Physics and biophysics of solvent induced forces: hydrophobic interactions and context-dependent hydration

Solvent induced forces (SIFs) among solutes derive from solvent structural modification due to solutes, and consequent thermodynamic drive towards minimization of related free energy costs. The role of SIFs in biomolecular conformation and function is appreciated by observing that typical SIF values fall within the 20–200 pN interval, and that proteins are stable by only a few kcal mol^–1 (1 kcal mol^–1 corresponds to 70 pN Å). Here we study SIFs, in systems of increasing complexity, using Molecular Dynamics (MD) simulations which give time- and space-resolved details on the biologically significant scale of single protein residues and sidechains. Of particular biological relevance among our results are a strong modulability of hydrophobic SIFs by electric charges and the dependence of this modulability upon charge sign. More generally, the present results extend our understanding of the recently reported strong context-dependence of SIFs and the related potential of mean force (PMF). This context-dependence can be strong enough to propagate (by relay action) along a composite solute, and to reverse SIFs acting on a given element, relative to expectations based on its specific character (hydrophobic/ philic, charged). High specificity such as that of SIFs highlighted by the present results is of course central to biological function. Biological implications of the present results cover issues such as biomolecular functional interactions and folding (including chaperoning and pathological conformational changes), coagulation, molecular recognition, effects of phosphorylation and more.     

Interaction of explicit solvent with hydrophobic/philic/charged residues of a protein: Residue character vs. conformational context

Molecular dynamics simulations of model solutes in explicit molecular water have recently elicited novel aspects of the strong nonpair additivity of the potential of mean force (PMF) and related solvent-induced forces (SIFs) and hydration. Here we present the results of the same type of work on SIFs acting on bovine pancreatic trypsin inhibitor (BPTI) at single residue/sidechain resolution. In this system, nonpair additivity and the consequent dependence of SIFs on the protein conformational context are sufficiently strong to overturn SIFs on some individual residues, relative to expectations based on their individual characters. This finding calls for a revisitation and offers a richer and diversified understanding of the role of hydrophobic/philic/charged groups in establishing the exquisite specificity of biomolecular folding and functional conformation. Its relevance is appreciated by noting that the work of a typical SIF acting on one residue, when displaced across a distance of 1 Å, is the equivalent of up to a few kcal/mol, which is the range of the stability/function free energy of a protein. Proteins 32:129–135, 1998. © 1998 Wiley-Liss, Inc.     

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.     

Experimental and computational studies of enantioseparation of structurally similar chiral compounds on amylose tris(3,5‐dimethylphenylcarbamate)

The enantioseparation of 14 structurally similar chiral solutes, with one or two chiral centers, are studied for a commercially important polysaccharide‐based chiral stationary phase, amylose tris(3,5‐dimethylphenylcarbamate) (ADMPC). Among these solutes, only two solutes show significant enantioresolutions of 2 to 2.5 in n‐hexane/2‐propanol (90/10, v/v) at 298 K. The retention factors of the chiral solutes vary significantly from 0.7 to 7.0, and they are compared with those of simpler nonchiral solutes having similar but fewer functional groups. The sorbent–solute H‐bonding interactions between the solute functional groups and the polymer C?O and NH functional groups are probed with attenuated total reflection infrared spectroscopy (ATR‐IR). The H‐bonding interactions of the polymer C?O and NH groups with the solutes result in changes in the IR amide band wavenumbers of ADMPC upon solute adsorption. The nanostructure of an ADMPC cavity and the potential interactions with the chiral solutes are proposed based on the sorbent–solute–solvent HPLC data, the sorbent–solute IR data, and the sorbent–solute molecular dynamics (MD) simulations. The results are consistent with the three point attachment hypothesis and indicate that a significant enantioresolution in ADMPC requires at least three different interaction sites for simultaneous H‐bonds and phenyl–phenyl interactions for phenylpropylamine (PPA) and various structurally similar chiral solutes. Chirality 2010. © 2009 Wiley‐Liss, Inc.     

Osmolyte trimethylamine-N-oxide does not affect the strength of hydrophobic interactions: origin of osmolyte compatibility

Osmolytes are small organic solutes accumulated at high concentrations by cells/tissues in response to osmotic stress. Osmolytes increase thermodynamic stability of folded proteins and provide protection against denaturing stresses. The mechanism of osmolyte compatibility and osmolyte-induced stability has, therefore, attracted considerable attention in recent years. However, to our knowledge, no quantitative study of osmolyte effects on the strength of hydrophobic interactions has been reported. Here, we present a detailed molecular dynamics simulation study of the effect of the osmolyte trimethylamine-N-oxide (TMAO) on hydrophobic phenomena at molecular and nanoscopic length scales. Specifically, we investigate the effects of TMAO on the thermodynamics of hydrophobic hydration and interactions of small solutes as well as on the folding-unfolding conformational equilibrium of a hydrophobic polymer in water. The major conclusion of our study is that TMAO has almost no effect either on the thermodynamics of hydration of small nonpolar solutes or on the hydrophobic interactions at the pair and many-body level. We propose that this neutrality of TMAO toward hydrophobic interactions-one of the primary driving forces in protein folding-is at least partially responsible for making TMAO a "compatible" osmolyte. That is, TMAO can be tolerated at high concentrations in organisms without affecting nonspecific hydrophobic effects. Our study implies that protein stabilization by TMAO occurs through other mechanisms, such as unfavorable water-mediated interaction of TMAO with the protein backbone, as suggested by recent experimental studies. We complement the above calculations with analysis of TMAO hydration and changes in water structure in the presence of TMAO molecules. TMAO is an amphiphilic molecule containing both hydrophobic and hydrophilic parts. The precise balance of the effects of hydrophobic and hydrophilic segments of the molecule appears to explain the virtual noneffect of TMAO on the strength of hydrophobic interactions.     

Some ways of looking at compensatory kosmotropes and different water environments

Hydration of macromolecular structures determines biological activity. Stabilizing solutes are kosmotropic (increase order of water) rather than chaotropic (decrease order). Preferential hydration of surfaces is a thermodynamic consequence of the solution behavior of kosmotropic solutes, but inconsistencies imply interactions such as the hydration of specific sites within macromolecules. Thermodynamic measures require bulk pure solutes; here simpler measures of the effects on bulk water, water at surfaces and hydration water of probes have been applied to solutes including natural stabilizers, analogues and example chaotropes. Changes in the near-infrared spectra, water proton NMR chemical shifts and relaxation times measure changes in the bulk liquid; HPLC-column retention of solutes indicate interactions with hydration water at different surfaces, and fluorescence probes detect effects on functional group hydration water. Ab initio calculations and Monte-Carlo simulations of the solutes in water measure the energetics of the solute-water interactions, the dipole moments of these molecules, their charge distributions and the effect of the solute molecules on the structure of water. The rankings of the test solutes by these measures are not consistent. Thus, stabilizing solutes are not interchangeable in biological systems and the intracellular replacement of one by another could affect the integration of cell metabolism.     

Description of hydration free energy density as a function of molecular physical properties

A method to calculate the solvation free energy density (SFED) at any point in the cavity surface or solvent volume surrounding a solute is proposed. In the special case in which the solvent is water, the SFED is referred to as the hydration free energy density (HFED). The HFED is described as a function of some physical properties of the molecules. These properties are represented by simple basis functions. The hydration free energy of a solute was obtained by integrating the HFED over the solvent volume surrounding the solute, using a grid model. Of 34 basis functions that were introduced to describe the HFED, only six contribute significantly to the HFED. These functions are representations of the surface area and volume of the solute, of the polarization and dispersion of the solute, and of two types of electrostatic interactions between the solute and its environment. The HFED is described as a linear combination of these basis functions, evaluated by summing the interaction energy between each atom of the solute with a grid point in the solvent, where each grid point is a representation of a finite volume of the solvent. The linear combination coefficients were determined by minimizing the error between the calculated and experimental hydration free energies of 81 neutral organic molecules that have a variety of functional groups. The calculated hydration free energies agree well with the experimental results. The hydration free energy of any other solute molecule can then be calculated by summing the product of the linear combination coefficients and the basis functions for the solute.     

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.     

Exclusion and retention of compensatory kosmotropes by HPLC columns

With water as the elution solvent, zwitterionic solutes and polyols were retained on HPLC columns, more than was water, by totally hydrophobic packing materials. Relative retentions were systematically affected by oxygen functional groups in the packing material, explicable as specific retention of water. Reproducible elution sequences of 20 solutes at a variety of hydrophobic surfaces (aromatic and both long- and short-alkyl aliphatic surfaces) showed there is a general process, consistent with interactions with hydration water at the surface having solvent properties distinct from bulk water. Early eluting solutes included glycine, sarcosine and taurine. Glycine betaine followed both these and N,N-dimethylglycine. The natural betaines propionobetaine and dimethylsulfoniopropionate also preceded glycine betaine. Dimethylsulfoxide was strongly retained, as (to a lesser extent) was proline betaine. Polyols eluted in the sequence sorbitol, trehalose, glycerol. Changes in the chemical nature of the surface or base material affected relative retentions of water and solutes. The presence of hydrogen-bonding functions increased retention of polyols, as well as water, relative to zwitterionic solutes. Specific effects with some solutes may be related to inconsistencies seen in biological systems. Pressures up to 8 MPa did not affect relative retention, constraining models based on the formation of low-density water.     

A desolvation barrier to hydrophobic cluster formation may contribute to the rate-limiting step in protein folding.

To gain insight into the free energy changes accompanying protein hydrophobic core formation, we have used computer simulations to study the formation of small clusters of nonpolar solutes in water. A barrier to association is observed at the largest solute separation that does not allow substantial solvent penetration. The barrier reflects an effective increase in the size of the cavity occupied by the expanded but water-excluding cluster relative to both the close-packed cluster and the fully solvated separated solutes; a similar effect may contribute to the barrier to protein folding/unfolding. Importantly for the simulation of protein folding without explicit solvent, we find that the interactions between nonpolar solutes of varying size and number can be approximated by a linear function of the molecular surface, but not the solvent-accessible surface of the solutes. Comparison of the free energy of cluster formation to that of dimer formation suggests that the assumption of pair additivity implicit in current protein database derived potentials may be in error.     

Effect of the solute molecular structure on its enantioresolution on cellulose tris(3,5-dimethylphenylcarbamate)

The effects of the molecular structures for 13 structurally similar chiral solutes on their HPLC retention and enantioresolutions on a commercially important polysaccharide-based chiral stationary phase, cellulose tris(3,5-dimethylphenylcarbamate) (CDMPC) are studied. Among these 13 solutes, only methyl ephedrine (MEph) shows significant enantioresolution. The retention factors of these chiral solutes vary significantly from 0.7 to 3.2 in n-hexane/2-propanol (90/10, v/v) at 298 K. The retention factors of some simpler non-chiral solutes having similar but fewer functional groups than their chiral counterparts are also studied under the same conditions and are compared to those of the chiral solutes. The H-bonding interactions between the functional groups of the solute and the C=O and NH functional groups of the polymer are probed with attenuated total reflection-infrared spectroscopy (ATR-IR) for the polymer, for binary sorbent-solute systems. The CDMPC IR amide band wavenumbers change significantly, indicating H-bonding interactions of the polymer C=O and NH groups with the solutes. The elution orders predicted for the enantiomers of these chiral solutes using molecular dynamics (MD) simulations of the polymer-solute binary systems are consistent with the HPLC results. The CDMPC cavity nano-structure and the potential interactions with chiral solutes are proposed based on HPLC data, IR data, and the simulations. The results are consistent with the three-point attachment model and support the hypothesis that significant enantioresolution requires at least three different synergistic interactions which can be a combination of steric hindrance, H-bonding, or pi-pi interactions.     

Temperature dependence of the solubility of non-polar gases in water

An explanation is provided for the experimentally observed temperature dependence of the solubility and the solubility minimum of non-polar gases in water. The influence of solute size and solute-water attractive interactions on the solubility minimum temperature is investigated. The transfer of a non-polar solute from the ideal gas into water is divided into two steps: formation of a cavity in water with the size and shape of the solute and insertion of the solute in this cavity which is equivalent to 'turning on' solute-water attractive interactions. This two step process divides the excess chemical potential of the non-polar solute in water into repulsive and attractive contributions, respectively. The reversible work for cavity formation is modeled using an information theory model of hydrophobic hydration. Attractive contributions are calculated by modeling the water structure in the vicinity of non-polar solutes. These models make a direct connection between microscopic quantities and macroscopic observables. Moreover, they provide an understanding of the peculiar temperature dependences of the hydration thermodynamics from properties of pure water; specifically, bulk water density and the water oxygen-oxygen radial distribution function.     

The effect of vicinal polar and charged groups on hydrophobic hydration.

The use of a linear relationship between free energy of hydrophobic hydration and solvent-accessible apolar surface area has been helpful in interpreting the thermodynamics of biological macromolecules. However, a recent study (Y.-K. Cheng, P. J. Rossky, Nature 1998, Vol. 392, pp. 696-699) has established a substantial enthalpic dependence on biomolecular surface topography, originating from solvent hydrogen-bonding loss in a restrictive geometry. In this study, we use molecular dynamics simulations of 2-Zn insulin in water solvent to explore the further effect of vicinal polar or charged groups on hydrophobic hydration at a biomolecular surface. In contrast to the case for solvent more isolated from such polar solute influences, the binding energies of the water that is proximal to the hydrophobic dimeric interface of insulin and vicinal to polar and charged groups are comparable to the bulk solvent value, a result of compensating interaction primarily with the solute counterions. The results suggest a special importance for such polar/charged groups in biological processes involving hydrophobic surface regions of restricted geometry and also suggest a general route for tuning the hydrophobicity of interfaces.     

Free energetics of rigid body association of ubiquitin binding domains: A biochemical model for binding mediated by hydrophobic interaction

Weak intermolecular interactions, such as hydrophobic associations, underlie numerous biomolecular recognition processes. Ubiquitin is a small protein that represents a biochemical model for exploring thermodynamic signatures of hydrophobic association as it is widely held that a major component of ubiquitin's binding to numerous partners is mediated by hydrophobic regions on both partners. Here, we use atomistic molecular dynamics simulations in conjunction with the Adaptive Biasing Force sampling method to compute potentials of mean force (the reversible work, or free energy, associated with the binding process) to investigate the thermodynamic signature of complexation in this well‐studied biochemical model of hydrophobic association. We observe that much like in the case of a purely hydrophobic solute (i.e., graphene, carbon nanotubes), association is favored by entropic contributions from release of water from the interprotein regions. Moreover, association is disfavored by loss of enthalpic interactions, but unlike in the case of purely hydrophobic solutes, in this case protein‐water interactions are lost and not compensated for by additional water‐water interactions generated upon release of interprotein and moreso, hydration, water. We further find that relative orientations of the proteins that mutually present hydrophobic regions of each protein to its partner are favored over those that do not. In fact, the free energy minimum as predicted by a force field based method recapitulates the experimental NMR solution structure of the complex. Proteins 2014; 82:1453–1468. © 2014 Wiley Periodicals, Inc.     

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.     

The non-polar solvent potential of mean force for the dimerization of alanine dipeptide: the role of solute-solvent van der Waals interactions

The non-polar component of the potential of mean force of dimerization of alanine dipeptide has been calculated in explicit solvent by free energy perturbation. We observe that the calculated PMF is inconsistent with a non-polar hydration free energy model based solely on the solute surface area. The non-linear behavior of the solute-solvent van der Waals energy is primarily responsible for the non-linear dependence of the potential of mean force with respect to the surface area. The calculated potential of mean force is reproduced by an implicit solvent model based on a solvent continuum model for the solute-solvent van der Waals interaction energy and the surface area for the work of forming the solute cavity.     

A comparison of DMPC- and DLPE-based lipid bilayers.

A 250 ps molecular dynamics simulation of the dimyristoylphosphatidylcholine (DMPC)-based lipid bilayer, including explicit water molecules, is reported. The solvent environment of the head groups and other structural properties of the bilayer have been analyzed and compared with experimental results as well as our previous simulation of the dilauroylphosphatidylethanolamine (DLPE)-based bilayer. From this comparison we find that the solvent structure around the DMPC head group (clathrate shell) is significantly different than that around the DLPE head group (typical hydrogen bonding interactions). We have modeled the probable relationship between the different solvent environments around the R-N(CH3)3+ (DMPC) and R-NH3+ (DLPE) head groups and the different interlammelar distances in these systems by performing potential of mean force (PMF) simulations on two N(CH3)4+ and NH4+ ions in water. From the PMF simulations it appears that the differences in the hydration of the DMPC and DLPE head groups is not responsible for the differences in the hydration force observed for these systems. We also find that the orientational polarization of DLPE and DMPC is similar, which suggests that solvent polarization is not responsible for the differences in the hydration repulsion behavior observed in these systems. We also examined the order parameters for DMPC and found them to be in reasonable agreement with experiment. Given the different characteristics of the DLPE and DMPC head groups, we suggest an explanation of the differences in the interlammellar spacings of bilayers composed of these like-charged lipids. From our DLPE simulations we find that the R-NH3+ head groups can interact with the nonesterified oxygens of the phosphate group in an intraleaflet or an interleaflet manner. For the latter a "cross link" between two leaflets can be formed, which causes a stabilization of the interlamellar spacings at fairly short distances. Moreover, due to the strong intraleaflet interaction we find that the DLPE interface is relatively "flat" (as opposed to DMPC-based bilayers), which results in a surface that has regions of positive and negative charge that reside in the same plane along the bilayer normal. Based on this we propose that the DLPE bilayer interface can correlate itself with another DLPE interface by alignment of the regions of positive (or negative) charge on one leaflet with the opposite charges on the opposing leaflet.     

Generation of multilamellar and unilamellar phospholipid vesicles

Multilamellar and unilamellar vesicles can be generated by a variety of techniques which lead to systems with differing lamellarity, size, trapped volume and solute distribution. The straight-forward hydration of lipid to produce multilamellar vesicles (MLVs) results in systems which exhibit low trapped volumes and where solutes contained in the aqueous buffer are partially excluded from the MLV interior. Large trapped volumes and equilibrium solute distributions can be achieved by freeze-thawing or by ‘reverse phase’ procedures where the lipid is hydrated after being solubilized in organic solvent. Unilamellar vesicles can be produced directly from MLVs by extrusion or sonication or, alternatively, can be obtained by reverse phase or detergent removal procedures. The advantages and limitations of these techniques are discussed.