| 166 |
|
|
| 167 |
|
\def\op#1{\hat{#1}} |
| 168 |
|
\begin{document} |
| 169 |
< |
\bibliographystyle{plain} |
| 169 |
> |
\bibliographystyle{unsrt} |
| 170 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 171 |
|
%%% Background %%% |
| 172 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 215 |
|
{\color{ndblue} |
| 216 |
|
|
| 217 |
|
A mesoscale model for phospholipids has been developed for molecular |
| 218 |
< |
dynamics simulations of lipid bilayers. The model makes several |
| 218 |
> |
dynamics simulations of phospholipid phase transitions. The model makes several |
| 219 |
|
simplifications to both the water and the phospholipids to reduce the |
| 220 |
|
computational cost of each force evaluation. The water was represented |
| 221 |
|
by the soft sticky dipole model of Ichiye \emph{et |
| 240 |
|
\label{sec:motivation} |
| 241 |
|
|
| 242 |
|
|
| 243 |
< |
Simulations of phospholipid bilayers are, by necessity, quite |
| 243 |
> |
Simulations of phospholipid phases are, by necessity, quite |
| 244 |
|
complex. The lipid molecules are large, and contain many |
| 245 |
|
atoms. Additionally, the head groups of the lipids are often |
| 246 |
|
zwitterions, and the large separation between charges results in a |
| 304 |
|
\end{kasten} |
| 305 |
|
|
| 306 |
|
\begin{kasten} |
| 307 |
< |
\subsection{{\color{ndblue}System Simplifications}} |
| 307 |
> |
\subsection{{\color{ndblue}Our Simplifications}} |
| 308 |
|
\begin{itemize} |
| 309 |
|
\item Unified atoms with fixed bond lengths replace groups of atoms. |
| 310 |
< |
\item Replace charge distributions with dipoles.(Eq.~\ref{eq:dipole} |
| 311 |
< |
vs. Eq.~\ref{eq:coloumb}) |
| 310 |
> |
\item Charge distributions are replaced with dipoles. |
| 311 |
|
\begin{itemize} |
| 312 |
|
\item Relatively short range, $\frac{1}{r^3}$, interactions allow |
| 313 |
< |
the application of computational simplification algorithms, |
| 315 |
< |
i.e. neighbor lists. |
| 313 |
> |
the application of neighbor lists. |
| 314 |
|
\end{itemize} |
| 315 |
|
\end{itemize} |
| 316 |
|
\begin{equation} |
| 323 |
|
{r^{5}_{ij}} \biggr] |
| 324 |
|
\label{eq:dipole} |
| 325 |
|
\end{equation} |
| 328 |
– |
\begin{equation} |
| 329 |
– |
V^{\text{ch}}_{ij}(\mathbf{r}_{ij}) = \frac{q_{i}q_{j}}% |
| 330 |
– |
{4\pi\epsilon_{0} r_{ij}} |
| 331 |
– |
\label{eq:coloumb} |
| 332 |
– |
\end{equation} |
| 326 |
|
\end{kasten} |
| 327 |
|
|
| 328 |
|
|
| 373 |
|
+ V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j}) |
| 374 |
|
\label{eq:ssdPot} |
| 375 |
|
\end{equation} |
| 376 |
< |
Where $V_{d\!p}(r_{i\!j}$ is given in Eq.~\ref{eq:dipole}, and $V_{L\!J}(r_{i\!j})$ is the Lennard-Jones potential: |
| 384 |
< |
\begin{equation} |
| 385 |
< |
V_{\text{LJ}} = |
| 386 |
< |
4\epsilon_{ij} \biggl[ |
| 387 |
< |
\biggl(\frac{\sigma_{ij}}{r_{ij}}\biggr)^{12} |
| 388 |
< |
- \biggl(\frac{\sigma_{ij}}{r_{ij}}\biggr)^{6} |
| 389 |
< |
\biggr] |
| 390 |
< |
\label{eq:lennardJonesPot} |
| 391 |
< |
\end{equation} |
| 392 |
< |
|
| 376 |
> |
Where $V_{d\!p}(r_{i\!j})$ is given in Eq.~\ref{eq:dipole}, and $V_{L\!J}(r_{i\!j})$ is the Lennard-Jones potential. |
| 377 |
|
\end{kasten} |
| 378 |
|
|
| 379 |
|
\begin{kasten} |
| 403 |
|
\sin\theta_{ij} \sin 2\theta_{ij} \cos 2\phi_{ij} |
| 404 |
|
+ \sin \theta_{ji} \sin 2\theta_{ji} \cos 2\phi_{ji} |
| 405 |
|
\label{eq:spPot2} |
| 406 |
< |
\end{equation}o |
| 406 |
> |
\end{equation} |
| 407 |
|
and |
| 408 |
|
\begin{equation} |
| 409 |
|
\begin{split} |
| 483 |
|
\end{center} |
| 484 |
|
|
| 485 |
|
\begin{itemize} |
| 486 |
< |
\item Head group replaced by a single Lennard-Jones sphere containing a dipole at its center |
| 486 |
> |
\item PC \& PE head groups are replaced by a Lennard-Jones sphere containing a dipole at its center |
| 487 |
|
\item Atoms in the tail chains modeled as unified groups of atoms |
| 488 |
|
\item Tail group interaction parameters based on those of TraPPE\cite{Siepmann1998} |
| 489 |
|
\end{itemize} |
| 524 |
|
\begin{kasten} |
| 525 |
|
|
| 526 |
|
\section{{\color{red}\underline{Initial Results}}} |
| 527 |
< |
\label{sec:results} |
| 528 |
< |
\subsection{{\color{ndblue}50 lipids randomly arranged in water}} |
| 545 |
< |
\label{sec:r50} |
| 546 |
< |
|
| 547 |
< |
\begin{center} |
| 548 |
< |
\begin{minipage}{130mm} |
| 549 |
< |
\begin{minipage}[t]{40mm} |
| 550 |
< |
\begin{itemize} |
| 551 |
< |
\item $N_{\mbox{lipids}} = 25$ |
| 552 |
< |
\end{itemize} |
| 553 |
< |
\end{minipage} |
| 554 |
< |
\begin{minipage}[t]{40mm} |
| 555 |
< |
\begin{itemize} |
| 556 |
< |
\item $N_{\mbox{H}_{2}\mbox{O}} = 1386$ |
| 557 |
< |
\end{itemize} |
| 558 |
< |
\end{minipage} |
| 559 |
< |
\begin{minipage}[t]{40mm} |
| 560 |
< |
\begin{itemize} |
| 561 |
< |
\item T = 300 K |
| 562 |
< |
\end{itemize} |
| 563 |
< |
\end{minipage} |
| 564 |
< |
\end{minipage} |
| 565 |
< |
\end{center} |
| 566 |
< |
|
| 567 |
< |
\end{kasten} |
| 568 |
< |
|
| 569 |
< |
\begin{kasten} |
| 570 |
< |
|
| 571 |
< |
\subsection{{\color{ndblue}Simulation Snapshots}} |
| 527 |
> |
\label{sec:results} |
| 528 |
> |
\subsection{{\color{ndblue}Simulation Snapshots:50 lipids in a sea of 1384 waters}} |
| 529 |
|
\label{sec:r50snapshots} |
| 530 |
|
|
| 531 |
|
\begin{center} |
| 585 |
|
system of 50 lipids was able to form micelles quickly, however |
| 586 |
|
bilayer formation was not seen on the time scale of the |
| 587 |
|
current simulation. Current simulations are exploring the |
| 588 |
< |
phase space of the model when the tail beads are larger than |
| 588 |
> |
parameter space of the model when the tail beads are larger than |
| 589 |
|
the head group. This should help to drive the system toward a |
| 590 |
|
bilayer rather than a micelle. Work is also being done on the |
| 591 |
|
simulation engine to allow for the box size of the system to |
