10 |
|
|
11 |
|
The 25 lipid system (scheme I) was initially started from an ordered |
12 |
|
configuration. The lipids were aligned in a 5x5 square with a side by |
13 |
< |
side spacing of $\approx\mbox{8\AA}$ (Fig.~\ref{fig:25lipidInit}) The |
13 |
> |
side spacing of $\sim \mbox{8\AA}$ (Fig.~\ref{fig:25lipidInit}) The |
14 |
|
box was then filled with water in an FCC lattice. The temperature was |
15 |
< |
then equilibrated to 300~K by resampling the atomic velocitiues from a |
15 |
> |
then equilibrated to 300~K by resampling the atomic velocities from a |
16 |
|
Maxwell-Boltzmann distribution. Once the temperature had been set, the |
17 |
< |
system was allowed to progress for $\approx 20$~ns. |
17 |
> |
system was allowed to progress for $\sim 20$~ns. |
18 |
|
|
19 |
|
\begin{figure} |
20 |
< |
\parbox{\linewidth}{Here is the initial 25 lipid configuration} |
21 |
< |
\caption[The initial configuration of scheme I]{The starting configuration of scheme I.} |
22 |
< |
\label{fig:25lipidinit} |
20 |
> |
\centering |
21 |
> |
\includegraphics[width=\linewidth]{5x5-initial_pre.eps} |
22 |
> |
\caption[The initial configuration of scheme I]{The starting configuration of scheme I after thermalization.} |
23 |
> |
\label{fig:25lipidInit} |
24 |
|
\end{figure} |
25 |
|
|
26 |
|
The 50 lipid system (scheme II) was initially started from a randomly |
27 |
< |
generarted configuration. A system box was initially filled with water |
27 |
> |
generated configuration. A system box was initially filled with water |
28 |
|
in an FCC lattice. The 50 lipid molecules were then sequentially |
29 |
< |
placed in the box with a random orientaion and position. If the lipid |
29 |
> |
placed in the box with a random orientation and position. If the lipid |
30 |
|
did not overlap with a previously placed one, its position was |
31 |
|
accepted, and the next lipid was placed. Once all 50 lipids were |
32 |
< |
positioned, any waters overlaping with the lipids were removed |
32 |
> |
positioned, any waters overlapping with the lipids were removed |
33 |
|
(Fig.~\ref{fig:r50Init}. The system was then equilibrated to 300~K in |
34 |
|
the same manner as scheme I. |
35 |
|
|
36 |
|
\begin{figure} |
37 |
< |
\parbox{\linewidth}{Here is the initial random 50 lipid configuration} |
38 |
< |
\caption[The initial configuration of scheme II]{The starting configuration of scheme II.} |
37 |
> |
\centering |
38 |
> |
\includegraphics[width=\linewidth]{r50-initial_pre.eps} |
39 |
> |
\caption[The initial configuration of scheme II]{The starting configuration of scheme II after thermalization} |
40 |
|
\label{fig:r50Init} |
41 |
|
\end{figure} |
42 |
|
|
44 |
|
\label{subSec:initSimsResults} |
45 |
|
|
46 |
|
Scheme I was found to split into two leaves within the first |
47 |
< |
5~ns. However, as the simulation progressed, it became appaarent that |
47 |
> |
5~ns. However, as the simulation progressed, it became apparent that |
48 |
|
the system was frustrated in its confined box. After 15~ns, the two |
49 |
< |
leaveswere still unable to form a bilayer. Instead, thew were only |
49 |
> |
leaves were still unable to form a bilayer. Instead, thew were only |
50 |
|
able to form two skewed layers (Fig.~\ref{fig:25lipidFinal}). |
51 |
|
|
52 |
< |
\begin{figure} |
53 |
< |
\parbox{\linewidth}{Here is the final 25 lipid configuration} |
54 |
< |
\caption[The final configuration of scheme I]{The final configuration of scheme I.} |
52 |
> |
\begin{figure} |
53 |
> |
\centering |
54 |
> |
\includegraphics[width=\linewidth]{5x5-montage_pre.eps} |
55 |
> |
\caption[The time evolution of scheme I]{The time evolution of scheme I.} |
56 |
|
\label{fig:25lipidFinal} |
57 |
|
\end{figure} |
58 |
+ |
|
59 |
+ |
Scheme II behaved similarly. Within the first 2~ns the system |
60 |
+ |
aggregated into lipid and water regions. After $\sim 5$~ns the lipid |
61 |
+ |
regions had become micelles. Over the course of the next 10~ns the |
62 |
+ |
micelles underwent little change. At 15~ns simulation time, we switched |
63 |
+ |
the ensemble to isobaric-isothermal, NPT. The new integrator had just |
64 |
+ |
been written, and allowed form isometric scaling of the simulation |
65 |
+ |
box. The new integrator allowed the system to relax more, and over the |
66 |
+ |
next 10~ns several of the micelles started to merge. However, no |
67 |
+ |
bilayer was formed. Fig.~\ref{fig:r50Final} shows the progression of |
68 |
+ |
the simulation. |
69 |
+ |
|
70 |
+ |
\begin{figure} |
71 |
+ |
\centering |
72 |
+ |
\includegraphics[width=\linewidth]{r50-montage_pre.eps} |
73 |
+ |
\caption[The time evolution of scheme II]{The time evolution of scheme II.} |
74 |
+ |
\label{fig:25lipidFinal} |
75 |
+ |
\end{figure} |
76 |
+ |
|
77 |
+ |
\begin{figure} |
78 |
+ |
\centering |
79 |
+ |
\subfigure[The self correlation of the phospholipid head groups. $g_{\text{Head,Head}}(r)$ is on the top, the bottom chart is the $\langle \cos \omega \rangle_{\text{Head,Head}}(r)$.]{% |
80 |
+ |
\label{fig:5x5HHCorr}% |
81 |
+ |
\includegraphics[angle=-90,width=0.49\linewidth]{all5x5-HEAD-HEAD.epsi}% |
82 |
+ |
} |
83 |
+ |
\subfigure[The $g_{\text{CH}_2\text{,CH}_2}(r)$ for the tail chains]{% |
84 |
+ |
\label{fig:5x5CCg}% |
85 |
+ |
\includegraphics[angle=-90,width=0.49\linewidth]{all5x5-CH2-CH2.epsi}} |
86 |
+ |
\subfigure% |
87 |
+ |
[The pair correlations between the head groups and the water]{% |
88 |
+ |
\label{fig:5x5HXCorr}% |
89 |
+ |
\includegraphics[angle=-90,width=0.49\linewidth]{all5x5-HEAD-X.epsi}} |
90 |
+ |
\caption[Scheme I pair correlations]{The pair correlation functions for scheme I.} |
91 |
+ |
\label{fig:5x5PairCorrs} |
92 |
+ |
\end{figure} |
93 |
+ |
|
94 |
+ |
Structural information about the simulations were calculated via the |
95 |
+ |
equations in Sec.~\ref{sec:analysis}. Fig.~\ref{fig:5x5HHCorr} shows |
96 |
+ |
$g_{\text{Head,Head}}(r)$ and $\langle \cos \omega |
97 |
+ |
\rangle_{\text{Head,Head}}(r)$ for scheme II. The |
98 |
+ |
first peak in the $g(r)$ at 4.03~$\mbox{\AA}$ is the nearest neighbor |
99 |
+ |
separation of the heads of two lipids. This corresponds to a maximum |
100 |
+ |
in the $\langle \cos \omega \rangle(r)$ which means that the two |
101 |
+ |
neighbors on the same leaf have their dipoles aligned. The broad peak |
102 |
+ |
at 6.5~$\mbox{\AA}$ is the inter-surface spacing. Here, there is a |
103 |
+ |
corresponding anti-alignment in the angular correlation. This means |
104 |
+ |
that although the dipoles are aligned on the same monolayer, the |
105 |
+ |
dipoles will orient themselves to be anti-aligned on a opposite facing |
106 |
+ |
monolayer. With this information, the two peaks at 7.0~$\mbox{\AA}$ |
107 |
+ |
and 7.4~$\mbox{\AA}$ are head groups on the same monolayer, and they |
108 |
+ |
are the second nearest neighbors to the head group. The peak is likely |
109 |
+ |
a split peak because of the small statistics of this system. Finally, |
110 |
+ |
the peak at 8.0~$\mbox{\AA}$ is likely the second nearest neighbor on |
111 |
+ |
the opposite monolayer because of the anti-alignment evident in the |
112 |
+ |
angular correlation. |
113 |
+ |
|
114 |
+ |
Fig.~\ref{fig:5x5CCg} shows the radial distribution function for the |
115 |
+ |
$\text{CH}_2$ unified atoms. The spacing of the atoms along the tail |
116 |
+ |
chains accounts for the regularly spaced sharp peaks, but the broad |
117 |
+ |
underlying peak with its maximum at 4.6~$\mbox{\AA}$ is the |
118 |
+ |
distribution of chain-chain distances between two lipids. The final |
119 |
+ |
figure, Fig.~\ref{fig:5x5HXCorr}, includes the correlation functions |
120 |
+ |
between the Head group and the SSD atoms. The peak in $g(r)$ at |
121 |
+ |
3.6~$\mbox{\AA}$ is the distance of closest approach between the two, |
122 |
+ |
and $\langle \cos \omega \rangle(r)$ shows that the SSD atoms will |
123 |
+ |
align their dipoles with the head groups at close distance. However, |
124 |
+ |
as one increases the distance, the SSD atoms are no longer aligned. |
125 |
+ |
|
126 |
+ |
\begin{figure} |
127 |
+ |
\centering |
128 |
+ |
\subfigure[The self correlation of the phospholipid head groups.]{% |
129 |
+ |
\label{fig:r50HHCorr}% |
130 |
+ |
\includegraphics[angle=-90,width=0.49\linewidth]{r50-HEAD-HEAD.epsi}% |
131 |
+ |
} |
132 |
+ |
\subfigure% |
133 |
+ |
[The pair correlations between the head groups and the water]{% |
134 |
+ |
\label{fig:r50HXCorr}% |
135 |
+ |
\includegraphics[angle=-90,width=0.49\linewidth]{r50-HEAD-X.epsi}% |
136 |
+ |
} |
137 |
+ |
\subfigure[The $g_{\text{CH}_2\text{,CH}_2}(r)$ for the tail chains]{% |
138 |
+ |
\label{fig:r50CCg}% |
139 |
+ |
\includegraphics[angle=-90,width=0.49\linewidth]{r50-CH2-CH2.epsi}} |
140 |
+ |
|
141 |
+ |
\caption[Scheme II pair correlations]{The pair correlation functions for scheme II} |
142 |
+ |
\label{fig:r50PairCorrs} |
143 |
+ |
\end{figure} |
144 |
+ |
|
145 |
+ |
Fig.~ \ref{fig:r50HHCorr}, \ref{fig:r50HXCorr}, and \ref{fig:r50CCg} |
146 |
+ |
are the same correlation functions for scheme II as for scheme I. What |
147 |
+ |
is most interesting to note, is the high degree of similarity between |
148 |
+ |
the correlation functions between systems. Even though scheme I formed |
149 |
+ |
a skewed bilayer and scheme II is still in the micelle stage, both |
150 |
+ |
have an inter-surface spacing of 6.5~$\mbox{\AA}$ with the same |
151 |
+ |
characteristic anti-alignment between surfaces. Not as surprising, is |
152 |
+ |
the consistency of the closest packing statistics between |
153 |
+ |
systems. Namely, a head-head closest approach distance of |
154 |
+ |
4~$\mbox{\AA}$, and similar findings for the chain-chain and |
155 |
+ |
head-water distributions as in scheme I. |