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 presented 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.

In Ch.~\ref{chap:md} we developed a more realistic model for lipid
molecules. To further address the dynamical properties of the
formation of the ripple phase, Molecular Dynamics was used to simulate
these systems. The lipid model consists of a dipolar head group and an
ellipsoidal tail.  Within the limits of this model, an explanation for
generalized membrane curvature is the 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. Symmetric and asymmetric ripple phases were observed to form in
the simulations.The structural properties of the ripple phase we
observed in the dynamics simulations are consistant with those we
observed in the Monte Carlo simuations of the simple point dipole
model.

To extend our simulations of lipid membranes to larger systems and
longer time scales, we developed an algorithm 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 simulation of the lipid bilayer was carried out that
was $9$ times the size of for 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 have been elucidated in this
dissertation. However, the biological importance of the ripple phase
is still a mystery. Additionally, experimental conformation of our
predictions (dipoles that align perpendicular to the membrane ripples)
is still required. Hopefully, this work can kindle some interest among
experimentalists. Further insights into the phase transitions of lipid
membranes can be obtained by applying more detailed molecular or
atomic scale 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	xsun	3375	Ch.~\ref{chap:mc}, we presented a simple model for dipolar elastic
6	xsun	3360	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	xsun	3375	In Ch.~\ref{chap:md} we developed a more realistic model for lipid
25			molecules. To further address the dynamical properties of the
26			formation of the ripple phase, Molecular Dynamics was used to simulate
27			these systems. The lipid model consists of a dipolar head group and an
28			ellipsoidal tail. Within the limits of this model, an explanation for
29			generalized membrane curvature is the simple mismatch in the size of
30			the heads with the width of the molecular bodies. The persistence of
31			a {\it bilayer} structure requires strong attractive forces between
32			the head groups. One feature of this model is that an energetically
33			favorable orientational ordering of the dipoles can be achieved by
34			out-of-plane membrane corrugation. The corrugation of the surface
35			stabilizes the long range orientational ordering for the dipoles in
36			the head groups which then adopt a bulk anti-ferroelectric
37			state. Symmetric and asymmetric ripple phases were observed to form in
38			the simulations.The structural properties of the ripple phase we
39			observed in the dynamics simulations are consistant with those we
40			observed in the Monte Carlo simuations of the simple point dipole
41			model.
42	xsun	3360
43	xsun	3375	To extend our simulations of lipid membranes to larger systems and
44			longer time scales, we developed an algorithm for carrying out
45			Langevin dynamics simulations on complex rigid bodies by incorporating
46			the hydrodynamic resistance tensors for arbitrary shapes into an
47			advanced symplectic integration scheme. The integrator gives
48	xsun	3360	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	xsun	3375	simulations. A simulation of the lipid bilayer was carried out that
53			was $9$ times the size of for the molecular dynamics simulations in
54			Ch.~\ref{chap:md}, the results show the structural stability of the
55	xsun	3360	ripple phase.
56
57			The structural properties and the formation mechanism for the ripple
58	xsun	3375	phase of lipid membranes have been elucidated in this
59			dissertation. However, the biological importance of the ripple phase
60			is still a mystery. Additionally, experimental conformation of our
61			predictions (dipoles that align perpendicular to the membrane ripples)
62			is still required. Hopefully, this work can kindle some interest among
63			experimentalists. Further insights into the phase transitions of lipid
64			membranes can be obtained by applying more detailed molecular or
65			atomic scale model with information of the fatty chains of the lipid
66			molecules.