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+\section{\label{lipidSection:introduction}Introduction}
-<
+\section{\label{lipidSection:model}Model}
->
+Under biologically relevant conditions, phospholipids are solvated
->
+in aqueous solutions at a roughly 25:1 ratio. Solvation can have a
->
+tremendous impact on transport phenomena in biological membranes
->
+since it can affect the dynamics of ions and molecules that are
->
+transferred across membranes. Studies suggest that because of the
->
+directional hydrogen bonding ability of the lipid headgroups, a
->
+small number of water molecules are strongly held around the
->
+different parts of the headgroup and are oriented by them with
->
+residence times for the first hydration shell being around 0.5 - 1
->
+ns\cite{Ho1992}. In the second solvation shell, some water molecules
->
+are weakly bound, but are still essential for determining the
->
+properties of the system. Transport of various molecular species
->
+into living cells is one of the major functions of membranes. A
->
+thorough understanding of the underlying molecular mechanism for
->
+solute diffusion is crucial to the further studies of other related
->
+biological processes. All transport across cell membranes takes
->
+place by one of two fundamental processes: Passive transport is
->
+driven by bulk or inter-diffusion of the molecules being transported
->
+or by membrane pores which facilitate crossing. Active transport
->
+depends upon the expenditure of cellular energy in the form of ATP
->
+hydrolysis. As the central processes of membrane assembly,
->
+translocation of phospholipids across membrane bilayers requires the
->
+hydrophilic head of the phospholipid to pass through the highly
->
+hydrophobic interior of the membrane, and for the hydrophobic tails
->
+to be exposed to the aqueous environment\cite{Sasaki2004}. A number
->
+of studies indicate that the flipping of phospholipids occurs
->
+rapidly in the eukaryotic endoplasmic reticulum and the bacterial
->
+cytoplasmic membrane via a bi-directional, facilitated diffusion
->
+process requiring no metabolic energy input. Another system of
->
+interest is the distribution of sites occupied by inhaled
->
+anesthetics in membrane. Although the physiological effects of
->
+anesthetics have been extensively studied, the controversy over
->
+their effects on lipid bilayers still continues. Recent deuterium
->
+NMR measurements on halothane on POPC lipid bilayers suggest the
->
+anesthetics are primarily located at the hydrocarbon chain
->
+region\cite{Baber1995}. However, infrared spectroscopy experiments
->
+suggest that halothane in DMPC lipid bilayers lives near the
->
+membrane/water interface\cite{Lieb1982}.
-<
+\section{\label{lipidSection:methods}Methods}
->
+Molecular dynamics simulations have proven to be a powerful tool for
->
+studying the functions of biological systems, providing structural,
->
+thermodynamic and dynamical information. Unfortunately, much of
->
+biological interest happens on time and length scales well beyond
->
+the range of current simulation technologies. Several schemes are
->
+proposed in this chapter to overcome these difficulties.
-+
+\section{\label{lipidSection:model}Model and Methodology}
-+
-+
+\subsection{\label{lipidSection:SSD}The Soft Sticky Dipole Water Model}
-+
-+
+In a typical bilayer simulation, the dominant portion of the
-+
+computation time will be spent calculating water-water interactions.
-+
+As an efficient solvent model, the Soft Sticky Dipole (SSD) water
-+
+model\cite{Chandra1999,Fennell2004} is used as the explicit solvent
-+
+in this project. Unlike other water models which have partial
-+
+charges distributed throughout the whole molecule, the SSD water
-+
+model consists of a single site which is a Lennard-Jones interaction
-+
+site, as well as a point dipole. A tetrahedral potential is added to
-+
+correct for hydrogen bonding. The following equation describes the
-+
+interaction between two water molecules:
-+
+\[
-+
+V_{SSD}  = V_{LJ} (r_{ij} ) + V_{dp} (r_{ij} ,\Omega _i ,\Omega _j )
-+
++ V_{sticky} (r_{ij} ,\Omega _i ,\Omega _j )
-+
+\]
-+
+where $r_{ij}$ is the vector between molecule $i$ and molecule $j$,
-+
+$\Omega _i$ and $\Omega _j$ are the orientational degrees of freedom
-+
+for molecule $i$ and molecule $j$ respectively.
-+
+\[
-+
+V_{LJ} (r_{ij} ) = 4\varepsilon _{ij} \left[ {\left( {\frac{{\sigma
-+
+_{ij} }}{{r_{ij} }}} \right)^{12}  - \left( {\frac{{\sigma _{ij}
-+
+}}{{r_{ij} }}} \right)^6 } \right]
-+
+\]
-+
+\[
-+
+V_{dp} (r_{ij} ,\Omega _i ,\Omega _j ) = \frac{1}{{4\pi \varepsilon
-+
+_0 }}\left[ {\frac{{\mu _i  \cdot \mu _j }}{{r_{ij}^3 }} -
-+
+\frac{{3\left( {\mu _i  \cdot r_{ij} } \right)\left( {\mu _i  \cdot
-+
+r_{ij} } \right)}}{{r_{ij}^5 }}} \right]
-+
+\]
-+
+\[
-+
+V_{sticky} (r_{ij} ,\Omega _i ,\Omega _j ) = v_0 [s(r_{ij} )w(r_{ij}
-+
+,\Omega _i ,\Omega _j ) + s'(r_{ij} )w'(r_{ij} ,\Omega _i ,\Omega _j
-+
+)]
-+
+\]
-+
+where $v_0$ is a strength parameter, $s$ and $s'$ are cubic
-+
+switching functions, while $w$   and $w'$  are responsible for the
-+
+tetrahedral potential and the short-range correction to the dipolar
-+
+interaction respectively.
-+
+\[
-+
+\begin{array}{l}
-+
+ w(r_{ij} ,\Omega _i ,\Omega _j ) = \sin \theta _{ij} \sin 2\theta _{ij} \cos 2\phi _{ij}  \\
-+
+ w'(r_{ij} ,\Omega _i ,\Omega _j ) = (\cos \theta _{ij}  - 0.6)^2 (\cos \theta _{ij}  + 0.8)^2  - w_0  \\
-+
+ \end{array}
-+
+\]
-+
+Although the dipole-dipole and sticky interactions are more
-+
+mathematically complicated than Coulomb interactions, the number of
-+
+pair interactions is reduced dramatically both because the model
-+
+only contains a single-point as well as "short range" nature of the
-+
+more expensive interaction.
-+
-+
+\subsection{\label{lipidSection:coarseGrained}The Coarse-Grained Phospholipid Model}
-+
-+
+Fig.~\ref{lipidFigure:coarseGrained} shows a schematic for our
-+
+coarse-grained phospholipid model. The lipid head group is modeled
-+
+by a linear rigid body which consists of three Lennard-Jones spheres
-+
+and a centrally located point-dipole. The backbone atoms in the
-+
+glycerol motif are modeled by Lennard-Jones spheres with dipoles.
-+
+Alkyl groups in hydrocarbon chains are replaced with unified
-+
+$\text{{\sc CH}}_2$ or $\text{{\sc CH}}_3$ atoms.
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=3in]{coarse_grained.eps}
-+
+\caption[A representation of coarse-grained phospholipid model]{A
-+
+representation of coarse-grained phospholipid model. The lipid
-+
+headgroup consists of $\text{{\sc PO}}_4$ group (yellow),
-+
+$\text{{\sc NC}}_4$ group (blue) and a united $\text{{\sc C}}$ atom
-+
+(gray) $ with a dipole, while the glycerol backbone includes dipolar
-+
+$\text{{\sc CE}}$ (red) and $\text{{\sc CK}}$ (pink) groups. Alkyl
-+
+groups in hydrocarbon chains are simply represented by gray united
-+
+atoms.} \label{lipidFigure:coarseGrained}
-+
+\end{figure}
-+
-+
+Accurate and efficient computation of electrostatics is one of the
-+
+most difficult tasks in molecular modeling. Traditionally, the
-+
+electrostatic interaction between two molecular species is
-+
+calculated as a sum of interactions between pairs of point charges,
-+
+using Coulomb's law:
-+
+\[
-+
+V = \sum\limits_{i = 1}^{N_A } {\sum\limits_{j = 1}^{N_B }
-+
+{\frac{{q_i q_j }}{{4\pi \varepsilon _0 r_{ij} }}} }
-+
+\]
-+
+where $N_A$ and $N_B$ are the number of point charges in the two
-+
+molecular species. Originally developed to study ionic crystals, the
-+
+Ewald sum method mathematically transforms this straightforward but
-+
+conditionally convergent summation into two more complicated but
-+
+rapidly convergent sums. One summation is carried out in reciprocal
-+
+space while the other is carried out in real space. An alternative
-+
+approach is the multipole expansion, which is based on electrostatic
-+
+moments, such as charge (monopole), dipole, quadrupole etc.
-+
-+
+Here we consider a linear molecule which consists of two point
-+
+charges $\pm q$ located at $ ( \pm \frac{d}{2},0)$. The
-+
+electrostatic potential at point $P$ is given by:
-+
+\[
-+
+\frac{1}{{4\pi \varepsilon _0 }}\left( {\frac{{ - q}}{{r_ -  }} +
-+
+\frac{{ + q}}{{r_ +  }}} \right) = \frac{1}{{4\pi \varepsilon _0
-+
+}}\left( {\frac{{ - q}}{{\sqrt {r^2  + \frac{{d^2 }}{4} + rd\cos
-+
+\theta } }} + \frac{q}{{\sqrt {r^2  + \frac{{d^2 }}{4} - rd\cos
-+
+\theta } }}} \right)
-+
+\]
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=3in]{charge_dipole.eps}
-+
+\caption[An illustration of split-dipole
-+
+approximation]{Electrostatic potential due to a linear molecule
-+
+comprising two point charges with opposite charges. }
-+
+\label{lipidFigure:chargeDipole}
-+
+\end{figure}
-+
-+
+The basic assumption of the multipole expansion is $r \gg d$ , thus,
-+
+$\frac{{d^2 }}{4}$ inside the square root of the denominator is
-+
+neglected. This is a reasonable approximation in most cases.
-+
+Unfortunately, in our headgroup model, the distance of charge
-+
+separation $d$ (4.63 $\AA$ in PC headgroup) may be comparable to
-+
+$r$. Nevertheless, we could still assume  $ \cos \theta  \approx 0$
-+
+in the central region of the headgroup. Using Taylor expansion and
-+
+associating appropriate terms with electric moments will result in a
-+
+"split-dipole" approximation:
-+
+\[
-+
+V(r) = \frac{1}{{4\pi \varepsilon _0 }}\frac{{r\mu \cos \theta
-+
+}}{{R^3 }}
-+
+\]
-+
+where$R = \sqrt {r^2  + \frac{{d^2 }}{4}}$ Placing a dipole at point
-+
+$P$ and applying the same strategy, the interaction between two
-+
+split-dipoles is then given by:
-+
+\[
-+
+V_{sd} (r_{ij} ,\Omega _i ,\Omega _j ) = \frac{1}{{4\pi \varepsilon
-+
+_0 }}\left[ {\frac{{\mu _i  \cdot \mu _j }}{{R_{ij}^3 }} -
-+
+\frac{{3\left( {\mu _i  \cdot r_{ij} } \right)\left( {\mu _i  \cdot
-+
+r_{ij} } \right)}}{{R_{ij}^5 }}} \right]
-+
+\]
-+
+where $\mu _i$  and  $\mu _j$ are the dipole moment of molecule $i$
-+
+and molecule $j$ respectively, $r_{ij}$ is vector between molecule
-+
+$i$ and molecule $j$, and $R_{ij}$ is given by,
-+
+\[
-+
+R_{ij}  = \sqrt {r_{ij}^2  + \frac{{d_i^2 }}{4} + \frac{{d_j^2
-+
+}}{4}}
-+
+\]
-+
+where $d_i$ and $d_j$ are the charge separation distance of dipole
-+
+and respectively. This approximation to the multipole expansion
-+
+maintains the fast fall-off of the multipole potentials but lacks
-+
+the normal divergences when two polar groups get close to one
-+
+another. The comparision between different electrostatic
-+
+approximation is shown in \ref{lipidFigure:splitDipole}. Due to the
-+
+divergence at the central region of the headgroup introduced by
-+
+dipole-dipole approximation, we discover that water molecules are
-+
+locked into the central region in the simulation. This artifact can
-+
+be corrected using split-dipole approximation or other accurate
-+
+methods.
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=\linewidth]{split_dipole.eps}
-+
+\caption[Comparison between electrostatic
-+
+approximation]{Electrostatic potential map for two pairs of charges
-+
+with different alignments: (a) illustration of different alignments;
-+
+(b) charge-charge interaction; (c) dipole-dipole approximation; (d)
-+
+split-dipole approximation.} \label{lipidFigure:splitDipole}
-+
+\end{figure}
-+
-+
+%\section{\label{lipidSection:methods}Methods}
-+
+\section{\label{lipidSection:resultDiscussion}Results and Discussion}
-+
-+
+\subsection{One Lipid in Sea of Water Molecules}
-+
-+
+To tune our parameters without the inter-headgroup interactions,
-+
+atomistic models of one lipid (DMPC or DLPE) in sea of water
-+
+molecules (TIP3P) were built and studied using atomistic molecular
-+
+dynamics. The simulation was analyzed using a set of radial
-+
+distribution functions, which give the probability of finding a pair
-+
+of molecular species a distance apart, relative to the probability
-+
+expected for a completely random distribution function at the same
-+
+density.
-+
-+
+\begin{equation}
-+
+g_{AB} (r) = \frac{1}{{\rho _B }}\frac{1}{{N_A }} < \sum\limits_{i
-+
+\in A} {\sum\limits_{j \in B} {\delta (r - r_{ij} )} }  >
-+
+\end{equation}
-+
+\begin{equation}
-+
+g_{AB} (r,\cos \theta ) = \frac{1}{{\rho _B }}\frac{1}{{N_A }} <
-+
+\sum\limits_{i \in A} {\sum\limits_{j \in B} {\delta (r - r_{ij} )}
-+
+} \delta (\cos \theta _{ij}  - \cos \theta ) >
-+
+\end{equation}
-+
-+
+From Fig.~\ref{lipidFigure:PCFAtom}, we can identify the first
-+
+solvation shell (3.5 $\AA$) and the second solvation shell (5.0
-+
+$\AA$) from both plots. However, the corresponding orientations are
-+
+different. In DLPE, water molecules prefer to sit around $\text{{\sc
-+
+NH}}_3$ group due to the hydrogen bonding. In contrast, because of
-+
+the hydrophobic effect of the $ {\rm{N(CH}}_{\rm{3}}
-+
+{\rm{)}}_{\rm{3}} $ group, the preferred position of water molecules
-+
+in DMPC is around the $\text{{\sc PO}}_4$ Group. When the water
-+
+molecules are far from the headgroup, the distribution of the two
-+
+angles should be uniform. The correlation close to center of the
-+
+headgroup dipole in both plots tells us that in the closely-bound
-+
+region, the dipoles of the water molecules are preferentially
-+
+anti-aligned with the dipole of headgroup. When the water molecules
-+
+are far from the headgroup, the distribution of the two angles
-+
+should be uniform. The correlation close to center of the headgroup
-+
+dipole in both plots tell us that in the closely-bound region, the
-+
+dipoles of the water molecules are preferentially aligned with the
-+
+dipole of headgroup.
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=\linewidth]{g_atom.eps}
-+
+\caption[The pair correlation functions for atomistic models]{The
-+
+pair correlation functions for atomistic models: (a)$g(r,\cos \theta
-+
+)$ for DMPC; (b) $g(r,\cos \theta )$ for DLPE; (c)$g(r,\cos \omega
-+
+)$ for DMPC; (d)$g(r,\cos \omega )$ for DLPE; (e)$g(\cos \theta,\cos
-+
+\omega)$ for DMPC; (f)$g(\cos \theta,\cos \omega)$ for DMLPE.}
-+
+\label{lipidFigure:PCFAtom}
-+
+\end{figure}
-+
-+
+The initial configurations of coarse-grained systems are constructed
-+
+from the previous atomistic ones. The parameters for the
-+
+coarse-grained model in Table~\ref{lipidTable:parameter} are
-+
+estimated and tuned using isothermal-isobaric molecular dynamics.
-+
+Pair distribution functions calculated from coarse-grained models
-+
+preserve the basic characteristics of the atomistic simulations. The
-+
+water density, measured in a head-group-fixed reference frame,
-+
+surrounding two phospholipid headgroups is shown in
-+
+Fig.~\ref{lipidFigure:PCFCoarse}. It is clear that the phosphate end
-+
+in DMPC and the amine end in DMPE are the two most heavily solvated
-+
+atoms.
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=\linewidth]{g_coarse.eps}
-+
+\caption[The pair correlation functions for coarse-grained
-+
+models]{The pair correlation functions for coarse-grained models:
-+
+(a)$g(r,\cos \theta )$ for DMPC; (b) $g(r,\cos \theta )$ for DLPE.}
-+
+\label{lipidFigure:PCFCoarse}
-+
+\end{figure}
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=\linewidth]{EWD_coarse.eps}
-+
+\caption[Excess water density of coarse-grained
-+
+phospholipids]{Excess water density of coarse-grained
-+
+phospholipids.} \label{lipidFigure:EWDCoarse}
-+
+\end{figure}
-+
-+
+\begin{table}
-+
+\caption{The Parameters For Coarse-grained Phospholipids}
-+
+\label{lipidTable:parameter}
-+
+\begin{center}
-+
+\begin{tabular}{|l|c|c|c|c|c|}
-+
+  \hline
-+
+  % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ...
-+
+  Atom type & Mass & $\sigma$ & $\epsilon$ & charge & Dipole \\
-+
+  $\text{{\sc CH}}_2$ & 14.03  & 3.95 & 0.0914 & 0 & 0 \\
-+
+  $\text{{\sc CH}}_3$ & 15.04  & 3.75 & 0.195  & 0 & 0 \\
-+
+  $\text{{\sc CE}}$   & 28.01  & 3.427& 0.294  & 0 & 1.693 \\
-+
+  $\text{{\sc CK}}$   & 28.01  & 3.592& 0.311  & 0 & 2.478 \\
-+
+  $\text{{\sc PO}}_4$ & 108.995& 3.9  & 1.88   & -1&  0 \\
-+
+  $\text{{\sc HDP}}$  & 14.03  & 4.0  & 0.13   & 0 &  0 \\
-+
+  $\text{{\sc NC}}_4$ & 73.137 & 4.9  & 0.88   & +1&  0 \\
-+
+  $\text{{\sc NH}}_3$ & 17.03  & 3.25 & 0.17   & +1&  0\\
-+
+  \hline
-+
+\end{tabular}
-+
+\end{center}
-+
+\end{table}
-+
-+
+\subsection{Bilayer Simulations Using Coarse-grained Model}
-+
-+
+A bilayer system consisting of 128 DMPC lipids and 3655 water
-+
+molecules has been constructed from an atomistic coordinate file.
-+
+The MD simulation is performed at constant temperature, T = 300K,
-+
+and constant pressure, p = 1 atm, and consisted of an equilibration
-+
+period of 2 ns. During the equilibration period, the system was
-+
+initially simulated at constant volume for 1 ns. Once the system was
-+
+equilibrated at constant volume, the cell dimensions of the system
-+
+was relaxed by performing under NPT conditions using Nos\'{e}-Hoover
-+
+extended system isothermal-isobaric dynamics. After equilibration,
-+
+different properties were evaluated over a production run of 5 ns.
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=\linewidth]{bilayer.eps}
-+
+\caption[Image of a coarse-grained bilayer system]{A coarse-grained
-+
+bilayer system consisting of 128 DMPC lipids and 3655 SSD water
-+
+molecules.}
-+
+\label{lipidFigure:bilayer}
-+
+\end{figure}
-+
-+
+\subsubsection{\textbf{Electron Density Profile (EDP)}}
-+
-+
+Assuming a gaussian distribution of electrons on each atomic center
-+
+with a variance estimated from the size of the van der Waals radius,
-+
+the EDPs which are proportional to the density profiles measured
-+
+along the bilayer normal obtained by x-ray scattering experiment,
-+
+can be expressed by\cite{Tu1995}
-+
+\begin{equation}
-+
+\rho _{x - ray} (z)dz \propto \sum\limits_{i = 1}^N {\frac{{n_i
-+
+}}{V}\frac{1}{{\sqrt {2\pi \sigma ^2 } }}e^{ - (z - z_i )^2 /2\sigma
-+
+^2 } dz},
-+
+\end{equation}
-+
+where $\sigma$ is the variance equal to the van der Waals radius,
-+
+$n_i$ is the atomic number of site $i$ and $V$ is the volume of the
-+
+slab between $z$ and $z+dz$ . The highest density of total EDP
-+
+appears at the position of lipid-water interface corresponding to
-+
+headgroup, glycerol, and carbonyl groups of the lipids and the
-+
+distribution of water locked near the head groups, while the lowest
-+
+electron density is in the hydrocarbon region. As a good
-+
+approximation to the thickness of the bilayer, the headgroup spacing
-+
+, is defined as the distance between two peaks in the electron
-+
+density profile, calculated from our simulations to be 34.1 $\AA$.
-+
+This value is close to the x-ray diffraction experimental value 34.4
-+
+$\AA$\cite{Petrache1998}.
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=\linewidth]{electron_density.eps}
-+
+\caption[The density profile of the lipid bilayers]{Electron density
-+
+profile along the bilayer normal. The water density is shown in red,
-+
+the density due to the headgroups in green, the glycerol backbone in
-+
+brown, $\text{{\sc CH}}_2$ in yellow, $\text{{\sc CH}}_3$ in cyan,
-+
+and total density due to DMPC in blue.}
-+
+\label{lipidFigure:electronDensity}
-+
+\end{figure}
-+
-+
+\subsubsection{\textbf{$\text{S}_{\text{{\sc cd}}}$ Order Parameter}}
-+
-+
+Measuring deuterium order parameters by NMR is a useful technique to
-+
+study the orientation of hydrocarbon chains in phospholipids. The
-+
+order parameter tensor $S$ is defined by:
-+
+\begin{equation}
-+
+S_{ij}  = \frac{1}{2} < 3\cos \theta _i \cos \theta _j  - \delta
-+
+_{ij}  >
-+
+\end{equation}
-+
+where $\theta$ is the angle between the  $i$th molecular axis and
-+
+the bilayer normal ($z$ axis). The brackets denote an average over
-+
+time and molecules. The molecular axes are defined:
-+
+\begin{itemize}
-+
+\item $\mathbf{\hat{z}}$ is the vector from $C_{n-1}$ to $C_{n+1}$.
-+
+\item $\mathbf{\hat{y}}$ is the vector that is perpendicular to $z$ and
-+
+in the plane through $C_{n-1}$, $C_{n}$, and $C_{n+1}$.
-+
+\item $\mathbf{\hat{x}}$ is the vector perpendicular to
-+
+$\mathbf{\hat{y}}$ and $\mathbf{\hat{z}}$.
-+
+\end{itemize}
-+
+In coarse-grained model, although there are no explicit hydrogens,
-+
+the order parameter can still be written in terms of carbon ordering
-+
+at each point of the chain\cite{Egberts1988}
-+
+\begin{equation}
-+
+S_{ij}  = \frac{1}{2} < 3\cos \theta _i \cos \theta _j  - \delta
-+
+_{ij}  >.
-+
+\end{equation}
-+
-+
+Fig.~\ref{lipidFigure:Scd} shows the order parameter profile
-+
+calculated for our coarse-grained DMPC bilayer system at 300K. Also
-+
+shown are the experimental data of Tu\cite{Tu1995}. The fact that
-+
+$\text{S}_{\text{{\sc cd}}}$ order parameters calculated from
-+
+simulation are higher than the experimental ones is ascribed to the
-+
+assumption of the locations of implicit hydrogen atoms which are
-+
+fixed in coarse-grained models at positions relative to the CC
-+
+vector.
-+
-+
+\begin{figure}
-+
+\centering
-+
+\includegraphics[width=\linewidth]{scd.eps}
-+
+\caption[$\text{S}_{\text{{\sc cd}}}$ order parameter]{A comparison
-+
+of $|\text{S}_{\text{{\sc cd}}}|$ between coarse-grained model
-+
+(blue) and DMPC\cite{Petrache2000} (black) near 300~K.}
-+
+\label{lipidFigure:Scd}
-+
+\end{figure}
-+
-+
+%\subsection{Bilayer Simulations Using Gay-Berne Ellipsoid Model}
-+
-+
+\section{\label{lipidSection:Conclusion}Conclusion}
-+
-+
+Atomistic simulations have been used in this study to determine the
-+
+preferred orientation and location of water molecules relative to
-+
+the location and orientation of the PC and PE lipid headgroups.
-+
+Based on the results from our all-atom simulations, we developed a
-+
+simple coarse-grained model which captures the essential features of
-+
+the headgroup solvation which is crucial to transport process in
-+
+membrane system. In addition, the model has been explored in a
-+
+bilayer system was shown to have reasonable electron density
-+
+profiles, $\text{S}_{\text{{\sc cd}}}$ order parameter and other
-+
+structural properties. The accuracy of this model is achieved by
-+
+matching atomistic result. It is also easy to represent different
-+
+phospholipids by changing a few parameters of the model. Another
-+
+important characteristic of this model distinguishing itself from
-+
+other models\cite{Goetz1998,Marrink2004} is the computational speed
-+
+gained by introducing a short range electrostatic approximation.
-+
+Further studies of this system using z-constraint method could
-+
+extend the time length of the simulations to study transport
-+
+phenomena in large-scale membrane systems.

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Comparing trunk/tengDissertation/Lipid.tex (file contents): Revision 2685 by tim, Mon Apr 3 18:07:54 2006 UTC vs. Revision 2881 by tim, Fri Jun 23 20:21:54 2006 UTC

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Comparing trunk/tengDissertation/Lipid.tex (file contents):
Revision 2685 by tim, Mon Apr 3 18:07:54 2006 UTC vs.
Revision 2881 by tim, Fri Jun 23 20:21:54 2006 UTC