insights that the acidic patches surrounding Tyr 83 have different electrostatic properties in plastocyanin a and b. The protonation states and the electrostatic interactions were numerically modeled on the existing plastocyanin a structure and on a homology model of plastocyanin b. The results of numerical calculations agree with the experimental findings and identify several differences in the titration behavior of the acidic patches. The difference of the tyrosine quenching pH profiles of the isoforms is rationalized by the differences in the calculated pK(a)'s of amino acids in the neighboring acidic clusters.

Functionality of Wrapping Defects in Soluble Proteins: What Cannot be Kept Dry Must be Conserved

Soluble proteins preserve their structure only if a sufficient number of non-polar groups are clustered around the backbone hydrogen bonds, protecting them from water attack. When these bonds are not properly wrapped or dehydrated intramolecularly, structural integrity can be preserved through binding partnerships. This is because insufficiently wrapped hydrogen bonds are inherently adhesive and become better shielded upon protein-ligand association. Thus, we postulate that deficiently wrapped hydrogen bonds are functionally relevant. Two findings that support this conjecture are: (a) there is a statistically relevant linear correlation between the number of defects in a folding domain and its proteomic connectivity, obtained from large-scale two-hybrid experiments; (b) the residues paired by under-wrapped hydrogen bonds are highly conserved. The high mutational sensitivity of under-wrapped regions can be rationalized, since their structural integrity relies on their propensity to behave as binding sites, in turn, a consequence of their adhesiveness. Thus, the regions in soluble protein structure that cannot be kept dry in water tend to be conserved.

Modeling loop reorganization free energies of acetylcholinesterase: A comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.

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.

Prediction of the multimeric assembly of staphylococcal enterotoxin A with cell-surface protein receptors

Staphylococcal enterotoxin A (SEA) cross-links two class II major histocompatibility complex (MHC) molecules and forms a multimeric assembly with T-cell receptors (TcRs). The X-ray crystal structure of SEA has been solved, yet details describing molecular recognition and association remain unclear. We present a structural model for the interactions of SEA with cell-surface proteins. Molecular docking calculations predicting SEA association with the class II MHC molecule HLA-DR1 were performed by using a rigid-body docking method. Docked orientations were evaluated by a Poisson-Boltzmann model for the electrostatic free energy of binding and the hydrophobic effect calculated from molecular surface areas. We found that the best-scoring SEA conformers for the DR1alpha interface display a binding mode similar to that determined crystallographically for staphylococcal enterotoxin B bound to HLA-DR1. For the zinc-binding site of SEA, docking DR1beta yielded several orientations exhibiting tetrahedral-like coordination geometries. Combining the two interfaces, tetramers were modeled by docking an alphabeta TcR with trimolecular complexes DR1beta-SEA-DR1alpha and SEA-betaDR1alpha-SEA. Our results indicate that the complex DR1beta-SEA-DR1alpha provides a more favorable assembly for the engagement of TcRs, forming SEA molecular contacts that are in accord with reported mutagenesis studies. In contrast, the cooperative association of two SEA molecules on a single DR1 molecule sterically inhibits interactions with TcRs. We suggest that signal transduction stimulated by SEA through large-scale assembly is limited to four or five TcR-(DR1beta-SEA-DR1alpha) tetramers and requires the dimerization of class II MHC molecules, while TcR dimerization is unlikely.

The effect of pH and various cations on the GTP hydrolysis of rice heterotrimeric G-protein alpha subunit expressed in Escherichia coli

Previously, we reported the biochemical properties of RGA1 that is expressed in Escherichia coli (Seo et al., 1997). The activities of RGA1 that hydrolyzes and binds guanine nucleotide were dependent on the MgCl(2) concentration. The steady state rate constant (k(cat) ) for GTP hydrolysis of RGA1 at 2 mM MgCl(2) was 0.0075 +/- 0.0001 min(-1). Here, we examined the effects of pH and cations on the GTPase activity. The optimum pH at 2 mM MgCl(2) was approximately 6.0; whereas, the pH at 2 mM NH(4)Cl was approximately 4.0. The result from the cation dependence on the GTPase (guanosine 5'-triphosphatase) activity of RGA1 under the same condition showed that the GTP hydrolysis rate (k(cat)= 0.0353 min(-1)) under the condition of 2 mM NH(4)Cl at pH 4.0 was the highest. It corresponded to about 3.24-fold of the k(cat) value of 0.0109 min(-1) in the presence of 2 mM MgCl(2) at pH 6.0.

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.

Protein-protein interactions: mechanisms and modification by drugs

Protein-protein interactions form the proteinaceous network, which plays a central role in numerous processes in the cell. This review highlights the main structures, properties of contact surfaces, and forces involved in protein-protein interactions. The properties of protein contact surfaces depend on their functions. The characteristics of contact surfaces of short-lived protein complexes share some similarities with the active sites of enzymes. The contact surfaces of permanent complexes resemble domain contacts or the protein core. It is reasonable to consider protein-protein complex formation as a continuation of protein folding. The contact surfaces of the protein complexes have unique structure and properties, so they represent prospective targets for a new generation of drugs. During the last decade, numerous investigations have been undertaken to find or design small molecules that block protein dimerization or protein(peptide)-receptor interaction, or on the other hand, induce protein dimerization.

MIAX: a new paradigm for modeling biomacromolecular interactions and complex formation in condensed phases

A new paradigm is proposed for modeling biomacromolecular interactions and complex formation in solution (protein-protein interactions so far in this report) that constitutes the scaffold of the automatic system MIAX (acronym for Macromolecular Interaction Assessment X). It combines in a rational way a series of computational methodologies, the goal being the prediction of the most native-like protein complex that may be formed when two isolated (unbound) protein monomers interact in a liquid environment. The overall strategy consists of first inferring putative precomplex structures by identification of binding sites or epitopes on the proteins surfaces and a simultaneous rigid-body docking process using geometric instances alone. Precomplex configurations are defined here as all those decoys the interfaces of which comply substantially with the inferred binding sites and whose free energy values are lower. Retaining all those precomplex configurations with low energies leads to a reasonable number of decoys for which a flexible treatment is amenable. A novel algorithm is introduced here for automatically inferring binding sites in proteins given their 3-D structure. The procedure combines an unsupervised learning algorithm based on the self-organizing map or Kohonen network with a 2-D Fourier spectral analysis. To model interaction, the potential function proposed here plays a central role in the system and is constituted by empirical terms expressing well-characterized factors influencing biomacromolecular interaction processes, essentially electrostatic, van der Waals, and hydrophobic. Each of these procedures is validated by comparing results with observed instances. Finally, the more demanding process of flexible docking is performed in MIAX embedding the potential function in a simulated annealing optimization procedure. Whereas search of the entire configuration hyperspace is a major factor precluding hitherto systems from efficiently modeling macromolecular interaction modes and complex structures, the paradigm presented here may constitute a step forward in the field because it is shown that a rational treatment of the information available from the 3-D structure of the interacting monomers combined with conveniently selected computational techniques can assist to elude search of regions of low probability in configuration space and indeed lead to a highly efficient system oriented to solve this intriguing and fundamental biologic problem.

Free-energy contributions to complex formation between botulinum neurotoxin type B and synaptobrevin fragment

Free-energy terms that contribute to complex formation between the catalytic domain of botulinum neurotoxin type B (BoNT/B-L(C)) and a 36-residue synaptobrevin fragment were estimated by using a combination of microscopic simulations and continuum methods. The complex for a non-hydrolyzed substrate was calculated by optimizing an energy function applied to the X-ray co-crystal structure of BoNT/B-L(C) bound with reaction products from a cleaved synaptobrevin peptide, refined to high crystallographic thermal factors. The estimated absolute binding affinity of the simulation structure is in good qualitative agreement with the experimental free energy of Michaelis complex formation, given the approximations of the model calculations. The simulation structure revealed significant complex stabilization from the hydrophobic effect, while the electrostatic cost of releasing water molecules from the interface determined to be highly unfavorable. By partitioning the total electrostatic and hydrophobic terms into residue free-energy contributions, a binding-affinity 'signature' for synaptobrevin was developed from the optimized conformation. The results demonstrate the effect of substrate length on complex formation and identify a peripheral high-affinity binding site near the N-terminal region that might initiate cooperative activation responsible for the large minimal substrate length requirement. The so-called SNARE motif is observed to contribute negligible free energy of binding.

Calculations of free-energy contributions to protein-RNA complex stabilization

The problem of calculating binding affinities of protein-RNA complexes is addressed by analyzing a computational strategy of modeling electrostatic free energies based on a nonlinear Poisson-Boltzmann (NLPB) model and linear response approximation (LRA). The underlying idea is to treat binding as a two-step process. Solutions to the NLPB equation calculate free energies arising from electronic polarizability and the LRA is constructed from molecular dynamics simulations to model reorganization free energies due to conformational transitions. By implementing a consistency condition of requiring the NLPB model to reproduce the solute-solvent free-energy transitions determined by the LRA, a "macromolecule dielectric constant" (epsilon(m)) for treating reorganization is obtained. The applicability of this hybrid approach was evaluated by calculating the absolute free energy of binding and free-energy changes for amino acid substitutions in the complex between the U1A spliceosomal protein and its cognate RNA hairpin. Depending on the residue substitution, epsilon(m) varied from 3 to 18, and reflected dipolar reorientation not included in the polarization modeled by epsilon(m) = 2. Although the changes in binding affinities from substitutions modeled strictly at the implicit level by the NLPB equation with epsilon(m) = 4 reproduced the experimental values with good overall agreement, substitutions problematic to this simple treatment showed significant improvement when solved by the NLPB-LRA approach.

What are the dielectric "constants" of proteins and how to validate electrostatic models?

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK(a) values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK(a) values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)-type models, and Tanford Kirkwwod (TK)-type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, epsilon(p), is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that epsilon(p) represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self-energies is not the optimal constant for charge-charge interactions.

Evaluation of protein-protein association energies by free energy perturbation calculations

The association energy upon binding of different amino acids in the specificity pocket of trypsin was evaluated by free energy perturbation calculations on complexes between bovine trypsin (BT) and bovine pancreatic trypsin inhibitor (BPTI). Three simulations of mutations of the primary binding residue (P(1)) were performed (P(1)-Ala to Gly, P(1)-Met to Gly and P(1)-Met to Ala) and the resulting differences in association energy (DeltaDeltaG(a)) are 2. 28, 5.08 and 2.93 kcal/mol for P(1)-Ala to Gly, P(1)-Met to Gly and to Ala with experimental values of 1.71, 4.62 and 2.91 kcal/mol, respectively. The calculated binding free energy differences are hence in excellent agreement with the experimental binding free energies. The binding free energies, however, were shown to be highly dependent on water molecules at the protein-protein interface and could only be quantitatively estimated if the correct number of such water molecules was included. Furthermore, the cavities that were formed when a large amino acid side-chain is perturbed to a smaller one seem to create instabilities in the systems and had to be refilled with water molecules in order to obtain reliable results. In addition, if the protein atoms that were perturbed away were not replaced by water molecules, the simulations dramatically overestimated the initial state of the free energy perturbations.

Modeling implicit reorganization in continuum descriptions of protein-protein interactions

The determination of free energies that govern protein-protein recognition is essential for a detailed molecular understanding of biological specificity. Continuum models of macromolecular interactions, in which the solvent is treated by an implicit representation and the proteins are treated semi-microscopically, are computationally tractable for estimating free energies, yet many questions remain concerning their accuracy. This article reports a continuum analysis of the free-energy changes underlying the binding of 31 interfacial alanine substitutions of two complexes of the antihen egg white lysozyme (HEL) antibody D1.3 bound with HEL or the antibody E5.2. Two implicit schemes for modeling the effects of protein and solvent relaxation were examined, in which the protein environment was treated as either homogeneous with a "protein dielectric constant" of epsilon(p) = 4 or inhomogeneous, with epsilon(p) = 4 for neutral residues and epsilon(p) = 25 for ionized residues. The results showed that the nonuniform dielectric model reproduced the experimental differences better, with an average absolute error of +/-1.1 kcal/mol, compared with +/-1.4 kcal/mol for the uniform model. More importantly, the error for charged residues in the nonuniform model is +/-0.8 kcal/mol and is nearly half of that corresponding to the uniform model. Several substitutions were clearly problematic in determining qualitative trends and probably required explicit structural reorganization at the protein-protein interface.

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.

How and why phosphotyrosine-containing peptides bind to the SH2 and PTB domains

BACKGROUND

Specific recognition of phosphotyrosine-containing protein segments by Src homology 2 (SH2) and phosphotyrosine-binding (PTB) domains plays an important role in intracellular signal transduction. Although many SH2/PTB-domain-containing receptor-peptide complex structures have been solved, little has been done to study the problem computationally. Prediction of the binding geometry and the binding constant of any peptide-protein pair is an extremely important problem.

RESULTS

A procedure to predict binding energies of phosphotyrosine-containing peptides with SH2/PTB domains was developed. The average deviation between experimentally measured binding energies and theoretical evaluations was 1.8 kcal/mol. Binding states of unphosphorylated peptides were also predicted reasonably well. Ab initio predictions of binding geometry of fully flexible peptides correctly identified conformations of two pentapeptides and a hexapeptide complexed with a v-Src SH2 domain receptor with root mean square deviations (rmsds) of 0.3 A, 1.2 A and 1.5 A, respectively.

CONCLUSIONS

The binding energies of phosphotyrosine-containing complexes can be effectively predicted using the procedure developed here. It was also possible to predict the bound conformations of flexible short peptides correctly from random starting conformations.

Free energy determinants of binding the rRNA substrate and small ligands to ricin A-chain

A continuum model is provided of the free energy terms that contribute to the molecular association of ricin A-chain (RTA) with the rRNA substrate and several small ligands. The model for RTA interactions with the RNA was taken from a previously proposed complex containing a 29-mer oligonucleotide hairpin (. Proteins 27:80-95), and models for the ligands were constructed from x-ray crystallographic structures. The calculated absolute free energies of complex formation for the RTA-RNA assembly and several single-residue substitutions are in good agreement with experimental data, given the approximations of evaluating the strain energy and conformational entropy. The free energy terms were found to resemble those of protein-protein complexes, with the net unfavorable electrostatic contribution offset by the favorable nonspecific hydrophobic effect. Decomposition of the RTA-RNA binding free energy into individual contributions revealed the electrostatic "hot" spots arising from charge-charge complementarity of the interfacial arginines with the RNA phosphate backbone. Base interactions of the GAGA loop structure dominate the hydrophobic complementarity. A linear-scaling model was parametrized for evaluating the binding of small ligands against the rRNA substrate and illustrates the free energy determinant required for designing specific RTA inhibitors.

Orientation, positional, additivity, and oligomerization-state effects of interhelical ion pairs in alpha-helical coiled-coils

The role of interhelical g-e' ion pairs in the dimerization specificity and stability of alpha-helical coiled-coils is highly controversial. Synthetic 35-residue coiled-coils based on the heptad repeat QgVaGbAcLdQeK f were used to investigate the effect of orientation of interhelical ion pairs between lysine and glutamic acid residues on coiled-coil stability. Stability was estimated from urea denaturation at 20 degreesC, monitoring unfolding with circular-dichroism spectroscopy. Double mutant cycles were employed to estimate the net interaction energy, Delta DeltaGuint, for the two orientations of the ion pair; Ee-Kg and Ke-Eg. Delta DeltaGuint was found to be about 1.4-fold higher for the Ee-Kg orientation in a coiled-coil containing an N-terminal disulfide bridge. The Delta DeltaGuint value was similar whether obtained from the middle heptad or averaged over all five heptads of the coiled-coil, suggesting that ion pairs contribute additively to coiled-coil stability. The effect of uncompensated charges was also illustrated by single substitutions of Gln with either Lys or Glu, resulting in Lys-Gln or Glu-Gln g-e' pairs. These substitutions were found to be twice as destabilizing at position g as at position e, and Lys was about twice as destabilizing as Glu at both positions e and g. In the absence of an interhelical disulfide bridge, Glu and Lys substitutions in the middle heptad were equally destabilizing at positions e and g (Lys continued to be more destabilizing than Glu) and the Delta DeltaGuint value for Lys-Glu ion pairs was not orientation dependent. These and previous results suggest the non-covalently-linked synthetic coiled-coils behave as molten globules, whereas a disulfide-bridge may "lock in" the structural differences between positions of the heptad repeat. Interhelical Lys-Glu ion pairs in either orientation promoted the formation of trimeric coiled-coils (in the absence of a disulfide bridge) while Gln-Gln g-e' interactions led to dimer formation. The results support a role for g-e' ionic attractions in controlling coiled-coil specificity, stability and oligomerization state, possibly through effects on the side-chain packing at the subunit interface.

Electrostatic effects in macromolecules: fundamental concepts and practical modeling

The past few years have seen an exponential growth in the calculations of electrostatic energies of macromolecules and an increased recognition of the crucial role of electrostatic effects. This review considers the current state of the field. Focus is placed on calculations of pKas, redox potentials and binding energies in macromolecules and clarification of the fact that the value of the dielectric 'constant' of a protein depends on its definition and that small dielectric constants should not be used in describing charge-charge interactions by current continuum models.