Lipid Bilayers
One of the primary research interests in our group is the utilization of computer simulations to study the phase behavior of lipids and lipid membranes. These are challenging systems to study due to the large size of the resulting structures and the time required for the phases of interest to develop. Since computer power is always a limitation, techniques need to be utilized that make these simulations more tractable. One method used by our group is coarse-grain simplification. In the case of lipids, the process is demonstrated in the figure to the right.

Here, we group the atoms of a multipoint molecule into fewer and fewer points. Decreasing the number of particles in the system reduces the number of interactions which need to be calculated, increasing our ability to explore the very large length and time scales needed to observe interesting lipid dynamics. By sacrificing some fine detail, we can improve our understanding of the larger-scale cooperative interactions that influence the phase behavior of these systems. Sometimes this loss of detail can be problematic, particularly in the case of water. For lipid systems, however, trying to understand the approximate behavior is our primary goal.

The Ripple Phase

Much of my group's research activity has been aimed at providing an explanation for the Pβ' ripple phase in lipid bilayers. We have developed a simple "web of dipoles" XYZ model which provides a relatively simple explanation. In this model, lipid molecules are treated as freely-rotating point dipoles which are translationally locked to lattice points in the XY plane, but which can move vertically. Each molecule is harmonically bonded to the surrounding lattice sites. The total potential for this model is given as a sum of dipole-dipole interactions and harmonic bonds between nearest neighbor sites,

Without translation in the z-axis, this model results in frustrated spin systems on hexagonal lattices and exhibits low-energy anti-ferroelectric states on non-hexagonal lattices. The flexibility in the Z-axis allows for spontaneous symmetry breaking which orders the dipoles in the low-energy anti-ferroelectric state at the same time the surface of the system undergoes a macroscopic rippling. With parameter choices (dipole strength, lattice spacing, elastic constants) that approximately match the phosphatidyl choline bilayer, we see macroscopic rippling that is reminiscent of the rippling in real bilayers. The figure on the right shows a hexagonal lattice (7 Å spacing) of dipoles (10 debye) which have formed into a stable macroscopic ripple at 300 K. There is a marked phase transition to a spin-disordered (fluid) phase at 340 K.

Aggregation of coarse-grain lipid models into a bilayer structure
Random Lipid Configuration
30 ns later
Dynamics of Aggregation and Permeation

We have done preliminary work on the aggregation dynamics of ball-and-chain models for lipids. These models were constructed from twinned chains of Lennard-Jones beads with a connecting or "head" bead which had a permanent dipole moment. 1024 of these molecules were embedded in a sea of 25,000 SSD/E water molecules and exhibited normal lipid-like behavior. From a random initial mixture of the ball-and-chain lipids in water, the model lipids collected into micelles within 5 ps and then into bilayer structures within 35 ns at room temperature and pressure. We are now investigating how small molecules (water, ethanol, xenon) which have been embedded in the bilayer will permeate through the bilayer, as well as how they alter the dynamics of inter- and intra-leaf lipid transport. The images to the left show the initial random configuration along with a configuration 30 ns into the trajectory.

These lipid water systems were simulated using the NPTxyz integrator in OOPSE. The NPTxyz integrator maintains an orthorhombic box while attempting to equalize the pressure in all three directions to atmospheric pressure. Because the head groups contain point-dipoles, the integrator also uses the DLM method for propagating orientational degrees of freedom.