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.
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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.
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