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Phospholipid bicelles serve as useful models in NMR
studies of membrane-associated biomolecules. The term bicelle refers
to a mixture of long-chain bilayer forming phospholipids and short-chain
micelle forming lipids of detergents. The structure feature of a
bicelle includes a central planar bilayer formed by long-chain phospholipids
surrounded by a rim of detergent that shields the long-chain lipid
tails from water. Depending on the concentration bicelles may adopt
an isotropic phase or a liquid crystalline phase composed of disk-
shaped particles. In the presence of a magnetic field the bicelle
disks will align with their bilayer normal perpendicular to the
direction of the magnetic field (without chemicals). However if
the disks are in an isotropic phase (non-preferred direction) may
carry a greater possibility of intersection. To examine this notion
we are developing a Monte Carlo simulation program. An essential
part of the program the algorithm to check for intersections of
two disks in a 3-dimensional space has been implemented. Results
from a preliminary study 2-dimensional version of the program offer
insight into spontaneous curvature effects on disk shape size and
orientation.
A phospholipid bilayer is a membrane lipid that consists
of double layers of polar hydrophilic heads that forms the outer
border and nonpolar hydrophobic tails that hide inside the bilayer.
Phospholipid bilayers are formed by a rapid spontaneous process
in a liquid medium where the structure of the bimolecular sheet
self-assembles to the structure of the constituent lipid molecule.
These structures have the tendency to cluster in water to possibly
minimize exposed hydrocarbon chains which result in the formation
of a bilayer compartment. Other important features of lipid bilayers
include their ability to self-seal and tendency to be extensive.
When a phospholipid bilayer come in contact with a micelle (globular
structure in which polar heads are on the surface and hydrocarbon
tails are inside the surface) the micelle tends to align around
the edges of the bilayer structure to form a bicelle or bilayered
micelle. To understand the bicelle’s unique structure one
must know that disk shaped bilayered micelles are formed by a mixture
of long (flat surface preferred) – short (curved surface preferred)
chain of phospholipids in an aqueous medium. Depending on the concentration
of the system bicelles mixtures can experience transitions between
two different phases. The isotropic is considered to be the lower
concentration phase where no positional or orientational order is
present and the disks may move about in a random fashion. Disks
in the nematic phase are exposed to an increased concentration in
which the orientation may be manipulated with a magnetic field.
This causes the disk to be oriented along the direction of that
magnetic field. Simulations using disk models of bicelles have been
used to study the self-assembly structure within a three dimensional
space and the transitions that occur upon concentration increases.
Currently the Kindt group is working on developing a program that
creates disks in a system chooses their position and tackles the
complexes involved in working with three dimensional structures.
My main concern regarding the program will be to develop a method
to test for intersections of disk once inserted into the system.
Method Development Kindt Group
The Kindt group is developing a program using a configurational
biased Monte Carlo Method algorithm that starts bicelles in an isotropic
phase and ends in the nematic phase. The way this works is by growing
polygonal shaped disk in a two dimensional form and transferring
them into three dimensional form. The next step in the program is
to choose the disks position (insert and removal) in the system.
Once a disk is inserted into the system a test must be done to determine
whether the disk intersects another disk or not. Before the intersection
test was derived made we look at different cases of intersection.
Figure 1 show the most important case of intersection of two disks
in a system.
Intersection Test
Mathematically we can tell whether the disks intersect
by taking the “dot product” of vectors on disk two with
the unit normal vector of disk one [Drawing- figure 2]. If the dot
product is positive then the vector points on the same side of the
plane as the unit normal vector; otherwise the dot product is negative
then there is not intersection. A reverse test is done on disk two.
Two-Dimensional Simulations
Two-Dimensional Simulations were adjusted and executed
similar to the three dimensional program in the making to investigate
changes involving the disks area position shape and size.
With a preferred angle of zero the program generates
a larger number of disks in the system than with an angle greater
than zero. In figure 4, the results suggest either larger disks
with more substance or an increase of smaller disk are being generated
in the system depending on the preferred angle. As disks approach
the preferred curve growth no longer continues. Results from figure
5 suggest that the formation domain contains disks of similar shapes
which does not influence packing.
The Kindt group will continue working on the algorithm for creating
disks in a 3-dimensional space. Results from a preliminary study
2-dimensional version of the program raises questions about the
growth of disks with a preferred bond angle. Increasing area fraction
in the system will be explored to see if disks stop growing once
they reach a preferred angle. Continuation of ways to explore spontaneous
curvature effects on disk shape size and orientation will be carried
out.
This material is based on work supported by the National Science
Foundation under Grant No. CHE- 0316076 and the SURE program of
Emory University.
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