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the ripple formation can be found in section |
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\ref{sec:discussion}. |
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|
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\section{Methodology and Model} |
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\section{Computational Model} |
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\label{sec:method} |
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|
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Our simple molecular-scale lipid model for studying the ripple phase |
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\end{eqnarray*} |
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the strength parameter has been adjusted as suggested by Cleaver {\it |
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et al.}\cite{Cleaver96} A switching function has been applied to all |
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potentials to smoothly turn off the interactions between a range of $22$ \AA\ and $25$ \AA. |
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potentials to smoothly turn off the interactions between a range of $22$ and $25$ \AA. |
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|
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The model of the solvent in our simulations is inspired by the idea of |
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``DPD'' water. Every four water molecules are reprsented by one |
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sphere. |
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The solvent model in our simulations is identical to one used by XXX |
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in their dissipative particle dynamics (DPD) simulation of lipid |
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bilayers.]cite{XXX} This solvent bead is a single site that represents |
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four water molecules (m = 72 amu) and has comparable density and |
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diffusive behavior to liquid water. However, since there are no |
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electrostatic sites on these beads, this solvent model cannot |
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replicate the dielectric properties of water. |
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|
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\begin{figure}[htb] |
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\centering |
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\includegraphics[height=4in]{lipidModel} |
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\includegraphics[width=\linewidth]{2lipidModel} |
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\caption{The parameters defining the behavior of the lipid |
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models. $\sigma_h / \sigma_0$ is the ratio of the head group to body |
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diameter. Molecular bodies all had an aspect ratio of 3.0. The |
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dipolar strength (and the temperature and pressure) wer the only other |
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parameters that wer varied systematically.\label{fig:lipidModel}} |
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diameter. Molecular bodies had a fixed aspect ratio of 3.0. The |
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solvent model was a simplified 4-water bead ($\sigma_w = 1.02 |
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> |
\sigma_0$) that has been used in other coarse-grained (DPD) simulations. |
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The dipolar strength (and the temperature and pressure) were the only |
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other parameters that were varied |
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systematically.\label{fig:lipidModel}} |
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\end{figure} |
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|
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\section{Experiment} |
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\section{Experimental Methodology} |
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\label{sec:experiment} |
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|
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To make the simulations less expensive and to observe long-time |
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behavior of the lipid membranes, all simulations were started from two |
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separate monolayers in the vaccum with $x-y$ anisotropic pressure |
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To create unbiased bilayers, all simulations were started from two |
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perfectly flat monolayers separated by a 20 \AA\ gap between the |
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> |
molecular bodies of the upper and lower leaves. The separated |
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monolayers were evolved in a vaccum with $x-y$ anisotropic pressure |
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|
coupling. The length of $z$ axis of the simulations was fixed and a |
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|
constant surface tension was applied to enable real fluctuations of |
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the bilayer. Periodic boundaries were used. There were $480-720$ lipid |
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molecules in the simulations depending on the size of the head |
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beads. All the simulations were equlibrated for $100$ ns at $300$ |
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K. The resulting structures were solvated in water ($6$ DPD |
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water/lipid molecule). These configurations were relaxed for another |
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$30$ ns relaxation. All simulations with water were carried out at |
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constant pressure ($P=1$ atm) by $3$D anisotropic coupling, and |
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constant surface tension ($\gamma=0.015$). Given the absence of fast |
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degrees of freedom in this model, a timestep of $50$ fs was |
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utilized. Simulations were performed by using OOPSE |
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package\cite{Meineke05}. |
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the bilayer. Periodic boundaries were used, and $480-720$ lipid |
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molecules were present in the simulations depending on the size of the |
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head beads. The two monolayers spontaneously collapse into bilayer |
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structures within 100 ps, and following this collapse, all systems |
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were equlibrated for $100$ ns at $300$ K. |
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|
|
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\section{Results and Analysis} |
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The resulting structures were then solvated at a ratio of $6$ DPD |
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solvent beads (24 water molecules) per lipid. These configurations |
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were then equilibrated for another $30$ ns. All simulations with |
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solvent were carried out at constant pressure ($P=1$ atm) by $3$D |
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> |
anisotropic coupling, and constant surface tension ($\gamma=0.015$ |
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> |
UNIT). Given the absence of fast degrees of freedom in this model, a |
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timestep of $50$ fs was utilized. Data collection for structural |
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properties of the bilayers was carried out during a final 5 ns run |
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> |
following the solvent equilibration. All simulations were performed |
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using the OOPSE molecular modeling program.\cite{Meineke05} |
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|
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\section{Results} |
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|
\label{sec:results} |
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|
|
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Snapshots in Figure \ref{fig:phaseCartoon} show that the membrane is |