| 1 |
\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 |
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 |
length scale would require approximately 1,300 lipid molecules in |
| 53 |
addition to all the water needed to fully solvate the bilayer. Another |
| 54 |
system of interest is water and proton diffusion through the |
| 55 |
membrane. Due to the fluid-like properties of a lipid membrane, not |
| 56 |
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 |
|
| 61 |
\label{sec:ssdModel} |
| 62 |
|
| 63 |
\begin{figure} |
| 64 |
\centering |
| 65 |
\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 |
\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 |
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 |
itself is then modeled as a chain of ``tail'' atoms attached to a |
| 89 |
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 |
|
| 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 |
route toward a bilayer. In the 50 lipid model system, the lipids show |
| 100 |
spontaneous aggregation into micelles from a random initial |
| 101 |
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 |
|
| 116 |
\bibliographystyle{achemso} |
| 117 |
\bibliography{application} |
| 118 |
\end{document} |
