Jocelyn M. Rodgers

Molecular Simulation of the DMPC-Cholesterol Phase Diagram

In this paper, we present a coarse-grained model of a hydrated saturated phospholipid bilayer (dimyristoylphosphatidylcholine, DMPC) containing cholesterol that we study using a hybrid dissipative particle dynamics-Monte Carlo method. This approach allows us to reach the time and length scales necessary to study structural and mechanical properties of the bilayer at various temperatures and cholesterol concentrations. The properties studied are the area per lipid, condensation, bilayer thickness, tail order parameters, bending modulus, and area compressibility. Our model quantitatively reproduces most of the experimental effects of cholesterol on these properties and reproduces the main features of the experimental phase and structure diagrams. We also present all-atom simulation results of the system and use these results to further validate the structure of our coarse-grained bilayer. On the basis of the changes in structural properties, we propose a temperature-composition structure diagram, which we compare with the experimental phase and structure diagrams. Attention is paid to the reliability and interpretation of the model and simulation method and of the different experimental techniques. The lateral organization of cholesterol in the bilayer is discussed.

Molecular Simulation of the Effect of Cholesterol on Lipid-Mediated Protein-Protein Interactions

Experiments and molecular simulations have shown that the hydrophobic mismatch between proteins and membranes contributes significantly to lipid-mediated protein-protein interactions. In this article, we discuss the effect of cholesterol on lipid-mediated protein-protein interactions as function of hydrophobic mismatch, protein diameter and protein cluster size, lipid tail length, and temperature. To do so, we study a mesoscopic model of a hydrated bilayer containing lipids and cholesterol in which proteins are embedded, with a hybrid dissipative particle dynamics-Monte Carlo method. We propose a mechanism by which cholesterol affects protein interactions: protein-induced, cholesterol-enriched, or cholesterol-depleted lipid shells surrounding the proteins affect the lipid-mediated protein-protein interactions. Our calculations of the potential of mean force between proteins and protein clusters show that the addition of cholesterol dramatically reduces repulsive lipid-mediated interactions between proteins (protein clusters) with positive mismatch, but does not affect attractive interactions between proteins with negative mismatch. Cholesterol has only a modest effect on the repulsive interactions between proteins with different mismatch.

Local molecular field theory for the treatment of electrostatics

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 interactions 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 σ, this equation may be solved more simply than the detailed simulation geometry might suggest. Proper choice of the smoothing length σ plays a major role in ensuring the accuracy of this approximation. We examine the results of a basic confinement of water between corrugated walls 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 σ. The slowly varying part of the restructured electrostatic potential will be more symmetric than the local details of confinements.

Interplay of local hydrogen-bonding and long-ranged dipolar forces in simulations of confined water.

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 errors 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 3 simple molecular systems that exhibit different aspects of the failure of a naïive 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.

Deconstructing Classical Water Models at Interfaces and in Bulk

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.

Molecular Monte Carlo Simulations Using Graphics Processing Units: To Waste Recycle or Not?

In the waste recycling Monte Carlo (WRMC) algorithm, (1) multiple trial states may be simultaneously generated and utilized during Monte Carlo moves to improve the statistical accuracy of the simulations, suggesting that such an algorithm may be well posed for implementation in parallel on graphics processing units (GPUs). In this paper, we implement two waste recycling Monte Carlo algorithms in CUDA (Compute Unified Device Architecture) using uniformly distributed random trial states and trial states based on displacement random-walk steps, and we test the methods on a methane-zeolite MFI framework system to evaluate their utility. We discuss the specific implementation details of the waste recycling GPU algorithm and compare the methods to other parallel algorithms optimized for the framework system. We analyze the relationship between the statistical accuracy of our simulations and the CUDA block size to determine the efficient allocation of the GPU hardware resources. We make comparisons between the GPU and the serial CPU Monte Carlo implementations to assess speedup over conventional microprocessors. Finally, we apply our optimized GPU algorithms to the important problem of determining free energy landscapes, in this case for molecular motion through the zeolite LTA.

Accurate thermodynamics for short-ranged truncations of Coulomb interactions in site-site molecular models

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 corrections for the thermodynamics of uniform truncated systems are possible. In particular, results for the simple point charge/extended (SPC/E) water model treated with spherically truncated Coulomb interactions suggested by local molecular field theory [J. M. Rodgers and J. D. Weeks, Proc. Natl. Acad. Sci. U.S.A. 105, 19136 (2008)] are presented. We extend the 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.

On the efficient and accurate short-ranged simulations of uniform polar molecular liquids

We show that spherical truncations of the 1/r interactions in models for water and acetonitrile yield very accurate results in bulk simulations for all site–site pair correlation functions as well as dipole–dipole correlation functions. This good performance in bulk simulations contrasts with the generally poor results found with the use of such truncations in nonuniform molecular systems. We argue that Local Molecular Field (LMF) theory provides a general theoretical framework that gives the necessary corrections to simple truncations in most nonuniform environments and explains the accuracy of spherical truncations in uniform environments by showing that these corrections are very small. LMF theory is derived from the exact Yvon–Born–Green (YBG) hierarchy by making physically-motivated and well-founded approximations. New and technically interesting derivations of both the YBG hierarchy and LMF theory for a variety of site–site molecular models are presented in appendices. The main paper focuses on understanding the accuracy of these spherical truncations in uniform systems both phenomenologically and quantitatively using LMF theory.

Waste-recycling Monte Carlo with optimal estimates: Application to free energy calculations in alloys

The estimator proposed recently by Delmas and Jourdain for waste-recycling Monte Carlo achieves variance reduction optimally with respect to a control variate that is evaluated directly using the simulation data. Here, the performance of this estimator is assessed numerically for free energy calculations in generic binary alloys and is compared to those of other estimators taken from the literature. A systematic investigation with varying simulation parameters of a simplified system, the anti-ferromagnetic Ising model, is first carried out in the transmutation ensemble using path-sampling. We observe numerically that (i) the variance of the Delmas-Jourdain estimator is indeed reduced compared to that of other estimators; and that (ii) the resulting reduction is close to the maximal possible one, despite the inaccuracy in the estimated control variate. More extensive path-sampling simulations involving an FeCr alloy system described by a many-body potential additionally show that (iii) gradual transmutations accommodate the atomic frustrations; thus, alleviating the numerical ergodicity issue present in numerous alloy systems and eventually enabling the determination of phase coexistence conditions.