| 110 |
|
glycerol motif are modeled by Lennard-Jones spheres with dipoles. |
| 111 |
|
Alkyl groups in hydrocarbon chains are replaced with unified |
| 112 |
|
$\text{{\sc CH}}_2$ or $\text{{\sc CH}}_3$ atoms. |
| 113 |
– |
|
| 113 |
|
\begin{figure} |
| 114 |
|
\centering |
| 115 |
|
\includegraphics[width=3in]{coarse_grained.eps} |
| 151 |
|
\theta } }} + \frac{q}{{\sqrt {r^2 + \frac{{d^2 }}{4} - rd\cos |
| 152 |
|
\theta } }}} \right) |
| 153 |
|
\] |
| 155 |
– |
|
| 154 |
|
\begin{figure} |
| 155 |
|
\centering |
| 156 |
|
\includegraphics[width=3in]{charge_dipole.eps} |
| 159 |
|
comprising two point charges with opposite charges. } |
| 160 |
|
\label{lipidFigure:chargeDipole} |
| 161 |
|
\end{figure} |
| 164 |
– |
|
| 162 |
|
The basic assumption of the multipole expansion is $r \gg d$ , thus, |
| 163 |
|
$\frac{{d^2 }}{4}$ inside the square root of the denominator is |
| 164 |
|
neglected. This is a reasonable approximation in most cases. |
| 209 |
|
split-dipole approximation.} \label{lipidFigure:splitDipole} |
| 210 |
|
\end{figure} |
| 211 |
|
|
| 215 |
– |
%\section{\label{lipidSection:methods}Methods} |
| 216 |
– |
|
| 212 |
|
\section{\label{lipidSection:resultDiscussion}Results and Discussion} |
| 213 |
|
|
| 214 |
|
\subsection{One Lipid in Sea of Water Molecules} |
| 220 |
|
distribution functions, which give the probability of finding a pair |
| 221 |
|
of molecular species a distance apart, relative to the probability |
| 222 |
|
expected for a completely random distribution function at the same |
| 223 |
< |
density. |
| 224 |
< |
|
| 225 |
< |
\begin{equation} |
| 226 |
< |
g_{AB} (r) = \frac{1}{{\rho _B }}\frac{1}{{N_A }} < \sum\limits_{i |
| 227 |
< |
\in A} {\sum\limits_{j \in B} {\delta (r - r_{ij} )} } > |
| 228 |
< |
\end{equation} |
| 234 |
< |
\begin{equation} |
| 235 |
< |
g_{AB} (r,\cos \theta ) = \frac{1}{{\rho _B }}\frac{1}{{N_A }} < |
| 223 |
> |
density |
| 224 |
> |
\begin{eqnarray} |
| 225 |
> |
g_{AB} (r) & = & \frac{1}{{\rho _B }}\frac{1}{{N_A }} < |
| 226 |
> |
\sum\limits_{i |
| 227 |
> |
\in A} {\sum\limits_{j \in B} {\delta (r - r_{ij} )} } >, \\ |
| 228 |
> |
g_{AB} (r,\cos \theta ) & = & \frac{1}{{\rho _B }}\frac{1}{{N_A }} < |
| 229 |
|
\sum\limits_{i \in A} {\sum\limits_{j \in B} {\delta (r - r_{ij} )} |
| 230 |
< |
} \delta (\cos \theta _{ij} - \cos \theta ) > |
| 231 |
< |
\end{equation} |
| 239 |
< |
|
| 230 |
> |
} \delta (\cos \theta _{ij} - \cos \theta ) >. |
| 231 |
> |
\end{eqnarray} |
| 232 |
|
From Fig.~\ref{lipidFigure:PCFAtom}, we can identify the first |
| 233 |
|
solvation shell (3.5 \AA) and the second solvation shell (5.0 \AA) |
| 234 |
|
from both plots. However, the corresponding orientations are |
| 247 |
|
dipole in both plots tell us that in the closely-bound region, the |
| 248 |
|
dipoles of the water molecules are preferentially aligned with the |
| 249 |
|
dipole of headgroup. |
| 258 |
– |
|
| 250 |
|
\begin{figure} |
| 251 |
|
\centering |
| 252 |
|
\includegraphics[width=\linewidth]{g_atom.eps} |
| 269 |
|
Fig.~\ref{lipidFigure:PCFCoarse}. It is clear that the phosphate end |
| 270 |
|
in DMPC and the amine end in DMPE are the two most heavily solvated |
| 271 |
|
atoms. |
| 281 |
– |
|
| 272 |
|
\begin{figure} |
| 273 |
|
\centering |
| 274 |
|
\includegraphics[width=\linewidth]{g_coarse.eps} |
| 277 |
|
(a)$g(r,\cos \theta )$ for DMPC; (b) $g(r,\cos \theta )$ for DLPE.} |
| 278 |
|
\label{lipidFigure:PCFCoarse} |
| 279 |
|
\end{figure} |
| 290 |
– |
|
| 280 |
|
\begin{figure} |
| 281 |
|
\centering |
| 282 |
|
\includegraphics[width=\linewidth]{EWD_coarse.eps} |
| 289 |
|
\caption{THE PARAMETERS FOR COARSE-GRAINED PHOSPHOLIPIDS} |
| 290 |
|
\label{lipidTable:parameter} |
| 291 |
|
\begin{center} |
| 292 |
< |
\begin{tabular}{|l|c|c|c|c|c|} |
| 292 |
> |
\begin{tabular}{lccccc} |
| 293 |
|
\hline |
| 294 |
|
% after \\: \hline or \cline{col1-col2} \cline{col3-col4} ... |
| 295 |
|
Atom type & Mass & $\sigma$ & $\epsilon$ & charge & Dipole \\ |
| 296 |
+ |
\hline |
| 297 |
|
$\text{{\sc CH}}_2$ & 14.03 & 3.95 & 0.0914 & 0 & 0 \\ |
| 298 |
|
$\text{{\sc CH}}_3$ & 15.04 & 3.75 & 0.195 & 0 & 0 \\ |
| 299 |
|
$\text{{\sc CE}}$ & 28.01 & 3.427& 0.294 & 0 & 1.693 \\ |
| 319 |
|
was relaxed by performing under NPT conditions using Nos\'{e}-Hoover |
| 320 |
|
extended system isothermal-isobaric dynamics. After equilibration, |
| 321 |
|
different properties were evaluated over a production run of 5 ns. |
| 332 |
– |
|
| 322 |
|
\begin{figure} |
| 323 |
|
\centering |
| 324 |
|
\includegraphics[width=\linewidth]{bilayer.eps} |
