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% temporary preamble |
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\documentclass{seminar} |
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\usepackage{amsmath} |
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\usepackage{epsf} |
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% ---------------------- |
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% | Title | |
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% ---------------------- |
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\title{A Coarse Grain 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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% Slide 1 |
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\begin{slide} {Talk Outline} |
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\begin{itemize} |
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\item Discussion of the research motivation and goals |
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\item Methodology |
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\item Discussion of current research and preliminary results |
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\item Future research |
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\end{itemize} |
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\end{slide} |
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% Slide 2 |
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\begin{slide}{Motivation} |
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\begin{itemize} |
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% make sure to come back and talk about the need for long time and length |
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% scales |
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\item Drug diffusion |
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\item ripple phase |
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\item bilayer formation dynamics |
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\end{itemize} |
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\end{slide} |
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% Slide 3 |
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\begin{slide}{Research Goals} |
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\begin{itemize} |
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\item |
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To develop a coarse-grain simulation model with which to simulate |
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phospholipid bilayers. |
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\item To use the model to observe: |
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\begin{itemize} |
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\item Phospholipid properties with long length scales |
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\begin{itemize} |
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\item The ripple phase. |
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\end{itemize} |
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\item Long time scale dynamics of biological relevance |
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\begin{itemize} |
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\item Trans-membrane diffusion of drug molecules |
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\end{itemize} |
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\end{itemize} |
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\end{itemize} |
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\end{slide} |
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% Slide 4 |
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\begin{slide}{Length Scale Simplification} |
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\begin{itemize} |
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\item |
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Replace any charged interactions of the system with dipoles. |
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\begin{itemize} |
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\item Allows for computational scaling aproximately by $N$ for |
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dipole-dipole interactions. |
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\item In contrast, the Ewald sum scales aproximately by $N \log N$. |
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\end{itemize} |
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\item |
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Use unified models for the water and the lipid chain. |
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\begin{itemize} |
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\item Drastically reduces the number of atoms to simulate. |
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\item Number of water interactions alone reduced by $\frac{1}{3}$. |
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\end{itemize} |
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\end{itemize} |
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\end{slide} |
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% Slide 5 |
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\begin{slide}{Time Scale Simplification} |
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\begin{itemize} |
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\item |
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No explicit hydrogens |
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\begin{itemize} |
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\item Hydrogen bond vibration is normally one of the fastest time |
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events in a simulation. |
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\end{itemize} |
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\item |
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Constrain all bonds to be of fixed length. |
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\begin{itemize} |
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\item As with the hydrgoens, bond vibrations are the fastest motion in |
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asimulation |
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\end{itemize} |
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\item |
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Allows time steps of up to 3 fs with the current integrator. |
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\end{itemize} |
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\end{slide} |
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% Slide 6 |
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\begin{slide}{Molecular Dynamics} |
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All of our simulations will be carried out using molcular |
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dymnamics. This involves solving Newton's equations of motion using |
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the classical \emph{Hamiltonian} as follows: |
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\begin{equation} |
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H(\vec{q},\vec{p}) = T(\vec{p}) + V(\vec{q}) |
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\end{equation} |
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Here $T(\vec{p})$ is the kinetic energy of the system which is a |
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function of momentum. In cartesian space, $T(\vec{p})$ can be |
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written as: |
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\begin{equation} |
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T(\vec{p}) = \sum_{i=1}^{N} \sum_{\alpha = x,y,z} \frac{p^{2}_{i\alpha}}{2m_{i}} |
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\end{equation} |
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\end{slide} |
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% Slide 7 |
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\begin{slide}{The Potential} |
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The main part of the simulation is then the calculation of forces from |
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the potential energy. |
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\begin{equation} |
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\vec{F}(\vec{q}) = - \nabla V(\vec{q}) |
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\end{equation} |
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The potential itself is made of several parts. |
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\begin{equation} |
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V_{tot} = |
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\overbrace{V_{l} + V_{\theta} + V_{\omega}}^{\mbox{bonded}} + |
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\overbrace{V_{l\!j} + V_{d\!p} + V_{s\!s\!d}}^{\mbox{non-bonded}} |
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\end{equation} |
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Where the bond interactions $V_{l}$, $V_{\theta}$, and $V_{\omega}$ are |
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the bond, bend, and torsion potentials, and the non-bonded |
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mmeineke |
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interactions $V_{l\!j}$, $V_{d\!p}$, and $V_{s\!p}$ are the |
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lenard-jones, dipole-dipole, and sticky potential interactions. |
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mmeineke |
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\end{slide} |
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mmeineke |
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% Slide 8 |
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mmeineke |
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mmeineke |
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\begin{slide}{Soft Sticky Dipole Model} |
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mmeineke |
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mmeineke |
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The soft sticky model consists of a |
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mmeineke |
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mmeineke |
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%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\end{document} |