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the ripple formation can be found in section |
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\ref{sec:discussion}. |
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|
| 133 |
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\section{Methodology and Model} |
| 133 |
> |
\section{Computational Model} |
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\label{sec:method} |
| 135 |
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|
| 136 |
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Our simple molecular-scale lipid model for studying the ripple phase |
| 271 |
|
\end{eqnarray*} |
| 272 |
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the strength parameter has been adjusted as suggested by Cleaver {\it |
| 273 |
|
et al.}\cite{Cleaver96} A switching function has been applied to all |
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< |
potentials to smoothly turn off the interactions between a range of $22$ \AA\ and $25$ \AA. |
| 274 |
> |
potentials to smoothly turn off the interactions between a range of $22$ and $25$ \AA. |
| 275 |
|
|
| 276 |
< |
The model of the solvent in our simulations is inspired by the idea of |
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``DPD'' water. Every four water molecules are reprsented by one |
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sphere. |
| 276 |
> |
The solvent model in our simulations is identical to one used by XXX |
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> |
in their dissipative particle dynamics (DPD) simulation of lipid |
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> |
bilayers.]cite{XXX} This solvent bead is a single site that represents |
| 279 |
> |
four water molecules (m = 72 amu) and has comparable density and |
| 280 |
> |
diffusive behavior to liquid water. However, since there are no |
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> |
electrostatic sites on these beads, this solvent model cannot |
| 282 |
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replicate the dielectric properties of water. |
| 283 |
|
|
| 284 |
|
\begin{figure}[htb] |
| 285 |
|
\centering |
| 286 |
< |
\includegraphics[height=4in]{lipidModel} |
| 286 |
> |
\includegraphics[width=\linewidth]{2lipidModel} |
| 287 |
|
\caption{The parameters defining the behavior of the lipid |
| 288 |
|
models. $\sigma_h / \sigma_0$ is the ratio of the head group to body |
| 289 |
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diameter. Molecular bodies all had an aspect ratio of 3.0. The |
| 290 |
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dipolar strength (and the temperature and pressure) wer the only other |
| 291 |
< |
parameters that wer varied systematically.\label{fig:lipidModel}} |
| 289 |
> |
diameter. Molecular bodies had a fixed aspect ratio of 3.0. The |
| 290 |
> |
solvent model was a simplified 4-water bead ($\sigma_w = 1.02 |
| 291 |
> |
\sigma_0$) that has been used in other coarse-grained (DPD) simulations. |
| 292 |
> |
The dipolar strength (and the temperature and pressure) were the only |
| 293 |
> |
other parameters that were varied |
| 294 |
> |
systematically.\label{fig:lipidModel}} |
| 295 |
|
\end{figure} |
| 296 |
|
|
| 297 |
< |
\section{Experiment} |
| 297 |
> |
\section{Experimental Methodology} |
| 298 |
|
\label{sec:experiment} |
| 299 |
|
|
| 300 |
< |
To make the simulations less expensive and to observe long-time |
| 301 |
< |
behavior of the lipid membranes, all simulations were started from two |
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< |
separate monolayers in the vaccum with $x-y$ anisotropic pressure |
| 300 |
> |
To create unbiased bilayers, all simulations were started from two |
| 301 |
> |
perfectly flat monolayers separated by a 20 \AA\ gap between the |
| 302 |
> |
molecular bodies of the upper and lower leaves. The separated |
| 303 |
> |
monolayers were evolved in a vaccum with $x-y$ anisotropic pressure |
| 304 |
|
coupling. The length of $z$ axis of the simulations was fixed and a |
| 305 |
|
constant surface tension was applied to enable real fluctuations of |
| 306 |
< |
the bilayer. Periodic boundaries were used. There were $480-720$ lipid |
| 307 |
< |
molecules in the simulations depending on the size of the head |
| 308 |
< |
beads. All the simulations were equlibrated for $100$ ns at $300$ |
| 309 |
< |
K. The resulting structures were solvated in water ($6$ DPD |
| 310 |
< |
water/lipid molecule). These configurations were relaxed for another |
| 303 |
< |
$30$ ns relaxation. All simulations with water were carried out at |
| 304 |
< |
constant pressure ($P=1$ atm) by $3$D anisotropic coupling, and |
| 305 |
< |
constant surface tension ($\gamma=0.015$). Given the absence of fast |
| 306 |
< |
degrees of freedom in this model, a timestep of $50$ fs was |
| 307 |
< |
utilized. Simulations were performed by using OOPSE |
| 308 |
< |
package\cite{Meineke05}. |
| 306 |
> |
the bilayer. Periodic boundaries were used, and $480-720$ lipid |
| 307 |
> |
molecules were present in the simulations depending on the size of the |
| 308 |
> |
head beads. The two monolayers spontaneously collapse into bilayer |
| 309 |
> |
structures within 100 ps, and following this collapse, all systems |
| 310 |
> |
were equlibrated for $100$ ns at $300$ K. |
| 311 |
|
|
| 312 |
< |
\section{Results and Analysis} |
| 312 |
> |
The resulting structures were then solvated at a ratio of $6$ DPD |
| 313 |
> |
solvent beads (24 water molecules) per lipid. These configurations |
| 314 |
> |
were then equilibrated for another $30$ ns. All simulations with |
| 315 |
> |
solvent were carried out at constant pressure ($P=1$ atm) by $3$D |
| 316 |
> |
anisotropic coupling, and constant surface tension ($\gamma=0.015$ |
| 317 |
> |
UNIT). Given the absence of fast degrees of freedom in this model, a |
| 318 |
> |
timestep of $50$ fs was utilized. Data collection for structural |
| 319 |
> |
properties of the bilayers was carried out during a final 5 ns run |
| 320 |
> |
following the solvent equilibration. All simulations were performed |
| 321 |
> |
using the OOPSE molecular modeling program.\cite{Meineke05} |
| 322 |
> |
|
| 323 |
> |
\section{Results} |
| 324 |
|
\label{sec:results} |
| 325 |
|
|
| 326 |
|
Snapshots in Figure \ref{fig:phaseCartoon} show that the membrane is |
