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Comparing trunk/mattDisertation/lipid.tex (file contents):
Revision 1025 by mmeineke, Sat Jan 31 22:10:21 2004 UTC vs.
Revision 1026 by mmeineke, Thu Feb 5 00:37:36 2004 UTC

+potential.
+The model used in this investigation adds more information to the
-<
+interactions than the previous two models,
->
+interactions than the previous two models, while still balancing the
->
+need for simplifications over atomistic detail.  The model uses
->
+Lennard-Jones spheres for the head and tail groups of the
->
+phopholipids, allowing for the ability to scale the parameters to
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+reflect various sized chain configurations while keeping the number of
->
+interactions small.  What sets this model apart, however, is the use
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+of dipoles to represent the electrosttaic nature of the
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+phospholipids. The dipole electrostatic interaction is shorter range
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+than coulombic ($\frac{1}{r^3}$ versus $\frac{1}{r}$), eliminating the
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+need for a costly Ewald sum.
-+
+Another key feature of this model, is the use of a dipolar water model
-+
+to represent the solvent. The soft sticky dipole ({\scssd})
-+
+water \cite{Liu:1996a} relies on the dipole for long range
-+
+electrostatic effects, butalso contains a short range correction for
-+
+hydrogen bonding. In this way the systems in this research mimic the
-+
+entropic contribution to the hydrophobic effect due to hydrogen-bond
-+
+network deformation around a non-polar entity, \emph{i.e.}~ the
-+
+phospholipid.
-+
-+
+The following is an outline of this chapter.
-+
+Sec.~\ref{lipoidSec:Methods} is an introduction to the lipid model
-+
+used in these simulations.  As well as clarification about the water
-+
+model and integration techniques.  The various simulation setups
-+
+explored in this research are outlined in
-+
+Sec.~\ref{lipidSec:ExpSetup}. Sec.~\ref{lipidSec:Results} and
-+
+Sec.~\ref{lipidSec:Discussion} give a summary of the results and
-+
+interpretation of those results respectively.  Finally, the
-+
+conclusions of this chapter are presented in
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+Sec.~\ref{lipidSec:Conclusion}.
-+
+\section{\label{lipidSec:Methods}Methods}
-–
+\subsection{\label{lipidSec:lipidMedel}The Lipid Model}
-+
-+
+\subsection{\label{lipidSec:lipidModel}The Lipid Model}
-+
+\begin{figure}
+\caption{Schematic diagram of the single chain phospholipid model}
+the same bond, bend, or torsion.  However, internal interactions not
+directly involved in a bonded pair are calculated.
-+
+All simulations presented here use a two chained lipid as pictured in
-+
+Fig.~\ref{lipidFig:twochain}.  The chains are both eight beads long,
-+
+and their mass and Lennard Jones parameters are summarized in
-+
+Table~\ref{lipidTable:tcLJParams}. The magnitude of the dipole moment
-+
+for the head bead is 10.6~Debye, and the bend and torsion parameters
-+
+are summarized in Table~\ref{lipidTable:teBTParams}.
-+
+\section{label{lipidSec:furtherMethod}Further Methodology}
-+
-+
+As mentioned previously, the water model used throughout these
-+
+simulations was the {\scssd} model of
-+
+Ichiye.\cite{liu:1996a,Liu:1996b,Chandra:1999} A discussion of the
-+
+model can be found in Sec.~\ref{oopseSec:SSD}. As for the integration
-+
+of the equations of motion, all simulations were performed in an
-+
+orthorhombic periodic box with a thermostat on velocities, and an
-+
+independent barostat on each cartesian axis $x$, $y$, and $z$.  This
-+
+is the $\text{NPT}_{xyz}$. ensemble described in Sec.~\ref{oopseSec:Ensembles}.
-+
-+
-+
+\subsection{\label{lipidSec:ExpSetup}Experimental Setup}
-+
-+
+Two main starting configuration classes were used in this research:
-+
+random and ordered bilayers.  The ordered bilayer starting
-+
+configurations were all started from an equilibrated bilayer at
-+
+~K. The original configuration for the first 300~K run was
-+
+assembled by placing the phospholipids centers of mass on a planar
-+
+hexagonal lattice.  The lipids were oriented with their long axis
-+
+perpendicular to the plane.  The second leaf simply mirrored the first
-+
+leaf, and the appropriate number of waters were then added above and
-+
+below the bilayer.
-+
-+
+The random configurations took more work to generate.  To begin, a
-+
+test lipid was placed in a simulation box already containing water at
-+
+the intended density.  The waters were then tested for overlap with
-+
+the lipid using a 5.0~$\mbox{\AA}$ buffer distance.  This gave an
-+
+estimate for the number of waters each lipid would displace in a
-+
+simulation box. A target number of waters was then defined which
-+
+included the number of waters each lipid would displace, the number of
-+
+waters desired to solvate each lipid, and a fudge factor to pad the
-+
+initialization.
-+
-+
+Next, a cubic simulation box was created that contained at least the
-+
+target number of waters in an FCC lattice (the lattice was for ease of
-+
+placement).  What followed was a RSA simulation similar to those of
-+
+Chapt.~\ref{chapt:RSA}. The lipids were sequentially given a random
-+
+position and orientation within the box.  If a lipid's position caused
-+
+atomic overlap with any previously adsorbed lipid, its position and
-+
+orientation were rejected, and a new random adsorption site was
-+
+attempted. The RSA simulation proceeded until all phospholipids had
-+
+been adsorbed.  After adsorption, all water molecules with locations
-+
+that overlapped with the atomic coordinates of the lipids were
-+
+removed.
-+
-+
+Finally, water molecules were removed one by one at random until the
-+
+desired number of waters per lipid was reached.  The typical low final
-+
+density for these initial configurations was not a problem, as the box
-+
+would shrink to an appropriate size within the first 50~ps of a
-+
+simulation in the $\text{NPT}_{xyz}$ ensemble.
-+
-+
+\subsection{\label{lipidSec:Configs}The simulation configurations}
-+
-+
+Table ~\ref{lipidTable:simNames} summarizes the names and important
-+
+details of the simulations.  The B set of simulations were all started
-+
+in an ordered bilayer and observed over a period of 10~ns. Simulution
-+
+RL was integrated for approximately 20~ns starting from a random
-+
+configuration as an example of spontaneous bilayer aggregation.
-+
+Lastly, simulation RH was also started from a random configuration,
-+
+but with a lesser water content and higher temperature to show the
-+
+spontaneous aggregation of an inverted hexagonal lamellar phase.

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Comparing trunk/mattDisertation/lipid.tex (file contents): Revision 1025 by mmeineke, Sat Jan 31 22:10:21 2004 UTC vs. Revision 1026 by mmeineke, Thu Feb 5 00:37:36 2004 UTC

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Comparing trunk/mattDisertation/lipid.tex (file contents):
Revision 1025 by mmeineke, Sat Jan 31 22:10:21 2004 UTC vs.
Revision 1026 by mmeineke, Thu Feb 5 00:37:36 2004 UTC