1 |
xsun |
3336 |
\chapter{\label{chap:conclusion}CONCLUSION} |
2 |
xsun |
3360 |
|
3 |
|
|
This dissertation has shown the efforts to the understanding of the |
4 |
|
|
structural properties and phase behavior of lipid membranes. In |
5 |
|
|
Ch.~\ref{chap:mc}, we present a simple model for dipolar elastic |
6 |
|
|
membranes that gives lattice-bound point dipoles complete |
7 |
|
|
orientational freedom as well as translational freedom along one |
8 |
|
|
coordinate (out of the plane of the membrane). There is an additional |
9 |
|
|
harmonic term which binds each of the dipoles to the six nearest |
10 |
|
|
neighbors on either triangular or distorted lattices. The |
11 |
|
|
translational freedom of the dipoles allows triangular lattices to |
12 |
|
|
find states that break out of the normal orientational disorder of |
13 |
|
|
frustrated configurations and which are stabilized by long-range |
14 |
|
|
anti-ferroelectric ordering. In order to break out of the frustrated |
15 |
|
|
states, the dipolar membranes form corrugated or ``rippled'' phases |
16 |
|
|
that make the lattices effectively non-triangular. We observe three |
17 |
|
|
common features of the corrugated dipolar membranes: 1) the corrugated |
18 |
|
|
phases develop easily when hosted on triangular lattices, 2) the wave |
19 |
|
|
vectors for the surface ripples are always found to be perpendicular |
20 |
|
|
to the dipole director axis, and 3) on triangular lattices, the dipole |
21 |
|
|
director axis is found to be parallel to any of the three equivalent |
22 |
|
|
lattice directions. |
23 |
|
|
|
24 |
|
|
Ch.~\ref{chap:md} we developed a more realistic model for lipid |
25 |
|
|
molecules compared to the simple point dipole one. To further address |
26 |
|
|
the dynamics properties of the ripple phase, the simulation method is |
27 |
|
|
switched to molecular dynamics. Symmetric and asymmetric ripple |
28 |
|
|
phases have been observed to form in the simulations. The lipid model |
29 |
|
|
consists of an dipolar head group and an ellipsoidal tail. Within the |
30 |
|
|
limits of this model, an explanation for generalized membrane |
31 |
|
|
curvature is a simple mismatch in the size of the heads with the width |
32 |
|
|
of the molecular bodies. The persistence of a {\it bilayer} structure |
33 |
|
|
requires strong attractive forces between the head groups. One |
34 |
|
|
feature of this model is that an energetically favorable orientational |
35 |
|
|
ordering of the dipoles can be achieved by out-of-plane membrane |
36 |
|
|
corrugation. The corrugation of the surface stabilizes the long range |
37 |
|
|
orientational ordering for the dipoles in the head groups which then |
38 |
|
|
adopt a bulk anti-ferroelectric state. The structural properties of |
39 |
|
|
the ripple phase we observed in the dynamics simulations are |
40 |
|
|
consistant to that we observed in the Monte Carlo simuations of the |
41 |
|
|
simple point dipole model. |
42 |
|
|
|
43 |
|
|
To extend our simulations of lipid membranes to larger system and |
44 |
|
|
longer time scale, an algorithm is developed in Ch.~\ref{chap:ld} for |
45 |
|
|
carrying out Langevin dynamics simulations on complex rigid bodies by |
46 |
|
|
incorporating the hydrodynamic resistance tensors for arbitrary shapes |
47 |
|
|
into an advanced symplectic integration scheme. The integrator gives |
48 |
|
|
quantitative agreement with both analytic and approximate hydrodynamic |
49 |
|
|
theories for a number of model rigid bodies, and works well at |
50 |
|
|
reproducing the solute dynamical properties (diffusion constants, and |
51 |
|
|
orientational relaxation times) obtained from explicitly-solvated |
52 |
|
|
simulations. A $9$ times larger simulation of the lipid bilayer are |
53 |
|
|
carried out for the comparison with the molecular dynamics simulations |
54 |
|
|
in Ch.~\ref{chap:md}, the results show the structural stability of the |
55 |
|
|
ripple phase. |
56 |
|
|
|
57 |
|
|
The structural properties and the formation mechanism for the ripple |
58 |
|
|
phase of lipid membranes are elucidated in this dissertation. However, |
59 |
|
|
the importance of the ripple phase in the experimental view is still a |
60 |
|
|
mystery, hopefully, this work can contribute some flame to the |
61 |
|
|
lighting of the experimental field. Further insights of the phase |
62 |
|
|
behavior of the lipid membranes can be obtained by applying a atomic |
63 |
|
|
or more detailed molecular model with information of the fatty chains |
64 |
|
|
of the lipid molecules. |