An understanding of the hydrophobicity of complex heterogeneous molecular assemblies is crucial to characterize and predict interactions between biomolecules. As such, uncovering the subtleties of assembly processes hinges on an accurate classificati
on of the relevant interfaces involved, and much effort has been spent on developing so-called hydrophobicity maps. In this work, we introduce a novel electrostatics-based mapping of aqueous interfaces that focuses on the collective, long-wavelength electrostatic response of water to the presence of nearby surfaces. In addition to distinguishing between hydrophobic and hydrophilic regions of heterogeneous surfaces, this electrostatic mapping can also differentiate between hydrophilic regions that polarize nearby waters in opposing directions. We therefore expect this approach to find use in predicting the location of possible water-mediated hydrophilic interactions, in addition to the more commonly emphasized hydrophobic interactions that can also be of significant importance.
We use appropriately defined short ranged reference models of liquid water to clarify the different roles local hydrogen bonding, van der Waals attractions, and long ranged electrostatic interactions play in the solvation and association of apolar so
lutes in water. While local hydrogen bonding in- teractions dominate hydrophobic effects involving small solutes, longer ranged electrostatic and dis- persion interactions are found to be increasingly important in the description of interfacial structure around large solutes. The hydrogen bond network sets the solute length scale at which a crossover in solvation behavior between these small and large length scale regimes is observed. Unbalanced long ranged forces acting on interfacial water molecules are also important in hydrophobic association, illustrated here by analysis of the association of model methane and buckminsterfullerene solutes.
Using concepts from perturbation and local molecular field theories of liquids we divide the potential of the SPC/E water model into short and long ranged parts. The short ranged parts define a minimal reference network model that captures very well
the structure of the local hydrogen bond network in bulk water while ignoring effects of the remaining long ranged interactions. This deconstruction can provide insight into the different roles that the local hydrogen bond network, dispersion forces, and long ranged dipolar interactions play in determining a variety of properties of SPC/E and related classical models of water. Here we focus on the anomalous behavior of the internal pressure and the temperature dependence of the density of bulk water. We further utilize these short ranged models along with local molecular field theory to quantify the influence of these interactions on the structure of hydrophobic interfaces and the crossover from small to large scale hydration behavior. The implications of our findings for theories of hydrophobicity and possible refinements of classical water models are also discussed.
Solvent structure and dynamics of acetonitrile at its liquid-vapor (LV) interface and at the acetonitrile-silica (LS) interface are studied by means of molecular dynamics simulations. We set up the interfacial system and treat the long-ranged electro
statics carefully to obtain both stable LV and LS interfaces within the same system. Single molecule (singlet) and correlated density orientational profiles and singlet and collective reorientational dynamics are reported for both interfaces. At the LS interface acetonitrile forms layers. The closest sublayer is dominated by nitrogen atoms bonding to the hydrogen sites of the silica surface. The singlet molecular reorientation is strongly hindered when close to the silica surface, but at the LV interface it relaxes much faster than in the bulk. Antiparallel correlations between acetonitrile molecules at the LV interface are even stronger than in the bulk liquid phase. This strong antiparallel correlation disappears at the LS interface. The collective reorientational relaxation of the first layer acetonitrile is much faster than the singlet reorientational relaxation but it is still slower than in the bulk. These results are interpreted with reference to a variety of recent experiments. We found that defining interface properties based on the distribution of positions of different choices of atoms or sites within the molecule leads to apparently different orientational profiles, especially at the LV interface. We provide a general formulation showing that this ambiguity arises when the size of the molecule is comparable to the interfacial width and is particularly significant when there is a large difference in density at the upper and lower boundaries of the interface. We finally analyze the effect of electrostatics to show the necessity of properly treating long-ranged electrostatics for simulations of interfacial systems.
We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method is illustr
ated by applications to dewetting of a hard sphere solute in a Lennard-Jones fluid, the interplay between local hydrogen bond structure and electrostatics for water confined between two hydrophobic walls, and to ion pairing in ionic solutions. Simulation time has been reduced by more than an order of magnitude over previous methods.
Coulomb interactions are present in a wide variety of all-atom force fields. Spherical truncations of these interactions permit fast simulations but are problematic due to their incorrect thermodynamics. Herein we demonstrate that simple analytical c
orrections for the thermodynamics of uniform truncated systems are possible. In particular results for the SPC/E water model treated with spherically-truncated Coulomb interactions suggested by local molecular field theory [Proc. Nat. Acad. Sci. USA 105, 19136 (2008)] are presented. We extend results developed by Chandler [J. Chem. Phys. 65, 2925 (1976)] so that we may treat the thermodynamics of mixtures of flexible charged and uncharged molecules simulated with spherical truncations. We show that the energy and pressure of spherically-truncated bulk SPC/E water are easily corrected using exact second-moment-like conditions on long-ranged structure. Furthermore, applying the pressure correction as an external pressure removes the density errors observed by other research groups in NPT simulations of spherically-truncated bulk species.
We extend results developed by Chandler [J. Chem. Phys. 65, 2925 (1976)] for the dielectric constant of neutral site-site molecular models to mixtures of both charged and uncharged molecules. This provides a unified derivation connecting the Stilling
er-Lovett moment conditions for ions to standard results for the dielectric constant for polar species and yields exact expressions for the small-k expansion of the two-point intermolecular charge-density function used to determine the total Coulomb energy. The latter is useful in determining corrections to the thermodynamics of uniform site-site molecular models simulated with spherically truncated Coulomb interactions.
We present results of molecular simulations of a model protein whose hydrophobic collapse proceeds as a cascade of downhill transitions between distinct intermediate states. Different intermediates are stabilized by means of appropriate harmonic cons
traints, allowing explicit calculation of the equilibrium free energy landscape. Nonequilibrium collapse trajectories are simulated independently and compared to diffusion on the calculated free energy surface. We find that collapse generally adheres to this surface, but quantitative agreement is complicated by nonequilibrium effects and by dependence of the diffusion coefficient on position on the surface.
We examine in detail the theoretical underpinnings of previous successful applications of local molecular field (LMF) theory to charged systems. LMF theory generally accounts for the averaged effects of long-ranged components of the intermolecular in
teractions by using an effective or restructured external field. The derivation starts from the exact Yvon-Born-Green hierarchy and shows that the approximation can be very accurate when the interactions averaged over are slowly varying at characteristic nearest-neighbor distances. Application of LMF theory to Coulomb interactions alone allows for great simplifications of the governing equations. LMF theory then reduces to a single equation for a restructured electrostatic potential that satisfies Poissons equation defined with a smoothed charge density. Because of this charge smoothing by a Gaussian of width sigma, this equation may be solved more simply than the detailed simulation geometry might suggest. Proper choice of the smoothing length sigma plays a major role in ensuring the accuracy of this approximation. We examine the results of a basic confinement of water between corrugated wall and justify the simple LMF equation used in a previous publication. We further generalize these results to confinements that include fixed charges in order to demonstrate the broader impact of charge smoothing by sigma. The slowly-varying part of the restructured electrostatic potential will be more symmetric than the local details of confinements.
Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However truncations are known to produce significant e
rrors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poissons equation defined with a Gaussian-smoothed charge density. We apply LMF theory to three simple molecular systems that exhibit different aspects of the failure of a naive application of spherical truncations -- water confined between hydrophobic walls, water confined between atomically-corrugated hydrophilic walls, and water confined between hydrophobic walls with an applied electric field. Spherical truncations of 1/r fail spectacularly for the final system in particular, and LMF theory corrects the failings for all three. Further, LMF theory provides a more intuitive way to understand the balance between local hydrogen bonding and longer-ranged electrostatics in molecular simulations involving water.
