matt_papers/SGI_Award_Application/application.tex

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\begin{document}


\title{A Mesoscale Model for Phospholipid Simulations}

\author{Matthew A. Meineke\\
Department of Chemistry and Biochemistry\\
University of Notre Dame\\
Notre Dame, Indiana 46556}

\date{\today}
\maketitle

\section{Research Summary}

Simulations of phospholipid bilayers are, by necessity, quite
complex. The lipid molecules are large, and contain many
atoms. Additionally, the head groups of the lipids are often
zwitterions, and the large separation between charges results in a
large dipole moment. Adding to the complexity are the number of water
molecules needed to properly solvate the lipid bilayer, typically 25
water molecules for every lipid molecule. These factors make it
difficult to study certain biologically interesting phenomena that
have large inherent length or time scale. One such phenomenon is the
existence of the ripple phase ($P_{\beta'}$) of the bilayer between
the gel phase ($L_{\beta'}$) and the fluid phase ($L_{\alpha}$). The
$P_{\beta'}$ phase has been shown to have a ripple period of
100-200~$\mbox{\AA}$.\cite{katsaras00,sengupta00} Simulations of this
length scale would require approximately 1,300 lipid molecules in
addition to all the water needed to fully solvate the bilayer. Another
system of interest is water and proton diffusion through the
membrane. Due to the fluid-like properties of a lipid membrane, not
all diffusion takes place at ion channels. It is therefore of interest
to study the dynamics of permeation through the membrane. These
molecules may then have appreciable residence times (on the order of
nanoseconds) within the bilayer.

\label{sec:ssdModel}

\begin{figure}
\centering
\includegraphics[width=35mm]{ssd.epsi}
\caption{The SSD model with the oxygen and hydrogen atoms drawn in for reference. Here, $\mu$ is the dipole moment of water, and $\sigma$ is the Length scale parameter used for the Lennard-Jones calculations.}
\label{fig:ssdModel}
\end{figure} 


\label{sec:lipidModel}

\begin{figure}
\centering
\includegraphics[angle=-90,width=80mm]{lipidModel.epsi}
\caption{A representation of the lipid model. $\phi$ is the torsion angle, $\theta$ is the bend angle, $\mu$ is the dipole moment of the head group, and n is the chain length.}
\label{fig:lipidModel}
\end{figure}

The mesoscale model used in this research is designed to simplify the
number of calculations needed to properly simulate a phospholipid
bilayer. The water molecules in the simulation are modeled using the
Soft Sticky Dipole (SSD) potential developed by Ichiye \emph{et
al}.\cite{liu96:new_model,liu96:monte_carlo,chandra99:ssd_md}
(Fig. \ref{fig:ssdModel}). This model reduces water to a single point
interaction, while still maintaining the hydrogen-bonding behavior of
water through special short range interactions. The lipid molecule
itself is then modeled as a chain of ``tail'' atoms attached to a
large ``head'' atom (Fig. \ref{fig:lipidModel}). The head atom
contains a freely rotating dipole to mimic the charge separation
present in phosphatidylcholine headgroups.

In the attached images, one can see that the model demonstrates very
promising initial results. In the images, the head atoms are colored
blue, the tail atoms are colored gray, and the water molecules reduced
in size for clarity. The actual simulation is enclosed within the
bounding box. In the simulation containing only 25 lipid models, the
system has demonstrated a spontaneous division into two leaflets, in
route toward a bilayer. In the 50 lipid model system, the lipids show
spontaneous aggregation into micelles from a random initial
configuration. It hould be noted that these initial simulations were
run using only a single processor. We are currently parallelizing the
simulation using the Message Passing Interface (MPI). By implementing
the force decomposition method of Plimpton\cite{plimpton93} to
calculate the long range forces, the size of the system studied will
be greatly expanded. Also, modifications to the model have been
implemented to constrain the dipole of the head group to remain
perpendicular to the tail chain. This will mimic what is seen
experimentally (i.e.~the dipole is aligned perpendicular to the
membrane normal vector). The dipole will be held in place through the
addition of a quadratic potential in the angle the dipole forms with
the tail chain. By varying the ``stiffness'' of the potential, the
effect of the dipole's range of motion on bilayer formation can be
studied.

\bibliographystyle{achemso} 
\bibliography{application}
\end{document}
Revision:	335
Committed:	Thu Mar 13 19:04:44 2003 UTC (21 years, 6 months ago) by mmeineke
Content type:	application/x-tex
File size:	5021 byte(s)
Log Message:	made som e revisions to the application.
#	User	Rev	Content
1	mmeineke	333	\documentclass[11pt]{article}
2
3			\usepackage{graphicx}
4			\usepackage{color}
5			\usepackage{floatflt}
6			\usepackage{amsmath}
7			\usepackage{amssymb}
8			\usepackage{subfigure}
9			\usepackage{palatino}
10			\usepackage[ref]{overcite}
11
12
13
14			\pagestyle{plain}
15			\pagenumbering{arabic}
16			\oddsidemargin 0.0cm \evensidemargin 0.0cm
17			\topmargin -21pt \headsep 10pt
18			\textheight 9.0in \textwidth 6.5in
19			\brokenpenalty=10000
20			\renewcommand{\baselinestretch}{1.2}
21			\renewcommand\citemid{\ } % no comma in optional reference note
22
23
24			\begin{document}
25
26
27			\title{A Mesoscale Model for Phospholipid Simulations}
28
29			\author{Matthew A. Meineke\\
30			Department of Chemistry and Biochemistry\\
31			University of Notre Dame\\
32			Notre Dame, Indiana 46556}
33
34			\date{\today}
35			\maketitle
36
37			\section{Research Summary}
38
39			Simulations of phospholipid bilayers are, by necessity, quite
40	mmeineke	335	complex. The lipid molecules are large, and contain many
41			atoms. Additionally, the head groups of the lipids are often
42			zwitterions, and the large separation between charges results in a
43			large dipole moment. Adding to the complexity are the number of water
44			molecules needed to properly solvate the lipid bilayer, typically 25
45			water molecules for every lipid molecule. These factors make it
46			difficult to study certain biologically interesting phenomena that
47			have large inherent length or time scale. One such phenomenon is the
48			existence of the ripple phase ($P_{\beta'}$) of the bilayer between
49			the gel phase ($L_{\beta'}$) and the fluid phase ($L_{\alpha}$). The
50			$P_{\beta'}$ phase has been shown to have a ripple period of
51			100-200~$\mbox{\AA}$.\cite{katsaras00,sengupta00} Simulations of this
52	mmeineke	333	length scale would require approximately 1,300 lipid molecules in
53			addition to all the water needed to fully solvate the bilayer. Another
54	mmeineke	335	system of interest is water and proton diffusion through the
55	mmeineke	333	membrane. Due to the fluid-like properties of a lipid membrane, not
56	mmeineke	335	all diffusion takes place at ion channels. It is therefore of interest
57			to study the dynamics of permeation through the membrane. These
58			molecules may then have appreciable residence times (on the order of
59			nanoseconds) within the bilayer.
60	mmeineke	333
61			\label{sec:ssdModel}
62
63			\begin{figure}
64			\centering
65	mmeineke	335	\includegraphics[width=35mm]{ssd.epsi}
66			\caption{The SSD model with the oxygen and hydrogen atoms drawn in for reference. Here, $\mu$ is the dipole moment of water, and $\sigma$ is the Length scale parameter used for the Lennard-Jones calculations.}
67	mmeineke	333	\label{fig:ssdModel}
68			\end{figure}
69
70
71			\label{sec:lipidModel}
72
73			\begin{figure}
74			\centering
75			\includegraphics[angle=-90,width=80mm]{lipidModel.epsi}
76			\caption{A representation of the lipid model. $\phi$ is the torsion angle, $\theta$ is the bend angle, $\mu$ is the dipole moment of the head group, and n is the chain length.}
77			\label{fig:lipidModel}
78			\end{figure}
79
80			The mesoscale model used in this research is designed to simplify the
81			number of calculations needed to properly simulate a phospholipid
82	mmeineke	335	bilayer. The water molecules in the simulation are modeled using the
83			Soft Sticky Dipole (SSD) potential developed by Ichiye \emph{et
84			al}.\cite{liu96:new_model,liu96:monte_carlo,chandra99:ssd_md}
85			(Fig. \ref{fig:ssdModel}). This model reduces water to a single point
86			interaction, while still maintaining the hydrogen-bonding behavior of
87			water through special short range interactions. The lipid molecule
88	mmeineke	333	itself is then modeled as a chain of ``tail'' atoms attached to a
89	mmeineke	335	large ``head'' atom (Fig. \ref{fig:lipidModel}). The head atom
90			contains a freely rotating dipole to mimic the charge separation
91			present in phosphatidylcholine headgroups.
92	mmeineke	333
93			In the attached images, one can see that the model demonstrates very
94			promising initial results. In the images, the head atoms are colored
95			blue, the tail atoms are colored gray, and the water molecules reduced
96			in size for clarity. The actual simulation is enclosed within the
97			bounding box. In the simulation containing only 25 lipid models, the
98			system has demonstrated a spontaneous division into two leaflets, in
99	mmeineke	335	route toward a bilayer. In the 50 lipid model system, the lipids show
100	mmeineke	333	spontaneous aggregation into micelles from a random initial
101	mmeineke	335	configuration. It hould be noted that these initial simulations were
102			run using only a single processor. We are currently parallelizing the
103			simulation using the Message Passing Interface (MPI). By implementing
104			the force decomposition method of Plimpton\cite{plimpton93} to
105			calculate the long range forces, the size of the system studied will
106			be greatly expanded. Also, modifications to the model have been
107			implemented to constrain the dipole of the head group to remain
108			perpendicular to the tail chain. This will mimic what is seen
109			experimentally (i.e.~the dipole is aligned perpendicular to the
110			membrane normal vector). The dipole will be held in place through the
111			addition of a quadratic potential in the angle the dipole forms with
112			the tail chain. By varying the ``stiffness'' of the potential, the
113			effect of the dipole's range of motion on bilayer formation can be
114			studied.
115	mmeineke	333
116			\bibliographystyle{achemso}
117			\bibliography{application}
118			\end{document}