2001
T. Ghosh, Angel E. Garcia, and S. Garde
"Enthalpy and Entropy Contributions to the Pressure Dependence of Hydrophobic Interactions"
submitted, (2001).We use long molecular dynamics simulations of methane molecules in TIP3P water at three different temperatures at pressures of 1 and 4000 atm to calculate entropic and enthalpic contributions to the the free energy of methane-methane association. In agreement with previous simulation studies, we find that the contact minimum is dominated by entropy whereas the solvent-separated minimum is stabilized by favorable enthalpy of association. Both the entropy and enthalpy at the contact minimum change negligibly with increasing pressure leading to the pressure insensitivity of the contact minimum configurations. In contrast, we find that the solvent separated configurations are increasingly stabilized at higher pressures by more favorable enthalpic contributions to the free energy. The desolvation barrier is dominated by unfavorable enthalpy of maintaining a dry volume between methanes. However, the increasing height of the desolvation barrier with increasing pressures results from entropy changes at the barrier configurations. Further resolution of the enthalpy of association shows that major contributions to the enthalpy arise from changes in water-water interactions and the mechanical work (PdV) expended in bringing the methanes to a separation of r. A connection of these thremodynamic features with the underlying changes in water structure is made by calculating methane-methane-water oxygen triplet correlation functions.
S. Garde, G. Hummer, and R. Khare
"Effect of Chain Length on Microscopic Density Fluctuations and Solvation in Polymeric Fluids", Polymeric Materials: Science and Engineering, accepted (2001).
T. Ghosh, Angel E. Garcia, and S. Garde
"Molecular Dynamics Simulations of Pressure Effects on Hydrophobic Interactions"
submitted, (2001).We report results on the pressure effects on hydrophobic interactions obtained from molecular dynamics simulations of aqueous solutions of methanes in water. A wide range of pressures that is relevant to pressure denaturation of proteins is investigated. The characteristic features of water-mediated interactions between hydrophobic solutes are found to be pressure dependent. In particular, with increasing pressure we find that (1) the solvent-separated configurations in the solute-solute potential of mean force (PMF) are stabilized with respect to the contact configurations; (2) the desolvation barrier increases monotonically with respect to both contact and solvent-separated configurations; (3) the locations of the minima and the barrier move toward shorter separations; and (4) pressure effects are considerably amplified for larger hydrophobic solutes. Together, these observations lend strong support to the picture of the pressure denaturation process proposed previously by Hummer et al. [Proc. Natl. Acad. Sci. USA., 95, 1552 (1998)]: with increasing pressure, the transfer of water into protein interior becomes key to the pressure denaturation process, leading to the dissociation of close hydrophobic contacts and subsequent swelling of the hydrophobic protein interior through insertions of water molecules. The pressure dependence of the PMF between larger hydrophobic solutes shows that pressure effects on the interaction between hydrophobic amino acids may be considerably amplified compared to those on the methane-methane
PMF.
A. Kalra, N. Tugcu, S. Cramer, and S. Garde
"Salting-in and Salting-out of Hydrophobic Solutes in Aqueous Salt Solutions"
Journal of Physical Chemistry B., in press, (2001).We present results on the thermodynamic and structural aspects of the hydration of hydrophobic solutes in three tetramethylammonium [-N(CH3)4+] salt solutions at various concentrations obtained from molecular dynamics simulations. Monovalent counterions of different sizes -- F-, Cl-, and a relatively large model ion BI- -- are chosen in order to cover a range of kosmotropic to chaotropic behaviors. Chemical potentials of hard-sphere solutes obtained using test particle insertions display both salting-in and salting-out effects depending on the type of salt. Water and salt-ion densities in the vicinity of hard-sphere solutes are calculated. Small and strongly hydrated F- ions (kosmotropes) are excluded from the vicinity of hydrophobic solutes, leading to an increase in local water densities near hydrophobic solutes (i.e., preferential hydration). This increases the excess chemical potential of hydrophobic solutes in solution which leads to salting-out. Opposite behavior is observed for large, less favorably hydrated BI- ions (chaotropes) which associate strongly with hydrophobic solutes. Compressive forces due to neighboring water molecules, cations, and anions on the surface of hard sphere solute are calculated. We find that water molecules make the most significant contribution towards the total compressive force. This explains the observed linear correlation between the extent of preferential hydration or dehydration of the solute surface and salting-out or salting-in effects. The trends in the thermodynamics of hydration of hydrophobic solutes upon addition of salts are explained in terms of the structural hydration of individual salt ions.
S. Garde and H. S. Ashbaugh
"Temperature Dependence of Hydrophobic Hydration and Entropy Convergence in an Isotropic Model of Water"
Journal of Chemical Physics, in press, (2001).We have investigated temperature dependence of hydrophobic hydration and molecular-scale density fluctuations in an isotropic single-site model of water originally devised by T. Head-Gordon and F. H. Stillinger [J. Chem. Phys., 98, 3313, 1993.] using Monte Carlo simulations. Our isotropic model of water, HGS water, has the same oxygen-oxygen radial distribution function as that of the simple point charge (SPC) water at room temperature and water density. For HGS water, we find that non-Gaussian occupancy fluctuations lead to cavity formation probabilities that are considerably lower than in SPC water. Wetting of a hard-sphere solute by HGS water is also found to be significantly greater than that by SPC water. These observations can be understood in terms of differences in Hamiltonians of the two water models. Despite these differences in the details of hydration, small hydrophobic solutes display many of the well-known thermodynamic finger prints of hydrophobic hydration once the variation of density with temperature, rho(T), along the saturation curve of real liquid water is followed for HGS water. For the hydration of small solutes, the ``entropy convergence'' is observed at temperatures of ~400 K. These observations emphasize that the phase behavior of liquid water contains crucial information regarding thermodynamics of solvation phenomena.
G. Hummer, A. E. García, and S. Garde
"Helix nucleation kinetics using molecular simulations in explicit solvent"
Proteins: Struct. Funct. Genet., 42, 77-84 (2001).We study the reversible folding/unfolding of short Ala and Gly-based peptides by molecular dynamics simulations of all-atom models in explicit water solvent. A kinetic analysis shows that the formation of a first alpha-helical turn occurs within 0.1-1 ns, in agreement with the analyses of laser temperature jump experiments. The unfolding times exhibit Arrhenius temperature dependence. For a rapidly nucleating all-Ala peptide, the helix nucleation time depends only weakly on temperature. For a peptide with enthalpically competing turn-like structures, helix nucleation exhibits an Arrhenius temperature dependence, corresponding to the unfolding of enthalpic traps in the coil ensemble. An analysis of structures in a "transition-state ensemble" shows that helix-to-coil transitions occur predominantly through breaking of hydrogen bonds at the helix ends, particularly at the C-terminus. The temperature dependence of the transition-state ensemble and the corresponding folding/unfolding pathways illustrate that folding mechanisms can change with temperature, possiblycomplicating the interpretation of high-temperature unfolding simulations. The timescale of helix formation is an essential factor in molecular models of protein folding. The rapid helix nucleation observed here suggests that transient helices form early in the folding event.
2000
G. Hummer, A. E. García, and S. Garde
"Conformational Diffusion and helix formation kinetics"
Phys. Rev. Lett., 85, 2637-2640 (2000).The lime, temperature, and sequence dependences of helix formation kinetics of fully atomistic peptide models in explicit solvent are described quantitatively by a diffusive search within the coil state with barrierless transitions into the helical state. Conformational diffusion leads to nonexponential kinetics and jump-width dependences in temperature jump experiments.
G. Hummer, S. Garde, A. E. García, and L. R. Pratt
"New Perspectives on Hydrophobic Effects"
Chemical Physics, 258, 349-370 (2000).Recent breakthroughs in the theory of hydrophobic effects permit new analyses of several characteristics of hydrophobic hydration and interaction. Heat capacities of non-polar solvation, and their temperature dependences, are analyzed within an information theory approach, using experimental information available from bulk liquid water. Non-polar solvation in aqueous electrolytes is studied by computer simulations, and interpreted within the information theory. We also study the preferential solvation of small non-polar molecules in heavy water (D2O) relative to light water (H2O) and find that this revealing difference can be explained by the higher compressibility of D2O. We develop a quasi-chemical description of hydrophobic hydration that incorporates the hydration structure and permits quantum-mechanical treatment ofthe solute. Finally, these new results are discussed in the context of hydrophobic effects in protein stability and folding, and of mesoscopic hydrophobic effects such as dewetting.
S. Garde, R. Khare, and G. Hummer
"Microscopic density fluctuations and solvation in polymeric fluids"
Journal of Chemical Physics., 112, 1574-1578 (2000).The information theory approach is used to study molecular-scale density fluctuations and solvation of hard-core molecules in a condensed polymeric system, supported by extensive computer simulations. In contrast to simple liquids, it is found that the bond connectivity in polymers leads to non-Gaussian density fluctuations in molecular volumes. We define "renormalized" polymers with a reduced number of monomers of increased effective size. This reduces correlations between monomers and simplifies the effective density fluctuations. Chemical potentials of hard-core solutes in polyethylene can then be calculated accurately using information theory.
1999
S. Garde, G. Hummer, and M. E. Paulaitis
"Hydration of tetramethylammonium ion: from water structure to the free energy of
hydration"
Proceedings of AIP Conference: Simulation and Theory of Electrostatic Interactions in Solution, L. R. Pratt and G. Hummer (eds.), Santa Fe, New Mexico, 202-224 (1999)We focus on prediction of structural organization of water in the vicinity of molecular ions and relating this water structure quantitatively to the ion hydration free energy. Analogous to results for clusters comprising covalently bonded nonpolar sites, we found that water structure near tetramethylammonium (TMA) ions in various charge states can be predicted sufficiently accurately by using proximity approximation. In particular, we show that a modified two-site proximity approximation that uses pair and triplet correlations with three nearest ion sites is able to capture details of water structure including asymmetry of hydration of positive and negative ions. We integrate the predicted charge densities along with a background charge applied uniformly within the integration sphere to calculate electrostatic potentials at the charge sites. The background charge density is chosen such that Stillinger-Lovett zeroth moment sum rule is satisfied within the integration sphere. Hydration free energies of TMA ion in seven different charge states (-3e, 2e,...,+3e) calculated using electrostatic potentials are in excellent agreement with molecular simulation results using Ewald summation technique and reproduce accurately the favorable hydration of negative ions with respect to positive ions.
H. S. Ashbaugh, S. Garde, G. Hummer, E. W. Kaler, and M. E. Paulaitis
"Conformational equilibria of hydrophobic solutes in aqueous solution: relationship to inhomogeneous water structure"
Biophysical Journal, 77, 645-654 (1999).Conformational free energies of butane, pentane, and hexane in water are calculated from molecular simulations with explicit waters and from a simple molecular theory in which the local hydration structure is estimated based on a proximity approximation. This proximity approximation uses only the two nearest carbon atoms on the alkane to predict the local water density at a given point in space. Conformational free energies of hydration are subsequently calculated using a free energy perturbation method. Quantitative agreement is found between the free energies obtained from simulations and theory. Moreover, free energy calculations using this proximity approximation are approximately four orders of magnitude faster than those based on explicit water simulations. Our results demonstrate the accuracy and utility of the proximity approximation for predicting water structure as the basis for a quantitative description of n-alkane conformational equilibria in water. In addition, the proximity approximation provides a molecular foundation for extending predictions of water structure and hydration thermodynamic properties of simple hydrophobic solutes to larger clusters or assemblies of hydrophobic solutes.
M. A. Gomez, L. R. Pratt, G. Hummer, and S. Garde
"Molecular realism in default models for information theories of hydrophobic effects"
Journal of Physical Chemistry B, 103, 3520 (1999).This letter considers several physical arguments about contributions to hydrophobic hydration of inert gases,
constructs default models to test them within information theories, and gives information theory predictions using those default models with moment information drawn from simulation of liquid water. Tested physical features include packing or steric effects, the role of attractive forces that lower the solvent pressure, and the roughly tetrahedral coordination of water molecules in liquid water. Packing effects (hard-sphere default model) and packing effects plus attractive forces (Lennard-Jones default model) are ineffective in improving the prediction of hydrophobic hydration free energies of inert gases over the previously used fiat default model. However, a conceptually simple cluster Poisson model that incorporates tetrahedral coordination structure in the default model is effective for these predictions. These results provide a partial rationalization of the remarkable performance of the flat default model with two moments in previous applications. The cluster Poisson default model thus will be the subject of further refinement.
S. Garde, A. E. García, L. R. Pratt, and G. Hummer
"Temperature dependence of the solubility of nonpolar gases inwater"
Biophys. Chem., 78, 21-32 (1999).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.
L. R. Pratt, S. Garde, and G. Hummer
"Theories of hydrophobic effects and the description
of free volume in complex liquids"
Proceedings of the NATO Advanced Study Institute
New approaches to and new problems in liquid state theory
C. Caccamo et al. (eds.), Kluwer Academic Publishers, the Netherlands (1999).
1998
G. Hummer, S. Garde, A. E. García, M. E. Paulaitis, and L. R. Pratt
"Hydrophobic Effects on a Molecular Scale"
Journal of Physical Chemistry (Feature Article) 102, 10469-10482 (1998).A theoretical approach is developed to quantify hydrophobic hydration and interactions on a molecular scale, with the goal of insight into the molecular origins of hydrophobic effects. The model is based on the fundamental relation between the probability for cavity formation in bulk water resulting from molecular-scale density fluctuations and the hydration free energy of the simplest hydrophobic solutes, hard particles. This probability is estimated using an information theory (IT) approach, incorporating experimentally available properties of bulk water: the density and radial distribution function. The IT approach reproduces the simplest hydrophobic effects: hydration of spherical nonpolar solutes, the potential of mean force (PMF) between methane molecules, and solvent contributions to the torsional equilibrium of butane. Applications of this approach to study temperature and pressure effects provide new insights into the thermodynamics and kinetics of protein folding. The IT model relates the hydrophobic-entropy convergence observed in protein unfolding experiments to the macroscopic isothermal compressibility of water. A novel explanation for pressure denaturation of proteins follows from an analysis of the pressure stability of hydrophobic aggregates, suggesting that water penetrates the hydrophobic core of proteins at high pressures. This resolves a long-standing puzzle, whether pressure denaturation contradicts the hydrophobic-core model of protein stability. Finally, issues of "dewetting" of molecularly large nonpolar solutes are discussed in the context of a recently developed perturbation theory approach.
G. Hummer, L. R. Pratt, A. E. García, S. Garde , B. J. Berne, and S. W. Rick
"Reply to comment on `Electrostatic potentials and free energies of solvation of polar and charged molecules"
Journal of Physical Chemistry B 102, 3841-3843 (1998).
G. Hummer and S. Garde
``Cavity expulsion and weak dewetting of hydrophobic solutes in water''
Physical Review Letters, 80, 4193-4196 (1998).Perturbation theory is used to study the solvation of nonpolar molecules in water, supported by extensive computer simulations. Two contributions to the solvent-mediated solute-water interactions an identified: a cavity potential of mean force that transforms by a simple translation when the solute size changes, and a solute-size-independent cavity-expulsion potential. The latter results in weak dewetting of the solute-water interface that can explain the approximate area dependence of solvation free energies with apparent surface
tensions similar to macroscopic values.
G. Hummer, S. Garde, A. E. García, M. E. Paulaitis, and L. R. Pratt
``The pressure dependence of hydrophobic interactions is consistent with the observed pressure denaturation of proteins''
Proc. Natl. Acad. Sci. USA, 95, 1552-1555 (1998).Proteins can be denatured by pressures of a few hundred MPa. This finding apparently contradicts the most widely used model of protein stability, where the formation of a hydrophobic core drives protein folding, The pressure denaturation puzzle is resolved by focusing on the pressure-dependent transfer of water into the protein interior, in contrast to the transfer of nonpolar residues into water, the approach commonly taken in models of protein unfolding, Pressure denaturation of proteins can then be explained by the pressure destabilization of hydrophobic aggregates by using an information theory model of hydrophobic interactions, Pressure-denatured proteins, unlike
heat-denatured proteins, retain a compact structure with water molecules penetrating their core, Activation volumes for hydrophobic contributions to protein folding and unfolding kinetics are positive. Clathrate hydrates are predicted to form by virtually the same mechanism that drives pressure denaturation of proteins.
S. Garde, G. Hummer, and M. E. Paulaitis
``Free energy of hydration of a molecular ionic solute: tetramethylammonium ion''
Journal of Chemical Physics 108, 1552-1561 (1998).We have performed Monte Carlo simulations of the tetramethylammonium ion, hydrated by 256 simple point charge (SPC) water molecules, as a function of total charge on the ion. The total charge was varied between -3e to +3e at intervals of 1e, and was distributed equally on the four methyl sites on the ion. Derivatives of the foe energy with respect to charge were related to the fluctuations in the ion-water interaction energies using a cumulant expansion. This derivative information for the different charge states was found to give an accurate description of the free energy of hydration. The calculated hydration foe energies were also found to be only weakly dependent on system size and the method used for calculating the electrostatic interactions (Ewald summation or generalized reaction field), when finite system size corrections are applied. The quadratic charge dependence was obtained for the free energy of hydration for both positive and negative ions as expected from the Born model. The hydration is, however, asymmetric. Negative ions are more favorably hydrated compared to positive ions. We relate this asymmetry of hydration to water structure; that is, to differences in the water oxygen and water hydrogen density
profiles surrounding positive and negative ions. Another manifestation of this asymmetry is seen in the positive electrostatic potential at the center of methyl sites in the uncharged state of the tetramethylammonium solute.
1997 and before
S. Garde, G. Hummer, and M. E. Paulaitis
``Hydrophobic interactions: conformational equilibria and the association of nonpolar molecules in water'' Faraday Discussions, 103, 125, (1996).Recently developed proximity approximations have been used to calculate inhomogeneous water density profiles around non-polar molecular solutes. Relative Helmholtz energies of hydrophobic hydration are calculated from these density profiles using two inherently different approaches: Helmholtz energy perturbation and a multiparticle correlation function expansion. Entropic contributions to the hydration Helmholtz energy are also calculated using the multiparticle correlation function expansion for the entropy truncated at the level of pair correlations. We show that the proximity approximations describe water structure around a tetramethylammonium ion in good agreement with neutron diffraction experiments, and provide an accurate description of water structure around simple alkanes and benzene as reflected in their entropies of hydration. Further, we reproduce two important features of hydrophobic interactions: a highly favoured contact minimum and a solvent separated minimum in the PMFs for methane-methane and neopentane-neopentane association in water. Our calculations also show that the more compact conformations of n-butane and n-pentane are favoured in water, as expected based on traditional ideas regarding hydrophobic interactions.
S. Garde, G. Hummer, A. E. García, M. E. Paulaitis, and L. R. Pratt
``Origin of the entropy convergence in hydrophobic hydration and protein folding''
Physical Review Letters, 77, 4966-4968, (1996).An information theory model is used to construct a molecular explanation why hydrophobic solvation entropies measured in calorimetry of protein unfolding converge at a common temperature. The entropy convergence follows from the weak temperature dependence of occupancy fluctuations for molecular-scale volumes in water. The macroscopic expression of the contrasting entropic behavior between water and common organic solvents is the relative temperature insensitivity of the water isothermal compressibility. The information theory model provides a quantitative description of small molecule hydration and predicts a negative entropy at convergence. Interpretations of entropic contributions to protein folding should account for this result.
M. E. Paulaitis, S. Garde, and H. S. Ashbaugh
``The hydrophobic effect''
Current Opinion in Colloids and Interfaces, 1, 376-383, (1996).Computer simulation and theoretical studies have improved significantly our understanding of the connection between the structural organization of water surrounding hydrophobic solutes and anomalous thermodynamic behavior associated with the 'hydrophobic effect'. Recent studies have yielded the quantitative temperature dependence of hydrophobic interactions and the dependence of hydration free energy on solute size and shape. The success of new proximity approximations, which assume that water organization is only locally sensitive to solute structure, has encouraged the study of the hydration of complex hydrophobic solutes.
G. Hummer, S. Garde, A. E. García, A. Pohorille, and L. R. Pratt
``An information theory model of hydrophobic interactions''
Proc. Natl. Acad. Sci. USA., 93, 8951-8955, (1996).
[See also: a commentary on this work by B. J. Berne in the same issue of PNAS].A molecular model of poorly understood hydrophobic effects is heuristically developed using the methods of information theory, Because primitive hydrophobic effects can be tied to the probability of observing a molecular-sized cavity in the solvent, the probability distribution of the number of solvent centers in a cavity volume is modeled on the basis of the two moments available from the density and radial distribution of oxygen atoms in liquid water. The modeled distribution then yields the probability that no solvent centers are found in the cavity volume, This model is shown to account quantitatively for the central hydrophobic phenomena of cavity formation and association of inert gas solutes. The connection of information theory to statistical thermodynamics provides a basis for clarification of hydrophobic effects. The simplicity and flexibility of the approach suggest that it should permit applications to conformational equilibria of nonpolar solutes and hydrophobic residues in biopolymers.
S. Garde, G. Hummer, A. E. García, L. R. Pratt, and M. E. Paulaitis
``Hydrophobic hydration: inhomogeneous water structure near nonpolar molecular solutes''
Physical Review E, 53, R4310-4313, (1996).A potential of mean force (PMF) expansion is used to predict the water structure near nonpolar solutes having different shapes and molecular conformations. The decomposition of n- particle PMFs into pair and triplet contributions describes well the hydration of those solutes consisting of nonbonded clusters, but not covalently bonded molecules. Alternative proximity approximations are devised based on the local dependence of the water structure on solute shape and excluded volume. Accurate predictions obtained using these proximity approximations demonstrate that water organization is only locally sensitive to structural details of nonpolar solutes.
M. E. Paulaitis, H. S. Ashbaugh, and S. Garde
``The entropy of hydration of simple hydrophobic solutes''
Biophysical Chemistry, 51, 349, (1994).Infinite-dilution partial molar entropies of solvation of simple, monatomic solutes in water are defined in terms of the entropy associated with (1) solute insertion at constant volume and at a fixed position in the solvent, and (2) expansion or contraction of the pure solvent to maintain constant pressure. A statistical mechanical expansion for the entropy of solution in terms of multiparticle correlation functions is applied tothis definition to identify three intrinsic contributions to the hydration entropy - solute-solvent pair correlations, rearrangement of solvent in the vicinity of the solute molecule, and expansion or contraction of the pure solvent - which we evaluate for the inert gases in water at 25 degrees C. For the smaller solutes, we find that the solventreorganization and solvent expansion contributions offset one another such that the entropy of hydration is determined almost exclusively by solute-water pair correlations. The solute-water pair correlation entropy also prevails as the primary factor determining entropies of hydration for the larger solutes; however, solvent reorganization now makes a small, negative contribution to the entropy.
Other Arcitles:
Tuhin Ghosh, Pawel Keblinski, and Shekhar Garde
Molecular Simulations "On the Fly"
CACHE Fall 2001 News LetterInteractive Web based tools possess enormous potential for being highly effective pedagogical tools. In particular, understanding of molecular-level phenomena that are hard to visualize can be made easy by employing such tools. Here we present application of Web based tools, especially for instructional purposes, and provide a brief primer on the ``nuts and bolts'' that go into their development. We also present representative instances of groups around the world that have contributed significantly towards making these tools available on the World Wide Web.