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This dissertation has shown the efforts to the understanding of the |
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structural properties and phase behavior of lipid membranes. In |
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Ch.~\ref{chap:mc}, we present a simple model for dipolar elastic |
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Ch.~\ref{chap:mc}, we presented a simple model for dipolar elastic |
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membranes that gives lattice-bound point dipoles complete |
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orientational freedom as well as translational freedom along one |
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coordinate (out of the plane of the membrane). There is an additional |
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director axis is found to be parallel to any of the three equivalent |
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lattice directions. |
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|
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Ch.~\ref{chap:md} we developed a more realistic model for lipid |
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molecules compared to the simple point dipole one. To further address |
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the dynamics properties of the ripple phase, the simulation method is |
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switched to molecular dynamics. Symmetric and asymmetric ripple |
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phases have been observed to form in the simulations. The lipid model |
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consists of an dipolar head group and an ellipsoidal tail. Within the |
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limits of this model, an explanation for generalized membrane |
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curvature is a simple mismatch in the size of the heads with the width |
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of the molecular bodies. The persistence of a {\it bilayer} structure |
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requires strong attractive forces between the head groups. One |
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feature of this model is that an energetically favorable orientational |
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ordering of the dipoles can be achieved by out-of-plane membrane |
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corrugation. The corrugation of the surface stabilizes the long range |
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orientational ordering for the dipoles in the head groups which then |
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adopt a bulk anti-ferroelectric state. The structural properties of |
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the ripple phase we observed in the dynamics simulations are |
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consistant to that we observed in the Monte Carlo simuations of the |
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simple point dipole model. |
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In Ch.~\ref{chap:md} we developed a more realistic model for lipid |
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molecules. To further address the dynamical properties of the |
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formation of the ripple phase, Molecular Dynamics was used to simulate |
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these systems. The lipid model consists of a dipolar head group and an |
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ellipsoidal tail. Within the limits of this model, an explanation for |
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generalized membrane curvature is the simple mismatch in the size of |
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the heads with the width of the molecular bodies. The persistence of |
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a {\it bilayer} structure requires strong attractive forces between |
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the head groups. One feature of this model is that an energetically |
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favorable orientational ordering of the dipoles can be achieved by |
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out-of-plane membrane corrugation. The corrugation of the surface |
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> |
stabilizes the long range orientational ordering for the dipoles in |
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> |
the head groups which then adopt a bulk anti-ferroelectric |
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> |
state. Symmetric and asymmetric ripple phases were observed to form in |
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> |
the simulations.The structural properties of the ripple phase we |
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> |
observed in the dynamics simulations are consistant with those we |
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observed in the Monte Carlo simuations of the simple point dipole |
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model. |
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|
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To extend our simulations of lipid membranes to larger system and |
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longer time scale, an algorithm is developed in Ch.~\ref{chap:ld} for |
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carrying out Langevin dynamics simulations on complex rigid bodies by |
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incorporating the hydrodynamic resistance tensors for arbitrary shapes |
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into an advanced symplectic integration scheme. The integrator gives |
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To extend our simulations of lipid membranes to larger systems and |
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longer time scales, we developed an algorithm for carrying out |
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Langevin dynamics simulations on complex rigid bodies by incorporating |
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the hydrodynamic resistance tensors for arbitrary shapes into an |
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> |
advanced symplectic integration scheme. The integrator gives |
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quantitative agreement with both analytic and approximate hydrodynamic |
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theories for a number of model rigid bodies, and works well at |
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reproducing the solute dynamical properties (diffusion constants, and |
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orientational relaxation times) obtained from explicitly-solvated |
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simulations. A $9$ times larger simulation of the lipid bilayer are |
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carried out for the comparison with the molecular dynamics simulations |
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in Ch.~\ref{chap:md}, the results show the structural stability of the |
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simulations. A simulation of the lipid bilayer was carried out that |
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was $9$ times the size of for the molecular dynamics simulations in |
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> |
Ch.~\ref{chap:md}, the results show the structural stability of the |
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ripple phase. |
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|
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The structural properties and the formation mechanism for the ripple |
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phase of lipid membranes are elucidated in this dissertation. However, |
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the importance of the ripple phase in the experimental view is still a |
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mystery, hopefully, this work can contribute some flame to the |
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lighting of the experimental field. Further insights of the phase |
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behavior of the lipid membranes can be obtained by applying a atomic |
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or more detailed molecular model with information of the fatty chains |
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of the lipid molecules. |
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> |
phase of lipid membranes have been elucidated in this |
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dissertation. However, the biological importance of the ripple phase |
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> |
is still a mystery. Additionally, experimental conformation of our |
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predictions (dipoles that align perpendicular to the membrane ripples) |
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is still required. Hopefully, this work can kindle some interest among |
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experimentalists. Further insights into the phase transitions of lipid |
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membranes can be obtained by applying more detailed molecular or |
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atomic scale model with information of the fatty chains of the lipid |
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molecules. |
