Solvation: how to obtain microscopic energies from partitioning and solvation experiments

Field theory description of ion association in re-entrant phase separation of polyampholytes

Phase separation of several different overall neutral polyampholyte species (with zero net charge) is studied in solution with two oppositely charged ion species that can form ion-pairs through an association reaction. A field theory description of the system, that treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is hereby given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently show evidence of a re-entrant polyampholyte phase separation at high ion concentrations when there is an overall decrease of volume upon ion-association. As an illustration of the ramifications of our theoretical framework, several polyampholyte concentration vs ion concentration phase diagrams under constant temperature conditions are presented to elucidate the dependence of phase separation behavior on polyampholyte sequence charge pattern as well as ion-pair dissociation constant, volumetric effects on ion association, solvent quality, and temperature.

A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and Its Ramifications for Dielectric Effects in Biomolecular Condensates

Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics, among other interaction types, being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is expected to be a relatively low-dielectric regime, which aside from its possible functional effects on client molecules should facilitate stronger electrostatic interactions among the scaffold IDPs. To gain insight into this LLPS-induced dielectric heterogeneity, addressing in particular whether a low-dielectric condensed phase entails more favorable LLPS than that posited by assuming IDP electrostatic interactions are uniformly modulated by the higher dielectric constant of the pure solvent, we consider a simplified multiple-chain model of polyampholytes immersed in explicit solvents that are either polarizable or possess a permanent dipole. Notably, simulated phase behaviors of these systems exhibit only minor to moderate differences from those obtained using implicit-solvent models with a uniform relative permittivity equals to that of pure solvent. Buttressed by theoretical treatments developed here using random phase approximation and polymer field-theoretic simulations, these observations indicate a partial compensation of effects between favorable solvent-mediated interactions among the polyampholytes in the condensed phase and favorable polyampholyte-solvent interactions in the dilute phase, often netting only a minor enhancement of overall LLPS propensity from the very dielectric heterogeneity that arises from the LLPS itself. Further ramifications of this principle are discussed.

Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.

Perplexing cooperative folding and stability of a low-sequence complexity, polyproline 2 protein lacking a hydrophobic core

The burial of hydrophobic side chains in a protein core generally is thought to be the major ingredient for stable, cooperative folding. Here, we show that, for the snow flea antifreeze protein (sfAFP), stability and cooperativity can occur without a hydrophobic core, and without α-helices or β-sheets. sfAFP has low sequence complexity with 46% glycine and an interior filled only with backbone H-bonds between six polyproline 2 (PP2) helices. However, the protein folds in a kinetically two-state manner and is moderately stable at room temperature. We believe that a major part of the stability arises from the unusual match between residue-level PP2 dihedral angle bias in the unfolded state and PP2 helical structure in the native state. Additional stabilizing factors that compensate for the dearth of hydrophobic burial include shorter and stronger H-bonds, and increased entropy in the folded state. These results extend our understanding of the origins of cooperativity and stability in protein folding, including the balance between solvent and polypeptide chain entropies.

The Hydrophobic Effect in Solute Partitioning and Interfacial Tension

Studies of the partitioning of hydrophobic solutes between water and nonpolar solvents provide estimates for the energy cost of creating hydrophobic-water contacts. This energy is a factor of three lower than the work of adhesion derived from interfacial tension measurements. This discrepancy noted by Tanford in 1979 is widely viewed as a serious challenge to our understanding of hydrophobic interactions. However, the interfacial energy of a water-alkane interface depends on chain length. A simple analysis of published data shows that the loss of rotational freedom of an alkane chain at an interface accounts quantitatively for the length-dependent contribution to interfacial tension, leaving a length-independent contribution very close to the free energy of transfer per unit of solvent accessible surface area. This analysis thus clarifies the discrepancy between the thermodynamic and interfacial tension measurements of hydrophobic interaction energy. Alkanes do not loose rotational freedom when transferred between two different liquid phases but they do at an interface. This reconciles the difference between microscopic and macroscopic measurements. Like the partitioning free energy, the work of adhesion also has a large entropy and small enthalpy at 20 ^oC.

Inferring the microscopic surface energy of protein-protein interfaces from mutation data

Mutations at protein-protein recognition sites alter binding strength by altering the chemical nature of the interacting surfaces. We present a simple surface energy model, parameterized with empirical ΔΔG values, yielding mean energies of -48 cal mol(-1) Å(-2) for interactions between hydrophobic surfaces, -51 to -80 cal mol(-1) Å(-2) for surfaces of complementary charge, and 66-83 cal mol(-1) Å(-2) for electrostatically repelling surfaces, relative to the aqueous phase. This places the mean energy of hydrophobic surface burial at -24 cal mol(-1) Å(-2) . Despite neglecting configurational entropy and intramolecular changes, the model correlates with empirical binding free energies of a functionally diverse set of rigid-body interactions (r = 0.66). When used to rerank docking poses, it can place near-native solutions in the top 10 for 37% of the complexes evaluated, and 82% in the top 100. The method shows that hydrophobic burial is the driving force for protein association, accounting for 50-95% of the cohesive energy. The model is available open-source from http://life.bsc.es/pid/web/surface_energy/ and via the CCharpPPI web server http://life.bsc.es/pid/ccharppi/.

Complexation-induced supramolecular assembly drives metal-ion extraction

Combining experiment with theory reveals the role of self-assembly and complexation in metal-ion transfer through the water-oil interface. The coordinating metal salt Eu(NO3)3 was extracted from water into oil by a lipophilic neutral amphiphile. Molecular dynamics simulations were coupled to experimental spectroscopic and X-ray scattering techniques to investigate how local coordination interactions between the metal ion and ligands in the organic phase combine with long-range interactions to produce spontaneous changes in the solvent microstructure. Extraction of the Eu(3+)-3(NO3(-)) ion pairs involves incorporation of the "hard" metal complex into the core of "soft" aggregates. This seeds the formation of reverse micelles that draw the water and "free" amphiphile into nanoscale hydrophilic domains. The reverse micelles interact through attractive van der Waals interactions and coalesce into rod-shaped polynuclear Eu(III) -containing aggregates with metal centers bridged by nitrate. These preorganized hydrophilic domains, containing high densities of O-donor ligands and anions, provide improved Eu(III) solvation environments that help drive interfacial transfer, as is reflected by the increasing Eu(III) partitioning ratios (oil/aqueous) despite the organic phase approaching saturation. For the first time, this multiscale approach links metal-ion coordination with nanoscale structure to reveal the free-energy balance that drives the phase transfer of neutral metal salts.

Mapping the hydropathy of amino acids based on their local solvation structure

In spite of its relevant biological role, no general consensus exists on the quantitative characterization of amino acid's hydropathy. In particular, many hydrophobicity scales exist, often producing quite different rankings for the amino acids. To make progress toward a systematic classification, we analyze amino acids' hydropathy based on the orientation of water molecules at a given distance from them as computed from molecular dynamics simulations. In contrast with what is usually done, we argue that assigning a single number is not enough to characterize the properties of an amino acid, in particular when both hydrophobic and hydrophilic regions are present in a residue. Instead we show that appropriately defined conditional probability densities can be used to map the hydrophilic and hydrophobic groups on the amino acids with greater detail than possible with other available methods. Three indicators are then defined based on the features of these probabilities to quantify the specific hydrophobicity and hydrophilicity of each amino acid. The characterization that we propose can be used to understand some of the ambiguities in the ranking of amino acids in the current scales. The quantitative indicators can also be used in combination with standard bioinformatics tools to predict the location of transmembrane regions of proteins. The method is sensitive to the specific environment of the amino acids and can be applied to unnatural and modified amino acids, as well as to other small organic molecules.

Mechanism of hydrophobic drug solubilization by small molecule hydrotropes

Drugs that are poorly soluble in water can be solubilized by the addition of hydrotropes. Albeit known for almost a century, how they work at a molecular basis is still controversial due to the lack of a rigorous theoretical basis. To clear up this situation, a combination of experimental data and Fluctuation Theory of Solutions (FTS) has been employed; information on the interactions between all the molecular species present in the solution has been evaluated directly. FTS has identified two major factors of hydrotrope-induced solubilization: preferential hydrotrope-solute interaction and water activity depression. The former is dominated by hydrotrope-solute association, and the latter is enhanced by ionic dissociation and hindered by the self-aggregation of the hydrotropes. Moreover, in stark contrast to previous hypotheses, neither the change of solute hydration nor the water structure accounts for hydrotropy. Indeed, the rigorous FTS poses serious doubts over the other common hypothesis: self-aggregation of the hydrotrope hinders, rather than promotes, solubilization.

Binding efficiency of protein-protein complexes

We examine the relationship between binding affinity and interface size for reversible protein-protein interactions (PPIs), using cytokines from the tumor necrosis factor (TNF) superfamily and their receptors as a test case. Using surface plasmon resonance, we measured single-site binding affinities for binding of the large receptor TNFR1 to its ligands TNFα (K(D) = 1.4 ± 0.4 nM) and lymphotoxin-α (K(D) = 50 ± 10 nM), and also for binding of the small receptor Fn14 to TWEAK (K(D) = 70 ± 10 nM). We additionally assembled data for all other TNF-TNFR family complexes for which reliable single-site binding affinities have been reported. We used these values to calculate the binding efficiencies, defined as binding energy per square angstrom of surface area buried at the contact interface, for nine of these complexes for which cocrystal structures are available, and compared the results to those for a set of 144 protein-protein complexes with published affinities. The results show that the most efficient PPI complexes generate ~20 cal mol(-1) Å(-2) of binding energy. A minimal contact area of ~500 Å(2) is required for a stable complex, required to generate sufficient interaction energy to pay the entropic cost of colocalizing two proteins from 1 M solution. The most compact and efficient TNF-TNFR complex was the BAFF-BR3 complex, which achieved ~80% of the maximal achievable binding efficiency. Other small receptors also gave high binding efficiencies, while the larger receptors generated only 44-49% of this limit despite interacting primarily through just a single small domain. The results provide new insight into how much binding energy can be generated by a PPI interface of a given size, and establish a quantitative method for predicting how large a natural or engineered contact interface must be to achieve a given level of binding affinity.

Contribution of hydrophobic interactions to protein stability

Our goal was to gain a better understanding of the contribution of hydrophobic interactions to protein stability. We measured the change in conformational stability, Δ(ΔG), for hydrophobic mutants of four proteins: villin headpiece subdomain (VHP) with 36 residues, a surface protein from Borrelia burgdorferi (VlsE) with 341 residues, and two proteins previously studied in our laboratory, ribonucleases Sa and T1. We compared our results with those of previous studies and reached the following conclusions: (1) Hydrophobic interactions contribute less to the stability of a small protein, VHP (0.6±0.3 kcal/mol per -CH(2)- group), than to the stability of a large protein, VlsE (1.6±0.3 kcal/mol per -CH(2)- group). (2) Hydrophobic interactions make the major contribution to the stability of VHP (40 kcal/mol) and the major contributors are (in kilocalories per mole) Phe18 (3.9), Met13 (3.1), Phe7 (2.9), Phe11 (2.7), and Leu21 (2.7). (3) Based on the Δ(ΔG) values for 148 hydrophobic mutants in 13 proteins, burying a -CH(2)- group on folding contributes, on average, 1.1±0.5 kcal/mol to protein stability. (4) The experimental Δ(ΔG) values for aliphatic side chains (Ala, Val, Ile, and Leu) are in good agreement with their ΔG(tr) values from water to cyclohexane. (5) For 22 proteins with 36 to 534 residues, hydrophobic interactions contribute 60±4% and hydrogen bonds contribute 40±4% to protein stability. (6) Conformational entropy contributes about 2.4 kcal/mol per residue to protein instability. The globular conformation of proteins is stabilized predominantly by hydrophobic interactions.

Underexposed polar residues and protein stabilization

Increasing protein stability is interesting for practical reasons and because it tests our understanding of protein energetics. We explore here the feasibility of stabilizing proteins by replacing underexposed polar residues by apolar ones of similar size and shape. We have compared the stability of wild-type apoflavodoxin with that of a few carefully selected mutants carrying Y → F, Q → L, T → V or K → M replacements. Although a clear inverse correlation between native solvent exposures of replaced polar residues and stability of mutants is observed, most mutations fail to stabilize the protein. The promising exceptions are the two Q → L mutations tested, which characteristically combine the greatest reduction in polar burial with the greatest increase in apolar burial relative to wild type. Analysis of published stability data corresponding to a variety of mutant proteins confirms that, unlike Y → F or T → V replacements, Q → L mutations tend to be stabilizing, and it suggests that N → L mutations might be stabilizing as well. On the other hand, we show that the stability changes associated to the apoflavodoxin mutations can be rationalized in terms of differential polar and apolar burials upon folding plus a generic destabilizing penalty term. Simple equations combining these contributions predict stability changes in a large data set of 113 mutants (Y → F, Q → L or T → V) similarly well as more complex algorithms available on the Internet.

Solvation theory to provide a molecular interpretation of the hydrophobic entropy loss of noble-gas hydration

An equation for the chemical potential of a dilute aqueous solution of noble gases is derived in terms of energies, force and torque magnitudes, and solute and water coordination numbers, quantities which are all measured from an equilibrium molecular dynamics simulation. Also derived are equations for the Gibbs free energy, enthalpy and entropy of hydration for the Henry's law process, the Ostwald process, and a third proposed process going from an arbitrary concentration in the gas phase to the equivalent mole fraction in aqueous solution which has simpler expressions for the enthalpy and entropy changes. Good agreement with experimental hydration free energies is obtained in the TIP4P and SPC/E water models although the solute's force field appears to affect the enthalpies and entropies obtained. In contrast to other methods, the approach gives a complete breakdown of the entropy for every degree of freedom and makes possible a direct structural interpretation of the well-known entropy loss accompanying the hydrophobic hydration of small non-polar molecules under ambient conditions. The noble-gas solutes experience only a small reduction in their vibrational entropy, with larger solutes experiencing a greater loss. The vibrational and librational entropy components of water actually increase but only marginally, negating any idea of water confinement. The term that contributes the most to the hydrophobic entropy loss is found to be water's orientational term which quantifies the number of orientational minima per water molecule and how many ways the whole hydrogen-bond network can form. These findings help resolve contradictory deductions from experiments that water structure around non-polar solutes is similar to bulk water in some ways but different in others. That the entropy loss lies in water's rotational entropy contrasts with other claims that it largely lies in water's translational entropy, but this apparent discrepancy arises because of different coordinate definitions and reference frames used to define the entropy terms.

Mechanisms of antimicrobial, cytolytic, and cell-penetrating peptides: from kinetics to thermodynamics

The mechanisms of six different antimicrobial, cytolytic, and cell-penetrating peptides, including some of their variants, are discussed and compared. The specificity of these polypeptides varies; however, they all form amphipathic alpha-helices when bound to membranes, and there are no striking differences in their sequences. We have examined the thermodynamics and kinetics of their interaction with phospholipid vesicles, namely, binding and peptide-induced dye efflux. The thermodynamics of binding calculated using the Wimley-White interfacial hydrophobicity scale are in good agreement with the values derived from experiment. The generally accepted view that binding affinity determines functional specificity is also supported by experiments in model membranes. We now propose the hypothesis that it is the thermodynamics of the insertion of the peptide into the membrane, from a surface-bound state, that determine the mechanism.

Redesign of a protein-peptide interaction: characterization and applications

The design of protein-peptide interactions has a wide array of practical applications and also reveals insight into the basis for molecular recognition. Here, we present the redesign of a tetratricopeptide repeat (TPR) protein scaffold, along with its corresponding peptide ligand. We show that the binding properties of these protein-peptide pairs can be understood, quantitatively, using straightforward chemical considerations. The recognition pairs we have developed are also practically useful for the specific identification of tagged proteins. We demonstrate the facile replacement of these proteins, which we have termed T-Mods (TPR-based recognition module), for antibodies in both detection and purification applications. The new protein-peptide pair has a dissociation constant that is weaker than typical antibody-antigen interactions, yet the recognition pair is highly specific and we have shown that this affinity is sufficient for both Western blotting and affinity purification. Moreover, we demonstrate that this more moderate affinity is actually advantageous for purification applications, because extremely harsh conditions are not required to dissociate the T-Mod-peptide interaction. The results we present are important, not only because they represent a successful application of protein design but also because they help define the properties that should be sought in other scaffolds that are being developed as antibody replacements.

Energetics of protein folding

The energetics of protein folding determine the 3D structure of a folded protein. Knowledge of the energetics is needed to predict the 3D structure from the amino acid sequence or to modify the structure by protein engineering. Recent developments are discussed: major factors are reviewed and auxiliary factors are discussed briefly. Major factors include the hydrophobic factor (burial of non-polar surface area) and van der Waals interactions together with peptide hydrogen bonds and peptide solvation. The long-standing model for the hydrophobic factor (free energy change proportional to buried non-polar surface area) is contrasted with the packing-desolvation model and the approximate nature of the proportionality between free energy and apolar surface area is discussed. Recent energetic studies of forming peptide hydrogen bonds (gas phase) are reviewed together with studies of peptide solvation in solution. Closer agreement is achieved between the 1995 values for protein unfolding enthalpies in vacuum given by Lazaridis-Archontis-Karplus and Makhatadze-Privalov when the solvation enthalpy of the peptide group is taken from electrostatic calculations. Auxiliary factors in folding energetics include salt bridges and side-chain hydrogen bonds, disulfide bridges, and propensities to form alpha-helices and beta-structure. Backbone conformational entropy is a major energetic factor which is discussed only briefly for lack of knowledge.

SIMPLE estimate of the free energy change due to aliphatic mutations: Superior predictions based on first principles

The bioinformatics revolution of the last decade has been instrumental in the development of empirical potentials to quantitatively estimate protein interactions for modeling and design. Although computationally efficient, these potentials hide most of the relevant thermodynamics in 5-to-40 parameters that are fitted against a large experimental database. Here, we revisit this longstanding problem and show that a careful consideration of the change in hydrophobicity, electrostatics, and configurational entropy between the folded and unfolded state of aliphatic point mutations predicts 20-30% less false positives and yields more accurate predictions than any published empirical energy function. This significant improvement is achieved with essentially no free parameters, validating past theoretical and experimental efforts to understand the thermodynamics of protein folding. Our first principle analysis strongly suggests that both the solute-solute van der Waals interactions in the folded state and the electrostatics free energy change of exposed aliphatic mutations are almost completely compensated by similar interactions operating in the unfolded ensemble. Not surprisingly, the problem of properly accounting for the solvent contribution to the free energy of polar and charged group mutations, as well as of mutations that disrupt the protein backbone remains open.

Pressure and temperature dependence of hydrophobic hydration: Volumetric, compressibility, and thermodynamic signatures

The combined effect of pressure and temperature on hydrophobic hydration of a nonpolar methanelike solute is investigated by extensive simulations in the TIP4P model of water. Using test-particle insertion techniques, free energies of hydration under a range of pressures from 1 to 3000 atm are computed at eight temperatures ranging from 278.15 to 368.15 K. Corresponding enthalpy, entropy, and heat capacity accompanying the hydration process are estimated from the temperature dependence of the free energies. Partial molar and excess volumes calculated using pressure derivatives of the simulated free energies are consistent with those determined by direct volume simulations; but direct volume determination offers more reliable estimates for compressibility. At 298.15 K, partial molar and excess isothermal compressibilities of methane are negative at 1 atm. Partial molar and excess adiabatic (isentropic) compressibilities are estimated to be also negative under the same conditions. But partial molar and excess isothermal compressibilities are positive at high pressures, with a crossover from negative to positive compressibility at approximately 100-1000 atm. This trend is consistent with experiments on aliphatic amino acids and pressure-unfolded states of proteins. For the range of pressures simulated, hydration heat capacity exhibits little pressure dependence, also in apparent agreement with experiment. When pressure is raised at constant room temperature, hydration free energy increases while its entropic component remains essentially constant. Thus, the increasing unfavorability of hydration under raised pressure is seen as largely an enthalpic effect. Ramifications of the findings of the authors for biopolymer conformational transitions are discussed.

Hydrophobic interaction and hydrogen-bond network for a methane pair in liquid water

We employ fully quantum-mechanical molecular dynamics simulations to evaluate the force between two methanes dissolved in water, as a model for hydrophobic association. A stable configuration is found near the methane-methane contact separation, while a shallow second potential minimum occurs for the solvent-separated configuration. The strength and shape of the potential of mean force are in conflict with earlier classical force-field simulations but agree well with a simple hydrophobic burial model which is based on solubility experiments. Examination of solvent dynamics reveals stable water cages at several specific methane-methane separations.

Energetics in correlation with structural features: the case of micellization

Understanding micellization processes at the molecular level has direct relevance for biological self-assembly, folding, and association processes. As such, it requires complete characterization of the micellization thermodynamics, including its correlation with the corresponding structural features. In this context, micellization of a series of model non-ionic surfactants (poly(ethylene glycol) monooctyl ethers, C(8)E(gamma)) was studied by isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC). The corresponding structural properties of C(8)E(gamma) micelles were investigated by small-angle X-ray scattering (SAXS). The C(8)E(gamma) micellization, characterized independently from ITC, DSC, and structural data, reveals that deltaH(M)(o) > 0, deltaS(M)(o) > 0, and deltaC(P)(M)(o) < 0, while the dissection of its energetics shows that it is primarily governed by the transfer of 20-30 C(8) alkyl chains from aqueous solution into the nonpolar core (r approximately 1.3 nm) of the spherical micelle. Moreover, thermodynamic parameters of micellization, estimated from the structural features related to the changes in solvent-accessible surface areas upon micellization, are in a good agreement with the corresponding parameters obtained from the analysis of ITC and DSC data. We have shown that the contributions to deltaS(M)(o) other than from hydration (deltaS(M)(other)(o)), estimated from experimental data, appear to be small (deltaS(M)(other)(o) < 0.1 deltaS(M)(other)(o)) and agree well with the theoretical estimates expressed as a sum of the corresponding translational, conformational, and size contributions. These deltaS(M)(other)(o) contributions are much less unfavorable than those estimated for a rigid-body association, which indicates the dynamic nature of the C(8)E(gamma) micellar aggregates. the dynamic nature of the C8EY micellar aggregates.

Transfer of lipophilic drugs between liposomal membranes and biological interfaces: Consequences for drug delivery

This review paper describes the present knowledge on the interaction of lipophilic, poorly water soluble, drugs with liposomal membranes and the reversibility of this interaction. This interaction is discussed in the context of equilibrium and spontaneous transfer kinetics of the drug, when the liposomes are brought in co-dispersion with other artificial or natural phospholipid membranes in an aqueous medium. The focus is on drugs, which have the potential to partition (dissolve) in a lipid membrane but do not perturb membranes. The degree of interaction is described as solubility of a drug in phospholipid membranes and the kinetics of transfer of a lipophilic drug between membranes. Finally, the consequences of these two factors on the design of lipid based carriers for oral, as well as parenteral use, for lipophilic drugs and lead selection of oral lipophilic drugs is described. Since liposomes serve as model-membranes for natural membranes, the assessment of lipid solubility and transfer kinetics of lipophilic drug using liposome formulations may additionally have predictive value for bioavailability and biodistribution and the pharmacokinetics of lipophilic drugs after parenteral as well as oral administration.

A novel method reveals that solvent water favors polyproline II over beta-strand conformation in peptides and unfolded proteins: conditional hydrophobic accessible surface area (CHASA)

In aqueous solution, the ensemble of conformations sampled by peptides and unfolded proteins is largely determined by their interaction with water. It has been a long-standing goal to capture these solute-water energetics accurately and efficiently in calculations. Historically, accessible surface area (ASA) has been used to estimate these energies, but this method breaks down when applied to amphipathic peptides and proteins. Here we introduce a novel method in which hydrophobic ASA is determined after first positioning water oxygens in hydrogen-bonded orientations proximate to all accessible peptide/protein backbone N and O atoms. This conditional hydrophobic accessible surface area is termed CHASA. The CHASA method was validated by predicting the polyproline-II (P(II)) and beta-strand conformational preferences of non-proline residues in the coil library (i.e., non-alpha-helix, non-beta-strand, non-beta-turn library derived from X-ray elucidated structures). Further, the method successfully rationalizes the previously unexplained solvation energies in polyalanyl peptides and compares favorably with published experimentally determined P(II) residue propensities. We dedicate this paper to Frederic M. Richards.

Environmental swap energy and role of configurational entropy in transfer of small molecules from water into alkanes

We studied the effect of segmented solvent molecules on the free energy of transfer of small molecules from water into alkanes (hexane, heptane, octane, decane, dodecane, tetradecane, and hexadecane). For these alkanes we measured partition coefficients of benzene, 3-methylindole (3MI), 2,3,4,6-tetrachlorophenol (TeCP), and 2,4,6-tribromophenol (TriBP) at 3, 11, 20, 33 [corrected], and 47 degrees C. For 3MI, TeCP, and TriBP the dependence of free energy of transfer on length of alkane chains was found to be very different from that for benzene. In contrast to benzene, the energy of transfer for 3MI, TeCP, and TriBP was independent of the number of carbons in alkanes. To interpret data, we used the classic Flory-Huggins (FH) theory of concentrated polymer solutions for the alkane phase. For benzene, the measured dependence of energy of transfer on the number of carbons in alkanes agreed well with predictions based on FH model in which the size of alkane segments was obtained from the ratio of molar volumes of alkanes and the solute. We show that for benzene, the energy of transfer can be divided into two components, one called environmental swap energy (ESE), and one representing the contribution of configurational entropy of alkane chains. For 3MI, TeCP, and TriBP the contribution of configurational entropy was not measurable even though the magnitude of the effect predicted from the FH model for short chain alkanes was as much as 20 times greater than experimental uncertainties. From the temperature dependence of ESE we obtained enthalpy and entropy of transfer for benzene, 3MI, TeCP, and TriBP. Experimental results are discussed in terms of a thermodynamic cycle considering creation of cavity, insertion of solute, and activation of solute-medium attractive interactions. Our results suggest that correcting experimental free energy of transfer by Flory-Huggins configurational entropy term is not generally appropriate and cannot be applied indiscriminately.

Computer simulations of membrane protein folding: structure and dynamics

A lattice model of membrane proteins with a composite energy function is proposed to study their folding dynamics and native structures using Monte Carlo simulations. This model successfully predicts the seven helix bundle structure of sensory rhodopsin I by practicing a three-stage folding. Folding dynamics of a transmembrane segment into a helix is further investigated by varying the cooperativity in the formation of alpha helices for both random folding and assisted folding. The chain length dependence of the folding time of a hydrophobic segment to a helical state is studied for both free and anchored chains. An unusual length dependence in the folding time of anchored chains is observed.

Stability scale and atomic solvation parameters extracted from 1023 mutation experiments

The stability scale of 20 amino acid residues is derived from a database of 1023 mutation experiments on 35 proteins. The resulting scale of hydrophobic residues has an excellent correlation with the octanol-to-water transfer free energy corrected with an additional Flory-Huggins molar-volume term (correlation coefficient r = 0.95, slope = 1.05, and a near zero intercept). Thus, hydrophobic contribution to folding stability is characterized remarkably well by transfer experiments. However, no corresponding correlation is found for hydrophilic residues. Both the hydrophilic portion and the entire scale, however, correlate strongly with average burial accessible surface (r = 0.76 and 0.97, respectively). Such a strong correlation leads to a near uniform value of the atomic solvation parameters for atoms C, S, O/N, O(-0.5), and N(+0.5,1). All are in the range of 12-28 cal x mol(-1) A(-2), close to the original estimate of hydrophobic contribution of 25-30 cal x mol(-1) A(-2) to folding stability. Without any adjustable parameters, the new stability scale and new atomic solvation parameters yielded an accurate prediction of protein-protein binding free energy for a separate database of 21 protein-protein complexes (r = 0.80 and slope = 1.06, and r = 0.83 and slope = 0.93, respectively).

Origins of protein denatured state compactness and hydrophobic clustering in aqueous urea: inferences from nonpolar potentials of mean force

Free energies of pairwise hydrophobic association are simulated in aqueous solutions of urea at concentrations ranging from 0-8 M. Consistent with the expectation that hydrophobic interactions are weakened by urea, the association of relatively large nonpolar solutes is destabilized by urea. However, the association of two small methane-sized nonpolar solutes in water has the opposite tendency of being slightly strengthened by the addition of urea. Such size effects and the dependence of urea-induced stability changes on the configuration of nonpolar solutes are not predicted by solvent accessible surface area approaches based on energetic parameters derived from bulk-phase solubilities of model compounds. Thus, to understand hydrophobic interactions in proteins, it is not sufficient to rely solely on transfer experiment data that effectively characterize a single nonpolar solute in an aqueous environment but not the solvent-mediated interactions among two or more nonpolar solutes. We find that the m-values for the rate of change of two-methane association free energy with respect to urea concentration is a dramatically nonmonotonic function of the spatial separation between the two methanes, with a distance-dependent profile similar to the corresponding two-methane heat capacity of association in pure water. Our results rationalize the persistence of residual hydrophobic contacts in some proteins at high urea concentrations and explain why the heat capacity signature (DeltaC(P)) of a compact denatured state can be similar to DeltaC(P) values calculated by assuming an open random-coil-like unfolded state.

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.

Thermodynamics of the hydrophobic effect. III. Condensation and aggregation of alkanes, alcohols, and alkylamines

Knowledge of the energetics of the low solubility of non-polar compounds in water is critical for the understanding of such phenomena as protein folding and biomembrane formation. Solubility in water can be considered as one leg of the three-part thermodynamic cycle - vaporization from the pure liquid, hydration of the vapor in aqueous solution, and aggregation of the substance back into initial pure form as an immiscible phase. Previous studies on the model compounds n-alkanes, 1-alcohols, and 1-aminoalkanes have noted that the thermodynamic parameters (Gibbs free energy, DeltaG; enthalpy, DeltaH; entropy, DeltaS; and heat capacity, DeltaC(p)) associated with these three processes are generally linear functions of the number of carbons in the alkyl chains. Here we assess the accuracy and limitations of the assumption of additivity of CH(2) group contributions to the thermodynamic parameters for vaporization, hydration, and aggregation. Processes of condensation from pure gas to liquid and aqueous solution to aggregate are compared. Hydroxy, amino, and methyl headgroup contributions are estimated, liquid and solid aggregates are distinguished. Most data in the literature were obtained for compounds with short aliphatic hydrocarbon tails. Here we emphasize long aliphatic chain behavior and include our recent experimental data on long chain alkylamine aggregation in aqueous solution obtained by titration calorimetry and van't Hoff analysis. Contrary to what is observed for short compounds, long aliphatic compound aggregation has a large exothermic enthalpy and negative entropy.

Implicit solvation in the self-consistent mean field theory method: sidechain modelling and prediction of folding free energies of protein mutants

The Atomic Solvation Parameter (ASP) model is one of the simplest models of solvation, in which the solvation free energy of a molecule is proportional to the solvent accessible surface area (SAS) of its atoms. However, until now this model had not been incorporated into the Self-Consistent Mean Field Theory (SCMFT) method for modelling sidechain conformations in proteins. The reason for this is that SAS is a many-body quantity and, thus, it is not obvious how to define it within the Mean Field (MF) framework, where multiple copies of each sidechain exist simultaneously. Here, we present a method for incorporating an SAS-based potential, such as the ASP model, into SCMFT. The theory on which the method is based is exact within the MF framework, that is, it does not depend on a pairwise or any other approximation of SAS. Therefore, SAS can be calculated to arbitrary accuracy. The method is computationally very efficient: only 7.6% slower on average than the method without solvation. We applied the method to the prediction of sidechain conformation, using as a test set high-quality solution structures of 11 proteins. Solvation was found to substantially improve the prediction accuracy of well-defined surface sidechains. We also investigated whether the methodology can be applied to prediction of folding free energies of protein mutants, using a set of barnase mutants. For apolar mutants, the modest correlation observed between calculated and observed folding free energies without solvation improved substantially when solvation was included, allowing the prediction of trends in the folding free energies of this type of mutants. For polar mutants, correlation was not significant even with solvation. Several other factors also responsible for the correlation were identified and analysed. From this analysis, future directions for applying and improving the present methodology are discussed.

Binding of small alcohols to a lipid bilayer membrane: does the partitioning coefficient express the net affinity?

The total vapor pressures at 26 degreesC of binary (water-alcohol) and ternary (water-alcohol-vesicle) systems were measured for six short chain alcohols. The vesicles were unilamellar dipalmitoyl phosphatidylcholine (DMPC). The data was used to evaluate the effect of vesicles on the chemical potential of alcohols expressed as the preferential binding parameter of the alcohol-lipid interaction, gamma23. This quantity is a thermodynamic (model-free) measure of the net strength of membrane-alcohol interactions. For the smaller investigated alcohols (methanol, ethanol and 1-propanol) gamma23 was negative. This is indicative of so-called preferential hydration, a condition where the affinity of the membrane for water is higher than the affinity for the alcohol. For the longer alcohols (1-butanol, 1-pentanol, 1-hexanol) gamma23 was positive and increasing with increasing chain length. This demonstrates preferential binding, i.e. enrichment of alcohol in the membrane and a concomitant depletion of the solute in the aqueous bulk. The measured values of gamma23 were compared to the number of alcohol-membrane contacts specified by partitioning coefficients from the literature. It was found that for the small alcohols the number of alcohol-membrane contacts is much larger than the number of preferentially bound solutes. This discrepancy, which is theoretically expected in cases of very weak binding, becomes less pronounced with increasing alcohol chain length, and when the partitioning coefficient exceeds approximately 3 on the molal scale (10(2) in mole fraction units) it vanishes. Based on this, relationships between structural and thermodynamic interpretations of membrane partitioning are discussed.

An amino acid code for protein folding

Direct structural information obtained for many proteins supports the following conclusions. The amino acid sequences of proteins can stabilize not only the final native state but also a small set of discrete partially folded native-like intermediates. Intermediates are formed in steps that use as units the cooperative secondary structural elements of the native protein. Earlier intermediates guide the addition of subsequent units in a process of sequential stabilization mediated by native-like tertiary interactions. The resulting stepwise self-assembly process automatically constructs a folding pathway, whether linear or branched. These conclusions are drawn mainly from hydrogen exchange-based methods, which can depict the structure of infinitesimally populated folding intermediates at equilibrium and kinetic intermediates with subsecond lifetimes. Other kinetic studies show that the polypeptide chain enters the folding pathway after an initial free-energy-uphill conformational search. The search culminates by finding a native-like topology that can support forward (native-like) folding in a free-energy-downhill manner. This condition automatically defines an initial transition state, the search for which sets the maximum possible (two-state) folding rate. It also extends the sequential stabilization strategy, which depends on a native-like context, to the first step in the folding process. Thus the native structure naturally generates its own folding pathway. The same amino acid code that translates into the final equilibrium native structure-by virtue of propensities, patterning, secondary structural cueing, and tertiary context-also produces its kinetic accessibility.

Dehydration-induced redistribution of amphiphilic molecules between cytoplasm and lipids is associated with desiccation tolerance in seeds

This study establishes a relationship between desiccation tolerance and the transfer of amphiphilic molecules from the cytoplasm into lipids during drying, using electron paramagnetic resonance spectroscopy of amphiphilic spin probes introduced into imbibed radicles of pea (Pisum sativum) and cucumber (Cucumis sativa) seeds. Survival following drying and a membrane integrity assay indicated that desiccation tolerance was present during early imbibition and lost in germinated radicles. In germinated cucumber radicles, desiccation tolerance could be re-induced by an incubation in polyethylene glycol (PEG) before drying. In desiccation-intolerant radicles, partitioning of spin probes into lipids during dehydration occurred at higher water contents compared with tolerant and PEG-induced tolerant radicles. The difference in partitioning behavior between desiccation-tolerant and -intolerant tissues could not be explained by the loss of water. Consequently, using a two-phase model system composed of sunflower or cucumber oil and water, physical properties of the aqueous solvent that may affect the partitioning of amphiphilic spin probes were investigated. A significant relationship was found between the partitioning of spin probes and the viscosity of the aqueous solvent. Moreover, in desiccation-sensitive radicles, the rise in cellular microviscosity during drying commenced at higher water contents compared with tolerant or PEG-induced tolerant radicles, suggesting that the microviscosity of the cytoplasm may control the partitioning behavior in dehydrating seeds.

Folding protein models with a simple hydrophobic energy function: the fundamental importance of monomer inside/outside segregation

The present study explores a "hydrophobic" energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its "hydrophobicity" and the number of contacts it makes, i.e., E(h,c) = -Sigma N/i=1 c(i)h(i) = -(h.c) is the negative scalar product between two vectors in N-dimensional cartesian space: h = (h1,., hN), which represents monomer hydrophobicities and is sequence-dependent; and c = (c(1),., c(N)), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c, the best sequence is a vector h on the direction upon which the projection of c - c is maximal, where c is the diagonal vector with components equal to c, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.

Thermodynamics of alcohol-lipid bilayer interactions: application of a binding model

Several recent reports have provided evidence that interactions of small alcohols with lipid bilayer membranes are dominated by adsorption to the membrane-water interface. This mode of interaction is better modeled by binding models than solution theories. In the present study, alcohol-membrane interactions are examined by applying the 'solvent exchange model' [J.A. Schellmann, Biophys. Chem. 37 (1990) 121] to calorimetric measurements. Binding constants (in mole fraction units) for small alcohols to unilamellar liposomes of dimyristoyl phosphatidylcholine were found to be close to unity, and in contrast to partitioning coefficients they decrease through the sequence ethanol, 1-propanol, 1-butanol. Thus, the direct (intrinsic) affinity of the bilayer for these alcohols is lower the longer the acyl chain. A distinction between binding and partitioning is discussed, and it is demonstrated that a high concentration of solute in the bilayer (large partitioning coefficients) can be obtained even in cases of weak binding. Other results from the model suggest that the number of binding sites on the lipid bilayer interface is 1-3 times the number of lipid molecules and that the binding is endothermic with an enthalpy change of 10-15 kJ/mol. Close to the main phase transition of the lipid bilayer the results suggest the presence of two distinct classes of binding sites: 'normal' sites similar to those observed at higher temperatures, and a lower number of high-affinity sites with binding constants larger by one or two orders of magnitude. The occurrence of high-affinity sites is discussed with respect to fluctuating gel and fluid domains in bilayer membranes close to the main phase transition.

Membrane protein folding and stability: physical principles

Stably folded membrane proteins reside in a free energy minimum determined by the interactions of the peptide chains with each other, the lipid bilayer hydrocarbon core, the bilayer interface, and with water. The prediction of three-dimensional structure from sequence requires a detailed understanding of these interactions. Progress toward this objective is summarized in this review by means of a thermodynamic framework for describing membrane protein folding and stability. The framework includes a coherent thermodynamic formalism for determining and describing the energetics of peptide-bilayer interactions and a review of the properties of the environment of membrane proteins--the bilayer milieu. Using a four-step thermodynamic cycle as a guide, advances in three main aspects of membrane protein folding energetics are discussed: protein binding and folding in bilayer interfaces, transmembrane helix insertion, and helix-helix interactions. The concepts of membrane protein stability that emerge provide insights to fundamental issues of protein folding.