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%% Load the necessary packages |
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%% |
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\usepackage{berkeley} |
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%%\usepackage{berkeley} |
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\usepackage{palatino} |
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\usepackage[latin1]{inputenc} |
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\usepackage{epsf} |
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\usepackage{graphicx,psfrag,color,pstcol,pst-grad} |
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\usepackage{multicol} |
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%% My Packages |
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< |
%%\usepackage{wrapfig} |
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\usepackage{wrapfig} |
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%% |
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%% Define the required numbers, lengths and boxes |
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} |
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\end{kasten} |
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|
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\begin{kasten} |
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\section{{\color{red}\underline{Introduction \& Background}}} |
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\label{sec:intro} |
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|
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\subsection{{\color{ndblue}Motivation}} |
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\label{sec:motivation} |
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|
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|
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Simulations of phospholipid bilayers are, by necessity, quite |
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complex. The lipid molecules are large, and contain many |
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atoms. Additionally, the head groups of the lipids are often |
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zwitterions, and the large separation between charges results in a |
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large dipole moment. Adding to the complexity are the number of water |
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molecules needed to properly solvate the lipid bilayer, typically 25 |
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water molecules for every lipid molecule. These factors make it |
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difficult to study certain biologically interesting phenomena that |
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have large inherent length or time scale. |
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|
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\end{kasten} |
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|
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\begin{kasten} |
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\subsection{{\color{ndblue}Ripple Phase}} |
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|
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\begin{wrapfigure}{o}{60mm} |
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\centering |
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\includegraphics[width=40mm]{ripple.epsi} |
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\end{wrapfigure} |
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|
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\mbox{} |
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\begin{itemize} |
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\item The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel to fluid phase. |
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\item Periodicity of 100 - 200 $\mbox{\AA}$\cite{Cevc87} |
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\item Current simulations have box sizes ranging from 50 - 100 $\mbox{\AA}$ on a side.\cite{saiz02,lindahl00,venable00} |
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\end{itemize} |
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|
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\label{sec:ripplePhase} |
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|
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\end{kasten} |
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|
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|
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\begin{kasten} |
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\subsection{{\color{ndblue}Diffusion \& Formation Dynamics}} |
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\begin{itemize} |
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|
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\item |
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Drug Diffusion |
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\begin{itemize} |
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\item |
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Some drug molecules may spend appreciable amounts of time in the |
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membrane |
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|
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\item |
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Long time scale dynamics are need to observe and characterize their |
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actions |
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\end{itemize} |
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|
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\item |
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Bilayer Formation Dynamics |
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\begin{itemize} |
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\item |
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Current lipid simulations indicate\cite{Marrink01}: |
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\begin{itemize} |
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\item Aggregation can happen as quickly as 200 ps |
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|
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\item Bilayers can take up to 20 ns to form completely |
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\end{itemize} |
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|
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\end{itemize} |
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\end{itemize} |
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\end{kasten} |
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|
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\begin{kasten} |
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\subsection{{\color{ndblue}System Simplfications}} |
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\begin{itemize} |
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\item Unified atoms with fixed bond lengths replace groups of atoms. |
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\item Replace charge distributions with dipoles.(Eq. \ref{eq:dipole} |
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vs. Eq. \ref{eq:coloumb}) |
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\begin{itemize} |
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\item Relatively short range, $\frac{1}{r^3}$, interactions allow |
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the application of computational simplification algorithms, |
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ie. neighbor lists. |
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\end{itemize} |
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\end{itemize} |
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\begin{equation} |
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V^{\text{dp}}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
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\boldsymbol{\Omega}_{j}) = \frac{1}{4\pi\epsilon_{0}} \biggl[ |
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\frac{\boldsymbol{\mu}_{i} \cdot \boldsymbol{\mu}_{j}}{r^{3}_{ij}} |
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- |
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\frac{3(\boldsymbol{\mu}_i \cdot \mathbf{r}_{ij}) % |
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(\boldsymbol{\mu}_j \cdot \mathbf{r}_{ij}) } |
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{r^{5}_{ij}} \biggr] |
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\label{eq:dipole} |
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\end{equation} |
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\begin{equation} |
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V^{\text{ch}}_{ij}(\mathbf{r}_{ij}) = \frac{q_{i}q_{j}}% |
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{4\pi\epsilon_{0} r_{ij}} |
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\label{eq:coloumb} |
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\end{equation} |
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\end{kasten} |
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%%% second column %%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{spalte} |
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\begin{kasten} |
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\section*{2 \hspace{0.1cm} {\color{ndblue}Ima second column holder}} |
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– |
hello |
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\begin{kasten} |
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\subsection{{\color{ndblue}Reduction in calculations}} |
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Unified water and lipid models and decrease the number of interactions |
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needed between two molecules. |
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|
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\begin{center} |
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\includegraphics[width=50mm,angle=-90]{reduction.epsi} |
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\end{center} |
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\end{kasten} |
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\begin{kasten} |
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\section{{\color{red}\underline{Models}}} |
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\label{sec:model} |
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\subsection{{\color{ndblue}Water Model}} |
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\label{sec:waterModel} |
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The waters in the simulation were modeled after the Soft Sticky Dipole |
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(SSD) model of Ichiye.\cite{liu96:new_model} Where: |
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|
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\begin{wrapfigure}[10]{o}{60mm} |
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\begin{center} |
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\includegraphics[width=40mm]{ssd.epsi} |
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\end{center} |
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\end{wrapfigure} |
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\mbox{} |
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\begin{itemize} |
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\item $\sigma$ is the Lennard-Jones length parameter. |
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\item $\boldsymbol{\mu}_i$ is the dipole vector of molecule $i$, |
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\item $\mathbf{r}_{ij}$ is the vector between molecules $i$ and $j$ |
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\item $\boldsymbol{\Omega}_i$ and $\boldsymbol{\Omega}_j$ are the Euler angles of molecule $i$ or $j$ respectively. |
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\end{itemize} |
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|
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It's potential is as follows: |
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|
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\begin{equation} |
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V_{s\!s\!d} = V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j}) |
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+ V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j}) |
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\end{equation} |
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\end{kasten} |
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\end{spalte} |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%% third column %%% |
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\begin{spalte} |
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\begin{kasten} |
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\section*{3 \hspace{0.1cm} {\color{ndblue}Ima third column holder}} |
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\section{{\color{ndblue}Ima third column holder}} |
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hello |
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\end{kasten} |
