Sagar A. Pandit

Parallel reactive molecular dynamics: Numerical methods and algorithmic techniques

Molecular dynamics modeling has provided a powerful tool for simulating and understanding diverse systems - ranging from materials processes to biophysical phenomena. Parallel formulations of these methods have been shown to be among the most scalable scientific computing applications. Many instances of this class of methods rely on a static bond structure for molecules, rendering them infeasible for reactive systems. Recent work on reactive force fields has resulted in the development of ReaxFF, a novel bond order potential that bridges quantum-scale and classical MD approaches by explicitly modeling bond activity (reactions) and charge equilibration. These aspects of ReaxFF pose significant challenges from a computational standpoint, both in sequential and parallel contexts. Evolving bond structure requires efficient dynamic data structures. Minimizing electrostatic energy through charge equilibration requires the solution of a large sparse linear system with a shielded electrostatic kernel at each sub-femtosecond long time-step. In this context, reaching spatio-temporal scales of tens of nanometers and nanoseconds, where phenomena of interest can be observed, poses significant challenges. In this paper, we present the design and implementation details of the Purdue Reactive Molecular Dynamics code, PuReMD. PuReMD has been demonstrated to be highly efficient (in terms of processor performance) and scalable. It extends current spatio-temporal simulation capability for reactive atomistic systems by over an order of magnitude. It incorporates efficient dynamic data structures, algorithmic optimizations, and effective solvers to deliver low per-time-step simulation time, with a small memory footprint. PuReMD is comprehensively validated for performance and accuracy on up to 3375 cores on a commodity cluster (Hera at LLNL-OCF). Potential performance bottlenecks to scalability beyond our experiments have also been analyzed. PuReMD is available over the public domain and has been used to model diverse systems, ranging from strain relaxation in Si-Ge nanobars, water-silica surface interaction, and oxidative stress in lipid bilayers (bio-membranes).

Molecular dynamics simulation of a dipalmitoylphosphatidylcholine bilayer with NaCl.

Molecular dynamics simulations are performed on two hydrated dipalmitoylphosphatidylcholine bilayer systems: one with pure water and one with added NaCl. Due to the rugged nature of the membrane/electrolyte interface, ion binding to the membrane surface is characterized by the loss of ion hydration. Using this structural characterization, binding of Na(+) and Cl(-) ions to the membrane is observed, although the binding of Cl(-) is seen to be slightly weaker than that of Na(+). Dehydration is seen to occur to a different extent for each type of ion. In addition, the excess binding of Na(+) gives rise to a net positive surface charge density just outside the bilayer. The positive density produces a positive electrostatic potential in this region, whereas the system without salt shows an electrostatic potential of zero.

An improved united atom force field for simulation of mixed lipid bilayers.

We introduce a new force field (43A1-S3) for simulation of membranes by the Gromacs simulation package. Construction of the force fields is by standard methods of electronic structure computations for bond parameters and charge distribution and specific volumes and heats of vaporization for small-molecule components of the larger lipid molecules for van der Waals parameters. Some parameters from the earlier 43A1 force field are found to be correct in the context of these calculations, while others are modified. The validity of the force fields is demonstrated by correct replication of X-ray form factors and NMR order parameters over a wide range of membrane compositions in semi-isotropic NTP 1 atm simulations. 43-A1-S3 compares favorably with other force fields used in conjunction with the Gromacs simulation package with respect to the breadth of phenomena that it accurately reproduces.

Complexation of Phosphatidylcholine Lipids with Cholesterol

It is postulated that the specific interactions between cholesterol and lipids in biological membranes are crucial in the formation of complexes leading subsequently to membrane domains (so-called rafts). These interactions are studied in molecular dynamics simulations performed on a dipalmitoylphosphatidylcholine (DPPC)-cholesterol bilayer mixture and a dilauroylphosphatidylcholine (DLPC)-cholesterol bilayer mixture, both having a cholesterol concentration of 40 mol %. Complexation of the simulated phospholipids with cholesterol is observed and visualized, exhibiting 2:1 and 1:1 stoichiometries. The most popular complex is found to be 1:1 in the case of DLPC, whereas the DPPC system carries a larger population of 2:1 complexes. This difference in the observed populations of complexes is shown to be a result of differences in packing geometry and phospholipid conformation due to the differing tail length of the two phosphatidylcholine lipids. Furthermore, aggregation of these complexes appears to form hydrogen-bonded networks in the system containing a mixture of cholesterol and DPPC. The CH...O hydrogen bond plays a crucial role in the formation of these complexes as well as the hydrogen bonded aggregates. The aggregation and extension of such a network implies a possible means by which phospholipid:cholesterol domains form.

Molecular Dynamics Simulation of Dipalmitoylphosphatidylserine Bilayer with Na+ Counterions

We performed a molecular dynamics simulation of dipalmitoylphosphatidylserine (DPPS) bilayer with Na+ counterions. We found that hydrogen bonding between the NH group and the phosphate group leads to a reduction in the area per headgroup when compared to the area in dipalmitoylphosphatidylcholine bilayer. The Na+ ions bind to the oxygen in the carboxyl group of serine, thus giving rise to a dipolar bilayer similar to dipalmitoylphosphatidylethanolamine bilayer. The results of the simulation show that counterions play a crucial role in determining the structural and electrostatic properties of DPPS bilayer.

Cholesterol Packing around Lipids with Saturated and Unsaturated Chains : A Simulation Study

The fundamental role of cholesterol in the regulation of eukaryotic membrane structure is well-established. However the manner in which atomic level interactions between cholesterol and lipids, with varying degrees of chain unsaturation and polar groups, affect the overall structure and organization of the bilayer is only beginning to be understood. In this paper we describe a series of Molecular Dynamics simulations designed to provide new insights into lipid-cholesterol interactions as a function of chain unsaturation. We have run simulations of varying concentrations of cholesterol in dipalmitoyl phosphatidylcholine (DPPC), palmitoyl-oleyol phosphatidylcholine (POPC), and dioleyol phosphatidylcholine (DOPC) bilayers. Structural analysis of the simulations reveals both atomistic and systemic details of the interactions and are presented here. In particular, we find that the minimum partial molecular area of cholesterol occurs in POPC-Chol mixtures implying the most favorable packing. Physically, this appears to be related to the fact that the two faces of the cholesterol molecule are different from each other and that the steric cross section of cholesterol molecules drops sharply near the small chain tails.

An algorithm to describe molecular scale rugged surfaces and its application to the study of a water/lipid bilayer interface

We propose an algorithm for the general description of rugged molecular scale interfacial surfaces. This algorithm was implemented in the description of a phospholipid membrane/water interface with the rugged surface defined by the phospholipid phosphorous atoms. The method allowed us to clearly discern four layered regions of water based upon the water local density as a function of the distance from the membrane surface. Furthermore, the water in each of the layered regions was found to have distinct orientational properties. The classification we make based on density due to our new algorithm is in agreement with that delineated in previous studies based on water orientation. The contribution of the different water regions to the total electrostatic potential reveals the particular way in which each layer’s water polarization contributes to the total dipole potential of the hydrated membrane.

A model for leveling coalitions among primate males: toward a theory of egalitarianism

We present a simple model of within-group leveling coalitions among male primates. The model assumes that the value of the coalition is the sum of the payoffs of its members, that the individual’s payoff is monotonically decreasing with its rank and that coalitions do not cause rank changes. It predicts that mainly mid- to low rankers engage in leveling coalitions, and that most coalition partners are of adjacent ranks. These predictions agree reasonably well with observations in nature. The model also makes the novel predictions that leveling coalitions are found where male mating competition has only a moderate contest component, and that male dominance ranks will become poorly differentiated where leveling coalitions are frequent. Both these predictions are consistent with observations on groups of macaques and baboons. The model also may account for leveling coalitions among egalitarian human foragers, without making additional assumptions about special human capabilities.

A model for within-group coalitionary aggression among males

Perhaps the most common form of cooperation among primates is the formation of coalitions. Competition among males within a group concerns a constant quantity of the limiting resource (fertilizations). Contest competition over fertilizations is known to produce payoffs that are distributed according to the priority-of-access model, and hence show an exponential decline in payoff with rank. We develop a model for rank-changing, within-group coalitions among primate males. For these coalitions to occur, they must be both profitable (i.e. improve fitness) for all coalition members and feasible (i.e. be able to beat the targets). We assume that the value of the coalition is the sum of the payoffs of the partners in their original ranks. We distinguish three basic coalition configurations, depending on the dominance ranks of the coalition partners relative to their target. We predict five basic coalition types. First, all-up, rank-changing coalitions targeting individuals ranking above all coalition partners; these are expected to involve coalition partners ranking just below their target, concern top rank, and be small, just two or three animals. Second, bridging, rank-changing coalitions, where higher-rankers support lower-rankers to rise to a rank below themselves; these are expected to be most common where a high-ranking male in a despotic system can support a low-ranking relative. Third, bridging non-rank-changing coalitions; these are expected to be common whenever high-ranking males have low-ranking close relatives. Fourth, non-rank-changing coalitions by high-rankers against lower-ranking targets; these are expected to serve to counteract or prevent the first type. Fifth, non-rank-changing, leveling coalitions, in which all partners rank below their target and which flatten the payoff distribution; these are expected to be large and mainly involve lower-ranking males. Bridging, rank-changing coalitions are expected in situations where contest is strong, all-up rank-changing coalitions where contest is intermediate, and leveling coalitions where contest is weak. We review the empirical patterns found among primates. The strong predictions of the model are confirmed by observational data on male-male coalitions in primates.

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.