trunk/xDissertation/Conclusion.tex

\chapter{\label{chap:conclusion}CONCLUSION}

This dissertation has shown the efforts to the understanding of the
structural properties and phase behavior of lipid membranes. In
Ch.~\ref{chap:mc}, we present a simple model for dipolar elastic
membranes that gives lattice-bound point dipoles complete
orientational freedom as well as translational freedom along one
coordinate (out of the plane of the membrane). There is an additional
harmonic term which binds each of the dipoles to the six nearest
neighbors on either triangular or distorted lattices.  The
translational freedom of the dipoles allows triangular lattices to
find states that break out of the normal orientational disorder of
frustrated configurations and which are stabilized by long-range
anti-ferroelectric ordering.  In order to break out of the frustrated
states, the dipolar membranes form corrugated or ``rippled'' phases
that make the lattices effectively non-triangular.  We observe three
common features of the corrugated dipolar membranes: 1) the corrugated
phases develop easily when hosted on triangular lattices, 2) the wave
vectors for the surface ripples are always found to be perpendicular
to the dipole director axis, and 3) on triangular lattices, the dipole
director axis is found to be parallel to any of the three equivalent
lattice directions.

Ch.~\ref{chap:md} we developed a more realistic model for lipid
molecules compared to the simple point dipole one. To further address
the dynamics properties of the ripple phase, the simulation method is
switched to molecular dynamics.  Symmetric and asymmetric ripple
phases have been observed to form in the simulations. The lipid model
consists of an dipolar head group and an ellipsoidal tail.  Within the
limits of this model, an explanation for generalized membrane
curvature is a simple mismatch in the size of the heads with the width
of the molecular bodies.  The persistence of a {\it bilayer} structure
requires strong attractive forces between the head groups.  One
feature of this model is that an energetically favorable orientational
ordering of the dipoles can be achieved by out-of-plane membrane
corrugation.  The corrugation of the surface stabilizes the long range
orientational ordering for the dipoles in the head groups which then
adopt a bulk anti-ferroelectric state. The structural properties of
the ripple phase we observed in the dynamics simulations are
consistant to that we observed in the Monte Carlo simuations of the
simple point dipole model.

To extend our simulations of lipid membranes to larger system and
longer time scale, an algorithm is developed in Ch.~\ref{chap:ld} for
carrying out Langevin dynamics simulations on complex rigid bodies by
incorporating the hydrodynamic resistance tensors for arbitrary shapes
into an advanced symplectic integration scheme.  The integrator gives
quantitative agreement with both analytic and approximate hydrodynamic
theories for a number of model rigid bodies, and works well at
reproducing the solute dynamical properties (diffusion constants, and
orientational relaxation times) obtained from explicitly-solvated
simulations. A $9$ times larger simulation of the lipid bilayer are
carried out for the comparison with the molecular dynamics simulations
in Ch.~\ref{chap:md}, the results show the structural stability of the
ripple phase.

The structural properties and the formation mechanism for the ripple
phase of lipid membranes are elucidated in this dissertation. However,
the importance of the ripple phase in the experimental view is still a
mystery, hopefully, this work can contribute some flame to the
lighting of the experimental field. Further insights of the phase
behavior of the lipid membranes can be obtained by applying a atomic
or more detailed molecular model with information of the fatty chains
of the lipid molecules.
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#	User	Rev	Content
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.