Solvation thermodynamics of biopolymers. I. Separation of the volume and surface interactions with estimates for proteins

Free-energy decomposition of salt effects on the solubilities of small molecules and the role of excluded-volume effects

The roles of cations and anions are different in the perturbation on solvation, and thus, the analyses of the separated contributions from cations and anions are useful to establish molecular pictures of ion-specific effects. In this work, we investigate the effects of cations, anions, and water separately in the solvation of n-alcohols and n-alkanes by free-energy decomposition. By utilising energy-representation theory of solvation, we address the contributions arising from the direct solute-solvent interactions and the excluded-volume effects. It is found that the change in solvation of n-alcohols and n-alkanes upon addition of salt depends primarily on the anion species. The direct interaction between the anion and solute is in agreement with the Setschenow coefficient in terms of the ranking of salting-in and salting-out for n-alkanes, which corresponds to the extent of accumulation of the anion on the solute surface. For each of the n-alcohols and n-alkanes examined, the excluded-volume component in the Setschenow coefficient is well correlated to the (total) Setschenow coefficient when the salt effects are concerned. The ranking of the excluded-volume component in the variation of the salt species is parallel to the water contribution, which is correlated further to the change in the water density upon the addition of the salt.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

Design of intrinsically disordered proteins that undergo phase transitions with lower critical solution temperatures

Many naturally occurring elastomers are intrinsically disordered proteins (IDPs) built up of repeating units and they can demonstrate two types of thermoresponsive phase behavior. Systems characterized by lower critical solution temperatures (LCST) undergo phase separation above the LCST whereas systems characterized by upper critical solution temperatures (UCST) undergo phase separation below the UCST. There is congruence between thermoresponsive coil-globule transitions and phase behavior whereby the theta temperatures above or below which the IDPs transition from coils to globules serve as useful proxies for the LCST / UCST values. This implies that one can design sequences with desired values for the theta temperature with either increasing or decreasing radii of gyration above the theta temperature. Here, we show that the Monte Carlo simulations performed in the so-called intrinsic solvation (IS) limit version of the temperature-dependent the ABSINTH (self-Assembly of Biomolecules Studied by an Implicit, Novel, Tunable Hamiltonian) implicit solvation model, yields a useful heuristic for discriminating between sequences with known LCST versus UCST phase behavior. Accordingly, we use this heuristic in a supervised approach, integrate it with a genetic algorithm, combine this with IS limit simulations, and demonstrate that novel sequences can be designed with LCST phase behavior. These calculations are aided by direct estimates of temperature dependent free energies of solvation for model compounds that are derived using the polarizable AMOEBA (atomic multipole optimized energetics for biomolecular applications) forcefield. To demonstrate the validity of our designs, we calculate coil-globule transition profiles using the full ABSINTH model and combine these with Gaussian Cluster Theory calculations to establish the LCST phase behavior of designed IDPs.

On the driving forces for protein-protein association

We analyze all the contributions to the standard free energy of association between two proteins. We find that the solvent-induced interactions between two (or more) hydrophilic groups can turn a highly unfavorable process of association into a highly favorable one. We therefore argue that in contrast to the generally accepted view, it is the hydrophilic rather than the hydrophobic effect that is dominant in biochemical processes such as protein-protein association, protein folding, and protein binding to DNA.

Excluded volume in solvation: sensitivity of scaled-particle theory to solvent size and density

Changes in solvent environment greatly affect macromolecular structure and stability. To investigate the role of excluded volume in solvation, scaled-particle theory is often used to calculate delta G(tr)(ev), the excluded-volume portion of the solute transfer free energy, delta G(tr). The inputs to SPT are the solvent radii and molarities. Real molecules are not spheres. Hence, molecular radii are not uniquely defined and vary for any given species. Since delta G(tr)(ev) is extremely sensitive to solvent radii, uncertainty in these radii causes a large uncertainty in delta G(tr)(ev)-several kcal/mol for amino acid solutes transferring from water to aqueous mixtures. This uncertainty is larger than the experimental delta G(tr) values. Also, delta G(tr)(ev) can be either positive or negative. Adding neutral crowding molecules may not necessarily reduce solubility. Lastly, delta G(tr)(ev) is very sensitive to solvent density, rho. A few percent error in rho may even cause qualitative deviations in delta G(tr)(ev). For example, if rho is calculated by assuming the hard-sphere pressure to be constant, then delta G(tr)(ev) values and uncertainties are now only tenths of a kcal/mol and are positive. Because delta G(tr)(ev) values calculated by scaled-particle theory are strongly sensitive to solvent radii and densities, determining the excluded-volume contribution to transfer free energies using SPT may be problematic.

Osmolyte-induced changes in protein conformational equilibria

Examining solute-induced changes in protein conformational equilibria is a long-standing method for probing the role of water in maintaining protein stability. Interpreting the molecular details governing the solute-induced effects, however, remains controversial. We present experimental and theoretical data for osmolyte-induced changes in the stabilities of the A and N states of yeast iso-1-ferricytochrome c. Using polyol osmolytes of increasing size, we observe that osmolytes alone induce A-state formation from acid-denatured cytochrome c and N state formation from the thermally denatured protein. The stabilities of the A and N states increase linearly with osmolyte concentration. Interestingly, osmolytes stabilize the A state to a greater degree than the N state. To interpret the data, we divide the free energy for the reaction into contributions from nonspecific steric repulsions (excluded volume effects) and from binding interactions. We use scaled particle theory (SPT) to estimate the free energy contributions from steric repulsions, and we estimate the contributions from water-protein and osmolyte-protein binding interactions by comparing the SPT calculations to experimental data. We conclude that excluded volume effects are the primary stabilizing force, with changes in water-protein and solute-protein binding interactions making favorable contributions to stability of the A state and unfavorable contributions to the stability of the N state. The validity of our interpretation is strengthened by analysis of data on osmolyte-induced protein stabilization from the literature, and by comparison with other analyses of solute-induced changes in conformational equilibria.

Analysis of protein-protein interactions and the effects of amino acid mutations on their energetics. The importance of water molecules in the binding epitope

A modeling analysis has been conducted to assess the determinants of binding strength and specificity for three crystal complexes; the anti-hen egg white lysozyme antibody D1.3 complexed with hen egg white lysozyme (HEL), the D1.3 antibody complexed with the anti-lysozyme antibody E5.2, and barnase complexed with barstar. The strengths of individual binding components within these interfaces are evaluated using a model of binding free energy that is based on pairwise surface preferences. In all cases the energetics of binding are dominated by a relatively small number of interfacial residues that define the binding epitope. A precise geometric arrangement of these residues was not found; they were either localized to one region, or distributed throughout the binding interface. Surprisingly, interfacial crystal water molecules were calculated to contribute around 25% of the total calculated binding strength. Theoretical alanine mutations were completed by atomic deletions of the wild-type complexes. Strong correlations were observed between the calculated changes in binding free energy (deltadeltaG(calculated)) and the experimental values (deltadeltaG(observed)) for all but three of the 30 single residue mutations in the D1.3-HEL, D1.3-E5.2 and barnase-barstar systems and for all of the double mutations in the barnase-barstar system. This analysis finds that the observed differences in binding strength are consistent with a model that accounts for the changes in binding energy from the direct contacts between each member of the complex and indirect changes due to released crystallographic water molecules that are near the mutation site. The observed energy changes for double mutations in the barnase-barstar system is fully accounted for by considering water molecules bound jointly by each member of the complex.

A possible involvement of solvent-induced interactions in drug design

We propose to study a new factor in designing new drugs. Most approaches to the drug design problem focus on the direct interactions between the drug and the corresponding target. We propose to study specific solvent-induced effects that can contribute to the binding Gibbs energy between the drug and its target. We estimate that these indirect effects will contribute significantly to the binding affinity and hopefully improve the clinical efficiency of the drugs.

A preference-based free-energy parameterization of enzyme-inhibitor binding. Applications to HIV-1-protease inhibitor design

The interface between protein receptor-ligand complexes has been studied with respect to their binary interatomic interactions. Crystal structure data have been used to catalogue surfaces buried by atoms from each member of a bound complex and determine a statistical preference for pairs of amino-acid atoms. A simple free energy model of the receptor-ligand system is constructed from these atom-atom preferences and used to assess the energetic importance of interfacial interactions. The free energy approximation of binding strength in this model has a reliability of about +/- 1.5 kcal/mol, despite limited knowledge of the unbound states. The main utility of such a scheme lies in the identification of important stabilizing atomic interactions across the receptor-ligand interface. Thus, apart from an overall hydrophobic attraction (Young L, Jernigan RL, Covell DG, 1994, Protein Sci 3:717-729), a rich variety of specific interactions is observed. An analysis of 10 HIV-1 protease inhibitor complexes is presented that reveals a common binding motif comprised of energetically important contacts with a rather limited set of atoms. Design improvements to existing HIV-1 protease inhibitors are explored based on a detailed analysis of this binding motif.

Stabilization of intermediate density states in globular proteins by homogeneous intramolecular attractive interactions

On-lattice simulations of two-dimensional self-avoiding chains subject to homogeneous intramolecular attractive interactions were performed as a model for studying various density regimes in globular proteins. For short chains of less than 15 units, all conformations were generated and classified by density. The range of intramolecular interactions was found to increase uniformly with density, and the average number of topological contacts is directly proportional to density. The uniform interaction energy increases the probability of high density states but does not necessarily lead to dominance of the highest density state. Typically, several large peaks appear in the probability distribution of packing densities, their location and amplitude being determined by the balance between entropic effects enhancing more expanded conformations and attractive interactions favoring compact forms. Also, the homogeneous interaction energy affects the distribution of most probable interacting points in favor of the longer range interactions over the short range ones, but in addition it introduces some more detailed preferences even among short range interactions. There are some implications about the characteristics of the intermediate density states and also for the likelihood that the native state does not correspond completely to the lowest energy conformation.

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.

Monte Carlo simulation of the water in a channel with charges

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.

Solvation effects on the sequence variability of DNA double helical conformations

The role of solvation on the sequence dependent conformational variabilities in DNA has been studied by calculating hydration free energies from solvent accessible surface areas for several base steps, as a function of various helical parameters, roll, twist and propeller twist. The results of roll calculations suggest opposite trends for AA and GG steps, with the former tending to have a compressed minor groove and the latter a compressed major groove. These trends are consistent with the experimental findings on sequence preferences and the nature of anisotropic bending of DNA observed in nucleosomes (Drew, H.R. and Travers, A.A., J. Mol. Biol. 186, 773-790 (1985); Satchwell, S.C., Drew, H.R. and Travers, A.A., J. Mol. Biol. 191, 659-675 (1986)) and CAP-DNA interactions (Gartenberg, M.R. and Crothers, D.M., Nature 333, 824-829, (1988)). Solvation energy profiles also indicate preferences for the base pairs in GG and AA steps to adopt low and high propeller twists, respectively. Such agreements may either reflect a coincidence of solvation effects with other energy terms or a dominance of solvent effects. The results are discussed in the context of the crystallographic observations of structural tendencies.

Solvent effect on binding thermodynamics of biopolymers

The indirect solvent-induced effect on the free energy of binding of biopolymers is examined within the framework of classical statistical mechanics. We focus specifically on the role of the solute-solvent hydrogen bonding. In particular, we have estimated the first order solvent effect on the indirect interaction between two biopolymers. We find that the solvent-induced interactions between two hydrophilic groups through water-bridged hydrogen bonds could significantly enhance the binding free energy. Some preliminary estimates indicate that this effect is significant and perhaps could be crucial in molecular recognition processes. Furthermore, we have calculated, from crystal structure data, the distance distribution between all the oxygens and nitrogens on the surface of some proteins that do not belong to the binding domain. In most cases we found an enhanced peak in the range of 4-5 A, which is where we expect to find strong solvent-induced interactions.