Reconciling the magnitude of the microscopic and macroscopic hydrophobic effects.

The magnitude of the hydrophobic effect, as measured from the surface area dependence of the solubilities of hydrocarbons in water, is generally thought to be about 25 calories per mole per square angstrom (cal mol-1 A-2). However, the surface tension at a hydrocarbon-water interface, which is a "macroscopic" measure of the hydrophobic effect, is approximately 72 cal mol-1 A-2. In an attempt to reconcile these values, alkane solubility data have been reevaluated to account for solute-solvent size differences, leading to a revised "microscopic" hydrophobic effect of 47 cal mol-1 A-2. This value, when used in a simple geometric model for the curvature dependence of the hydrophobic effect, predicts a macroscopic alkane-water surface tension that is close to the macroscopic value.

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.

Entropy in protein folding and in protein-protein interactions.

The reduction of conformational entropy is a major barrier that has to be overcome in protein folding and binding. Changes in solvent entropy are also a major factor. Recent advances include clarification of the fundamental issues concerning the separation of entropy into components, the treatment of association entropy in binding, and the role of size and shape effects in solvation entropy. Advances in the application of entropy calculations include an emerging consensus for estimates of backbone and sidechain entropy loss in protein folding via use of numerically intensive methods for sampling, and use of the expanding protein-structure database.

Salt effects on nucleic acids.

Salt-dependent electrostatic effects are a major factor in determining the stability, structure, reactivity, and binding behavior of nucleic acids. Increasingly detailed theoretical methods, especially those based on Monte Carlo and Poisson-Boltzmann methodologies, combined with powerful computational algorithms are being used to examine how the shape, charge distribution and dielectric properties of the molecules affect the ion distribution in the surrounding aqueous solution, and how they play a role in ligand binding, structural transitions and other biologically important reactions. These studies indicate that inclusion of detailed structural information about the nucleic acid and its ligands is crucial for improving models of nucleic acid electrostatics, and that better treatment of the ion atmosphere and dielectric effects is also of major importance.

Decomposition of interaction free energies in proteins and other complex systems.

A recent analysis of Mark and van Gunsteren has questioned the validity of separating different free energy components in proteins, or indeed in any complex system. The separability of free energy terms is re-examined from both a theoretical and a numerical perspective. Using a power series expansion of the free energy, it is found that the leading terms are free energy components that arise from individual contributions to the Hamiltonian ("in situ" free energies). The energetic part of an in situ free energy component is given by the ensemble average of the corresponding Hamiltonian component, while the leading term in the entropic part, which was missing in the analysis of Mark and van Gunsteren, is given by the mean square fluctuation. In addition there are correlations between fluctuations in each Hamiltonian component, which give rise to a coupling, or correlation entropy. A simple system, whose configurational degrees of freedom can be completely sampled, was examined in order to determine the relative sizes of these different contributions to the free energy. Under certain conditions, the change in system free energy observed when a particular component of the Hamiltonian is removed or altered is well approximated by the change in the in situ free energy of that component. In practical terms, this allows one in these cases to separate out different free energy contributions.

Analysis of the heat capacity dependence of protein folding.

This paper presents an analysis of plots of enthalpy versus heat capacity change at 25 degrees C for the unfolding of proteins and for the dissolution of gaseous, liquid and solid solutes, first reported by Murphy, Privalov & Gill. The negative slope in the enthalpy plot for proteins is interpreted as arising from a large penalty associated with burying polar groups in the protein interior. The small enthalpy changes that accompany protein unfolding at 25 degrees C are also discussed. It is argued that the combined effects of hydrogen bond formation and close packing predict a large positive enthalpy of unfolding. Electrostatic calculations indicate that the penalty associated with burying polar groups is large enough to effectively cancel these terms, leading to the small net enthalpy changes that are observed. The free energy changes associated with protein folding are also discussed. The free energy cost of burying polar groups largely compensates for the stabilizing contribution of the hydrophobic effect and would appear to account for the fact that proteins are marginally stable, independent of their size and of their relative hydrophobicities.

On the decomposition of free energies.

The decomposition of free energies and entropies into components has recently been discussed within the framework of the free energy perturbation (FEP) and thermodynamic integration (TI) methods. In FEP, the cumulant expansion of the excess free energy contains coupling terms in second and higher orders. It is shown here that this expansion can be expressed in terms of temperature derivatives of the mean energy, suggesting a natural decomposition of the free energy into components corresponding to each term in the Hamiltonian. This result is derived in such a way that it establishes the equivalence to a particular form of component analysis based on TI in which all terms in the interaction energy are turned on simultaneously using 1/kT as the coupling parameter.

Empirical free energy calculations: a blind test and further improvements to the method.

Empirical Gibbs functions estimate free energies of non-covalent reactions (deltaG) from atomic coordinates of reaction products (e.g. antibody-antigen complexes). The function previously developed by us has four terms that quantify the effects of hydrophobic, electrostatic and entropy changes (conformational, association) upon complexation. The function was used to calculate delta deltaG of ten lysozyme mutants affecting the stability of the HyHEL-10 antibody-lysozyme complex. The mutants were computer-modeled from the X-ray structure of the wild-type, and free energy calculations produced a correlation coefficient of 0.5 with the experimental delta deltaG data (average absolute error +/-3 kcal). The following changes were then introduced into the Gibbs function: (1) the hydrophobic force was made proportional to the molecular surface, as calculated by the GEPOL93 algorithm, with the scaling constant of 70 cal/mol/A2; (2) calculation of the electrostatics of binding was carried out by the finite difference Poisson-Boltzmann algorithm, which employed uniform grid charging, dielectric boundary smoothing and charge anti-aliasing; and (3) side-chain conformational entropy was estimated from the CONGEN sampling of torsional degrees of freedom. In the new calculations, correlation with experimental data improved to 0.6 or 0.8 if a single outlying mutant, K96M, was neglected. Analysis of the errors remaining in our calculations indicated that molecular mechanics-based modeling of the mutants, rather than the form of our amended Gibbs function, was the main factor limiting the accuracy of the free energy estimates.

Salt effects on ligand-DNA binding. Minor groove binding antibiotics.

Salt dependent electrostatic effects play a central role in intermolecular interactions involving nucleic acids. In this paper, the finite-difference solution to the nonlinear Poisson-Boltzmann (NLPB) equation is used to evaluate the salt dependent contribution to the electrostatic binding free energy of the minor groove binding antibiotics DAPI, Hoechst 33258 and netropsin to DNA using detailed molecular structures of the complexes. For each of these systems, a treatment based on the NLPB equation accurately describes the variation of the experimentally observed binding constant with bulk salt concentration. A solvation formalism is developed in which salt effects are described in terms of three free energy contributions: the electrostatic ion-molecule interaction free energy, delta delta G degrees im; the electrostatic ion-ion interaction free energy, delta delta G degrees ii; and the entropic ion organization free energy, delta delta G degrees org. The electrostatic terms, delta delta G degrees im and delta delta G degrees ii, have both enthalpic and entropic components, while the term delta delta G degrees org is purely a cratic entropy. Each of these terms depends significantly on salt dependent changes in the counterion and coion concentrations around the DNA. In each of the systems studied, univalent ions substantially destabilize charged ligand-DNA complexes at physiological salt concentrations. This effect involves a salt dependent redistribution of counterions near the DNA. The free energy associated with the redistribution of counterions upon binding is dominated by the unfavorable change in the electrostatic ion-molecule interactions, delta delta G degrees im, rather than the change in the cratic entropy of ion organization, delta delta G degrees org. In addition, the observed slope of the salt dependence of the free energy is determined by electrostatic ion-molecule and ion-ion interactions as well as the cratic entropy of ion release. These findings are in contrast to models in which the cratic entropy of counterion release drives binding.

Salt effects on protein-DNA interactions. The lambda cI repressor and EcoRI endonuclease.

In this paper, finite-difference solutions to the nonlinear Poisson-Boltzmann (NLPB) equation are used to calculate the salt dependent contribution to the electrostatic DNA binding free energy for both the lambda cI repressor and the EcoRI endonuclease. For the protein-DNA systems studied, the NLPB method describes nonspecific univalent salt dependent effects on the binding free energy which are in excellent agreement with experimental results. In these systems, the contribution of the ion atmosphere to the binding free energy substantially destabilizes the protein-DNA complexes. The magnitude of this effect involves a macromolecular structure dependent redistribution of both cations and anions around the protein and the DNA which is dominated by long range electrostatic interactions. We find that the free energy associated with global ion redistribution upon binding is more important than changes associated with local protein-DNA interactions (ion-pairs) in determining salt effects. The NLPB model reveals how long range salt effects can play a significant role in the relative stability of protein-DNA complexes with different structures.

The role of protonation and metal chelation preferences in defining the properties of mercury-binding coiled coils.

To define the delicate interplay between metal chelation, protein folding and function in metalloproteins, a family of de novo-designed peptides was synthesized that self-assemble in aqueous solution to form two and three-stranded alpha-helical coiled coils. Each peptide contains a single Cys residue at an a or d position of the heptad repeat. Peptide association thus produces a Cys-rich coordination environment that has been used to bind Hg(II) ions. These peptides display a pH-dependent association, with trimers observed above the pKa of Glu side-chains and dimers below this value. Finite-difference Poisson-Boltzmann calculations suggest that the dimeric state decreases the unfavorable electrostatic interactions between positively charged Lys side-chains (relative to the trimer). The Cys-containing peptides bind Hg(II) in a position-dependent fashion. Cys at a positions form three-coordinate Hg complexes at high pH where the trimeric aggregation state predominates, and two-coordinate complexes at lower pH. A d position Cys, however, is only able to generate the two-coordinate complex, illustrating the difference in coordination geometry between the two positions in the coiled coil. The binding of Hg(II) was also shown to substantially increase the stability of the helical aggregates.

Electrostatic interactions in hirudin-thrombin binding.

Hirudin is a good anticoagulant owing to potent inhibition of the serine protease thrombin. An aspartate- and glutamate-rich portion of hirudin plays an important part in its tight binding to thrombin through a ladder of salt bridges, and these residues have previously been mutated to asparagine or glutamine. Detailed calculations of the electrostatic contribution to changes in binding from these mutations have been performed using the finite-difference Poisson-Boltzmann method which include charge--charge interactions, solvation interactions, the residual electrostatic interaction of mutant residues, pKa shifts, and ionic strength. Single mutant effects on binding energy were close to experimental values, except for the D55N mutant whose effect is overestimated, perhaps because of displacement of a bound chloride ion from the site where it binds. Multiple mutation values were generally overestimated. The effect of pKa shifts upon the binding is significant for one hirudin residue E58, but this appears to be due to a poor salt bridge with thrombin caused by crystal contacts. Electrostatic interaction between the acidic residues is unfavorable. However, analysis of experimental multiple mutation/single mutation data shows apparently negative interactions between these residues, from which it is concluded that structural changes can occur in the complex to relieve an unfavorable interaction when more than one acidic residue is mutated. In all cases, there is a loss in stability of the complex from mutations due to loss of favorable charge--charge interactions with thrombin, but this is largely compensated for by reduced unfavorable desolvation interactions, and by residual polar interactions in the Asn/Gln mutants.

Correlating solvation free energies and surface tensions of hydrocarbon solutes.

A simple equation relating ratios of transfer free energies and solvation free energies to surface tension is derived. When applied to hydrocarbons in water, experimental values for macroscopic surface tension yield remarkably accurate predictions of a ratio involving microscopic quantities, if one uses transfer free energies which have been adjusted for the effects of solute/solvent volume differences. The results support the validity of applying macroscopic concepts such as interfacial free energy at the molecular level. They further suggest that molecular volume as well as surface area contributes to the solubility of hydrocarbons in water.

Effect of charge interactions on the carboxylate vibrational stretching frequency in c-type cytochromes investigated by continuum electrostatic calculations and FTIR spectroscopy.

The FTIR spectra of the asymmetric carboxylate absorption region of three c-type cytochromes--namely horse heart, yeast and bonito cytochromes c--as well as continuum electrostatic calculations performed on their respective protein matrices, show that these combined methods can target specific protein regions and yield pertinent protein charge information that correlates with the observed spectral data. Deconvolution of the IR carboxylate stretch frequency region (1525-1675 cm-1) in the three cytochromes yield different v(oco)a distributions. In the case of the bonito cytochrome c carboxylates, two v(oco)a populations are clearly distinguishable in the deconvoluted spectra--which is not the case for the more complex v(oco)a deconvolutions of the other two cytochromes. The frequency distributions of the calculated potentials are consistent with the experimental observations and we conclude that the IR carboxylate absorption in proteins can be modified by the electrostatic environment.

Identification of additional IDH mutations associated with oncometabolite R(-)-2-hydroxyglutarate production.

Mutations in cytosolic isocitrate dehydrogenase 1 (IDH1) or its mitochondrial homolog IDH2 can lead to R(-)-2-hydroxyglutarate (2HG) production. To date, mutations in three active site arginine residues, IDH1 R132, IDH2 R172 and IDH2 R140, have been shown to result in the neomorphic production of 2HG. Here we report on three additional 2HG-producing IDH1 mutations: IDH1 R100, which is affected in adult glioma, IDH1 G97, which is mutated in colon cancer cell lines and pediatric glioblastoma, and IDH1 Y139. All these new mutants stereospecifically produced 2HG's (R) enantiomer. In contrast, we find that the IDH1 SNPs V71I and V178I, as well as a number of other single-sample reports of IDH non-synonymous mutation, did not elevate cellular 2HG levels in cells and retained the wild-type ability for isocitrate-dependent NADPH production. Finally, we report the existence of additional rare, but recurring mutations found in lymphoma and thyroid cancer, which while failing to elevate 2HG nonetheless displayed loss of function, indicating a possible tumorigenic mechanism for a non-2HG-producing subset of IDH mutations in some malignancies. These data broaden our understanding of how IDH mutations may contribute to cancer through either neomorphic R(-)-2HG production or reduced wild-type enzymatic activity, and highlight the potential value of metabolite screening in identifying IDH-mutated tumors associated with elevated oncometabolite levels.

Calculation of HyHel10-lysozyme binding free energy changes: effect of ten point mutations.

The change in free energy of binding of hen egg white lysozyme (HEL) to the antibody HyHel-10 arising from ten point mutations in HEL (D101K, D101G, K96M, K97D, K97G, K97G, R21E, R21K, W62Y, and W63Y) was calculated using a combination of the finite difference Poisson-Boltzmann method for the electrostatic contribution, a solvent accessible surface area term for the non-polar contribution, and rotamer counting for the sidechain entropy contribution. Comparison of experimental and calculated results indicate that because of pKa shifts in some of the mutated residues, primarily those involving Aspartate or Glutamate, proton uptake or release occurs in binding. When this effect was incorporated into the binding free energy calculations, the agreement with experiment improved significantly, and resulted in a mean error of about 1.9 kcal/mole. Thus these calculations predict that there should be a significant pH dependence to the change in binding caused by these mutations. The other major contributions to binding energy changes comes from solvation and charge charge interactions, which tend to oppose each other. Smaller contributions come from nonpolar interactions and sidechain entropy changes. The structures of the HyHel-10-HEL complexes with mutant HEL were obtained by modeling, and the effect of the modeled structure on the calculations was also examined. "Knowledge based" modeling and automatic generation of models using molecular mechanics produced comparable results.

Calculation of electron transfer reorganization energies using the finite difference Poisson-Boltzmann model.

A description is given of a method to calculate the electron transfer reorganization energy (lambda) in proteins using the linear or nonlinear Poisson-Boltzmann (PB) equation. Finite difference solutions to the linear PB equation are then used to calculate lambda for intramolecular electron transfer reactions in the photosynthetic reaction center from Rhodopseudomonas viridis and the ruthenated heme proteins cytochrome c, myoglobin, and cytochrome b and for intermolecular electron transfer between two cytochrome c molecules. The overall agreement with experiment is good considering both the experimental and computational difficulties in estimating lambda. The calculations show that acceptor/donor separation and position of the cofactors with respect to the protein/solvent boundary are equally important and, along with the overall polarizability of the protein, are the major determinants of lambda. In agreement with previous studies, the calculations show that the protein provides a low reorganization environment for electron transfer. Agreement with experiment is best if the protein polarizability is modeled with a low (<8) average effective dielectric constant. The effect of buried waters on the reorganization energy of the photosynthetic reaction center was examined and found to make a contribution ranging from 0.05 eV to 0.27 eV, depending on the donor/acceptor pair.

Calculation of the electrophoretic mobility of a particle bearing bound polyelectrolyte using the nonlinear poisson-boltzmann equation.

A numerical method for determining the electrophoretic mobility of a polyelectrolyte-coated particle is presented. The particle surface is modeled as having a permeable layer of polyelectrolyte molecules anchored to its surface. Fluid flow within the polyelectrolyte layer is subject to Stokes drag arising from the polyelectrolyte segments. The method allows arbitrary distribution of polymer segments and charge density normal to the surface to be used. The hydrodynamic plane of shear may also be varied. The potential profile is determined by a numerical solution to the nonlinearized Poisson-Boltzmann equation. The potential profile is then used in a numerical solution to the Navier-Stokes equation to give the required mobility. The use of the nonlinearized Poisson-Boltzmann equation extends the results to higher charge density/lower ionic strength conditions than previous treatments. The surface potentials and mobilities for three limiting charge distributions are compared for both the linear and nonlinear treatments to delimit the range of validity of the linear treatment. The utility of the numerical, nonlinear treatment is demonstrated by an improved fit to the electrophoretic mobility of human erythrocytes as a function of ionic strength in the range 10 to 150 mM.

Hydration heat capacity of nucleic acid constituents determined from the random network model.

The heat capacities of hydration (dCp) of the five nucleic acid bases A, G, C, T, and U, the sugars ribose and deoxyribose, and the phosphate backbone were determined using Monte Carlo simulations and the random network model. Solute-induced changes in the mean length and root mean square angle of hydrogen bonds between hydration shell waters were used to compute dCp for these solutes. For all solutes the dCp is significantly more positive than predicted from accessible surface area (ASA) models of heat capacity. In ASA models, nitrogen, oxygen, and phosphorus atoms are considered as uniformly polar, therefore making a negative contribution to dCp. However, the simulations show that many of these polar atoms are hydrated by water whose hydrogen bonds are less distorted than in bulk, leading to a positive dCp. This is in contrast to the effect of polar groups seen previously in small molecules and amino acids, which increase the water H-bond distortion, giving negative dCp contributions. Our results imply that dCp accompanying DNA dehydration in DNA-ligand and DNA-protein binding reactions may be significantly more negative than previously believed and that dehydration is a significant contributor to the large decrease in heat capacity seen in experiments.

Energetics of cyclic dipeptide crystal packing and solvation.

Calculations of the thermodynamics of transfer of the cyclic alanine-alanine (cAA) and glycine-glycine (cGG) dipeptides between the gas, water, and crystal phases were carried out using a combination of molecular mechanics, normal mode analysis, and continuum electrostatics. The experimental gas-to-water solvation free energy and the enthalpy of gas-to-crystal transfer of cGG are accurately reproduced by the calculations. The enthalpies of cGG and cAA crystal-to-water transfer are close to the experimental values. A combination of experimental data and normal mode analysis of cGG provides an accurate estimate of the association entropy penalty (loss of rational and translational entropy and gain in vibrational entropy) for "binding" in the crystalline phase of -14.1 cal/mol/k. This is a smaller number than most previous theoretical estimates, but it is similar to previous experimental estimates. Calculated entropies of the crystal phase underestimate the experimental entropy by about 15 cal/mol/k because of neglect of long-range lattice motions. Comparison of the intermolecular interactions in the crystals of cGG and cAA provides a possible explanation of the puzzling decrease in enthalpy, with increasing hydrophobicity seen previously for both cyclic dipeptide dissolution and protein unfolding. This decrease arises from a favorable long-range electrostatic interaction between dipeptide molecules in the crystals, which is attenuated by the more hydrophobic side chains.