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% ---------------------- |
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% | Title | |
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% ---------------------- |
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\title{A Mezzoscale Model for Phospholipid MD Simulations} |
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\author{Matthew A. Meineke\\ |
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Department of Chemistry and Biochemistry\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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\date{\today} |
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%------------------------------------------------------------------- |
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% Begin Document |
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\begin{document} |
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%\maketitle |
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\nobibliography{canidacy_slides} |
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\bibliographystyle{jurabib} |
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% Slide 0 Title slide |
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\begin{slide} |
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\begin{center} |
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\bfseries |
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\fontsize{24pt}{30pt}\selectfont \color{Black} |
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A Mesoscale Model for Phospholipid Simulations \par |
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\fontsize{16pt}{20pt}\selectfont \color{Green3} |
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Matthew A. Meineke\par |
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\fontsize{12pt}{15pt}\selectfont \color{Purple2} |
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Department of Chemistry and Biochemistry \par |
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University of Notre Dame \par |
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Notre Dame, IN 46556 \par |
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\fontsize{12pt}{15pt}\selectfont \color{Red} \date{today} \par |
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\end{center} |
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\end{slide} |
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|
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|
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% Slide 1 |
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\begin{slide} {\LARGE Talk Outline} |
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\begin{itemize} |
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|
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\item Discussion of the research motivation and goals |
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\item Methodology |
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|
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\item Discussion of current research and preliminary results |
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|
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\item Future research |
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|
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\end{itemize} |
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\end{slide} |
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|
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|
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% Slide 2 |
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|
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\begin{slide} |
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|
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\centerline{\LARGE Motivation A: Long Length Scales} |
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|
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\begin{wrapfigure}{r}{60mm} |
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|
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\epsfxsize=45mm |
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\epsfbox{ripple.epsi} |
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|
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\end{wrapfigure} |
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|
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\mbox{} |
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Ripple phase: |
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\begin{itemize} |
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|
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\item |
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The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel |
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to fluid phase. |
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|
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\item |
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Periodicity of 100 - 200 $\mbox{\AA}$\footcite{Cevc87} |
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|
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\item |
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Current simulations have box sizes ranging from 50 - 100 $\mbox{\AA}$ |
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on a side.\footcite{Venable93}\footcite{Heller93} |
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|
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\end{itemize} |
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\vspace{10mm} |
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\end{slide} |
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|
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|
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\begin{slide}{\LARGE Motivation B: Long Time Scales} |
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|
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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\footcite{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{slide} |
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|
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|
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% Slide 4 |
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|
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\begin{slide}{\LARGE Length Scale Simplification I} |
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|
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|
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Replace charge distriibutions of the system with dipoles. |
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|
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\begin{itemize} |
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\item Allows for computational scaling approximately by $N$ for |
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dipole-dipole interactions. |
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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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|
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\item In contrast, the Ewald sum, needed for calculating charge - charge |
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interactions, scales approximately by $N \log N$. |
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\end{itemize} |
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|
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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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\end{equation} |
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|
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\begin{center} |
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\vspace{4mm} |
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vs. |
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\end{center} |
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|
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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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\end{equation} |
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|
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\end{slide} |
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|
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\begin{slide}{\LARGE Length Scale Simplification II} |
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|
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Use unified models for the water and the lipid chain. |
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|
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\begin{itemize} |
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\item |
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Drastically reduces the number of atoms and interactions to simulate. |
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|
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\end{itemize} |
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|
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|
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|
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\begin{figure} |
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%\epsfxsize=30mm |
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%\leavevmode |
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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{figure} |
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|
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|
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\end{slide} |
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|
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|
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% Slide 5 |
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|
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\begin{slide}{Time Scale Simplification} |
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\begin{itemize} |
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\item |
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Constrain all bonds to be of fixed length. |
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|
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\begin{itemize} |
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\item bond vibrations are the fastest motion in |
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a simulation |
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\end{itemize} |
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|
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\item |
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Allows time steps of up to 3 fs with the current integrator. In |
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contrast, a time step of 1 fs is usually required for energy conservation. |
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|
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\end{itemize} |
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\end{slide} |
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|
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% Slide 8 |
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|
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\begin{slide}{Soft Sticky Dipole Model\footcite{Liu96}} |
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|
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\begin{figure} |
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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{figure} |
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|
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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{slide} |
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|
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|
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% Slide 9 |
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\begin{slide}{Hydrogen Bonding in SSD} |
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|
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The SSD model's $V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})$ recreates |
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the hydrogen bonding network of water. |
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|
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|
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\begin{figure} |
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\begin{center} |
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\mbox{% |
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\subfigure[SSD relaxed on a diamond lattice]{% |
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\mbox{\includegraphics[angle=-90,width=55mm]{ssd_ice.epsi}}}% |
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\hspace{4mm} |
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\subfigure[Stockmayer spheres relaxed on a diamond lattice]{% |
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\mbox{\includegraphics[angle=-90,width=55mm]{dipole_ice.epsi}}}% |
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} |
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|
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\end{center} |
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\end{figure} |
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|
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\end{slide} |
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|
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|
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% Slide 10 |
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|
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\begin{slide}{The Lipid Model} |
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|
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\begin{figure} |
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\begin{center} |
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|
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\includegraphics[width=40mm,angle=-90]{lipidModel.epsi} |
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|
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\end{center} |
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\end{figure} |
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|
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\begin{equation} |
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V_{\mbox{lipid}} = \overbrace{% |
| 444 |
V_{\mbox{bend}}(\theta_{ijk}) + V_{\mbox{tors.}}(\phi_{ijkl})% |
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}^{bonded} |
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+ \overbrace{% |
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V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})% |
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}^{non-bonded} |
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\end{equation} |
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|
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\begin{itemize} |
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\item |
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Tail forcefield parameters taken from TraPPE\footcite{Siepmann1998} |
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\end{itemize} |
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|
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\end{slide} |
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|
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|
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|
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% Slide 12 |
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|
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\begin{slide}{Initial Runs: 25 Lipids in water} |
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|
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\begin{wrapfigure}{r}{60mm} |
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|
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\includegraphics[width=55mm]{5x5-initial.eps} |
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|
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\end{wrapfigure} |
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|
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\textbf{Simulation Parameters:} |
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|
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\begin{itemize} |
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|
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\item $N_{\mbox{lipids}} = 25$ |
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|
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\item $N_{\mbox{H}_{2}\mbox{O}} = 1386$ |
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|
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\item Water to lipid ratio of 55.4:1 or 70% wt. |
| 479 |
|
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\item Lipid had only a single saturated chain of 16 carbons |
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|
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\item Box Size: 34.5~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$ |
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|
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\item T = 300 K |
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|
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\item NVE ensemble |
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|
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\item Periodic boundary conditions |
| 489 |
\end{itemize} |
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|
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\end{slide} |
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|
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\begin{slide}{5x5: Final} |
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|
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|
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\begin{figure} |
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\begin{center} |
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\includegraphics[angle=-90,width=75mm]{5x5-3.6ns.epsi} |
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\end{center} |
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\end{figure} |
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|
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\begin{center} |
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The configuration at 3.6 ns. |
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\end{center} |
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|
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\end{slide} |
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|
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|
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% Slide 14 |
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|
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\begin{slide}{5x5: Head to Head $g(r)$} |
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|
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\begin{figure} |
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\begin{center} |
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\includegraphics[width=55mm,angle=-90]{all5x5-HEAD-HEAD.GofR.eps} |
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\end{center} |
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\end{figure} |
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|
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\begin{equation} |
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g(r) = \frac{V}{N(N-1)}\langle \sum_{i} \sum_{j \neq i} \delta(|\mathbf{r} |
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- \mathbf{r}_{ij}|) \rangle |
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\end{equation} |
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|
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|
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\end{slide} |
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|
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\begin{slide}{5x5: Head to Water $g(r)$} |
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|
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|
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\begin{figure} |
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\begin{center} |
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\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-X.GofR.eps} |
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\end{center} |
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\end{figure} |
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|
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\end{slide} |
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|
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|
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% Slide 15 |
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|
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\begin{slide}{5x5: Head to Head $\cos$ correlation} |
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|
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\begin{figure} |
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\begin{center} |
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\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-HEAD.cosCorr.eps} |
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\end{center} |
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\end{figure} |
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|
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\end{slide} |
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|
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\begin{slide}{5x5: Head to Water $\cos$ correlation} |
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|
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\begin{figure} |
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\begin{center} |
| 555 |
\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-X.cosCorr.eps} |
| 556 |
\end{center} |
| 557 |
\end{figure} |
| 558 |
|
| 559 |
\end{slide} |
| 560 |
|
| 561 |
|
| 562 |
% Slide 16 |
| 563 |
|
| 564 |
\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water} |
| 565 |
|
| 566 |
\begin{wrapfigure}{r}{40mm} |
| 567 |
|
| 568 |
\includegraphics[angle=-90,width=35mm]{r50-initial.eps} |
| 569 |
|
| 570 |
\end{wrapfigure} |
| 571 |
|
| 572 |
\textbf{Simulation Parameters:} |
| 573 |
|
| 574 |
\begin{itemize} |
| 575 |
|
| 576 |
\item $N_{\mbox{lipids}} = 50$ |
| 577 |
|
| 578 |
\item $N_{\mbox{H}_{2}\mbox{O}} = 1384$ |
| 579 |
|
| 580 |
\item Water to lipid ratio of 27:1 or 54\% wt. |
| 581 |
|
| 582 |
\item Lipid had only a single saturated chain of 16 carbons |
| 583 |
|
| 584 |
\item Box Size: 26.6 $\mbox{\AA}$ x 26.6 $\mbox{\AA}$ x 108.4 $\mbox{\AA}$ |
| 585 |
|
| 586 |
\item T = 300 K |
| 587 |
|
| 588 |
\item NVE ensemble |
| 589 |
|
| 590 |
\item Periodic boundary conditions |
| 591 |
|
| 592 |
\end{itemize} |
| 593 |
|
| 594 |
\end{slide} |
| 595 |
|
| 596 |
\begin{slide}{R-50: Final} |
| 597 |
|
| 598 |
|
| 599 |
\begin{figure} |
| 600 |
\begin{center} |
| 601 |
\includegraphics[angle=-90,width=110mm]{r50_1.3ns.epsi} |
| 602 |
\end{center} |
| 603 |
\end{figure} |
| 604 |
|
| 605 |
\begin{center} |
| 606 |
The configuration at 1.3 ns |
| 607 |
\end{center} |
| 608 |
|
| 609 |
\end{slide} |
| 610 |
|
| 611 |
|
| 612 |
% Slide 18 |
| 613 |
|
| 614 |
\begin{slide}{R-50: Head to Head $g(r)$} |
| 615 |
|
| 616 |
|
| 617 |
\begin{figure} |
| 618 |
\begin{center} |
| 619 |
\includegraphics[width=70mm,angle=-90]{r50-HEAD-HEAD.GofR.eps} |
| 620 |
\end{center} |
| 621 |
\end{figure} |
| 622 |
|
| 623 |
\end{slide} |
| 624 |
|
| 625 |
|
| 626 |
\begin{slide}{R-50: Head to Water $g(r)$} |
| 627 |
|
| 628 |
|
| 629 |
\begin{figure} |
| 630 |
\begin{center} |
| 631 |
\includegraphics[width=70mm,angle=-90]{r50-HEAD-X.GofR.eps} |
| 632 |
\end{center} |
| 633 |
\end{figure} |
| 634 |
|
| 635 |
\end{slide} |
| 636 |
|
| 637 |
|
| 638 |
% Slide 19 |
| 639 |
|
| 640 |
\begin{slide}{R-50: Head to Head $\cos$ correlation} |
| 641 |
|
| 642 |
|
| 643 |
\begin{figure} |
| 644 |
\begin{center} |
| 645 |
\includegraphics[width=70mm,angle=-90]{r50-HEAD-HEAD.cosCorr.eps} |
| 646 |
\end{center} |
| 647 |
\end{figure} |
| 648 |
|
| 649 |
\end{slide} |
| 650 |
|
| 651 |
\begin{slide}{R-50: Head to Water $\cos$ correlation} |
| 652 |
|
| 653 |
\begin{figure} |
| 654 |
\begin{center} |
| 655 |
\includegraphics[width=70mm,angle=-90]{r50-HEAD-X.cosCorr.eps} |
| 656 |
\end{center} |
| 657 |
\end{figure} |
| 658 |
|
| 659 |
\end{slide} |
| 660 |
|
| 661 |
|
| 662 |
% Slide 20 |
| 663 |
|
| 664 |
\begin{slide}{Future Directions} |
| 665 |
|
| 666 |
\begin{itemize} |
| 667 |
|
| 668 |
\item |
| 669 |
Simulation of a lipid with 2 chains, or perhaps expand the current |
| 670 |
unified chain atoms to take up greater steric bulk. |
| 671 |
|
| 672 |
\item |
| 673 |
Incorporate constant pressure and constant temperature into the ensemble. |
| 674 |
\begin{itemize} |
| 675 |
\item Start initial configuration in the gas phase, and |
| 676 |
compress the system to STP. |
| 677 |
\end{itemize} |
| 678 |
|
| 679 |
\item |
| 680 |
Parallelize the code. |
| 681 |
|
| 682 |
\item |
| 683 |
Explore and map the phase diagram for our model. |
| 684 |
|
| 685 |
\item |
| 686 |
Observe how modification of our model might affect the phase diagram. |
| 687 |
|
| 688 |
\item |
| 689 |
Add biologicaly interesting molecules to the system and observe |
| 690 |
transport properties. |
| 691 |
|
| 692 |
\end{itemize} |
| 693 |
\end{slide} |
| 694 |
|
| 695 |
|
| 696 |
% Slide 21 |
| 697 |
|
| 698 |
\begin{slide}{Acknowledgements} |
| 699 |
|
| 700 |
\begin{itemize} |
| 701 |
|
| 702 |
\item Dr. J. Daniel Gezelter |
| 703 |
\item Christopher Fennell |
| 704 |
\item Charles Vardeman |
| 705 |
\item Teng Lin |
| 706 |
\item Megan Sprauge |
| 707 |
\item Patrick Conforti |
| 708 |
\item Dan Combest |
| 709 |
|
| 710 |
\end{itemize} |
| 711 |
|
| 712 |
Funding by: |
| 713 |
\begin{itemize} |
| 714 |
\item NSF |
| 715 |
\end{itemize} |
| 716 |
|
| 717 |
\end{slide} |
| 718 |
|
| 719 |
|
| 720 |
%%%%%%%%%%%%%%%%%%%%%%%%%% Auxillary Slides %%%%%%%%%%%%%%%%%%%%%%%% |
| 721 |
|
| 722 |
\begin{slide}{Sticky Potential I} |
| 723 |
|
| 724 |
\begin{equation} |
| 725 |
V_{s\!p}(\mathbf{r}_{i\!j},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) = |
| 726 |
v^{\circ}[s(r_{ij})w_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
| 727 |
\boldsymbol{\Omega}_{j}) |
| 728 |
+ |
| 729 |
s'(r_{ij})w^{x}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
| 730 |
\boldsymbol{\Omega}_{j})] |
| 731 |
\end{equation} |
| 732 |
where |
| 733 |
\begin{equation} |
| 734 |
w_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) = |
| 735 |
\sin\theta_{ij} \sin 2\theta_{ij} \cos 2\phi_{ij} |
| 736 |
+ \sin \theta_{ji} \sin 2\theta_{ji} \cos 2\phi_{ji} |
| 737 |
\end{equation} |
| 738 |
and $w^{x}_{ij}$ is a correction function for when $\theta_{ij}$ is |
| 739 |
$0^{\circ}$ or $180^{\circ}$. Its form is: |
| 740 |
\begin{equation} |
| 741 |
\begin{split} |
| 742 |
w^{x}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) &= |
| 743 |
(\cos\theta_{ij}-0.6)^2(\cos\theta_{ij} + 0.8)^2 \\ |
| 744 |
&\phantom{=} + (\cos\theta_{ji}-0.6)^2(\cos\theta_{ji} + 0.8)^2 - 2w^{\circ} |
| 745 |
\end{split} |
| 746 |
\end{equation} |
| 747 |
|
| 748 |
|
| 749 |
\end{slide} |
| 750 |
|
| 751 |
|
| 752 |
|
| 753 |
|
| 754 |
|
| 755 |
%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 756 |
|
| 757 |
\end{document} |
