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Revision 734 by mmeineke, Wed Aug 27 19:32:40 2003 UTC vs.
Revision 753 by mmeineke, Tue Sep 9 16:35:31 2003 UTC

# Line 10 | Line 10 | side spacing of $\approx\mbox{8\AA}$ (Fig.~\ref{fig:25
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  
# Line 42 | Line 44 | Scheme I was found to split into two leaves within the
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.

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