| 1 |
|
|
| 2 |
|
|
| 3 |
< |
\chapter{\label{chapt:lipid}Phospholipid Simulations} |
| 3 |
> |
\chapter{\label{chapt:lipid}PHOSPHOLIPID SIMULATIONS} |
| 4 |
|
|
| 5 |
|
\section{\label{lipidSec:Intro}Introduction} |
| 6 |
|
|
| 10 |
|
simulation of the gel ($L_{\beta}$) phase of |
| 11 |
|
dipalmitoylphosphatidylcholine (DPPC),\cite{lindahl00} to the |
| 12 |
|
spontaneous aggregation of DPPC molecules into fluid phase |
| 13 |
< |
($L_{\alpha}$) bilayers.\cite{marrink01} With the exception of a few |
| 13 |
> |
($L_{\alpha}$) bilayers.\cite{Marrink01} With the exception of a few |
| 14 |
|
ambitious |
| 15 |
|
simulations, \cite{marrink01:undulation,marrink:2002,lindahl00} most |
| 16 |
|
investigations are limited to a range of 64 to 256 |
| 17 |
< |
phospholipids.\cite{lindahl00,sum:2003,venable00,gomez:2003,smondyrev:1999,marrink01} |
| 17 |
> |
phospholipids.\cite{lindahl00,sum:2003,venable00,gomez:2003,smondyrev:1999,Marrink01} |
| 18 |
|
The expense of the force calculations involved when performing these |
| 19 |
|
simulations limits the system size. To properly hydrate a bilayer, one |
| 20 |
|
typically needs 25 water molecules for every lipid, bringing the total |
| 131 |
|
4\epsilon_{ij} \biggl[ |
| 132 |
|
\biggl(\frac{\sigma_{ij}}{r_{ij}}\biggr)^{12} |
| 133 |
|
- \biggl(\frac{\sigma_{ij}}{r_{ij}}\biggr)^{6} |
| 134 |
< |
\biggr] |
| 134 |
> |
\biggr], |
| 135 |
|
\label{lipidEq:LJpot} |
| 136 |
|
\end{equation} |
| 137 |
|
and |
| 141 |
|
\boldsymbol{\hat{u}}_{i} \cdot \boldsymbol{\hat{u}}_{j} |
| 142 |
|
- |
| 143 |
|
3(\boldsymbol{\hat{u}}_i \cdot \mathbf{\hat{r}}_{ij}) % |
| 144 |
< |
(\boldsymbol{\hat{u}}_j \cdot \mathbf{\hat{r}}_{ij} )\biggr] |
| 144 |
> |
(\boldsymbol{\hat{u}}_j \cdot \mathbf{\hat{r}}_{ij} )\biggr]. |
| 145 |
|
\label{lipidEq:dipolePot} |
| 146 |
|
\end{equation} |
| 147 |
< |
Where $V_{\text{LJ}}$ is the Lennard-Jones potential and |
| 147 |
> |
Here $V_{\text{LJ}}$ is the Lennard-Jones potential and |
| 148 |
|
$V_{\text{dipole}}$ is the dipole-dipole potential. As previously |
| 149 |
|
stated, $\sigma_{ij}$ and $\epsilon_{ij}$ are the Lennard-Jones |
| 150 |
|
parameters which scale the length and depth of the interaction |
| 162 |
|
algorithm.\cite{andersen83} The bends are subject to a harmonic |
| 163 |
|
potential: |
| 164 |
|
\begin{equation} |
| 165 |
< |
V_{\text{bend}}(\theta) = k_{\theta}( \theta - \theta_0 )^2 |
| 165 |
> |
V_{\text{bend}}(\theta) = k_{\theta}( \theta - \theta_0 )^2, |
| 166 |
|
\label{lipidEq:bendPot} |
| 167 |
|
\end{equation} |
| 168 |
|
where $k_{\theta}$ scales the strength of the harmonic well, and |
| 177 |
|
molecule. The torsion potential is given by: |
| 178 |
|
\begin{equation} |
| 179 |
|
V_{\text{torsion}}(\phi) = |
| 180 |
< |
k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0 |
| 180 |
> |
k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0. |
| 181 |
|
\label{lipidEq:torsionPot} |
| 182 |
|
\end{equation} |
| 183 |
|
Here, the parameters $k_0$, $k_1$, $k_2$, and $k_3$ fit the cosine |
| 207 |
|
\ref{lipidTable:tcTorsionParams}. |
| 208 |
|
|
| 209 |
|
\begin{table} |
| 210 |
< |
\caption[Lennard-Jones parameters for the two chain phospholipids]{THE LENNARD JONES PARAMETERS FOR THE TWO CHAIN PHOSPHOLIPIDS} |
| 210 |
> |
\caption{THE LENNARD JONES PARAMETERS FOR THE TWO CHAIN PHOSPHOLIPIDS} |
| 211 |
|
\label{lipidTable:tcLJParams} |
| 212 |
|
\begin{center} |
| 213 |
|
\begin{tabular}{|l|c|c|c|c|} |
| 224 |
|
\end{table} |
| 225 |
|
|
| 226 |
|
\begin{table} |
| 227 |
< |
\caption[Bend Parameters for the two chain phospholipids]{BEND PARAMETERS FOR THE TWO CHAIN PHOSPHOLIPIDS} |
| 227 |
> |
\caption{BEND PARAMETERS FOR THE TWO CHAIN PHOSPHOLIPIDS} |
| 228 |
|
\label{lipidTable:tcBendParams} |
| 229 |
|
\begin{center} |
| 230 |
|
\begin{tabular}{|l|c|c|} |
| 244 |
|
\end{table} |
| 245 |
|
|
| 246 |
|
\begin{table} |
| 247 |
< |
\caption[Torsion Parameters for the two chain phospholipids]{TORSION PARAMETERS FOR THE TWO CHAIN PHOSPHOLIPIDS} |
| 247 |
> |
\caption{TORSION PARAMETERS FOR THE TWO CHAIN PHOSPHOLIPIDS} |
| 248 |
|
\label{lipidTable:tcTorsionParams} |
| 249 |
|
\begin{center} |
| 250 |
|
\begin{tabular}{|l|c|c|c|c|} |
| 280 |
|
its equilibrium value by $\sim 0.6\%$, temperature fluctuations are |
| 281 |
|
about $\sim 1.4\%$ of their set value, and pressure fluctuations are |
| 282 |
|
the largest, varying as much as $\pm 250$~atm. However, such large |
| 283 |
< |
fluctuations in pressure are typical for liquid state simulations. |
| 283 |
> |
fluctuations in pressure are typical for liquid state simulations.\cite{leach01:mm} |
| 284 |
|
|
| 285 |
|
|
| 286 |
|
\subsection{\label{lipidSec:ExpSetup}Experimental Setup} |
| 354 |
|
Fig.~\ref{lipidFig:densityProfile} illustrates the densities of the |
| 355 |
|
atoms in the bilayer systems normalized by the bulk density as a |
| 356 |
|
function of distance from the center of the box. The profile is taken |
| 357 |
< |
along the bilayer normal (in this case the $z$ axis). The profile at |
| 358 |
< |
270~K shows several structural features that are largely smoothed out |
| 359 |
< |
at 300~K. The left peak for the {\sc head} atoms is split at 270~K, |
| 360 |
< |
implying that some freezing of the structure into a gel phase might |
| 361 |
< |
already be occurring at this temperature. However, movies of the |
| 362 |
< |
trajectories at this temperature show that the tails are very fluid, |
| 363 |
< |
and have not gelled. But this profile could indicate that a phase |
| 364 |
< |
transition may simply be beyond the time length of the current |
| 365 |
< |
simulation, and that given more time the system may tend towards a gel |
| 366 |
< |
phase. In all profiles, the water penetrates almost 5~$\mbox{\AA}$ |
| 367 |
< |
into the bilayer, completely solvating the {\sc head} atoms. The |
| 368 |
< |
$\text{{\sc ch}}_3$ atoms, although mainly centered at the middle of |
| 369 |
< |
the bilayer, show appreciable penetration into the head group |
| 370 |
< |
region. This indicates that the chains have enough flexibility to bend |
| 371 |
< |
back upward to allow the ends to explore areas around the {\sc head} |
| 372 |
< |
atoms. It is unlikely that this is penetration from a lipid of the |
| 373 |
< |
opposite face, as the lipids are only 12~$\mbox{\AA}$ in length, and |
| 374 |
< |
the typical leaf spacing as measured from the {\sc head-head} spacing |
| 375 |
< |
in the profile is 17.5~$\mbox{\AA}$. |
| 357 |
> |
along the bilayer normal (in this case the $z$ axis). The first interesting point to note is the penetration of water into the membrane. Water penetrates about 5~$\mbox{\AA}$ into the bilayer, completely solvating the head groups. This is common in atomistic and some coarse grain simulations of phospholipid bilayers.\cite{Marrink01,marrink04,klein01} It is an indication that the water molecules are very attracted to the polar head region, yet there is still enough of a hydrophobic effect to exclude water from the inside of the bilayer. |
| 358 |
|
|
| 359 |
+ |
Another interesting point is the fluidity of the chains. Although the ends of the tails, the $\text{{\sc ch}}_3$ atoms, are mostly concentrated at the centers of the bilayers, they have a significant density around the head regions. This indicates that there is much freedom of movement in the chains of our model. Typical atomistic simulations of DPPC show the terminal groups concentrated at the center of the bilayer.\cite{marrink03:vesicles} This is most likely an indication that our chain lengths are too small, and given longer chains, the tail groups would stay more deeply buried in the bilayer. |
| 360 |
+ |
|
| 361 |
+ |
The last point to consider is the splitting in the density peak of the {\sc head} atom at 270~K. This implies that there is some freezing of structure at this temperature. By 280~K, this feature is smoothed out, demonstrating a more fluid phase in the bilayer. Within the time scale of the simulation, the gel phase has not formed at 270~K, so this splitting in the peak is likely a glassy transition in the head groups, and could possibly indicate that we are simulating in a super cooled region of our phospholipid model. |
| 362 |
+ |
|
| 363 |
|
\begin{figure} |
| 364 |
|
\centering |
| 365 |
|
\includegraphics[width=\linewidth]{densityProfile.eps} |
| 374 |
|
the experimental characterizations of phospholipids. It is obtained |
| 375 |
|
through deuterium NMR, and measures the ordering of the carbon |
| 376 |
|
deuterium bond in relation to the bilayer normal at various points |
| 377 |
< |
along the chains. In our model, there are no explicit hydrogens, but |
| 377 |
> |
along the chains. The order parameter has a range of $[1,-\frac{1}{2}]$. A value of 1 |
| 378 |
> |
implies full order aligned to the bilayer axis, 0 implies full |
| 379 |
> |
disorder, and $-\frac{1}{2}$ implies full order perpendicular to the |
| 380 |
> |
bilayer axis. The {\sc cd} bond vector for carbons near the head group |
| 381 |
> |
are usually ordered perpendicular to the bilayer normal, with tails |
| 382 |
> |
farther away tending toward disorder. This makes the order parameter |
| 383 |
> |
negative for most carbons, and as such $|S_{\text{{\sc cd}}}|$ is more |
| 384 |
> |
commonly reported than $S_{\text{{\sc cd}}}$. |
| 385 |
> |
|
| 386 |
> |
In our model, there are no explicit hydrogens, but |
| 387 |
|
the order parameter can be written in terms of the carbon ordering at |
| 388 |
|
each point in the chain:\cite{egberts88} |
| 389 |
|
\begin{equation} |
| 390 |
< |
S_{\text{{\sc cd}}} = \frac{2}{3}S_{xx} + \frac{1}{3}S_{yy} |
| 390 |
> |
S_{\text{{\sc cd}}} = \frac{2}{3}S_{xx} + \frac{1}{3}S_{yy}, |
| 391 |
|
\label{lipidEq:scd1} |
| 392 |
|
\end{equation} |
| 393 |
< |
Where $S_{ij}$ is given by: |
| 393 |
> |
where $S_{ij}$ is given by: |
| 394 |
|
\begin{equation} |
| 395 |
|
S_{ij} = \frac{1}{2}\Bigl\langle(3\cos\Theta_i\cos\Theta_j |
| 396 |
< |
- \delta_{ij})\Bigr\rangle |
| 396 |
> |
- \delta_{ij})\Bigr\rangle. |
| 397 |
|
\label{lipidEq:scd2} |
| 398 |
|
\end{equation} |
| 399 |
|
Here, $\Theta_i$ is the angle the $i$th axis in the reference frame of |
| 400 |
|
the carbon atom makes with the bilayer normal. The brackets denote an |
| 401 |
|
average over time and molecules. The carbon atom axes are defined: |
| 402 |
|
\begin{itemize} |
| 403 |
< |
\item $\mathbf{\hat{z}}\rightarrow$ vector from $C_{n-1}$ to $C_{n+1}$ |
| 404 |
< |
\item $\mathbf{\hat{y}}\rightarrow$ vector that is perpendicular to $z$ and |
| 405 |
< |
in the plane through $C_{n-1}$, $C_{n}$, and $C_{n+1}$ |
| 406 |
< |
\item $\mathbf{\hat{x}}\rightarrow$ vector perpendicular to |
| 403 |
> |
\item $\mathbf{\hat{z}}$ is the vector from $C_{n-1}$ to $C_{n+1}$. |
| 404 |
> |
\item $\mathbf{\hat{y}}$ is the vector that is perpendicular to $z$ and |
| 405 |
> |
in the plane through $C_{n-1}$, $C_{n}$, and $C_{n+1}$. |
| 406 |
> |
\item $\mathbf{\hat{x}}$ is the vector perpendicular to |
| 407 |
|
$\mathbf{\hat{y}}$ and $\mathbf{\hat{z}}$. |
| 408 |
|
\end{itemize} |
| 409 |
|
This assumes that the hydrogen atoms are always in a plane |
| 410 |
|
perpendicular to the $C_{n-1}-C_{n}-C_{n+1}$ plane. |
| 411 |
|
|
| 417 |
– |
The order parameter has a range of $[1,-\frac{1}{2}]$. A value of 1 |
| 418 |
– |
implies full order aligned to the bilayer axis, 0 implies full |
| 419 |
– |
disorder, and $-\frac{1}{2}$ implies full order perpendicular to the |
| 420 |
– |
bilayer axis. The {\sc cd} bond vector for carbons near the head group |
| 421 |
– |
are usually ordered perpendicular to the bilayer normal, with tails |
| 422 |
– |
farther away tending toward disorder. This makes the order parameter |
| 423 |
– |
negative for most carbons, and as such $|S_{\text{{\sc cd}}}|$ is more |
| 424 |
– |
commonly reported than $S_{\text{{\sc cd}}}$. |
| 425 |
– |
|
| 412 |
|
Fig.~\ref{lipidFig:scdFig} shows the $S_{\text{{\sc cd}}}$ order |
| 413 |
|
parameters for the bilayer system at 300~K. There is no appreciable |
| 414 |
|
difference in the plots for the various temperatures, however, there |
| 419 |
|
group separating the chains from the top of the lipid. In DMPC, with |
| 420 |
|
the flexibility inherent in a multiple atom head group, as well as a |
| 421 |
|
glycerol linkage between the head group and the acyl chains, there is |
| 422 |
< |
more loss of ordering by the point when the chains start. |
| 422 |
> |
more loss of ordering by the point when the chains start. Also, there is more ordering in the model due to the our assumptions about the locations of the hydrogen atoms. Our method assumes a rigid location for each hydrogen atom based on the carbon positions. This does not allow for any small fluctuations in their positions that would be inherent in an atomistic simulation or in experiments. These small fluctuations would serve to lower the ordering measured in the $S_{\text{{\sc cd}}}$. |
| 423 |
|
|
| 424 |
|
\begin{figure} |
| 425 |
|
\centering |
| 447 |
|
u_{ix}u_{ix}-\frac{1}{3} & u_{ix}u_{iy} & u_{ix}u_{iz} \\ |
| 448 |
|
u_{iy}u_{ix} & u_{iy}u_{iy}-\frac{1}{3} & u_{iy}u_{iz} \\ |
| 449 |
|
u_{iz}u_{ix} & u_{iz}u_{iy} & u_{iz}u_{iz}-\frac{1}{3} % |
| 450 |
< |
\end{pmatrix} |
| 450 |
> |
\end{pmatrix}, |
| 451 |
|
\label{lipidEq:po1} |
| 452 |
|
\end{equation} |
| 453 |
< |
Where the $u_{i\alpha}$ is the $\alpha$ element of the unit vector |
| 453 |
> |
where the $u_{i\alpha}$ is the $\alpha$ element of the unit vector |
| 454 |
|
$\mathbf{\hat{u}}_i$, and the sum over $i$ averages over the whole |
| 455 |
|
collection of unit vectors. This allows the tensor to be written: |
| 456 |
|
\begin{equation} |
| 457 |
|
\overleftrightarrow{\mathsf{Q}} = \frac{1}{N}\sum_i^N \biggl[ |
| 458 |
|
\mathbf{\hat{u}}_i \otimes \mathbf{\hat{u}}_i |
| 459 |
< |
- \frac{1}{3} \cdot \mathsf{1} \biggr] |
| 459 |
> |
- \frac{1}{3} \cdot \mathsf{1} \biggr]. |
| 460 |
|
\label{lipidEq:po2} |
| 461 |
|
\end{equation} |
| 462 |
|
|
| 467 |
|
vectors. The director axis is the average direction all of the unit vectors |
| 468 |
|
are pointing. The $P_2$ order parameter is then simply |
| 469 |
|
\begin{equation} |
| 470 |
< |
\langle P_2 \rangle = \frac{3}{2}\lambda_{\text{max}} |
| 470 |
> |
\langle P_2 \rangle = \frac{3}{2}\lambda_{\text{max}}. |
| 471 |
|
\label{lipidEq:po3} |
| 472 |
|
\end{equation} |
| 473 |
|
|
| 474 |
|
Table~\ref{lipidTab:blSummary} summarizes the $P_2$ values for the |
| 475 |
< |
bilayers, as well as the dipole orientations. The unit vector for the |
| 475 |
> |
bilayers, as well as for the dipole orientations. The unit vector for the |
| 476 |
|
lipid molecules was defined by finding the moment of inertia for each |
| 477 |
|
lipid, then setting $\mathbf{\hat{u}}$ to point along the axis of |
| 478 |
< |
minimum inertia. For the {\sc head} atoms, the unit vector simply |
| 478 |
> |
minimum inertia (the long axis). For the {\sc head} atoms, the unit vector simply |
| 479 |
|
pointed in the same direction as the dipole moment. For the lipid |
| 480 |
|
molecules, the ordering was consistent across all temperatures, with |
| 481 |
|
the director pointed along the $z$ axis of the box. More |
| 482 |
|
interestingly, is the high degree of ordering the dipoles impose on |
| 483 |
|
the {\sc head} atoms. The directors for the dipoles themselves |
| 484 |
< |
consistently pointed along the plane of the bilayer, with the |
| 499 |
< |
directors anti-aligned on the top and bottom leaf. |
| 484 |
> |
consistently pointed along the plane of the bilayer, with head groups lining up in rows of alternating alignment. The ordering implies that the dipole interaction is a little too strong, or that perhaps the dipoles are allowed to approach each other a bit too closely. A possible change in future models would alter the size or shape of the head group to discourage too rigid ordering of the dipoles. |
| 485 |
|
|
| 486 |
|
\begin{table} |
| 487 |
< |
\caption[Structural properties of the bilayers]{BILAYER STRUCTURAL PROPERTIES AS A FUNCTION OF TEMPERATURE} |
| 487 |
> |
\caption{BILAYER STRUCTURAL PROPERTIES AS A FUNCTION OF TEMPERATURE} |
| 488 |
|
\label{lipidTab:blSummary} |
| 489 |
|
\begin{center} |
| 490 |
|
\begin{tabular}{|c|c|c|c|c|} |
| 523 |
|
is given by the following Einstein relation:\cite{allen87:csl} |
| 524 |
|
\begin{equation} |
| 525 |
|
D_L = \lim_{t\rightarrow\infty}\frac{1}{4t}\langle |\mathbf{r}(t) |
| 526 |
< |
- \mathbf{r}(0)|^2\rangle |
| 526 |
> |
- \mathbf{r}(0)|^2\rangle, |
| 527 |
|
\end{equation} |
| 528 |
< |
Where $\mathbf{r}(t)$ is the $xy$ position of the lipid at time $t$ |
| 529 |
< |
(assuming the $z$-axis is parallel to the bilayer normal). |
| 528 |
> |
where $\mathbf{r}(t)$ is the $xy$ position of the lipid at time $t$ |
| 529 |
> |
(assuming the $z$-axis is parallel to the bilayer normal). Calculating the $D_L$ involves first plotting the mean square displacement, $\langle |\mathbf{r}(t) - \mathbf{r}(0)|^2\rangle$, finding the slope at long times, and dividing the slope by 4 to give the diffusion constant (Fig.~\ref{lipidFig:msdFig}). When finding the slope only the 1~ns to 3~ns times are considered. Points at the longer times are not included due to the lack of good statistics at long time intervals. |
| 530 |
|
|
| 531 |
|
Fig.~\ref{lipidFig:diffusionFig} shows the lateral diffusion constants |
| 532 |
|
as a function of temperature. There is a definite increase in the |
| 533 |
|
lateral diffusion with higher temperatures, which is exactly what one |
| 534 |
|
would expect with greater fluidity of the chains. However, the |
| 535 |
< |
diffusion constants are two orders of magnitude smaller than those |
| 536 |
< |
typical of DPPC.\cite{Cevc87} This is counter-intuitive as the DPPC |
| 537 |
< |
molecule is sterically larger and heavier than our model. This could |
| 553 |
< |
be an indication that our model's chains are too interwoven and hinder |
| 554 |
< |
the motion of the lipid or that the dipolar head groups are too |
| 555 |
< |
tightly bound to each other. In contrast, the diffusion constant of |
| 535 |
> |
diffusion constants are two orders of magnitude larger than those |
| 536 |
> |
typical of DPPC ($\sim10^{-9}\text{cm}^2/\text{s}$ over this temperature range).\cite{Cevc87} This is what one would expect as the DPPC |
| 537 |
> |
molecule is sterically larger and heavier than our model, indicating that further modifications to the model should increase the lengths of the tail chains, and perhaps explore larger, more massive head groups. In contrast, the diffusion constant of |
| 538 |
|
the {\sc ssd} water, $9.84\times 10^{-6}\,\text{cm}^2/\text{s}$, is |
| 539 |
|
reasonably close to the bulk water diffusion constant ($2.2999\times |
| 540 |
|
10^{-5}\,\text{cm}^2/\text{s}$).\cite{Holz00} |
| 541 |
|
|
| 542 |
|
\begin{figure} |
| 543 |
|
\centering |
| 544 |
+ |
\includegraphics[width=\linewidth]{msdFig.eps} |
| 545 |
+ |
\caption[Lateral mean square displacement for the phospholipid at 300~K]{This is a representative lateral mean square displacement for the center of mass motion of the phospholipid model. This particular example is from the 300~K simulation. The box is drawn about the region used in the calculation of the diffusion constant.} |
| 546 |
+ |
\label{lipidFig:msdFig} |
| 547 |
+ |
\end{figure} |
| 548 |
+ |
|
| 549 |
+ |
\begin{figure} |
| 550 |
+ |
\centering |
| 551 |
|
\includegraphics[width=\linewidth]{diffusionFig.eps} |
| 552 |
|
\caption[The lateral diffusion constants versus temperature]{The lateral diffusion constants for the bilayers as a function of temperature.} |
| 553 |
|
\label{lipidFig:diffusionFig} |
| 558 |
|
A very important accomplishment for our model is its ability to |
| 559 |
|
spontaneously form bilayers from a randomly dispersed starting |
| 560 |
|
configuration. Fig.~\ref{lipidFig:blImage} shows an image sequence for |
| 561 |
< |
the bilayer aggregation. After 3.0~ns, the basic form of the bilayer |
| 573 |
< |
can already be seen. By 7.0~ns, the bilayer has a lipid bridge |
| 574 |
< |
stretched across the simulation box to itself that will turn out to be |
| 575 |
< |
very long lived ($\sim$20~ns), as well as a water pore, that will |
| 576 |
< |
persist for the length of the current simulation. At 24~ns, the lipid |
| 577 |
< |
bridge has broken, and the bilayer is still integrating the lipid |
| 578 |
< |
molecules from the bridge into itself. However, the water pore is |
| 579 |
< |
still present at 24~ns. |
| 561 |
> |
the bilayer aggregation. After 1.0~ns, bulk aggregation has occured. By 5.0~ns, the basic bilayer aggregation can be seen, however there is a vertical lipid bridge connecting the periodic image of the bilayer to itself. At 15.0~ns, the lipid bridge has finally broken up, and the lipid molecules are starting to re-incorporate themselves into the bilayer. A water pore is still present through the membrane. In the last frame at 42.0~ns, the water pore is still present, although does show some signs of rejoining the bulk water section. These behaviors are typical for coarse grain model simulations, which can have lipid bridge lifetimes of up to 20~ns, and water pores typically lasting 3 to 25~ns.\cite{marrink04} |
| 562 |
|
|
| 563 |
|
\begin{figure} |
| 564 |
|
\centering |
| 575 |
|
1.5~ns, The main body of water in the system has already collected |
| 576 |
|
into a central water channel. By 10.0~ns, the channel has widened |
| 577 |
|
slightly, but there are still many water molecules permeating the |
| 578 |
< |
lipid macro-structure. At 23.0~ns, the central water channel has |
| 578 |
> |
lipid macro-structure. At 35.0~ns, the central water channel has |
| 579 |
|
stabilized and several smaller water channels have been absorbed by |
| 580 |
|
the main one. However, there is still an appreciable water |
| 581 |
|
concentration throughout the lipid structure. |
| 592 |
|
We have presented a simple unified-atom phospholipid model capable of |
| 593 |
|
spontaneous aggregation into a bilayer and an inverted rod |
| 594 |
|
structure. The time scales of the macro-molecular aggregations are |
| 595 |
< |
approximately 24~ns. In addition the model's properties have been |
| 595 |
> |
approximately 24~ns, with water permeation of the structures persisting for times longer than the scope of both aggregations. In addition the model's properties have been |
| 596 |
|
explored over a range of temperatures through prefabricated |
| 597 |
|
bilayers. No freezing transition is seen in the temperature range of |
| 598 |
|
our current simulations. However, structural information from 270~K |
