| 355 |
|
bilayer structure does not persist; all lipid molecules are solvated |
| 356 |
|
directly in the water. The critial value of the strength of the dipole |
| 357 |
|
depends on the head size. The perfectly flat surface melts at $5$ |
| 358 |
< |
debye, the asymmetric rippled surfaces melt at $8$ debye, the |
| 359 |
< |
symmetric rippled surfaces melt at $10$ debye. The ordering of the |
| 360 |
< |
tails is the same as the ordering of the dipoles except for the flat |
| 361 |
< |
phase. Since the surface is already perfect flat, the order parameter |
| 362 |
< |
does not change much until the strength of the dipole is $15$ |
| 363 |
< |
debye. However, the order parameter decreases quickly when the |
| 364 |
< |
strength of the dipole is further increased. The head groups of the |
| 365 |
< |
lipid molecules are brought closer by stronger interactions between |
| 366 |
< |
them. For a flat surface, a large amount of free volume between the |
| 367 |
< |
head groups is available, but when the head groups are brought closer, |
| 368 |
< |
the tails will splay outward, forming an inverse micelle. For rippled |
| 369 |
< |
surfaces, there is less free volume available between the head |
| 370 |
< |
groups. Therefore there is little effect on the structure of the |
| 371 |
< |
membrane due to increasing dipolar strength. Unlike other systems that |
| 372 |
< |
melt directly when the interaction is weak enough, for |
| 373 |
< |
$\sigma_h=1.41\sigma_0$, part of the membrane melts into itself |
| 374 |
< |
first. The upper leaf of the bilayer becomes totally interdigitated |
| 375 |
< |
with the lower leaf. This is different behavior than what is exhibited |
| 376 |
< |
with the interdigitated lines in the rippled phase where only one |
| 377 |
< |
interdigitated line connects the two leaves of bilayer. |
| 358 |
> |
$0.03$ debye, the asymmetric rippled surfaces melt at $8$ $0.04$ |
| 359 |
> |
$0.03$ debye, the symmetric rippled surfaces melt at $10$ $0.04$ |
| 360 |
> |
debye. The ordering of the tails is the same as the ordering of the |
| 361 |
> |
dipoles except for the flat phase. Since the surface is already |
| 362 |
> |
perfect flat, the order parameter does not change much until the |
| 363 |
> |
strength of the dipole is $15$ debye. However, the order parameter |
| 364 |
> |
decreases quickly when the strength of the dipole is further |
| 365 |
> |
increased. The head groups of the lipid molecules are brought closer |
| 366 |
> |
by stronger interactions between them. For a flat surface, a large |
| 367 |
> |
amount of free volume between the head groups is available, but when |
| 368 |
> |
the head groups are brought closer, the tails will splay outward, |
| 369 |
> |
forming an inverse micelle. When $\sigma_h=1.28\sigma_0$, the $P_2$ |
| 370 |
> |
order parameter decreases slightly after the strength of the dipole is |
| 371 |
> |
increased to $16$ debye. For rippled surfaces, there is less free |
| 372 |
> |
volume available between the head groups. Therefore there is little |
| 373 |
> |
effect on the structure of the membrane due to increasing dipolar |
| 374 |
> |
strength. However, the increase of the $P_2$ order parameter implies |
| 375 |
> |
the membranes are flatten by the increase of the strength of the |
| 376 |
> |
dipole. Unlike other systems that melt directly when the interaction |
| 377 |
> |
is weak enough, for $\sigma_h=1.41\sigma_0$, part of the membrane |
| 378 |
> |
melts into itself first. The upper leaf of the bilayer becomes totally |
| 379 |
> |
interdigitated with the lower leaf. This is different behavior than |
| 380 |
> |
what is exhibited with the interdigitated lines in the rippled phase |
| 381 |
> |
where only one interdigitated line connects the two leaves of bilayer. |
| 382 |
|
\begin{figure}[htb] |
| 383 |
|
\centering |
| 384 |
|
\includegraphics[width=\linewidth]{sP2} |
| 390 |
|
temperature. The behavior of the $P_2$ order paramter is |
| 391 |
|
straightforward. Systems are more ordered at low temperature, and more |
| 392 |
|
disordered at high temperatures. When the temperature is high enough, |
| 393 |
< |
the membranes are instable. Since our model lacks the detailed |
| 394 |
< |
information on lipid tails, we can not simulate the fluid phase with |
| 395 |
< |
melted fatty acid chains. Moreover, the formation of the tilted |
| 396 |
< |
$L_{\beta'}$ phase also depends on the organization of fatty groups on |
| 397 |
< |
tails. |
| 393 |
> |
the membranes are instable. For flat surfaces ($\sigma_h=1.20\sigma_0$ |
| 394 |
> |
and $\sigma_h=1.28\sigma_0$), when the temperature is increased to |
| 395 |
> |
$310$, the $P_2$ order parameter increases slightly instead of |
| 396 |
> |
decreases like ripple surface. This is an evidence of the frustration |
| 397 |
> |
of the dipolar ordering in each leaf of the lipid bilayer, at low |
| 398 |
> |
temperature, the systems are locked in a local minimum energy state, |
| 399 |
> |
with increase of the temperature, the system can jump out the local |
| 400 |
> |
energy well to find the lower energy state which is the longer range |
| 401 |
> |
orientational ordering. Like the dipolar ordering of the flat |
| 402 |
> |
surfaces, the ordering of the tails of the lipid molecules for ripple |
| 403 |
> |
membranes ($\sigma_h=1.35\sigma_0$ and $\sigma_h=1.41\sigma_0$) also |
| 404 |
> |
show some nonthermal characteristic. With increase of the temperature, |
| 405 |
> |
the $P_2$ order parameter decreases firstly, and increases afterward |
| 406 |
> |
when the temperature is greater than $290 K$. The increase of the |
| 407 |
> |
$P_2$ order parameter indicates a more ordered structure for the tails |
| 408 |
> |
of the lipid molecules which corresponds to a more flat surface. Since |
| 409 |
> |
our model lacks the detailed information on lipid tails, we can not |
| 410 |
> |
simulate the fluid phase with melted fatty acid chains. Moreover, the |
| 411 |
> |
formation of the tilted $L_{\beta'}$ phase also depends on the |
| 412 |
> |
organization of fatty groups on tails. |
| 413 |
|
\begin{figure}[htb] |
| 414 |
|
\centering |
| 415 |
|
\includegraphics[width=\linewidth]{tP2} |
