Brad A. Bauer

Exploring Ion Permeation Energetics in Gramicidin A Using Polarizable Charge Equilibration Force Fields

All-atom molecular dynamics simulations have been applied in the recent past to explore the free energetics underlying ion transport processes in biological ion channels. Roux and co-workers, Kuyucak and co-workers, Busath and co-workers, and others have performed rather elegant and extended time scale molecular dynamics simulations using current state-of-the-art fixed-charge (nonpolarizable) force fields to calculate the potential of mean force defining the equilibrium flux of ions through prototypical channels such as gramicidin A. An inescapable conclusion of such studies has been the gross overestimation of the equilibrium free energy barrier, generally predicted to be from 10 to 20 kcal/mol depending on the force field and simulation protocol used in the calculation; this translates to an underestimation of experimentally measurable single channel conductances by several orders of magnitude. Next-generation polarizable force fields have been suggested as possible alternatives for more quantitative predictions of the underlying free energy surface in such systems. (1) Presently, we consider ion permeation energetics in the gramicidin A channel using a novel polarizable force field. Our results predict a peak barrier height of 6 kcal/mol relative to the channel entrance; this is significantly lower than the uncorrected value of 12 kcal/mol for nonpolarizable force fields such as GROMOS and CHARMM27 which do not account for electronic polarization. These results provide promising initial indications substantiating the long-conjectured importance of polarization effects in describing ion-protein interactions in narrow biological channels.

Molecular dynamics simulations of aqueous ions at the liquid-vapor interface accelerated using graphics processors.

Molecular dynamics (MD) simulations are a vital tool in chemical research, as they are able to provide an atomistic view of chemical systems and processes that is not obtainable through experiment. However, large‐scale MD simulations require access to multicore clusters or supercomputers that are not always available to all researchers. Recently, scientists have returned to exploring the power of graphics processing units (GPUs) for various applications, such as MD, enabled by the recent advances in hardware and integrated programming interfaces such as NVIDIAs CUDA platform. One area of particular interest within the context of chemical applications is that of aqueous interfaces, the salt solutions of which have found application as model systems for studying atmospheric process as well as physical behaviors such as the Hoffmeister effect. Here, we present results of GPU‐accelerated simulations of the liquid–vapor interface of aqueous sodium iodide solutions. Analysis of various properties, such as density and surface tension, demonstrates that our model is consistent with previous studies of similar systems. In particular, we find that the current combination of water and ion force fields coupled with the ability to simulate surfaces of differing area enabled by GPU hardware is able to reproduce the experimental trend of increasing salt solution surface tension relative to pure water. In terms of performance, our GPU implementation performs equivalent to CHARMM running on 21 CPUs. Finally, we address possible issues with the accuracy of MD simulaions caused by nonstandard single‐precision arithmetic implemented on current GPUs.

Properties of water along the liquid-vapor coexistence curve via molecular dynamics simulations using the polarizable TIP4P-QDP-LJ water model

We present an extension of the TIP4P-QDP model, TIP4P-QDP-LJ, that is designed to couple changes in repulsive and dispersive nonbond interactions to changes in polarizability. Polarizability is intimately related to the dispersion component of classical force field models of interactions, and we explore the effect of incorporating this connection explicitly on properties along the liquid-vapor coexistence curve of pure water. Parametrized to reproduce condensed-phase liquid water properties at 298 K, the TIP4P-QDP-LJ model predicts density, enthalpy of vaporization, self-diffusion constant, and the dielectric constant at ambient conditions to about the same accuracy as TIP4P-QDP but shows remarkable improvement in reproducing the liquid-vapor coexistence curve. TIP4P-QDP-LJ predicts critical constants of T(c)=623 K, rho(c)=0.351 g/cm(3), and P(c)=250.9 atm, which are in good agreement with experimental values of T(c)=647.1 K, rho(c)=0.322 g/cm(3), and P(c)=218 atm, respectively. Applying a scaling factor correction (obtained by fitting the experimental vapor-liquid equilibrium data to the law of rectilinear diameters using a three-term Wegner expansion) the model predicts critical constants (T(c)=631 K and rho(c)=0.308 g/cm(3)). Dependence of enthalpy of vaporization, self-diffusion constant, surface tension, and dielectric constant on temperature are shown to reproduce experimental trends. We also explore the interfacial potential drop across the liquid-vapor interface for the temperatures studied. The interfacial potential demonstrates little temperature dependence at lower temperatures (300-450 K) and significantly enhanced (exponential) dependence at elevated temperatures. Terms arising from the decomposition of the interfacial potential into dipole and quadrupole contributions are shown to monotonically approach zero as the temperature approaches the critical temperature. Results of this study suggest that self-consistently treating the coupling of phase-dependent polarizability with dispersion interactions in classical water force fields may be an important effect for the extension of polarizable water force fields to reproduce properties along the liquid-vapor coexistence envelope as well as near critical conditions. More importantly, the present study demonstrates the rather remarkable transferability of a water model parametrized to a single state point to other thermodynamic states. Further studies are recommended.

Recent applications and developments of charge equilibration force fields for modeling dynamical charges in classical molecular dynamics simulations

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, in our hands those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for small molecules, proteins, lipids, and lipid bilayers and recently have begun work on carbohydrate force fields. The latter area has been relatively untouched by force field developers with particular focus on polarizable, non-additive interaction potential models. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration method for phase-dependent polarizable force fields, lipid molecules, and small-molecule carbohydrates. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields.

Structural, dynamic, and electrostatic properties of fully hydrated DMPC bilayers from molecular dynamics simulations accelerated with graphical processing units (GPUs)

We present results of molecular dynamics simulations of fully hydrated DMPC bilayers performed on graphics processing units (GPUs) using current state‐of‐the‐art non‐polarizable force fields and a local GPU‐enabled molecular dynamics code named FEN ZI. We treat the conditionally convergent electrostatic interaction energy exactly using the particle mesh Ewald method (PME) for solution of Poissons Equation for the electrostatic potential under periodic boundary conditions. We discuss elements of our implementation of the PME algorithm on GPUs as well as pertinent performance issues. We proceed to show results of simulations of extended lipid bilayer systems using our program, FEN ZI. We performed simulations of DMPC bilayer systems consisting of 17,004, 68,484, and 273,936 atoms in explicit solvent. We present bilayer structural properties (atomic number densities, electron density profiles), deuterium order parameters (SCD), electrostatic properties (dipole potential, water dipole moments), and orientational properties of water. Predicted properties demonstrate excellent agreement with experiment and previous all‐atom molecular dynamics simulations. We observe no statistically significant differences in calculated structural or electrostatic properties for different system sizes, suggesting the small bilayer simulations (less than 100 lipid molecules) provide equivalent representation of structural and electrostatic properties associated with significantly larger systems (over 1000 lipid molecules). We stress that the three system size representations will have differences in other properties such as surface capillary wave dynamics or surface tension related effects that are not probed in the current study. The latter properties are inherently dependent on system size. This contribution suggests the suitability of applying emerging GPU technologies to studies of an important class of biological environments, that of lipid bilayers and their associated integral membrane proteins. We envision that this technology will push the boundaries of fully atomic‐resolution modeling of these biological systems, thus enabling unprecedented exploration of meso‐scale phenomena (mechanisms, kinetics, energetics) with atomic detail at commodity hardware prices.

Variation of ion polarizability from vacuum to hydration: insights from Hirshfeld partitioning.

The results of iterative Hirshfeld partitioning on the polarizability of monovalent anions (F(-), Cl(-), and Br(-)) and Na(+) in water clusters ranging from n = 0 to n = 25 are presented. In each case, the ions reach a limiting intrinsic polarizability in the fully hydrated state. For F(-), Cl(-), and Br(-) using B3LYP/aug-cc-pVDZ, the intrinsic polarizabilities in the condensed-phase limit are 47.2 +/- 0.7%, 47.2 +/- 0.3%, and 54.2 +/- 0.4% of their gas-phase value at the corresponding level of theory. The extent of this scaling depends on the basis set (we also consider B3LYP/aug-cc-pVTZ), but intrinsic polarizabilities are generally within 35-55% of the gas-phase value. The sodium cation is the least polarizable in the condensed-phase limit. The average intrinsic polarizability of water in these clusters decreases with the size of the cluster, which is consistent with earlier Hirshfeld analysis of intrinsic polarizabilities of pure water (Krishtal, A.; Senet, P.; Yang, M.; van Alsenoy, C. J. Chem. Phys. 2006, 125, 034312). Further analysis demonstrates that water molecules near ions in sufficiently large clusters (n = 25) have intrinsic polarizabilities similar to those of water molecules fully coordinated in a pure aqueous cluster. The observed binodal distribution of the water intrinsic polarizability within the cluster is attributed to polarizability differences between interior and exterior water molecules. This observation is in qualitative agreement with arguments based on Paulis exclusion principle that suggest a reduced polarizability for condensed-phase water relative to the vacuum value.

Free Energetics of Carbon Nanotube Association in Pure and Aqueous Ionic Solutions

Carbon nanotubes are a promising platform across a broad spectrum of applications ranging from separations technology, drug delivery, to bio(electronic) sensors. Proper dispersion of carbon nanotube materials is important to retaining the electronic properties of nanotubes. Experimentally it has been shown that salts can regulate the dispersing properties of CNTs in aqueous system with surfactants (Niyogi, S.; Densmore, C. G.; Doorn, S. K. J. Am. Chem. Soc.2009, 131, 1144-1153); details of the physicochemical mechanisms underlying such effects continue to be explored. We address the effects of inorganic monovalent salts (NaCl and NaI) on dispersion stability of carbon nanotubes.We perform all-atom molecular dynamics simulations using nonpolarizable interaction models to compute the potential of mean force between two (10,10) single-walled carbon nanotubes (SWNTs) in the presence of NaCl/NaI and compare to the potential of mean force between SWNTs in pure water. Addition of salts enhances stability of the contact state between two SWNTs on the order of 4 kcal/mol. The ion-specific spatial distribution of different halide anions gives rise to starkly different contributions to the free energy stability of nanotubes in the contact state. Iodide anion directly stabilizes the contact state to a much greater extent than chloride anion. The enhanced stability arises from the locally repulsive forces imposed on nanotubes by the surface-segregated iodide anion. Within the time scale of our simulations, both NaI and NaCl solutions stabilize the contact state by equivalent amounts. The marginally higher stability for contact state in salt solutions recapitulates results for small hydrophobic solutes in NaCl solutions (Athawale, M. V.; Sarupria, S.; Garde, S. J. Phys. Chem. B2008, 112, 5661-5670) as well as single-walled carbon nanotubes in NaCl and CaCl2 aqueous solutions.

Free energetics and the role of water in the permeation of methyl guanidinium across the bilayer-water interface: insights from molecular dynamics simulations using charge equilibration potentials.

Combining umbrella sampling molecular dynamics (MD) simulations, the weighted histogram analysis method (WHAM) for unbiasing probabilities, and polarizable charge equilibration force fields, we compute the potential of mean force for the reversible transfer of methyl guanidinium from bulk solution to the center of a model DPPC bilayer. A 5 kcal/mol minimum in the potential of mean force profile for membrane permeation suggests that the analogue will preferentially reside in the headgroup region of the lipid, qualitatively in agreement with previously published results. We find the potential of mean force for permeation to be approximately 28 kcal/mol (relative to the minimum in the headgroups), within the range of values reported for similar types of simulations using fixed-charge force fields. From analysis of the lipid structure, we find that the lipid deformation leads to a substantial destabilizing contribution to the free energy of the methyl guanidinium as it resides in the bilayer center, though this deformation allows more efficient stabilization by water defects and transient pores. Water in the bilayer core stabilizes the charged residue. The role of water in stabilizing or destabilizing the solute as it crosses the bilayer depends on bulk electrolyte concentration. In 1 M KCl solution, the water contribution to the potential of mean force is stabilizing over the entire range of the permeation coordinate, with the sole destabilizing force originating from the anionic species in solution. Conversely, methyl guanidinium experiences net destabilization from water in the absence of electrolyte. The difference in solvent contributions to permeation free energy is traced to a local effect arising from differences in water density in the bilayer-water solution interface, thus leading to starkly opposite net forces on the permeant. The origin of the local water density differential rests with the penetration of hydrated chloride anions into the solution-bilayer interface. Finally, water permeation into the bilayer is required for the deformation of individual lipid molecules and permeation of ions into the membrane. From simulations where water is first excluded from the bilayer center where methyl guanidinium is restrained and then, after equilibration, allowed to enter the bilayer, we find that in the absence of any water defects/permeation into the bilayer, the lipid headgroups do not follow the methyl guanidinium. Only when water enters the bilayer do we see deformation of individual lipid molecules to associate with the amino acid analogue at bilayer center.

Charge equilibration force fields for molecular dynamics simulations of lipids, bilayers, and integral membrane protein systems.

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for lipids and lipid bilayers. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration (CHEQ) method for lipid molecules. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields. Application areas include DPPC-water monolayers, potassium ion permeation free energetics in the gramicidin A bacterial channel, and free energetics of permeation of charged amino acid analogs across the water-bilayer interface. This article is part of a Special Issue entitled: Membrane protein structure and function.

Solvation properties of N‐acetyl‐β‐glucosamine: Molecular dynamics study incorporating electrostatic polarization

N‐Acetyl‐β‐glucosamine (NAG) is an important moiety of glycoproteins and is involved in many biological functions. However, conformational and dynamical properties of NAG molecules in aqueous solution, the most common biological environment, remain ambiguous due to limitations of experimental methods. Increasing efforts are made to probe structural properties of NAG and NAG‐containing macromolecules, like peptidoglycans and polymeric chitin, at the atomic level using molecular dynamics simulations. In this work, we develop a polarizable carbohydrate force field for NAG and contrast simulation results of various properties using this novel force field and an analogous nonpolarizable (fixed charge) model. Aqueous solutions of NAG and its oligomers are investigated; we explore conformational properties (rotatable bond geometry), electrostatic properties (dipole moment distribution), dynamical properties (self‐diffusion coefficient), hydrogen bonding (water bridge structure and dynamics), and free energy of hydration. The fixed‐charge carbohydrate force field exhibits deviations from the gas phase relative rotation energy of exocyclic hydroxymethyl side chain and of chair/boat ring distortion. The polarizable force field predicts conformational properties in agreement with corresponding first‐principles results. NAG–water hydrogen bonding pattern is studied through radial distribution functions (RDFs) and correlation functions. Intermolecular hydrogen bonding between solute and solvent is found to stabilize NAG solution structures while intramolecular hydrogen bonds define glycosidic linkage geometry of NAG oligomers. The electrostatic component of hydration free energy is highly dependent on force field atomic partial charges, influencing a more favorable free energy of hydration in the fixed‐charge model compared to the polarizable model.