| 598 |
|
\begin{figure}[htb] |
| 599 |
|
\centering |
| 600 |
|
\includegraphics[width=\linewidth]{tP2} |
| 601 |
< |
\caption{The $P_2$ order parameter as a funtion of |
| 601 |
> |
\caption{The $P_2$ order parameter as a function of |
| 602 |
|
temperature.\label{fig:tP2}} |
| 603 |
|
\end{figure} |
| 604 |
|
|
| 605 |
|
\section{Discussion} |
| 606 |
|
\label{sec:discussion} |
| 607 |
+ |
|
| 608 |
+ |
The ripple phases have been observed in our molecular dynamic |
| 609 |
+ |
simulations using a simple molecular lipid model. The lipid model |
| 610 |
+ |
consists of an anisotropic interacting dipolar head group and an |
| 611 |
+ |
ellipsoid shape tail. According to our simulations, the explanation of |
| 612 |
+ |
the formation for the ripples are originated in the size mismatch |
| 613 |
+ |
between the head groups and the tails. The ripple phases are only |
| 614 |
+ |
observed in the studies using larger head group lipid models. However, |
| 615 |
+ |
there is a mismatch betweent the size of the head groups and the size |
| 616 |
+ |
of the tails in the simulations of the flat surface. This indicates |
| 617 |
+ |
the competition between the anisotropic dipolar interaction and the |
| 618 |
+ |
packing of the tails also plays a major role for formation of the |
| 619 |
+ |
ripple phase. The larger head groups provide more free volume for the |
| 620 |
+ |
tails, while these hydrophobic ellipsoids trying to be close to each |
| 621 |
+ |
other, this gives the origin of the spontanous curvature of the |
| 622 |
+ |
surface, which is believed as the beginning of the ripple phases. The |
| 623 |
+ |
lager head groups cause the spontanous curvature inward for both of |
| 624 |
+ |
leaves of the bilayer. This results in a steric strain when the tails |
| 625 |
+ |
of two leaves too close to each other. The membrane has to be broken |
| 626 |
+ |
to release this strain. There are two ways to arrange these broken |
| 627 |
+ |
curvatures: symmetric and asymmetric ripples. Both of the ripple |
| 628 |
+ |
phases have been observed in our studies. The difference between these |
| 629 |
+ |
two ripples is that the bilayer is continuum in the symmetric ripple |
| 630 |
+ |
phase and is disrupt in the asymmetric ripple phase. |
| 631 |
+ |
|
| 632 |
+ |
Dipolar head groups are the key elements for the maintaining of the |
| 633 |
+ |
bilayer structure. The lipids are solvated in water when lowering the |
| 634 |
+ |
the strength of the dipole on the head groups. The long range |
| 635 |
+ |
orientational ordering of the dipoles can be achieved by forming the |
| 636 |
+ |
ripples, although the dipoles are likely to form head-to-tail |
| 637 |
+ |
configurations even in flat surface, the frustration prevents the |
| 638 |
+ |
formation of the long range orientational ordering for dipoles. The |
| 639 |
+ |
corrugation of the surface breaks the frustration and stablizes the |
| 640 |
+ |
long range oreintational ordering for the dipoles in the head groups |
| 641 |
+ |
of the lipid molecules. Many rows of the head-to-tail dipoles are |
| 642 |
+ |
parallel to each other and adopt the antiferroelectric state as a |
| 643 |
+ |
whole. This is the first time the organization of the head groups in |
| 644 |
+ |
ripple phases of the lipid bilayer has been addressed. |
| 645 |
|
|
| 646 |
+ |
The most important prediction we can make using the results from this |
| 647 |
+ |
simple model is that if dipolar ordering is driving the surface |
| 648 |
+ |
corrugation, the wave vectors for the ripples should always found to |
| 649 |
+ |
be {\it perpendicular} to the dipole director axis. This prediction |
| 650 |
+ |
should suggest experimental designs which test whether this is really |
| 651 |
+ |
true in the phosphatidylcholine $P_{\beta'}$ phases. The dipole |
| 652 |
+ |
director axis should also be easily computable for the all-atom and |
| 653 |
+ |
coarse-grained simulations that have been published in the literature. |
| 654 |
+ |
|
| 655 |
+ |
Although our model is simple, it exhibits some rich and unexpected |
| 656 |
+ |
behaviors. It would clearly be a closer approximation to the reality |
| 657 |
+ |
if we allowed greater translational freedom to the dipoles and |
| 658 |
+ |
replaced the somewhat artificial lattice packing and the harmonic |
| 659 |
+ |
elastic tension with more realistic molecular modeling potentials. |
| 660 |
+ |
What we have done is to present a simple model which exhibits bulk |
| 661 |
+ |
non-thermal corrugation, and our explanation of this rippling |
| 662 |
+ |
phenomenon will help us design more accurate molecular models for |
| 663 |
+ |
corrugated membranes and experiments to test whether rippling is |
| 664 |
+ |
dipole-driven or not. |
| 665 |
+ |
|
| 666 |
|
\newpage |
| 667 |
|
\bibliography{mdripple} |
| 668 |
|
\end{document} |
