Hidden thermodynamics of mutant proteins: a molecular dynamics analysis

Structure-based drug design approaches for predicting binding affinities of HIV1 protease inhibitors

Computational assessment of the binding affinity of enzyme inhibitors prior to synthesis is an important component of computer-assisted drug design (CADD) paradigms. The free energy perturbation (FEP) methodology is the most accurate means of estimating relative binding affinities between two inhibitors. However, due to its complexity and computation-intensive nature, practical applications are restricted to analysis of structurally-related inhibitors. Accordingly, there is a need for methods that enable rapid assessment of large number of structurally-unrelated molecules in a suitably accurate manner. In this review, the FEP method is compared with regression-based methods that employ multivariate models to assess the advantages of each in the estimation of relative binding affinities of inhibitors to an enzyme. Semiquantitative predictions of relative binding free energies of human immunodeficiency virus 1 (HIV1) protease inhibitors are also presented and compared with the corresponding FEP results. The results indicate that the regression-based methods and the FEP method are useful in the semi-quantitative and quantitative assessment of relative binding affinities of enzyme inhibitors, respectively, prior to synthesis.

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.

Computational studies on mutant protein stability: The correlation between surface thermal expansion and protein stability

Thermal stability of mutant proteins has been investigated using temperature dependent molecular dynamics (MD) simulations in vacuo. The numerical modeling was aimed at mimicking protein expansion upon heating. After the conditions for an expanding protein accessible surface area were established for T4 lysozyme and barnase wild-type proteins, MD simulations were carried out under the same conditions using the crystal structures of several mutant proteins. The computed thermal expansion of the accessible surface area of mutant proteins was found to be strongly correlated with their experimentally measured stabilities. A similar, albeit weaker, correlation was observed for model mutant proteins. This opens the possibility of obtaining stability information directly from protein structure.

Protein-protein recognition: an experimental and computational study of the R89K mutation in Raf and its effect on Ras binding

Binding of the protein Raf to the active form of Ras promotes activation of the MAP kinase signaling pathway, triggering cell growth and differentiation. Raf/Arg89 in the center of the binding interface plays an important role determining Ras-Raf binding affinity. We have investigated experimentally and computationally the Raf-R89K mutation, which abolishes signaling in vivo. The binding to [gamma-35S]GTP-Ras of a fusion protein between the Raf-binding domain (RBD) of Raf and GST was reduced at least 175-fold by the mutation, corresponding to a standard binding free energy decrease of at least 3.0 kcal/mol. To compute this free energy and obtain insights into the microscopic interactions favoring binding, we performed alchemical simulations of the RBD, both complexed to Ras and free in solution, in which residue 89 is gradually mutated from Arg into Lys. The simulations give a standard binding free energy decrease of 2.9+/-1.9 kcal/mol, in agreement with experiment. The use of numerous runs with three different force fields allows insights into the sources of uncertainty in the free energy and its components. The binding decreases partly because of a 7 kcal/mol higher cost to desolvate Lys upon binding, compared to Arg, due to better solvent interactions with the more concentrated Lys charge in the unbound state. This effect is expected to be general, contributing to the lower propensity of Lys to participate in protein-protein interfaces. Large contributions to the free energy change also arise from electrostatic interactions with groups up to 8 A away, namely residues 37-41 in the conserved effector domain of Ras (including 4 kcal/mol from Ser39 which loses a bifurcated hydrogen bond to Arg89), the conserved Lys84 and Lys87 of Raf, and 2-3 specific water molecules. This analysis will provide insights into the large experimental database of Ras-Raf mutations.

Specific amino acid recognition by aspartyl-tRNA synthetase studied by free energy simulations

Specific amino acid binding by aminoacyl-tRNA synthetases is necessary for correct translation of the genetic code. To obtain insight into the origin of the specificity, the binding to aspartyl-tRNA synthetase (AspRS) of the negatively charged substrate aspartic acid and the neutral analogue asparagine are compared by use of molecular dynamics and free energy simulations. Simulations of the Asn-AspRS complex show that although Asn cannot bind in the same position as Asp, several possible positions exist 1.5 to 2 A away from the Asp site. The binding free energy of Asn in three of these positions was compared to that of Asp through alchemical free energy simulations, in which Asp is gradually mutated ito Asn in the complex with the enzyme. To correctly account for the electrostatic interactions in the system (including bulk solvent), a recently developed hybrid approach was used, in which the region of the mutation site is treated microscopically, whereas distant protein and solvent are treated by continuum electrostatics. Seven free energy simulations were performed in the protein and two in solution. The various Asn positions and orientations sampled at the Asn endpoints of the protein simulations yielded very similar free energy differences. The calculated Asp-->Asn free energy change is 79.8(+/-1.5) kcal/mol in solution and 95.1(+/-2.8) kcal/mol in the complex with the protein. Thus, the substrate Asp is predicted to bind much more strongly than Asn, with a binding free energy difference of 15.3 kcal/mol. This implies that erroneous binding of Asn by AspRS is highly improbable, and cannot account for any errors in the translation of the genetic code. Almost all of the protein contributions to the Asp versus Asn binding free energy difference arise from an arginine and a lysine residue that hydrogen bond to the substrate carboxylate group and an Asp and a Glu that hydrogen bond to these; all four amino acid residues are completely conserved in AspRSs. The protein effectively "solvates" the Asp side-chain more strongly than water does. The simulations are analyzed to determine the interactions that Asn is able to make in the binding pocket, and which sequence differences between AspRS and the highly homologous AsnRS are important for modifying the amino acid specificity. A double or triple mutation of AspRS that could make it specific for Asn is proposed, and supported by preliminary simulations of a mutant complex.

The nature of trypsin-pancreatic trypsin inhibitor binding: free energy calculation of Tyr39-->Phe39 mutation in trypsin

The main goal of this work is the detailed study of the binding interactions in the trypsin-pancreatic trypsin inhibitor (PTI) complex and, here, we present how meaningful the Tyr39-Ile19 interaction is to the stability of that particular complex using free energy methods. This knowledge should be very important in the design of new inhibitors for trypsin and enzymes homologous to it. In particular, it could help to decide whether it is possible to produce selective inhibitors for these enzymes by appropriate mutations of residues in the contact region of PTI.

Quaternary structure sensitive tyrosine interactions in hemoglobin: a UV resonance Raman study of the double mutant rHb (beta99Asp-->Asn, alpha42Tyr-->Asp)

Two interactions involving tyrosines have been implicated in the communication pathway that links ligand binding to quaternary state changes in hemoglobin. Tyr alpha(1)42 stabilizes the alpha1beta2 T state interface through the formation of a hydrogen bond to Asp beta(2)99. The side chains of the penultimate Tyr residues (alpha140 and beta145) occupy the pockets made by helicies F and H in the deoxy form with the phenolic hydroxyl hydrogen bonded to the carbonyl group of Val FG5. Early crystallographic studies indicated that in the R form the penultimate Tyr is expelled out of the pocket, thus eliminating the hydrogen bond. This hydrogen bond has been considered to play an important role in maintaining the low-oxygen-affinity state (T state) in deoxy HbA, but a later higher resolution crystallographic study (Shannon, 1983) failed to reveal such movement of this Tyr during the R --> T transition. Nevertheless, conversion of this Tyr to Phe increases oxygen affinity considerably, suggesting that hydrogen bonding is involved in oxygen affinity modulation. Earlier ultraviolet resonance Raman results reported by Spiro and co-workers [Rodgers et al. (1992) J. Am. Chem. Soc. 114, 3697-3709] were used to conclude that the significant quaternary structure dependent changes observed in tyrosine Raman bands are due to the formation of the T state hydrogen bond with Tyr alpha42 acting as a proton acceptor rather than being the anticipated proton donor, as would be expected if Asp beta99 were ionized. This surprising result rests on the assumption that changes in the environment of Tyr alpha42 are the overwhelming contributor to the R - T UV Raman difference spectrum. In this study, a cooperative double mutant lacking Tyr alpha42, [rHb (Asp beta99 --> Asn, Tyr alpha42 --> Asp)], is used to determine the relative contributions of Tyr alpha42 and the penultimate tyrosines to the R - T UV resonance Raman difference spectrum. The results both directly support the claim that Tyr alpha42 is the proton acceptor in the T state and expose the potential role of the penultimate tyrosines in coupling the quaternary state to the ligand reactivity.

Highly potent, selective, and low cost bis-tetrahydroaminacrine inhibitors of acetylcholinesterase. Steps toward novel drugs for treating Alzheimer's disease

We report highly potent, selective, and low cost bifunctional acetylcholinesterase (AChE) inhibitors developed by our two-step prototype optimization strategy utilizing computer modeling of ligand docking with target proteins: 1) identify low affinity sites normally missed by x-ray crystallography; and 2) design bifunctional analogs capable of simultaneous binding at the computer-determined low affinity site and the x-ray-identified high affinity site. Applying this strategy to 9-amino-1,2,3,4-tetrahydroacridine (THA), a drug for Alzheimer's disease, we obtained alkylene linked bis-THA analogs. These analogs were up to 10,000-fold more selective and 1,000-fold more potent than THA in inhibiting rat AChE and yet required one simple reaction to synthesize. Additionally, alkylene linked benzyl-THA analogs were developed to examine the specificity of the docking-derived low affinity THA peripheral site in AChE. The present work and our previous computational studies strongly suggest that a low affinity THA peripheral site exists in AChE. This peripheral site provides a structural basis for design of improved cholinesterase ligands for treating Alzheimer's disease and for other health-related purposes.

Free energy simulations of axial contacts in sickle-cell hemoglobin

Molecular dynamics simulations have been used to investigate the thermodynamic stability of axial contacts in sickle-cell hemoglobin (HbS). Free energy changes were evaluated for the point mutation beta 121 Glu --> Gln in the axial contact region of HbS crystals. The calculations predict a free energy change of-3.6 kcal/mol per contact for the mutation, which is in qualitative agreement with experimental observations of aggravated sickling found in the double mutant Hb D Los Angeles (beta 6 Glu --> Val. beta 121 Glu --> Gln) relative to HbS (beta 6 Glu --> Val). The beta 121 Glu is sequestered in a salt link with beta 17 Lys located on the same polypeptide chain, making the Glu interactions with its surroundings similar in aggregates and individual hemoglobins. Due to this cancellation of the large electrostatic Glu contributions, the weak nonspecific interactions between the Gln and the neighboring polypeptide chain are the main contributing factor to the enhanced aggregation of Hb D Los Angeles relative to HbS. Together with the previous study of the lateral contact [K. Kuczera et al. (1990) Proceedings of the National Academy of Science USA, Vol. 87, pp, 8481-8485], the present results provide a more complete picture of the forces driving the sickling aggregation. A comparison of different treatments of internal flexibility in free energy simulations and analysis of rate of convergence of the different calculated properties has also been performed.

Free energy perturbation techniques applied to subtilisin BPN' stability

The inability to predict the effect of specific mutations on protein stability has been an area of concern to researchers in the field of protein engineering. Small stabilization free energies (5 to 15 kcal/mol) distinguish the native and the denatured states of a protein, making the rational design of protein stability a difficult challenge. Free Energy Perturbation Technique (FEPT) appears to be a method that will be important for protein engineering to meet this challenge. Not only is it a method to evaluate potential sites for mutation prior to synthesis, it identifies important atomic contributions that are responsible for the free energy changes of interest. Accuracy and speed are the principal limitations of the technique, but the powerful combination of structure, energy, dynamics and solvent make the investment of time and effort very attractive. Our examples illustrate both the power and limitations of FEPT. Using the program CHARMm, FEPT has been applied to the well known stabilizing mutations--asparagine to Serine--at residue 218 in subtilisin BPN'. In analyzing the atomic contributions that result in the increase in stability, two mutations at residue 203 were chosen to test the predictive power of FEPT. Sometimes extraordinary measures must be undertaken to sample sufficient conformational space to achieve accurate FEPT results. However we believe the method will be invaluable in the development of rules for designing a more stable subtilisin BPN'.

FT-IR difference spectroscopy of hemoglobins A and Kempsey: evidence that a key quaternary interaction induces protonation of Asp beta 99

Fourier transform infrared difference spectra are reported for the CO adduct of human hemoglobin versus deoxyHb, in H2O and D2O. In addition to the well-known CO stretching and S-H(D) stretching bands, the difference spectra reveal numerous bands in the 1200-1700 cm-1 region, a number of which are assigned. Several amide modes are identified via their frequencies and D2O sensitivities. Bands arising from histidine protonation have also been found via comparison of the difference spectra at different pH(D) values, with the aid of aqueous histidine spectra. Of particular interest is the observation of a negative band at 1697 cm-1, which is assigned to the C = O stretch of carboxylic acid. This carboxylic acid is tentatively identified as the side chain of Asp beta 99, because it is missing in the difference spectrum of Hb Kempsey, a mutant in which Asp beta 99 is replaced by Asn. Asp beta 99 forms a critical contact with Tyr alpha 42 across the alpha 1 beta 2 interface in deoxyHb, which is broken upon ligation. Protonation of Asp beta 99 in deoxyHb is consistent with UV resonance Raman evidence that Tyr alpha 42 is the acceptor rather than the donor of the quaternary H-bond.

Ion transport in the gramicidin channel: molecular dynamics study of single and double occupancy

The structural and thermodynamic factors responsible for the singly and doubly occupied saturation states of the gramicidin channel are investigated with molecular dynamics simulations and free energy perturbation methods. The relative free energy of binding of all of the five common cations Li+, Na+, K+, Rb+, and Cs+ is calculated in the singly and doubly occupied channel and in bulk water. The atomic system, which includes the gramicidin channel, a model membrane made of neutral Lennard-Jones particles and 190 explicit water molecules to form the bulk region, is similar to the one used in previous work to calculate the free energy profile of a Na+ ion along the axis of the channel. In all of the calculations, the ions are positioned in the main binding sites located near the entrances of the channel. The calculations reveal that the doubly occupied state is relatively more favorable for the larger ions. Thermodynamic decomposition is used to show that the origin of the trend observed in the calculations is due to the loss of favorable interactions between the ion and the single file water molecules inside the channel. Small ions are better solvated by the internal water molecules in the singly occupied state than in the doubly occupied state; bigger ions are solvated almost as well in both occupation states. Water-channel interactions play a role in the channel response. The observed trends are related to general thermodynamical properties of electrolyte solutions.

How much is a stabilizing bond worth?

It is commonly supposed that the contribution of a bond to protein or nucleic acid stability is equal to the in situ stability of the bond itself. This is not true for the noncovalent bonds that stabilize molecular folding. In general, a bonding interaction contributes a free energy increment to protein or nucleic acid stability that is larger, an enthalpy increment that is smaller, and entropy and heat capacity increments that are more positive than the corresponding bond parameter.

Restoring allosterism with compensatory mutations in hemoglobin

Abnormal human hemoglobins (HBs) with amino acid substitutions in the alpha 1 beta 2 interface have very high oxygen affinity and greatly reduced cooperativity in O2 binding compared to normal human Hb. In such abnormal Hbs with mutations at position beta 99, the intersubunit hydrogen bonds between Asp-beta 99 and Tyr-alpha 42 and between Asp-beta 99 and Asn-alpha 97 are broken, thus destabilizing the deoxyquaternary structure of these Hbs. A molecular dynamics method has been used to design compensatory amino acid substitutions in these Hbs that can restore their allosteric properties. We have designed a compensatory mutation in a naturally occurring mutant Hb, Hb Kempsey (Asp-beta 99-->Asn), and have produced it using our Escherichia coli expression plasmid pHE2. We have determined the O2 binding properties of this recombinant double mutant Hb, Hb(Asp-beta 99-->Asn and Tyr-alpha 42-->Asp) and have used 1H NMR spectroscopy to investigate the tertiary structures around the heme groups and the quaternary structure in the alpha 1 beta 2 subunit interface. Our results clearly show that the Tyr-alpha 42-->Asp replacement can substantially compensate for the functional defect of Hb Kempsey caused by the Asp-beta 99-->Asn substitution. The structural and functional information derived from this recombinant Hb provides insights into the structural basis of allosterism and the design of compensatory amino acid substitutions to restore the functional properties of other abnormal HBs associated with hemoglobinopathies.

Free energy simulations: the meaning of the individual contributions from a component analysis

A theoretical analysis is made of the decomposition into contributions from individual interactions of the free energy calculated by thermodynamic integration. It is demonstrated that such a decomposition, often referred to as "component analysis," is meaningful, even though it is a function of the integration path. Moreover, it is shown that the path dependence can be used to determine the relation of the contribution of a given interaction to the state of the system. To illustrate these conclusions, a simple transformation (Cl- to Br- in aqueous solution) is analyzed by use of the Reference Interaction Site Model-Hypernetted Chain Closure integral equation approach; it avoids the calculational difficulties of macromolecular simulation while retaining their conceptual complexity. The difference in the solvation free energy between chloride and bromide is calculated, and the contributions of the Lennard-Jones and electrostatic terms in the potential function are analyzed by the use of suitably chosen integration paths. The model is also used to examine the path dependence of individual contributions to the double free energy differences (delta delta G or delta delta A) that are often employed in free energy simulations of biological systems. The alchemical path, as contrasted with the experimental path, is shown to be appropriate for interpreting the effects of mutations on ligand binding and protein stability. The formulation is used to obtain a better understanding of the success of the Poisson-Boltzmann continuum approach for determining the solvation properties of polar and ionic systems.

Helix-capping interaction in lambda Cro protein: a free energy simulation analysis

The stability mutant Tyr-26-->Asp was studied in the Cro protein from bacteriophage lambda using free energy molecular dynamics simulations. The mutant was calculated to be more stable than the wild type by 3.0 +/- 1.7 kcal/mol/monomer, in reasonable agreement with experiment (1.4 kcal/mol/monomer). Moreover, the aspartic acid in the mutant was found to form a capping interaction with the amino terminus of the third alpha-helix of Cro. The simulations were analyzed to understand better the source of the stability of this helix-capping interaction and to examine the results in light of previous explanations of stabilizing helix caps--namely, a model of local unsatisfied hydrogen bonds at the helix termini and the helix macrodipole model. Analysis of the simulations shows that the stabilizing effect of this charged helical cap is due both to favorable hydrogen bonds with backbone NH groups at the helix terminus and to favorable electrostatic interactions (but not hydrogen bonds) with their carbonyls (effectively the next row of local dipoles in the helix). However, electrostatic interactions are weak or negligible with backbone dipolar groups in the helix further away from the terminus. Moreover, the importance of other local electrostatic interactions with polar side chains near the helix terminus, which are neglected in most treatments of this effect, are shown to be important. Thus, the results support a model that is intermediate between the two previous explanations: both unsatisfied hydrogen bonds at the helix terminus and other, local preoriented dipolar groups stabilize the helix cap. These findings suggest that similar interactions with preoriented dipolar groups may be important for cooperativity in other charge-dipole interactions and may be employed to advantage for molecular design.

Synthesis of a self-contained concept of the molecular mechanism of energy interconversion by H(+)-transporting ATP synthase

The original aim of the review has been to probe into the validity of the paradigm on the high energy-carrier function of ATP. It seemed to be called into question on the basis of findings with H(+)-transporting ATP synthase suggesting the formation of ATP from ADP and Pi without energy input. Thus, ATP appeared as a low-energy compound. Starting from the current, rich knowledge of the molecular structure and the inviting thinking on the mechanism of H(+)-transporting ATP synthase, we have endeavoured to freshly interpret and integrate the pertinent observations in the light of the comprehensively derived model of the molecular mechanism of energy interconversion by Na+/K(+)-transporting ATPase. In this way, we have uncovered the common mechanistic elements of the two energy-interconverting enzymes. The emerging purpose of the present paper has been the 'synthesis' of a self-contained concept of the molecular mechanism of the interconversion of electrochemical and chemical Gibbs energies by H(+)-transporting ATP synthase. The outcome is reflected in the following tentative evaluations. 1. In ATP hydrolysis, the great Gibbs energy change which is observed in solution, is largely conserved by the F1 sector of ATP synthase as mechanical Gibbs energy in the enzyme's protein fabric, so that it can be utilized in the resynthesis of ATP from enzyme-bound ADP and Pi. The plainly measured low Gibbs energy change results from large compensating enthalpy and entropy changes that reflect the underlying changes in protein conformation. 2. In stoichiometric ATP synthesis by F1 sector from ADP and Pi bound to the catalytic centre, their intrinsic binding energy brings about a loss of peptide chain entropy that makes possible an entropy-driven ATP formation. 3. The driving force for ATP synthesis cannot be the high Gibbs energy change on binding of product ATP; the tight ATP-enzyme complex rather is a low Gibbs energy intermediate from which escape is difficult. 4. The catalytic centre exists either in an open state unable to firmly bind the substrate-product couple, or in a closed state protecting formed ATP from facile hydrolysis by ambient water. 5. The cleft closure, induced by binding of Pi and ADP or ATP, does not necessarily need external energy supply, because the cleft closure proceeds from rigid domain rotations which can occur rather spontaneously. In further analogy to adenylate kinase, the driving force of this domain movement presumably comes from the electrostatic interactions between phosphate moieties and arginine side chains in the catalytic centre.(ABSTRACT TRUNCATED AT 400 WORDS)

Molecular recognition in proteins. Simulation analysis of substrate binding by a tyrosyl-tRNA synthetase mutant

Alchemical molecular dynamics simulations are performed to determine the difference in the free energy of binding of the tyrosine substrate between the wild type of tyrosyl-tRNA synthetase (TyrRS) from Bacillus stearothermophilus and the mutant Tyr169-->Phe. The results are of general interest because the Tyr169 hydroxyl group interacts with the ammonium group of the substrate in a manner corresponding to that found in other amino acid binding proteins (e.g. the Asp receptor of the chemotactic bacterium Salmonella typhimurium and class I major histocompatibility complex molecules). The calculated free-energy change due to the Tyr169-->Phe mutation is 3.4 kcal/mol (the statistical error is +/- 0.5 kcal/mol) in satisfactory agreement with the experimental value of 3(+/- 0.5) kcal/mol. By use of thermodynamic integration, the contribution of the different terms to the free energy change are estimated. The path dependence of such a decomposition is discussed and it is suggested that the alchemical choice is of primary interest for understanding the interactions involved. There are large protein contributions to the alchemical free energy difference of the bound and free enzyme that cancel in the overall result. Due to this cancellation, the essential interactions contributing to the free-energy change are those between the OH group of Tyr169 and water in the free enzyme and those between the OH group of Tyr169 and the ammonium group of the substrate in the bound system. The results thus support simple models based on a balance of hydrogen bonding interactions.

Do salt bridges stabilize proteins? A continuum electrostatic analysis

The electrostatic contribution to the free energy of folding was calculated for 21 salt bridges in 9 protein X-ray crystal structures using a continuum electrostatic approach with the DELPHI computer-program package. The majority (17) were found to be electrostatically destabilizing; the average free energy change, which is analogous to mutation of salt bridging side chains to hydrophobic isosteres, was calculated to be 3.5 kcal/mol. This is fundamentally different from stability measurements using pKa shifts, which effectively measure the strength of a salt bridge relative to 1 or more charged hydrogen bonds. The calculated effect was due to a large, unfavorable desolvation contribution that was not fully compensated by favorable interactions within the salt bridge and between salt-bridge partners and other polar and charged groups in the folded protein. Some of the salt bridges were studied in further detail to determine the effect of the choice of values for atomic radii, internal protein dielectric constant, and ionic strength used in the calculations. Increased ionic strength resulted in little or no change in calculated stability for 3 of 4 salt bridges over a range of 0.1-0.9 M. The results suggest that mutation of salt bridges, particularly those that are buried, to "hydrophobic bridges" (that pack at least as well as wild type) can result in proteins with increased stability. Due to the large penalty for burying uncompensated ionizable groups, salt bridges could help to limit the number of low free energy conformations of a molecule or complex and thus play a role in determining specificity (i.e., the uniqueness of a protein fold or protein-ligand binding geometry).

Application of molecular dynamics and free energy perturbation methods to metalloporphyrin-ligand systems II: CO and dioxygen binding to myoglobin

The protein contribution to the relative binding affinity of the ligands CO and O2 toward myoglobin (Mb) has been simulated using free energy perturbation calculations. The tautomers of the His E7 residue are different for the oxymyoglobin (MbO2) and carboxymyoglobin (MbCO) systems. This was modeled by performing two-step calculations that mutate the ligand and mutate the His E7 tautomers in separate steps. Differences in hydrogen bonding to the O2 and CO ligands were incorporated into the model. The O2 complex was calculated to be 2-3 kcal/mol more stable than the corresponding CO complex when compared to the same difference in an isolated heme control. This value agrees well with the experimental value of 2.0 kcal/mol. In qualitative agreement with experiments, the Fe-C-O bond is found to be bent (theta = 159.8 degrees) with a small tilt (theta = 6.2 degrees). The contributions made by each of the 29 residues--within the 9.0-A radius of the iron atom--to the free energy difference are separated into van der Waals and electrostatic contributions; the latter contributions are dominant. Aside from the proximal histidine and the heme group, the residues having the largest difference in free energy in mutating MbO2-->MbCO are His E7, Phe CD1, Phe CD4, Val E11, and Thr E10.

Single-site modifications of half-ligated hemoglobin reveal autonomous dimer cooperativity within a quaternary T tetramer

The patterns of energetic response elicited by single-site hemoglobin mutations and chemical modifications have been determined in order to probe the dimer-dimer interface of the half-ligated tetramer (species [21]) that was previously shown to behave as allosterically distinct from both the unligated and fully ligated molecules. In this study the free energies of quaternary assembly (dimers to tetramers) were determined for a series of 24 tetrameric species in which one dimeric half-molecule is ligated (cyanomet hemes) while the adjacent alpha beta dimer is unligated and contains a single amino acid modification. Assembly energies have also been determined for tetramers bearing the same amino acid modifications but where the hemesites were completely vacant and additionally where they were fully occupied. A total of 72 molecular species were thus characterized. It was found that mutationally induced perturbations to the free energy of quaternary assembly were identical for the half-ligated tetramers and the unligated tetramers over the entire spatial distribution of altered sites, but exhibited a radically different pattern from that of the fully ligated molecules. These results indicate that the dimer-dimer interface of the half-ligated tetramer (species [21]) has the same quaternary structure as that of the unligated molecule, i.e., "quaternary T." This quaternary structure assignment of species [21] strongly supports the operation of a Symmetry Rule which translates changes in hemesite ligation into six T-->R quaternary switchpoints. Analysis of the observed Symmetry Rule behavior in relation to the measured distribution of cooperative free energies for the partially ligated species reveals significant cooperativity between alpha and beta subunits of the dimeric half-tetramer within quaternary T. The mutational results indicate that these interactions are not "paid for" by breaking or making noncovalent bonds at the dimer-dimer interface (alpha 1 beta 2). They arise from structural and energetic changes that are "internal" to the ligated dimer even though its association with the unligated dimer is required for the cooperativity to occur. Free energy of "tertiary constraint" is thus generated by the first binding step and is propagated to the second hemesite while the dimer-dimer interface alpha 1 beta 2 serves as a constraint. The "sequential" cooperativity that occurs within the half-molecule is thus preconditioned by the constraint of a quaternary T interface; release of this constraint by dissociation produces only noncooperative dimers.(ABSTRACT TRUNCATED AT 400 WORDS)

Free energy component analysis: application to the "Z-phobicity" of A-T base pairs

We have carried out molecular dynamics/free energy perturbation calculations on the double helical hexamer d(CGCGCG)2 in both B and Z forms. The third C.G base pair was "mutated" to T-A in both B and Z-DNA. It is known experimentally that replacement of a C.G with a T-A base pair in an alternating CG sequence raises the energy of the Z form relative to the B form by approximately 1 kcal mole-1. We have carried out free energy component calculations to assess the reason for the "Z-phobicity" of T-A base pairs. There are two major contributions. The primary contribution is from the intra-base pair interactions of the mutated base pair itself which disfavor T-A relative to C.G in the Z form by congruent to 1.4 kcal mole-1. A secondary contribution of 0.4 kcal mole-1 arises because the two cytosines on the strand where G is mutated to A disfavor T-A relative to C.G in the Z form by 1.9 kcal mole-1, while the guanines flanking the C on the complementary strand stabilize the T-A base pair relative to the C.G in the Z form by 1.5 kcal mole-1. The effect of the phosphates, non-neighboring nucleotides and intramolecular energies of the base pair being mutated are all small and come close to canceling each other, leading to a net calculated free energy for T-A Z-phobicity of 1.7 kcal mole-1.

What determines the strength of noncovalent association of ligands to proteins in aqueous solution?

Free energy perturbation methods using molecular dynamics have been used to calculate the absolute free energy of association of two ligand-protein complexes. The calculations reproduce the significantly more negative free energy of association of biotin to streptavidin, compared to N-L-acetyltryptophanamide/alpha-chymotrypsin. This difference in free energy of association is due to van der Waals/dispersion effects in the nearly ideally performed cavity that streptavidin presents to biotin, which involves four tryptophan residues.

An approximate but efficient method to calculate free energy trends by computer simulation: application to dihydrofolate reductase-inhibitor complexes

Derivatives of free energy differences have been calculated by molecular dynamics techniques. The systems under study were ternary complexes of Trimethoprim (TMP) with dihydrofolate reductases of E. coli and chicken liver, containing the cofactor NADPH. Derivatives are taken with respect to modification of TMP, with emphasis on altering the 3-, 4- and 5-substituents of the phenyl ring. A linear approximation allows the encompassing of a whole set of modifications in a single simulation, as opposed to a full perturbation calculation, which requires a separate simulation for each modification. In the case considered here, the proposed technique requires a factor of 1000 less computing effort than a full free energy perturbation calculation. For the linear approximation to yield a significant result, one has to find ways of choosing the perturbation evolution, such that the initial trend mirrors the full calculation. The generation of new atoms requires a careful treatment of the singular terms in the non-bonded interaction. The result can be represented by maps of the changed molecule, which indicate whether complex formation is favoured under movement of partial charges and change in atom polarizabilities. Comparison with experimental measurements of inhibition constants reveals fair agreement in the range of values covered. However, detailed comparison fails to show a significant correlation. Possible reasons for the most pronounced deviations are given.

Crystal structure of CTP-ligated T state aspartate transcarbamoylase at 2.5 A resolution: implications for ATCase mutants and the mechanism of negative cooperativity

The X-ray crystal structure of CTP-ligated T state aspartate transcarbamoylase has been refined to an R factor of 0.182 at 2.5 A resolution using the computer program X-PLOR. The structure contains 81 sites for solvent and has rms deviations from ideality in bond lengths and bond angles of 0.018 A and 3.722 degrees, respectively. The cytosine base of CTP interacts with the main chain carbonyl oxygens of rTyr-89 and rIle-12, the main chain NH of rIle-12, and the amino group of rLys-60. The ribose hydroxyls form polar contacts with the amino group of rLys-60, a carboxylate oxygen of rAsp-19, and the main chain carbonyl oxygen of rVal-9. The phosphate oxygens of CTP interact with the amino group of rLys-94, the hydroxyl of rThr-82, and an imidazole nitrogen of rHis-20. Recent mutagenesis experiments evaluated in parallel with the structure reported here indicate that alterations in the hydrogen bonding environment of the side chain of rAsn-111 may be responsible for the homotropic behavior of the pAR5 mutant of ATCase. The location of the first seven residues of the regulatory chain has been identified for the first time in a refined ATCase crystal structure, and the proximity of this portion of the regulatory chain to the allosteric site suggests a potential role for these residues in nucleotide binding to the enzyme. Finally, a series of amino acid side chain rearrangements leading from the R1 CTP allosteric to the R6 CTP allosteric site has been identified which may constitute the molecular mechanism of distinct CTP binding sites on ATCase.

Mutagenic dissection of hemoglobin cooperativity: effects of amino acid alteration on subunit assembly of oxy and deoxy tetramers

Free energies of oxygen-linked subunit assembly and cooperative interaction have been determined for 34 molecular species of human hemoglobin, which differ by amino acid alterations as a result of mutation or chemical modification at specific sites. These studies required the development of extensions to our earlier methodology. In combination with previous results they comprise a data base of 60 hemoglobin species, characterized under the same conditions. The data base was analyzed in terms of the five following issues. (1) Range and sensitivity to site modifications. Deoxy tetramers showed greater average energetic response to structural modifications than the oxy species, but the ranges are similar for the two ligation forms. (2) Structural localization of cooperative free energy. Difference free energies of dimer-tetramer assembly (oxy minus deoxy) yielded delta Gc for each hemoglobin, i.e., the free energy used for modulation of oxygen affinity over all four binding steps. A structure-energy map constructed from these results shows that the alpha 1 beta 2 interface is a unique structural location of the noncovalent bonding interactions that are energetically coupled to cooperativity. (3) Relationship of cooperativity to intrinsic binding. Oxygen binding energetics for dissociated dimers of mutants strongly indicates that cooperativity and intrinsic binding are completely decoupled by tetramer to dimer dissociation. (4) Additivity, site-site coupling and adventitious perturbations. All these are exhibited by individual-site modifications of this study. Large nonadditivity may be correlated with global (quaternary) structure change. (5) Residue position vs. chemical nature. Functional response is solely dictated by structural location for a subset of the sites, but varies with side-chain type at other sites. The current data base provides a unique framework for further analyses and modeling of fundamental issues in the structural chemistry of proteins and allosteric mechanisms.

A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations

A Monte Carlo quantum mechanical-molecular mechanical (QM-MM) simulation method was used to determine the contributions of the solvent polarization effect to the total interaction energies between solute and solvent for amino acid side chains and nucleotide bases in aqueous solution. In the present AM1-TIP3P approach, the solute molecule is characterized by valence electrons and nucleus cores with Hartree-Fock theory incorporating explicit solvent effects into the total Hamiltonian, while the solvent is approximated by the three-point charge TIP3P model. The polarization energy contributes 10 to 20 percent of the total electrostatic energy in these systems. The performance of the hybrid AM1-TIP3P model was further validated by consideration of bimolecular complexes with water and by computation of the free energies of solvation of organic molecules using statistical perturbation theory. Excellent agreement with ab initio 6-31G(d) results and experimental solvation free energies was obtained.

High-resolution X-ray study of deoxyhemoglobin Rothschild 37 beta Trp----Arg: a mutation that creates an intersubunit chloride-binding site

The mutation site in hemoglobin Rothschild (37 beta Trp----Arg) is located in the "hinge region" of the alpha 1 beta 2 interface, a region that is critical for normal hemoglobin function. The mutation results in greatly reduced cooperativity and an oxygen affinity similar to that of hemoglobin A [Gacon, G., Belkhodja, O., Wajcman, H., & Labie, D. (1977) FEBS Lett. 82, 243-246]. Crystal were grown under "low-salt" conditions [100 mM Cl- in 10 mM phosphate buffer at pH 7.0 with poly(ethylene glycol) as a precipitating agent]. The crystal structure of deoxyhemoglobin Rothschild and the isomorphous crystal structure of deoxyhemoglobin A were refined at resolutions of 2.0 and 1.9 A, respectively. The mutation-induced structural changes were partitioned into components of (1) tetramer rotation, (2) quaternary structure rearrangement, and (3) deformations of tertiary structure. The quaternary change involves a 1 degree rotation of the alpha subunit about the "switch region" of the alpha 1 beta 2 interface. The tertiary changes are confined to residues at the alpha 1 beta 2 interface, with the largest shifts (approximately 0.4 A) located across the interface from the mutation site at the alpha subunit FG corner-G helix boundary. Most surprising was the identification of a mutation-generated anion-binding site in the alpha 1 beta 2 interface. Chloride binds at this site as a counterion for Arg 37 beta. The requirement of a counterion implies that the solution properties of hemoglobin Rothschild, in particular the dimer-tetramer equilibrium, should be very dependent upon the concentration and type of anions present.

Evaluating the effects of a single amino acid substitution on both the native and denatured states of a protein

For proteins that contain a disulfide bond, stability is linked thermodynamically to thiol-disulfide exchange. We use this relationship to obtain unfolding free energies for both the reduced and oxidized forms of Escherichia coli thioredoxin from measurements of the effective concentrations of protein thiols. We then evaluate the effect of an amino acid substitution on disulfide bond formation in both the native and denatured states of the protein. Although the Pro-34----Ser substitution in thioredoxin results in a decrease of the effective concentration of protein thiols in the native state, the effective concentration increases in the denatured state. The net effect of the amino acid substitution is to increase the stability of reduced thioredoxin by approximately 2.4 kcal/mol, whereas the stability of the oxidized protein remains the same. By assuming a two-state unfolding equilibrium and a mutation free energy of -7.7 kcal/mol for the Pro-34----Ser substitution in the reduced, urea-unfolded state (based on estimates of solvation and entropic changes), we obtained relative free energies for the native and denatured states of the mutant and wild-type proteins, in both the reduced and oxidized forms.

Contribution of the hydrophobic effect to protein stability: analysis based on simulations of the Ile-96----Ala mutation in barnase

Molecular dynamics simulations have been used to compute the difference in the unfolding free energy between wild-type barnase and the mutant in which Ile-96 is replaced by alanine. The simulations yield results (-3.42 and -5.21 kcal/mol) that compare favorably with experimental values (-3.3 and -4.0 kcal/mol). The major contributions to the free energy difference arise from bonding terms involving degrees of freedom of the mutated side chain and from nonbonded interactions of that side chain with its environment in the folded protein. By comparison with simulations of an extended peptide in the absence of solvent, used as a reference state, hydration effects are shown to play a minor role in the overall free energy balance for the Ile----Ala transformation. The implications of these results for our understanding of the hydrophobic effect and its contribution to protein stability are discussed.

Relative differences in the binding free energies of human immunodeficiency virus 1 protease inhibitors: a thermodynamic cycle-perturbation approach

Peptidomimetic inhibitors of the human immunodeficiency virus 1 protease show considerable promise for treatment of AIDS. We have, therefore, been seeking computer-assisted drug design methods to aid in the systematic design of such inhibitors from a lead compound. Here we report thermodynamic cycle-perturbation calculations (using molecular dynamics simulations) to compute the relative difference in free energy of binding that results when one entire residue (valine) is deleted from one such inhibitor. In particular, we studied the "alchemic" mutation of the inhibitor Ac-Ser-Leu-Asn-(Phe-Hea-Pro)-Ile-Val-OMe (S1) to Ac-Ser-Leu-Asn-(Phe-Hea-Pro)-Ile-OMe (S2), where Hea is hydroxyethylamine, in two different (R and S) diastereomeric configurations of the hydroxyethylene group. The calculated (averaged for R and S) difference in binding free energy [3.3 +/- 1.1 kcal/mol (mean +/- SD); 1 cal = 4.184 J] is in good agreement with the experimental value of 3.8 +/- 1.3 kcal/mol, obtained from the measured Ki values for an equilibrium mixture of R and S configurations. Precise testing of our predictions will be possible when binding data become available for the two disastereomers separately. The observed binding preference for S1 is explained by the stronger ligand-protein interaction, which dominates an opposing contribution arising from the large desolvation penalty of S1 relative to S2. This calculation suggests that the thermodynamic cycle-perturbation approach can be useful even when a relatively large change in the ligand is simulated and supports the use of the thermodynamic cycle-perturbation algorithm for screening proposed derivatives of a lead inhibitor/drug prior to their synthesis.