Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603.

The study of antibody-antigen interactions should greatly benefit from the development of quantitative models for the evaluation of binding free energies in proteins. The present work addresses this challenge by considering the test case of the binding free energies of phosphorylcholine analogs to the murine myeloma protein McPC603. This includes the evaluation of the differential binding energy as well as the absolute binding energies and their corresponding electrostatic contributions. Four different approaches are examined: the Protein Dipoles Langevin Dipoles (PDLD) method, the semi-microscopic PDLD (PDLD/S) method, a free energy perturbation (FEP) method based on an adiabatic charging procedure and a linear response approximation that accelerates the FEP calculation. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions. The determination of the hydrophobic energy involves an approach which considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. This treatment, which considers the protein as a harmonic system, views the steric forces as the restoring forces for the electrostatic interactions. The FEP method is found to give unreliable results with regular cut-off radii and starts to give quantitative results only in very expensive treatment with very large cut-off radii. The PDLD and PDLD/S methods are much faster than the FEP approach and give reasonable results for both the relative and absolute binding energies. The speed and simplicity of the PDLD/S method make it an effective strategy for interactive docking studies and indeed such an option is incorporated in the program MOLARIS. A component analysis of the different energy contributions of the FEP treatment and a similar PDLD analysis indicate that electrostatic effects provide the largest contribution to the differential binding energy, while the hydrophobic and steric contributions are much smaller. This finding lends further support to the idea that electrostatic interactions play a major role in determining the antigen specificity of McPC603.     

Protein control of iron-sulfur cluster redox potentials.

The relationship between the three-dimensional structures of iron-sulfur proteins and the redox potentials of their iron-sulfur clusters is of fundamental importance. We report calculations of the redox potentials of the [Fe4S4(S-cys)4]-2/-3 couple in four crystallographically characterized proteins: Azotobacter vinelandii ferredoxin I, Peptococcus aerogenes ferredoxin, Bacillus thermoproteolyticus ferredoxin, and Chromatium vinosum high potential iron protein (HiPIP). Our calculations use the "protein dipoles Langevin dipoles" microscopic electrostatic model, which includes both protein and solvent water. The variations in calculated redox potentials are in excellent agreement with experimental data. In particular, our results confirm the important role of amide groups close to the cluster in separating the potential of C. vinosum HiPIP from those of the other three proteins. However, the potentials of these latter exhibit a substantial range despite extremely similar amide group environments of their clusters. Our results show that the potentials in these proteins are tuned in part by varying the access of solvent water to the neighborhood of the cluster. Our calculations provide the first successful quantitative modeling of the protein control of iron-sulfur cluster redox potentials.     

Absolute binding free energy calculations: On the accuracy of computational scoring of protein–ligand interactions

Calculating the absolute binding free energies is a challenging task. Reliable estimates of binding free energies should provide a guide for rational drug design. It should also provide us with deeper understanding of the correlation between protein structure and its function. Further applications may include identifying novel molecular scaffolds and optimizing lead compounds in computer‐aided drug design. Available options to evaluate the absolute binding free energies range from the rigorous but expensive free energy perturbation to the microscopic linear response approximation (LRA/β version) and related approaches including the linear interaction energy (LIE) to the more approximated and considerably faster scaled protein dipoles Langevin dipoles (PDLD/S‐LRA version) as well as the less rigorous molecular mechanics Poisson–Boltzmann/surface area (MM/PBSA) and generalized born/surface area (MM/GBSA) to the less accurate scoring functions. There is a need for an assessment of the performance of different approaches in terms of computer time and reliability. We present a comparative study of the LRA/β, the LIE, the PDLD/S‐LRA/β, and the more widely used MM/PBSA and assess their abilities to estimate the absolute binding energies. The LRA and LIE methods perform reasonably well but require specialized parameterization for the nonelectrostatic term. The PDLD/S‐LRA/β performs effectively without the need of reparameterization. Our assessment of the MM/PBSA is less optimistic. This approach appears to provide erroneous estimates of the absolute binding energies because of its incorrect entropies and the problematic treatment of electrostatic energies. Overall, the PDLD/S‐LRA/β appears to offer an appealing option for the final stages of massive screening approaches. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Control of the redox potential of cytochrome c and microscopic dielectric effects in proteins

X-ray structural information provides the opportunity to explore quantitatively the relation between the microenvironments of heme proteins and their redox potentials. This can be done by considering the protein as a "solvent" for its redox center and calculating the difference between the electrostatic energy of the reduced and oxidized heme. Such calculations are presented here, applying the protein dipoles-Langevin dipoles (PDLD) model to cytochrome c. The calculations focus on an evaluation of the difference between the redox potentials of cytochrome c and the octapeptide-methionine complex formed by hydrolysis of cytochrome c. The corresponding difference (approximately 7 kcal/mol) is accounted for by the PDLD calculations. It is found that the protein provides basically a low dielectric environment for the heme, which destabilizes the oxidized heme (relative to its energy in water). The effect of the charged propionic acids on the heme is examined in a preliminary way. It is found that the negative charges of these groups are in a hydrophilic rather than a hydrophobic environment and that the protein-water system provides an effective high dielectric constant for their interaction with the heme. The dual nature of the dielectric effect of the cytochrome (a low dielectric constant for the self-energy of the heme and a high dielectric constant for charge-charge interactions) is discussed. The findings of this work are consistent with the difference between the folding energies of the reduced and oxidized cytochrome c.     

Crystal structures of the Met148Leu and Ser86Asp mutants of rusticyanin from Thiobacillus ferrooxidans: insights into the structural relationship with the cupredoxins and the multi copper proteins

The crystal structures of the Met148Leu and Ser86Asp mutants of rusticyanin are presented at 1.82 and 1.65 A resolution, respectively. Both of these structures have two molecules in the asymmetric unit compared to the one present in the crystal form of the native protein. This provides an opportunity to investigate intramolecular electron transfer pathways in rusticyanin. The redox potential of the Met148Leu mutant ( approximately 800 mV) is elevated compared to that of the native protein ( approximately 670 mV at pH 3.2) while that of the Ser86Asp mutant ( approximately 623 mV at pH 3.2) is decreased. The effect of the Ser86Asp mutation on the hydrogen bonding near the type 1 Cu site is discussed and hence its role in determining acid stability is examined. The type 1 Cu site of Met148Leu mimics the structural and biochemical characteristics of those found in domain II of ceruloplasmin and fungal laccase. Moreover, the native rusticyanin's cupredoxin core and the type 1 Cu site closely resemble those found in ascorbate oxidase and nitrite reductase. Structure based phylogenetic trees have been re-examined in view of the additional structural data on rusticyanin and fungal laccase. We confirm that rusticyanin is in the same class as nitrite reductase domain 2, laccase domain 3 and ceruloplasmin domains 2, 4 and 6.     

Contribution of amino acid substitutions at two different interior positions to the conformational stability of human lysozyme.

To elucidate correlative relationships between structural change and thermodynamic stability in proteins, a series of mutant human lysozymes modified at two buried positions (Ile56 and Ile59) were examined. Their thermodynamic parameters of denaturation and crystal structures were studied by calorimetry and X-ray crystallography. The mutants at positions 56 and 59 exhibited different responses to a series of amino acid substitutions. The changes in stability due to substitutions showed a linear correlation with changes in hydrophobicity of substituted residues, having different slopes at each mutation site. However, the stability of each mutant was found to be represented by a unique equation involving physical properties calculated from mutant structures. By fitting present and previous stability data for mutant human lysozymes substituted at various positions to the equation, the magnitudes of the hydrophobicity of a carbon atom and the hydrophobicity of nitrogen and neutral oxygen atoms were found to be 0.178 and -0.013 kJ/mol.A(2), respectively. It was also found that the contribution of a hydrogen bond with a length of 3.0 A to protein stability was 5.1 kJ/mol and the entropy loss of newly introduction of a water molecules was 7.8 kJ/mol.     

Atomic resolution crystal structures, EXAFS, and quantum chemical studies of rusticyanin and its two mutants provide insight into its unusual properties

Rusticyanin from the extremophile Thiobacillus ferrooxidans is a blue copper protein with unusually high redox potential and acid stability. We present the crystal structures of native rusticyanin and of its Cu site mutant His143Met at 1.27 and 1.10 A, respectively. The very high resolution of these structures allows a direct comparison with EXAFS data and with quantum chemical models of the oxidized and reduced forms of the proteins, based upon both isolated and embedded clusters and density functional theory (DFT) methods. We further predict the structure of the Cu(II) form of the His143Met mutant which has been experimentally inaccessible due to its very high redox potential. We also present metrical EXAFS data and quantum chemical calculations for the oxidized and reduced states of the Met148Gln mutant, this protein having the lowest redox potential of all currently characterized mutants of rusticyanin. These data offer new insights into the structural factors which affect the redox potential in this important class of proteins. Calculations successfully predict the structure and the order of redox potentials for the three proteins. The calculated redox potential of H143M ( approximately 400 mV greater than native rusticyanin) is consistent with the failure of readily available chemical oxidants to restore a Cu(II) species of this mutant. The structural and energetic effects of mutating the equatorial cysteine to serine, yet to be studied experimentally, are predicted to be considerable by our calculations.     

Decrease in protein solubility and cataract formation caused by the Pro23 to Thr mutation in human gamma D-crystallin

The P23T mutation in the human gammaD-crystallin gene has in recent years been associated with a number of well known cataract phenotypes. To understand the molecular mechanism of lens opacity caused by this mutation, we expressed human gammaD-crystallin (HGD), the P23T mutant, and other related mutant proteins in Escherichia coli and compared the structures and thermodynamic properties of these proteins in vitro. The results show that the cataract-causing mutation P23T does not exhibit any significant structural change relative to the native protein. However, in marked contrast to the native protein, the mutant shows a dramatically lowered solubility. The reduced solubility results from the association of the P23T mutant to form a new condensed phase that contains clusters of the mutant protein. The monomer-cluster equilibrium is represented by a solubility curve in the phase diagram. When the solubility limit is exceeded, the mutant protein forms the condensed phase after a nucleation time of 10-20 min. We found that the solubility of the P23T mutant exhibits an inverse dependence on temperature, i.e., the protein clusters are increasingly soluble as the temperature of the solution decreases. The solubility of P23T can be substantially altered by the introduction of specific mutations at or in the immediate vicinity of residue 23. We examined the mutants P23S, P23V, P23TInsP24, and P23TN24K and found that the latter two mutations can restore the solubility of the P23T mutant. These findings may help develop a strategy for the rational design of small molecule inhibitors of this type of condensed phase.     

Influence of the redox potential of the primary quinone electron acceptor on photoinhibition in photosystem II

We report the characterization of the effects of the A249S mutation located within the binding pocket of the primary quinone electron acceptor, Q(A), in the D2 subunit of photosystem II in Thermosynechococcus elongatus. This mutation shifts the redox potential of Q(A) by approximately -60 mV. This mutant provides an opportunity to test the hypothesis, proposed earlier from herbicide-induced redox effects, that photoinhibition (light-induced damage of the photosynthetic apparatus) is modulated by the potential of Q(A). Thus the influence of the redox potential of Q(A) on photoinhibition was investigated in vivo and in vitro. Compared with the wild-type, the A249S mutant showed an accelerated photoinhibition and an increase in singlet oxygen production. Measurements of thermoluminescence and of the fluorescence yield decay kinetics indicated that the charge-separated state involving Q(A) was destabilized in the A249S mutant. These findings support the hypothesis that a decrease in the redox potential of Q(A) causes an increase in singlet oxygen-mediated photoinhibition by favoring the back-reaction route that involves formation of the reaction center chlorophyll triplet. The kinetics of charge recombination are interpreted in terms of a dynamic structural heterogeneity in photosystem II that results in high and low potential forms of Q(A). The effect of the A249S mutation seems to reflect a shift in the structural equilibrium favoring the low potential form.     

Probing the general base catalysis in the first step of BamHI action by computer simulations.

BamHI is a type II restriction endonuclease that catalyzes the scission of the phoshodiester bond in the GAGTCC cognate sequence in the presence of two divalent metal ions. The first step of the reaction is the preparation of water for nucleophilic attack by Glu-113, which has been proposed to abstract the proton from the attacking water molecule. Alternatively, the 3'-phosphate group to the susceptible phosphodiester bond has been suggested to play a role as the general base. The two hypotheses have been tested by computer simulations using the semiempirical protein dipoles Langevin dipoles (PDLD/S) method. Deprotonation of water by Glu-113 has been found to be less favorable by 5.7 kcal/mol than metal-catalyzed deprotonation with a concomitant proton transfer to bulk solvent. The preparation of the nucleophile by the 3'-phosphate group is less favorable by 12.3 kcal/mol. These results suggest that both the general base and the substrate-assisted mechanisms in the first step of BamHI action are less likely than the metal-catalyzed reaction. The metal ions in the active site of BamHI make the largest contributions to the reduction of the free energy of hydroxide ion formation. On the basis of these findings we propose that the first step of endonuclease catalysis does not require a general base; rather, the essential attacking nucleophile in BamHI catalytic action is stabilized by the metal ions.     

The role of residue stability in transient protein–protein interactions involved in enzymatic phosphate hydrolysis. A computational study

Finding why protein–protein interactions (PPIs) are so specific can provide a valuable tool in a variety of fields. Statistical surveys of so‐called transient complexes (like those relevant for signal transduction mechanisms) have shown a tendency of polar residues to participate in the interaction region. Following this scheme, residues in the unbound partners have to compete between interacting with water or interacting with other residues of the protein. On the other hand, several works have shown that the notion of active site electrostatic preorganization can be used to interpret the high efficiency in enzyme reactions. This preorganization can be related to the instability of the residues important for catalysis. In some enzymes, in addition, conformational changes upon binding to other proteins lead to an increase in the activity of the enzymatic partner. In this article the linear response approximation version of the semimacroscopic protein dipoles Langevin dipoles (PDLD/S‐LRA) model is used to evaluate the stability of several residues in two phosphate hydrolysis enzymes upon complexation with their activating partners. In particular, the residues relevant for PPI and for phosphate hydrolysis in the CDK2/Cyclin A and Ras/GAP complexes are analyzed. We find that the evaluation of the stability of residues in these systems can be used to identify not only active site regions but it can also be used as a guide to locate “hot spots” for PPIs. We also show that conformational changes play a major role in positioning interfacing residues in a proper “energetic” orientation, ready to interact with the residues in the partner protein surface. Thus, we extend the preorganization theory to PPIs, extrapolating the results we obtained from the above‐mentioned complexes to a more general case. We conclude that the correlation between stability of a residue in the surface and the likelihood that it participates in the interaction can be a general fact for transient PPIs. Proteins 2006. © 2005 Wiley‐Liss, Inc.     

Heat capacity of protein folding.

We construct a Hamiltonian for a single domain protein where the contact enthalpy and the chain entropy decrease linearly with the number of native contacts. The hydration effect upon protein unfolding is included by modeling water as ideal dipoles that are ordered around the unfolded surfaces, where the influence of these surfaces, covered with an "ice-like" shell of water, is represented by an effective field that directs the water dipoles. An intermolecular pair interaction between water molecules is also introduced. The heat capacity of the model exhibits, the common feature of small globular proteins, two peaks corresponding to cold and warm unfolding, respectively. By introducing ad hoc vibrational modes, we obtain quantitatively good accordance with experiments on myoglobin.     

Contact potential that recognizes the correct folding of globular proteins.

We have devised a continuous function of interresidue contacts in globular proteins such that the X-ray crystal structure has a lower function value than that of thousands of protein-like alternative conformations. Although we fit the adjustable parameters of the potential using only 10,000 alternative structures for a selected training set of 37 proteins, a grand total of 530,000 constraints was satisfied, derived from 73 proteins and their numerous alternative conformations. In every case where the native conformation is adequately globular and compact, according to objective criteria we have developed, the potential function always favors the native over all alternatives by a substantial margin. This is true even for an additional three proteins never used in any way in the fitting procedure. Conformations differing only slightly from the native, such as those coming from crystal structures of the same protein complexed with different ligands or from crystal structures of point mutants, have function values very similar to the native's and always less than those of alternatives derived from substantially different crystal structures. This holds for all 95 structures that are homologous to one or another of various proteins we used. Realizing that this potential should be useful for modeling the conformation of new protein sequences from the body of protein crystal structures, we suggest a test for deciding whether a nearly correct approximation to the native conformation has been found.     

Dipole lattice membrane model for protein calculations

A dipole lattice model for lipid membranes and their interactions with peptides is presented. It uses the Langevin dipole method to calculate electrostatic interactions in the heterogeneous membrane environment. A series of test cases are presented, including spherical charges, dipoles, side chain analogs, and helical peptides. The model consistently produces qualitatively correct results.     

The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins.

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (epsilon(eff)) is examined by the semimicroscopic version of the Protein Dipole Langevin Dipoles (PDLD/S) method within the framework of the Linear Response Approximation (LRA). This is done by evaluating the interactions between ionized residues in the reaction center of Rhodobacter sphaeroides, while taking into account the protein reorganization energy. It is found that an explicit consideration of the protein relaxation leads to a significant increase in epsilon(eff) and that semimicroscopic models that do not take this relaxation into account force one to use a large value for the so-called "protein dielectric constant," epsilon(p), of the Poisson-Boltzmann model or for the corresponding epsilon(in) in the PDLD/S model. An additional increase in epsilon(eff) is expected from the reorganization of ionized residues and from changes in the degree of water penetration. This finding provides further support for the idea that epsilon(in) (or epsilon(p)) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of epsilon(eff), supporting our previously reported view that charge-charge interactions correspond to a large value of this "dielectric constant," even in protein interiors. It is also pointed out that epsilon(eff) for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, epsilon'(eff), that determines the free energy of ion pairs in proteins (epsilon'(eff) reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general epsilon(in) are discussed. It is clarified that the epsilon(in) that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the epsilon(in) that reproduces the corresponding effect upon formation of individual charges. This reflects fundamental inconsistencies in attempts to cast microscopic concepts in a macroscopic model. Thus one should either use a large epsilon(in) for charge-charge interactions and a small epsilon(in) for charge-dipole interactions or consider the protein relaxation microscopically.     

Cytochrome b562 variants: a library for examining redox potential evolution

A general understanding of how cytochromes evolve within a fixed structure to optimize redox potential for specific bioenergetic processes does not exist. Toward this end, a library approach is used to investigate the range and distribution of redox potential which occurs when all sequence space available through mutation at two positions is examined within a fixed structural motif. Random mutation of Phe61 and Phe65 of cytochrome b562 (E. coli), and subsequent examination of a statistically significant sampling of this library, demonstrates that the redox potential can vary over 100 mV (>25% of the known accessible potential in native proteins with axial His-Met ligation) through mutation at these two positions. The redox potential of the wild-type protein occurs at an extremum of the distribution observed, indicating that Phe61 and Phe65 were most likely naturally selected to differentially stabilize the reduced state of the protein. At the other extremum, a compositionally conservative set of mutations (F61I, F65Y) leads to a 100 mV shift in the redox equilibrium toward the oxidized state. NMR analyses indicate that a charge-dipole interaction which results from mutation of phenylalanine to tyrosine at position 65 may be responsible.     

A positive charge at position 33 of thioredoxin primarily affects its interaction with other proteins but not redox potential

Oxidoreductases of the thioredoxin superfamily possess the C-X-X-C motif. The redox potentials vary over a wide range for these proteins. A crucial determinant of the redox potential has been attributed to the variation of the X-X dipeptide. Here, we substitute Lys for Gly at the first X of Escherichia coli thioredoxin to investigate how a positive charge would affect the redox potential. The substitution does not affect the protein's redox potential. The equilibrium constant obtained from pairwise reaction between the mutant and wild-type proteins equals 1.1, indicating that the replacement does not significantly affect the thiol-disulfide redox equilibrium. However, the catalytic efficiency of thioredoxin reductase on the G33K mutant decreases approximately 2.8 times compared to that of the wild type. The mutation mainly affects K(m), with little effect on k(cat). The mutation also inhibits thioredoxin's ability to reduce insulin disulfide by approximately one-half. Whether the mutant protein supports the growth of phages T3/7 and f1 was tested. The efficiency of plating (EOP) of T3/7 on the mutant strain decreases 5 times at 37 degrees C and 3 x 10(4) times at 42 degrees C relative to that of the wild-type strain, suggesting that interaction between phage gene 5 protein and thioredoxin is hindered. The mutation also reduces the EOP of phage f1 by 8-fold at 37 degrees C and 1.5-fold at 42 degrees C. The global structure of the mutant protein does not change when studied by CD and fluorescence spectra. Therefore, G33K does not significantly affect the overall structure or redox potential of thioredoxin, but primarily interferes with its interaction with other proteins. Together with the G33D mutation, the overall results show that a charged residue at the first X has a greater influence on the molecular interaction of the protein than the redox potential.     

A Pro to His mutation in active site of thioredoxin increases its disulfide-isomerase activity 10-fold. New refolding systems for reduced or randomly oxidized ribonuclease.

Thioredoxin (Trx) from Escherichia coli was compared with bovine protein disulfide-isomerase (PDI) for its ability to catalyze native disulfide formation in either reduced or randomly oxidized (scrambled) ribonuclease A (RNase). On a molar basis, a 100-fold higher concentration of Trx than of PDI was required to give the same rate of native disulfide formation measured as recovery of RNase activity. A Pro-34 to His (P34H Trx) mutation in the active site of E. coli Trx (WCGPC), mimicking the two suggested active sites in PDI (WCGHC), increased the catalytic activity in disulfide formation about 10-fold. The mutant P34H Trx displayed a 35-mV higher redox potential (E'0) of the active site disulfide/dithiol relative to wild type Trx, making it more similar to the redox potential observed for PDI. This higher redox potential correlates well with the enhanced activity and suggests a role for the histidine side chain. Enzymatic isomerization of disulfides in scrambled, oxidized RNase requires the presence of a catalytic thiol such as GSH to initiate the thiol-disulfide interchange. Bovine thioredoxin reductase, together with NADPH, could replace GSH. For oxidative folding of reduced RNase in air with Trx, P34H Trx, or PDI, catalytic amounts of sodium selenite (1 microM) resulted in rapid disulfide formation and high yields of ribonuclease activity equivalent to previously known redox buffers of GSH and GSSG. These results demonstrate no obligatory role for glutathione in disulfide formation. A possible mechanism for the unknown thiol oxidative process accompanying folding and protein disulfide formation in vivo is discussed.