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

Research progress on non covalent interaction dissolution characterization of insoluble wheat protein based on swelling

The non covalent interactions of proteins are usually characterized by solubility, which is based on the principle that specific solvents can disrupt non covalent interactions and promote protein dissolution. However, this method is generally applicable to highly soluble protein materials. The solubility of wheat protein is poor. When using this method to characterize non covalent interactions, there is always a portion of protein aggregates that can only reach a swollen state and cannot be completely dissolved. At present, there are no research reports on the role of non covalent interactions in swelling. In view of this, this article first reviews the swelling and dissolution processes of insoluble proteins such as wheat protein in solvents, focusing on the characterization mechanisms and influencing factors of three non covalent interactions using solubility characterization. At the same time, this article also explores the potential of swelling in characterizing non covalent interactions, aiming to improve the characterization methods of non covalent interactions between wheat proteins and provide methodological support for analyzing processing differences from the hierarchical analysis of wheat protein interactions in the future.

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions

A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.

Influence of denaturants on amyloid β42 aggregation kinetics

Amyloid formation is linked to devastating neurodegenerative diseases, motivating detailed studies of the mechanisms of amyloid formation. For Aβ, the peptide associated with Alzheimer's disease, the mechanism and rate of aggregation have been established for a range of variants and conditions in vitro and in bodily fluids. A key outstanding question is how the relative stabilities of monomers, fibrils and intermediates affect each step in the fibril formation process. By monitoring the kinetics of aggregation of Aβ42, in the presence of urea or guanidinium hydrochloride (GuHCl), we here determine the rates of the underlying microscopic steps and establish the importance of changes in relative stability induced by the presence of denaturant for each individual step. Denaturants shift the equilibrium towards the unfolded state of each species. We find that a non-ionic denaturant, urea, reduces the overall aggregation rate, and that the effect on nucleation is stronger than the effect on elongation. Urea reduces the rate of secondary nucleation by decreasing the coverage of fibril surfaces and the rate of nucleus formation. It also reduces the rate of primary nucleation, increasing its reaction order. The ionic denaturant, GuHCl, accelerates the aggregation at low denaturant concentrations and decelerates the aggregation at high denaturant concentrations. Below approximately 0.25 M GuHCl, the screening of repulsive electrostatic interactions between peptides by the charged denaturant dominates, leading to an increased aggregation rate. At higher GuHCl concentrations, the electrostatic repulsion is completely screened, and the denaturing effect dominates. The results illustrate how the differential effects of denaturants on stability of monomer, oligomer and fibril translate to differential effects on microscopic steps, with the rate of nucleation being most strongly reduced.

Effect of urea on the hydration and aggregation of hydrophobic and amphiphilic solute models: Implications to protein aggregation

Despite the emergence of a molecular picture of urea's protein unfolding mechanism in the past few decades, less is known about its action mechanism on protein aggregation. This is especially relevant for understanding the aggregation of amyloid proteins and peptides, implicated in several neurodegenerative diseases. While urea is believed to weaken the hydrophobic effect, a picture consistent with the decrease in the excess chemical potential of sufficiently large alkanes, interactions with protein polar side chains and backbone atoms are also important. Here, we study, through molecular dynamics, the hydration and aggregation of several alkanes and amphiphilic "mutants" of n-dodecane, in an 8M aqueous urea solution, aiming at getting insight into urea's mode of action. A size-dependent crossover temperature is found, above which the hydration of the alkanes is favored in the aqueous urea solution. The hydration of the alkanes is enhanced via entropy, with the enthalpy opposing hydration, consistent with experiments. The reason is that although solute-solvent interactions are favorable, these are overwhelmed by urea-water and urea-urea interactions. In contrast, water-water interactions and entropy are favored by a water depletion around the solute and a reduced water depletion around methane explains its exceptional solubility decrease. Furthermore, we show that while urea favors the hydration of n-dodecane and the amphiphilic mutants, it slightly enhances and reduces, respectively, the aggregation of the alkanes and the amphiphilic mutants. Thus, opposite to the common view, our results show that urea does not necessarily weaken hydrophobic interactions despite solvation being favored.

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

Breakdown of classical paradigms in relation to membrane structure and functions

Updates of the mosaic fluid membrane model implicitly sustain the paradigms that bilayers are closed systems conserving a state of fluidity and behaving as a dielectric slab. All of them are a consequence of disregarding water as part of the membrane structure and its essential role in the thermodynamics and kinetics of membrane response to bioeffectors. A correlation of the thermodynamic properties with the structural features of water makes possible to introduce the lipid membrane as a responsive structure due to the relaxation of water rearrangements in the kinetics of bioeffectors' interactions. This analysis concludes that the lipid membranes are open systems and, according to thermodynamic of irreversible formalism, bilayers and monolayers can be reasonable compared under controlled conditions. The inclusion of water in the complex structure makes feasible to reconsider the concept of dielectric slab and fluidity.

Urea-aromatic interactions in biology

Noncovalent interactions are key determinants in both chemical and biological processes. Among such processes, the hydrophobic interactions play an eminent role in folding of proteins, nucleic acids, formation of membranes, protein-ligand recognition, etc.. Though this interaction is mediated through the aqueous solvent, the stability of the above biomolecules can be highly sensitive to any small external perturbations, such as temperature, pressure, pH, or even cosolvent additives, like, urea-a highly soluble small organic molecule utilized by various living organisms to regulate osmotic pressure. A plethora of detailed studies exist covering both experimental and theoretical regimes, to understand how urea modulates the stability of biological macromolecules. While experimentalists have been primarily focusing on the thermodynamic and kinetic aspects, theoretical modeling predominantly involves mechanistic information at the molecular level, calculating atomistic details applying the force field approach to the high level electronic details using the quantum mechanical methods. The review focuses mainly on examples with biological relevance, such as (1) urea-assisted protein unfolding, (2) urea-assisted RNA unfolding, (3) urea lesion interaction within damaged DNA, (4) urea conduction through membrane proteins, and (5) protein-ligand interactions those explicitly address the vitality of hydrophobic interactions involving exclusively the urea-aromatic moiety.

Distinct and Nonadditive Effects of Urea and Guanidinium Chloride on Peptide Solvation

Using enhanced-sampling replica exchange fully atomistic molecular dynamics simulations, we show that, individually, urea and guanidinium chloride (GdmCl) denature the Trpcage protein, but remarkably, the helical segment ¹NLYIQWL⁷ of the protein is stabilized in mixed denaturant solutions. GdmCl induces protein denaturation via a combination of direct and indirect effects involving dehydration of the protein and destabilization of stabilizing salt bridges. In contrast, urea denatures the protein through favorable protein-urea preferential interactions, with peptide-specific indirect effects of urea on the water structure around the protein. In the case of the helical segment of Trpcage, urea "oversolvates" the peptide backbone by reorganizing water molecules from the peptide side chains to the peptide backbone. An intricate nonadditive thermodynamic balance between GdmCl-induced dehydration of the peptide and the urea-induced changes in solvation structure triggers partial counteraction to urea denaturation and stabilization of the helix.

Temperature, Hydrostatic Pressure, and Osmolyte Effects on Liquid-Liquid Phase Separation in Protein Condensates: Physical Chemistry and Biological Implications

Liquid-liquid phase separation (LLPS) of proteins and other biomolecules play a critical role in the organization of extracellular materials and membrane-less compartmentalization of intra-organismal spaces through the formation of condensates. Structural properties of such mesoscopic droplet-like states were studied by spectroscopy, microscopy, and other biophysical techniques. The temperature dependence of biomolecular LLPS has been studied extensively, indicating that phase-separated condensed states of proteins can be stabilized or destabilized by increasing temperature. In contrast, the physical and biological significance of hydrostatic pressure on LLPS is less appreciated. Summarized here are recent investigations of protein LLPS under pressures up to the kbar-regime. Strikingly, for the cases studied thus far, LLPSs of both globular proteins and intrinsically disordered proteins/regions are typically more sensitive to pressure than the folding of proteins, suggesting that organisms inhabiting the deep sea and sub-seafloor sediments, under pressures up to 1 kbar and beyond, have to mitigate this pressure-sensitivity to avoid unwanted destabilization of their functional biomolecular condensates. Interestingly, we found that trimethylamine-N-oxide (TMAO), an osmolyte upregulated in deep-sea fish, can significantly stabilize protein droplets under pressure, pointing to another adaptive advantage for increased TMAO concentrations in deep-sea organisms besides the osmolyte's stabilizing effect against protein unfolding. As life on Earth might have originated in the deep sea, pressure-dependent LLPS is pertinent to questions regarding prebiotic proto-cells. Herein, we offer a conceptual framework for rationalizing the recent experimental findings and present an outline of the basic thermodynamics of temperature-, pressure-, and osmolyte-dependent LLPS as well as a molecular-level statistical mechanics picture in terms of solvent-mediated interactions and void volumes.

Conformational Heterogeneity and FRET Data Interpretation for Dimensions of Unfolded Proteins

A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible-heterogeneous as well as homogeneous-conformational distributions are taken into account without prejudgment, a single value of average transfer efficiency 〈E〉 between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration 〈R_g〉. Here we utilize unbiased conformational statistics from a coarse-grained explicit-chain model to establish a general logical framework to quantify this fundamental ambiguity in smFRET inference. As an application, we address the long-standing controversy regarding the denaturant dependence of 〈R_g〉 of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that 〈R_g〉 of unfolded Protein L is highly sensitive to [GuHCl], but data from SAXS suggested a near-constant 〈R_g〉 irrespective of [GuHCl]. Strikingly, our analysis indicates that although the reported 〈E〉 values for Protein L at [GuHCl] = 1 and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian R_g² distributions consistent with these two 〈E〉 values overlap by as much as 75%. Our findings suggest, in general, that the smFRET-SAXS discrepancy regarding unfolded protein dimensions likely arise from highly heterogeneous conformational ensembles at low or zero denaturant, and that additional experimental probes are needed to ascertain the nature of this heterogeneity.

How Osmolytes Counteract Pressure Denaturation on a Molecular Scale

Life in the deep sea exposes enzymes to high hydrostatic pressure, which decreases their stability. For survival, deep sea organisms tend to accumulate various osmolytes, most notably trimethylamine N-oxide used by fish, to counteract pressure denaturation. However, exactly how these osmolytes work remains unclear. Here, a rigorous statistical thermodynamics approach is used to clarify the mechanism of osmoprotection. It is shown that the weak, nonspecific, and dynamic interactions of water and osmolytes with proteins can be characterized only statistically, and that the competition between protein-osmolyte and protein-water interactions is crucial in determining conformational stability. Osmoprotection is driven by a stronger exclusion of osmolytes from the denatured protein than from the native conformation, and water distribution has no significant effect on these changes at low osmolyte concentrations.

Under-folded proteins: Conformational ensembles and their roles in protein folding, function, and pathogenesis

For decades, protein function was intimately linked to the presence of a unique, aperiodic crystal‐like structure in a functional protein. The two only places for conformational ensembles of under‐folded (or partially folded) protein forms in this picture were either the end points of the protein denaturation processes or transiently populated folding intermediates. Recent years witnessed dramatic change in this perception and conformational ensembles, which the under‐folded proteins are, have moved from the shadow. Accumulated to date data suggest that a protein can exist in at least three global forms–functional and folded, functional and intrinsically disordered (nonfolded), and nonfunctional and misfolded/aggregated. Under‐folded protein states are crucial for each of these forms, serving as important folding intermediates of ordered proteins, or as functional states of intrinsically disordered proteins (IDPs) and IDP regions (IDPRs), or as pathology triggers of misfolded proteins. Based on these observations, conformational ensembles of under‐folded proteins can be classified as transient (folding and misfolding intermediates) and permanent (IDPs and stable misfolded proteins). Permanently under‐folded proteins can further be split into intentionally designed (IDPs and IDPRs) and unintentionally designed (misfolded proteins). Although intrinsic flexibility, dynamics, and pliability are crucial for all under‐folded proteins, the different categories of under‐foldedness are differently encoded in protein amino acid sequences. © 2013 Wiley Periodicals, Inc. Biopolymers 99: 870–887, 2013.

Molecular Thermodynamics of Methane Solvation in tert-Butanol-Water Mixtures

We studied solvation structure and thermodynamics of methane in mixtures of tert-butanol and water using computer simulations. We show that for alcohol mole fractions below 20%, methane is preferentially solvated by hydrated alcohol clusters. Because methane expels water molecules from these clusters, a large endothermic solvent reorganization enthalpy occurs. This process is responsible for the experimentally observed maximum of the heat of methane solvation close to 5% alcohol in the mixture and contributes to a positive entropy change relative to solvation in pure water. Because the structural solvent reorganization enthalpy is enthalpy-entropy compensating, the methane solvation free energy is a smoothly varying function of the alcohol/water solution composition.

Salting-Out of Methane in the Aqueous Solutions of Urea and Glycine-Betaine

We have studied the hydrophobic association and solvation of methane molecules in aqueous solutions of urea and glycine betaine (GB). We have calculated the potentials of mean force (PMFs) between methane molecules in water, aqueous GB, aqueous urea and aqueous urea-GB mixtures. The PMFs and equilibrium constants indicate that both urea and GB increase the hydrophobic association of methane. Calculation of thermodynamic parameters shows that the association of methane is stabilized by entropy whereas solvation is favored by enthalpy. In the case of the water-urea-GB mixture, both hydrophobic association and solvation are stabilized by entropy. From the investigation of radial distribution functions, running coordination numbers and excess coordination numbers, we infer that both urea and GB are preferentially excluded from methane surface in the mixtures of osmolytes and methane is preferentially solvated by water molecules in all the mixtures. The favorable exclusion of both urea and GB from the methane surface suggests that both urea and GB increase the interaction between methane molecules, i.e., salting-out of methane. We observe that addition of both urea and GB to water enhances local water structure. The calculated values of diffusion constants of water also suggest enhanced water-water interactions in the presence of urea and GB. The calculated free energies of methane in these mixtures show that methane is less soluble in the mixtures of urea and GB than in water. The data on solvation free energies support the observations obtained from the PMFs of methane molecules.

Caffeine dimerization: effects of sugar, salts, and water structure

Sugars and salts strongly affect the dimerization of caffeine in water. Such a change of dimerization, considered to be crucial for bitter taste suppression, has long been rationalized by the change of "water structure" induced by the additives; "kosmotropic" (water structure enhancing) salts and sugars promote dimerization, whereas "chaotropic" (water structure breaking) salts suppress dimerization. Based on statistical thermodynamics, here we challenge this consensus; we combine the rigorous Kirkwood-Buff theory of solution with the classical isodesmic model of caffeine association. Instead of the change of water structure, we show that the enhancement of caffeine dimerization is due to the exclusion of additives from caffeine, and that the weakening of dimerization is due to the binding of additives on caffeine.

Cosolvent effects on protein stability

Proteins are marginally stable, and the folding/unfolding equilibrium of proteins in aqueous solution can easily be altered by the addition of small organic molecules known as cosolvents. Cosolvents that shift the equilibrium toward the unfolded ensemble are termed denaturants, whereas those that favor the folded ensemble are known as protecting osmolytes. Urea is a widely used denaturant in protein folding studies, and the molecular mechanism of its action has been vigorously debated in the literature. Here we review recent experimental as well as computational studies that show an emerging consensus in this problem. Urea has been shown to denature proteins through a direct mechanism, by interacting favorably with the peptide backbone as well as the amino acid side chains. In contrast, the molecular mechanism by which the naturally occurring protecting osmolyte trimethylamine N-oxide (TMAO) stabilizes proteins is not clear. Recent studies have established the strong interaction of TMAO with water. Detailed molecular simulations, when used with force fields that incorporate these interactions, can provide insight into this problem. We present the development of a model for TMAO that is consistent with experimental observations and that provides physical insight into the role of cosolvent-cosolvent interaction in determining its preferential interaction with proteins.

Direct Measurement of the Kinetics and Thermodynamics of Association of Hydrophobic Molecules from Molecular Dynamics Simulations

A detailed study of the kinetics and thermodynamics of associations of model hydrophobic molecules is likely to be valuable for understanding the fundamental driving forces for processes such as protein folding and protein-protein association. To this end, we present results from a series of 500 ns long molecular dynamics (MD) simulations examining associations of 13 types of different alkane pairs in explicit water. In addition to providing accurate measurements of the association thermodynamics, the unbiased nature of the configurational sampling in the MD simulations allows the association and dissociation kinetics to be directly quantified. We show that by choosing a suitable reaction coordinate, the computed free energies of all of the alkane-alkane complexes can be linearly related to their buried molecular surface areas, that their dissociation kinetics can be reliably estimated from the height of the barrier on the computed free energy surfaces, and that their association kinetics are effectively diffusion-limited.

Understanding protein non-folding

This review describes the family of intrinsically disordered proteins, members of which fail to form rigid 3-D structures under physiological conditions, either along their entire lengths or only in localized regions. Instead, these intriguing proteins/regions exist as dynamic ensembles within which atom positions and backbone Ramachandran angles exhibit extreme temporal fluctuations without specific equilibrium values. Many of these intrinsically disordered proteins are known to carry out important biological functions which, in fact, depend on the absence of a specific 3-D structure. The existence of such proteins does not fit the prevailing structure-function paradigm, which states that a unique 3-D structure is a prerequisite to function. Thus, the protein structure-function paradigm has to be expanded to include intrinsically disordered proteins and alternative relationships among protein sequence, structure, and function. This shift in the paradigm represents a major breakthrough for biochemistry, biophysics and molecular biology, as it opens new levels of understanding with regard to the complex life of proteins. This review will try to answer the following questions: how were intrinsically disordered proteins discovered? Why don't these proteins fold? What is so special about intrinsic disorder? What are the functional advantages of disordered proteins/regions? What is the functional repertoire of these proteins? What are the relationships between intrinsically disordered proteins and human diseases?

Equilibrium study of protein denaturation by urea

Though urea is commonly used to denature proteins, the molecular mechanism of its denaturing ability is still a subject of considerable debate. Previous molecular dynamics simulation studies have sought to elucidate the mechanism of urea denaturation by focusing on the pathway of denaturation rather than examining the effect of urea on the folding/unfolding equilibrium, which is commonly measured in experiment. Here we report the reversible folding/unfolding equilibrium of Trp-cage miniprotein in the presence of urea, over a broad range of urea concentrations, using all-atom Replica exchange MD simulations. The simulations capture the experimentally observed linear dependence of unfolding free energy on urea concentration. We find that the denaturation is driven by favorable direct interaction of urea with the protein through both electrostatic and van der Waals forces and quantify their contribution. Though the magnitude of direct electrostatic interaction of urea is larger than van der Waals, the difference between unfolded and folded ensembles is dominated by the van der Waals interaction. We also find that hydrogen bonding of urea to the peptide backbone does not play a dominant role in denaturation. The unfolded ensemble sampled depends on urea concentration, with greater urea concentration favoring conformations with greater solvent exposure. The m-value is predicted to increase with temperature and more strongly so with pressure.

Structural evolution during protein denaturation as induced by different methods

Small-angle neutron scattering (SANS) and dynamic light scattering (DLS) have been used to study conformational changes in protein bovine serum albumin (BSA) due to perturbation in its native structure as induced by varying temperature and pressure, and in presence of protein denaturating agents urea and surfactant. BSA has prolate ellipsoidal shape at ambient temperature and we observe no effect of temperature on its structure up to a temperature of about 60 degrees C . At temperatures beyond 60 degrees C , protein denaturation leads to aggregation. The protein solution exhibits a fractal structure at temperatures above 64 degrees C , and its fractal dimension increases with temperature. This is an indication of aggregation followed by gelation that evolves with increasing temperature. It is known for some of the proteins (e.g., Staphylococcal Nuclease) that pressure of 200 MPa can unfold the protein, whereas BSA does not show any protein unfolding even up to the pressure of 450 MPa . In presence of urea, the BSA protein unfolds for urea concentrations greater than 4M and acquires a random coil configuration. We make use of the dilution method to show the reversibility of protein unfolding with urea. The addition of surfactant denaturates the protein by the formation of micellelike aggregates of surfactants along the unfolded polypeptide chains of the protein. We show such structure of the protein-surfactant complex can be stabilized at higher temperatures, which is not the case for pure protein.

Generalized solvation heat capacities

The partial molar heat capacity associated with a constant-pressure solvation process is extended to define a total of six generalized solvation heat capacities, each of which contain unique physical information. These arise from all the possible cross derivatives of the reversible heat of solvation (with respect to T and N), each evaluated at either constant pressure or constant volume. The resulting quantities may be interconverted using expressions that depend on the solvent equation of state and the solute partial molar volume. Moreover, contributions to each of the solvation heat capacities arising from the temperature dependence of the solute-solvent interaction energy and the solvent-reorganization energy (at either constant pressure or constant volume) are formally identified. For the self-solvation of a molecule in its own pure fluid, the latter quantities may be extracted directly from experimental data, while for more general solvation processes additional input is required, either from computer simulation or from theoretical approximations. The results are used to experimentally quantify the generalized heat capacities pertaining to the self-solvation of xenon, difluoromethane, n-hexane, and water, as well as the hydration of xenon, cyclohexane, and three hard sphere solutes (of about the same size as water, xenon, and cyclohexane).

The influence of urea and trimethylamine-N-oxide on hydrophobic interactions

Molecular dynamics simulations are used to obtain potentials of mean force for pairs of neopentane molecules immersed in aqueous solutions containing urea, trimethylamine-N-oxide (TMAO), or both solutes at once. It is shown that the hydrophobic attraction acting between neopentane pairs in pure water and in water-urea solution is completely destroyed by the addition of TMAO. This strongly suggests that TMAO does not counter the protein denaturing effect of urea by enhancing hydrophobic attraction amongst nonpolar groups.

Simple solvation potential for coarse-grained models of proteins

We formulate a simple solvation potential based on a coarsed-grained representation of amino acids with two spheres modeling the C(alpha) atom and an effective side-chain centroid. The potential relies on a new method for estimating the buried area of residues, based on counting the effective number of burying neighbors in a suitable way. This latter quantity shows a good correlation with the buried area of residues computed from all atom crystallographic structures. We check the discriminatory power of the solvation potential alone to identify the native fold of a protein from a set of decoys and show the potential to be considerably selective.

Absolute free energy calculations by thermodynamic integration in four spatial dimensions

An optimized technique for calculating the excess chemical potential of small molecules in dense liquids and the binding affinity of molecular ligands to biomolecules is reported. In this method, a molecular species is coupled to the system of interest via a nonphysical fourth spatial dimension w through which insertion or extraction can be carried out [R. Pomes, E. Eisenmesser, C. B. Post et al., J. Chem. Phys. 111, 3387 (1999)]. Molecular simulations are used to compute the potential of mean force (PMF) acting on the solute molecule in the fourth dimension. The excess chemical potential of that molecule is obtained as the difference in the PMF between fully coupled and fully decoupled systems. The simplicity, efficiency, and generality of the method are demonstrated for the calculation of the hydration free energies of water and methanol as well as sodium, cesium, and chloride ions. A significant advantage over other methods is that the 4D-PMF approach provides a single effective and general route for decoupling all nonbonded interactions (i.e., both Lennard-Jones and Coulombic) at once for both neutral and charged solutes. Direct calculation of the mean force from thermodynamic integration is shown to be more computationally efficient than calculating the PMF from umbrella sampling. Statistical error analysis suggests a simple strategy for optimizing sampling. The detailed analysis of systematic errors arising from the truncation of Coulombic interactions in a solvent droplet of finite size leads to straightforward corrections to ionic hydration free energies.

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.

The Hofmeister series and protein-salt interactions

In order to understand the origin of the Hofmeister series, a statistical-mechanical analysis, based upon the Kirkwood-Buff (KB) theory, has been performed to extract information regarding protein hydration and water-mediated protein-salt interactions from published experimental data-preferential hydration and volumetric data for bovine serum albumin in the presence of a wide range of salts. The analysis showed a linear correlation between the preferential hydration parameter and the protein-cosolvent KB parameter. The same linear correlation holds even when nonelectrolyte cosolvents, such as polyethelene glycol, have been incorporated. These results suggest that the Hofmeister series is due to a wide variation of the water-mediated protein-cosolvent interaction (but not the change of protein hydration) and that this mechanism is a special case of a more general scenario common even to the macromolecular crowding.

Effective interactions between chaotropic agents and proteins

Chaotropic agents are cosolutes that can disrupt the hydrogen bonding network between water molecules and reduce the stability of the native state of proteins by weakening the hydrophobic effect. In this work, we represent the chaotropic agent as a factor that reduces the amount of order in the structures formed by water molecules, both in the bulk and the hydration shells around hydrophobic amino acids. In this framework we show that low chaotrope concentrations lead to a destabilization of the native state of proteins, and that high concentrations induce complete denaturation. We also find that the reduction of the number of bulk ordered states of water molecules can give origin to an effective interaction between chaotropic molecules and proteins.