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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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% 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 Mezzoscale Model for Phospholipid MD 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 Biochemisty \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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% 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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|
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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: |
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Long Length Scales} |
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\begin{wrapfigure}{r}{60mm} |
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\epsfxsize=45mm |
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\epsfbox{ripple.epsi} |
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\end{wrapfigure} |
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%\epsfbox{ripple.epsi} |
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%\begin{floatingfigure}{0.45\linewidth} |
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% \incffig{ripple.epsi} |
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%\end{floatingfigure} |
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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{Berne90} |
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|
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\end{itemize} |
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\vspace{30mm} |
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\end{slide} |
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|
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\begin{slide}{Motivation} |
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|
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There is a strong need in phospholipid bilayer simulations for the |
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capability to simulate both long time and length scales. Consider the |
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following: |
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|
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\begin{itemize} |
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|
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\item Drug diffusion |
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\begin{itemize} |
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\item Some drug molecules may spend an appreciable time in the |
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membrane. Long time scale dynamics are needed to observe and |
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characterize their actions. |
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\end{itemize} |
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|
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\item Ripple phase |
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\begin{itemize} |
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\item Between the bilayer gel and fluid phase there exists a ripple |
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phase. This phase has a period of about 100 - 200 $\mbox{\AA}$. |
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\end{itemize} |
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|
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\item Bilayer formation dynamics |
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\begin{itemize} |
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\item Initial simulations show that bilayers can take upwards of |
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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{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}{Length Scale Simplification} |
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\begin{itemize} |
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|
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\item |
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Replace any charged interactions 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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\item In contrast, the Ewald sum scales approximately by $N \log N$. |
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\end{itemize} |
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|
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\item |
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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 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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|
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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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|
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\item |
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No explicit hydrogens |
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|
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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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|
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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 As with the hydrogens, 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. |
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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 6 |
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\begin{slide}{Molecular Dynamics} |
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|
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All of our simulations will be carried out using molecular |
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dynamics. This involves solving Newton's equations of motion using |
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the classical \emph{Hamiltonian} as follows: |
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|
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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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|
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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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|
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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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|
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\end{slide} |
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|
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% Slide 7 |
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\begin{slide}{The Potential} |
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|
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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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|
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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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|
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The potential itself is made of several parts. |
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|
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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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|
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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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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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|
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\end{slide} |
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|
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% Slide 8 |
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\begin{slide}{Soft Sticky Dipole Model} |
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The Soft-Sticky model for water is a reduced model. |
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\begin{itemize} |
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\item |
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The model is represented by a single point mass at the water's center |
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of mass. |
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|
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\item |
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The point mass contains a fixed dipole of 2.35 D pointing from the |
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oxygens toward the hydrogens. |
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|
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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{slide} |
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|
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% Slide 8b |
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|
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\begin{slide}{SSD Diagram} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=50mm |
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\epsfbox{ssd.epsi} |
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\end{figure} |
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\end{center} |
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|
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A Diagram of the SSD model. |
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\end{slide} |
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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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It is important to note that SSD has a potential specifically to |
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recreate the hydrogen bonding network of water. |
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|
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|
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ICE SSD |
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|
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ICE point Dipole |
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|
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|
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The importance of the hydrogen bond network is it's significant |
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contribution to the hydrophobic driving force of bilayer formation. |
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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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To eliminate the need for charge-charge interactions, our lipid model |
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replaces the phospholipid head group with a single large head group |
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atom containing a freely oriented dipole. The tail is a simple alkane chain. |
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|
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Lipid Properties: |
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\begin{itemize} |
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\item $|\vec{\mu}_{\text{HEAD}}| = 20.6\ \text{D}$ |
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\item $m_{\text{HEAD}} = 196\ \text{amu}$ |
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\item Tail atoms are unified CH, $\text{CH}_2$, and $\text{CH}_3$ atoms |
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\begin{itemize} |
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\item Alkane forcefield parameters taken from TraPPE |
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\end{itemize} |
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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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% Slide 11 |
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|
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\begin{slide}{Lipid Model} |
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\end{slide} |
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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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\textbf{Simulation Parameters:} |
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|
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\begin{itemize} |
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|
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\item Starting Configuration: |
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\begin{itemize} |
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\item 25 lipid molecules arranged in a 5 x 5 square |
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\item square was surrounded by a sea of 1386 waters |
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\begin{itemize} |
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\item final water to lipid ratio was 55.4:1 |
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\end{itemize} |
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\end{itemize} |
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|
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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 dt = 2.0 - 3.0 fs |
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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 |
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\end{itemize} |
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|
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\end{slide} |
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|
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% Slide 13 |
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\begin{slide}{5x5: Initial} |
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\begin{center} |
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\begin{figure} |
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\epsfxsize=50mm |
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\epsfbox{5x5-initial.eps} |
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\end{figure} |
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\end{center} |
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|
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The initial configuration |
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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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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{5x5-1.7ns.eps} |
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\end{figure} |
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\end{center} |
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|
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The final configuration at 1.7 ns. |
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\end{slide} |
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% Slide 14 |
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|
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\begin{slide}{5x5: $g(r)$} |
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{all5x5-HEAD-HEAD-gr.eps} |
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\end{figure} |
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\end{center} |
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\end{slide} |
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\begin{slide}{5x5: $g(r)$} |
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{all5x5-HEAD-X-gr.eps} |
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\end{figure} |
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\end{center} |
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\end{slide} |
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% Slide 15 |
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|
| 576 |
\begin{slide}{5x5: $\cos$ correlations} |
| 577 |
|
| 578 |
\begin{center} |
| 579 |
\begin{figure} |
| 580 |
\epsfxsize=60mm |
| 581 |
\epsfbox{all5x5-HEAD-HEAD-cr.eps} |
| 582 |
\end{figure} |
| 583 |
\end{center} |
| 584 |
|
| 585 |
\end{slide} |
| 586 |
|
| 587 |
\begin{slide}{5x5: $\cos$ correlations} |
| 588 |
|
| 589 |
\begin{center} |
| 590 |
\begin{figure} |
| 591 |
\epsfxsize=60mm |
| 592 |
\epsfbox{all5x5-HEAD-X-cr.eps} |
| 593 |
\end{figure} |
| 594 |
\end{center} |
| 595 |
|
| 596 |
\end{slide} |
| 597 |
|
| 598 |
|
| 599 |
% Slide 16 |
| 600 |
|
| 601 |
\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water} |
| 602 |
|
| 603 |
\textbf{Simulation Parameters:} |
| 604 |
|
| 605 |
\begin{itemize} |
| 606 |
|
| 607 |
\item Starting Configuration: |
| 608 |
\begin{itemize} |
| 609 |
\item 50 lipid molecules arranged randomly in a rectangular box |
| 610 |
\item The box was then filled with 1384 waters |
| 611 |
\begin{itemize} |
| 612 |
\item final water to lipid ratio was 27:1 |
| 613 |
\end{itemize} |
| 614 |
\end{itemize} |
| 615 |
|
| 616 |
\item Lipid had only a single saturated chain of 16 carbons |
| 617 |
|
| 618 |
\item Box Size: 26.6 $\mbox{\AA}$ x 26.6 $\mbox{\AA}$ x 108.4 $\mbox{\AA}$ |
| 619 |
|
| 620 |
\item dt = 2.0 - 3.0 fs |
| 621 |
|
| 622 |
\item T = 300 K |
| 623 |
|
| 624 |
\item NVE ensemble |
| 625 |
|
| 626 |
\item Periodic boundary conditions |
| 627 |
|
| 628 |
\end{itemize} |
| 629 |
|
| 630 |
\end{slide} |
| 631 |
|
| 632 |
|
| 633 |
% Slide 17 |
| 634 |
|
| 635 |
\begin{slide}{R-50: Initial} |
| 636 |
|
| 637 |
\begin{center} |
| 638 |
\begin{figure} |
| 639 |
\epsfxsize=100mm |
| 640 |
\epsfbox{r50-initial.eps} |
| 641 |
\end{figure} |
| 642 |
\end{center} |
| 643 |
|
| 644 |
The initial configuration |
| 645 |
|
| 646 |
\end{slide} |
| 647 |
|
| 648 |
\begin{slide}{R-50: Final} |
| 649 |
|
| 650 |
\begin{center} |
| 651 |
\begin{figure} |
| 652 |
\epsfxsize=100mm |
| 653 |
\epsfbox{r50-521ps.eps} |
| 654 |
\end{figure} |
| 655 |
\end{center} |
| 656 |
|
| 657 |
The fianl configuration at 521 ps |
| 658 |
|
| 659 |
\end{slide} |
| 660 |
|
| 661 |
|
| 662 |
% Slide 18 |
| 663 |
|
| 664 |
\begin{slide}{R-50: $g(r)$} |
| 665 |
|
| 666 |
|
| 667 |
\begin{center} |
| 668 |
\begin{figure} |
| 669 |
\epsfxsize=60mm |
| 670 |
\epsfbox{r50-HEAD-HEAD-gr.eps} |
| 671 |
\end{figure} |
| 672 |
\end{center} |
| 673 |
|
| 674 |
\end{slide} |
| 675 |
|
| 676 |
|
| 677 |
\begin{slide}{R-50: $g(r)$} |
| 678 |
|
| 679 |
|
| 680 |
\begin{center} |
| 681 |
\begin{figure} |
| 682 |
\epsfxsize=60mm |
| 683 |
\epsfbox{r50-HEAD-X-gr.eps} |
| 684 |
\end{figure} |
| 685 |
\end{center} |
| 686 |
|
| 687 |
\end{slide} |
| 688 |
|
| 689 |
|
| 690 |
% Slide 19 |
| 691 |
|
| 692 |
\begin{slide}{R-50: $\cos$ correlations} |
| 693 |
|
| 694 |
|
| 695 |
\begin{center} |
| 696 |
\begin{figure} |
| 697 |
\epsfxsize=60mm |
| 698 |
\epsfbox{r50-HEAD-HEAD-cr.eps} |
| 699 |
\end{figure} |
| 700 |
\end{center} |
| 701 |
|
| 702 |
\end{slide} |
| 703 |
|
| 704 |
\begin{slide}{R-50: $\cos$ correlations} |
| 705 |
|
| 706 |
|
| 707 |
\begin{center} |
| 708 |
\begin{figure} |
| 709 |
\epsfxsize=60mm |
| 710 |
\epsfbox{r50-HEAD-X-cr.eps} |
| 711 |
\end{figure} |
| 712 |
\end{center} |
| 713 |
|
| 714 |
\end{slide} |
| 715 |
|
| 716 |
|
| 717 |
% Slide 20 |
| 718 |
|
| 719 |
\begin{slide}{Future Directions} |
| 720 |
|
| 721 |
\begin{itemize} |
| 722 |
|
| 723 |
\item |
| 724 |
Simulation of a lipid with 2 chains, or perhaps expand the current |
| 725 |
unified chain atoms to take up greater steric bulk. |
| 726 |
|
| 727 |
\item |
| 728 |
Incorporate constant pressure and constant temperature into the ensemble. |
| 729 |
|
| 730 |
\item |
| 731 |
Parrellize the code. |
| 732 |
|
| 733 |
\end{itemize} |
| 734 |
\end{slide} |
| 735 |
|
| 736 |
|
| 737 |
% Slide 21 |
| 738 |
|
| 739 |
\begin{slide}{Acknowledgements} |
| 740 |
|
| 741 |
\begin{itemize} |
| 742 |
|
| 743 |
\item Dr. J. Daniel Gezelter |
| 744 |
\item Christopher Fennel |
| 745 |
\item Charles Vardeman |
| 746 |
\item Teng Lin |
| 747 |
|
| 748 |
\end{itemize} |
| 749 |
|
| 750 |
Funding by: |
| 751 |
\begin{itemize} |
| 752 |
\item Dreyfus New Faculty Award |
| 753 |
\end{itemize} |
| 754 |
|
| 755 |
\end{slide} |
| 756 |
|
| 757 |
|
| 758 |
|
| 759 |
|
| 760 |
|
| 761 |
|
| 762 |
|
| 763 |
|
| 764 |
%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 765 |
|
| 766 |
\end{document} |
