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.

Molecular dynamics simulation of hydrated DPPC monolayers using charge equilibration force fields.

We present results of molecular dynamics simulations of a model DPPC-water monolayer using charge equilibration (CHEQ) force fields, which explicitly account for electronic polarization in a classical treatment of intermolecular interactions. The surface pressure, determined as the difference between the monolayer and pure water surface tensions at 323 K, is predicted to be 22.92 ±1.29 dyne/cm, just slightly below the broad range of experimental values reported for this system. The surface tension for the DPPC-water monolayer is predicted to be 42.35 ±1.16 dyne/cm, in close agreement with the experimentally determined value of 40.9 dyne/cm. This surface tension is also consistent with the value obtained from DPPC monolayer simulations using state-of-the-art nonpolarizable force fields. The current results of simulations predict a monolayer-water potential difference relative to the pure water-air interface of 0.64 ±0.02 Volts, an improved prediction compared to the fixed-charge CHARMM27 force field, yet still overestimating the experimental range of 0.3 to 0.45 Volts. As the charge equilibration model is a purely charge-based model for polarization, the current results suggest that explicitly modeled polarization effects can offer improvements in describing interfacial electrostatics in such systems.

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 Poisson's 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 (S(CD)), 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.

Water Permeation Through DMPC Lipid Bilayers using Polarizable Charge Equilibration Force Fields.

We investigate permeation energetics of water entering a model dimyristoylphosphatidylcholine (DMPC) bilayer via molecular dynamics simulations using polarizable Charge Equilibration (CHEQ) models. Potentials of mean force show 4.5-5.5 kcal/mol barriers for water permeation into bilayers. Barriers are highest when water coordination within the bilayer is prevented, and also when using force fields that accurately reproduce experimental alkane hydration free energies. The magnitude of the average water dipole moment decreases from 2.6 Debye (in bulk) to 1.88 Debye (in membrane interior). This variation correlates with the change in a water molecule's coordination number.

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 Pauli's exclusion principle that suggest a reduced polarizability for condensed-phase water relative to the vacuum value.