matt_papers/canidacy_talk/canidacy_slides.tex

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% ----------------------
% |      Title         |
% ----------------------

\title{A Mezzoscale Model for Phospholipid MD Simulations}

\author{Matthew A. Meineke\\
Department of Chemistry and Biochemistry\\
University of Notre Dame\\
Notre Dame, Indiana 46556}

\date{\today}

%-------------------------------------------------------------------
%                       Begin Document

\begin{document}

%\maketitle


\nobibliography{canidacy_slides}
\bibliographystyle{jurabib}


% Slide 0 Title slide
\begin{slide}
  \begin{center}
    \bfseries
    \fontsize{24pt}{30pt}\selectfont \color{Black}
    A Mesoscale Model for Phospholipid Simulations  \par
    \fontsize{16pt}{20pt}\selectfont \color{Green3}
     Matthew A. Meineke\par
    \fontsize{12pt}{15pt}\selectfont \color{Purple2}
    Department of Chemistry and Biochemistry \par
    University of Notre Dame \par
    Notre Dame, IN 46556 \par
    \fontsize{12pt}{15pt}\selectfont \color{Red} \date{today} \par
  \end{center}
 \end{slide}


% Slide 1
\begin{slide} {\LARGE Talk Outline}
\begin{itemize}

\item Discussion of the research motivation and goals

\item Methodology

\item Discussion of current research and preliminary results

\item Future research

\end{itemize}
\end{slide}


% Slide 2

\begin{slide}

\centerline{\LARGE Motivation A: Long Length Scales}

\begin{wrapfigure}{r}{60mm}

    \epsfxsize=45mm
    \epsfbox{ripple.epsi}

\end{wrapfigure}

\mbox{}
Ripple phase:
\begin{itemize}

\item
The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel
to fluid phase.

\item
Periodicity of 100 - 200 $\mbox{\AA}$\footcite{Cevc87}

\item
Current simulations have box sizes ranging from 50 - 100 $\mbox{\AA}$
on a side.\footcite{Venable93}\footcite{Heller93}

\end{itemize}
\vspace{10mm}
\end{slide}


\begin{slide}{\LARGE Motivation B: Long Time Scales}

\begin{itemize}

\item
Drug Diffusion
        \begin{itemize}
        \item 
        Some drug molecules may spend appreciable amounts of time in the
        membrane

        \item
        Long time scale dynamics are need to observe and characterize their
        actions
        \end{itemize}

\item
Bilayer Formation Dynamics
        \begin{itemize}
        \item
        Current lipid simulations indicate\footcite{Marrink01}:
                \begin{itemize} 
                \item Aggregation can happen as quickly as 200 ps

                \item Bilayers can take up to 20 ns to form completely
                \end{itemize}

        \end{itemize}
\end{itemize}
\end{slide}


% Slide 4

\begin{slide}{\LARGE Length Scale Simplification I}


Replace charge distriibutions of the system with dipoles.

\begin{itemize}
\item Allows for computational scaling approximately by $N$ for
      dipole-dipole interactions.
        \begin{itemize}
        \item Relatively short range, $\frac{1}{r^3}$, interactions allow
        the application of computational simplification algorithms,
        ie. neighbor lists.
        \end{itemize}

\item In contrast, the Ewald sum, needed for calculating charge - charge 
        interactions, scales approximately by $N \log N$.
\end{itemize}

\begin{equation}
V^{\text{dp}}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},
        \boldsymbol{\Omega}_{j}) = \frac{1}{4\pi\epsilon_{0}} \biggl[
        \frac{\boldsymbol{\mu}_{i} \cdot \boldsymbol{\mu}_{j}}{r^{3}_{ij}}
        -
        \frac{3(\boldsymbol{\mu}_i \cdot \mathbf{r}_{ij}) %
                (\boldsymbol{\mu}_j \cdot \mathbf{r}_{ij}) }
                {r^{5}_{ij}} \biggr]
\end{equation}

\begin{center}
\vspace{4mm}
vs.
\end{center}

\begin{equation}
V^{\text{ch}}_{ij}(\mathbf{r}_{ij}) = \frac{q_{i}q_{j}}%
        {4\pi\epsilon_{0} r_{ij}}
\end{equation} 

\end{slide}

\begin{slide}{\LARGE Length Scale Simplification II}

Use unified models for the water and the lipid chain.

\begin{itemize}
\item 
Drastically reduces the number of atoms and interactions to simulate.

\end{itemize}


\begin{figure}
%\epsfxsize=30mm
%\leavevmode
\begin{center}
\includegraphics[width=50mm,angle=-90]{reduction.epsi}
\end{center}
\end{figure}


\end{slide}


% Slide 5

\begin{slide}{Time Scale Simplification}
\begin{itemize}
\item
Constrain all bonds to be of fixed length.

        \begin{itemize}
        \item bond vibrations are the fastest motion in
         a simulation
        \end{itemize}

\item
Allows time steps of up to 3 fs with the current integrator. In
contrast, a time step of 1 fs is usually required for energy conservation.

\end{itemize}
\end{slide}

% Slide 8

\begin{slide}{Soft Sticky Dipole Model\footcite{Liu96}}

\begin{figure}
\begin{center}
\includegraphics[width=40mm]{ssd.epsi}
\end{center}
\end{figure}


It's potential is as follows:

\begin{equation}
V_{s\!s\!d} = V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
        + V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
\end{equation}
\end{slide}


% Slide 9
\begin{slide}{Hydrogen Bonding in SSD}

The SSD model's $V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})$ recreates
the hydrogen bonding network of water.


\begin{figure}
\begin{center}
\mbox{%
        \subfigure[SSD relaxed on a diamond lattice]{%
                \mbox{\includegraphics[angle=-90,width=55mm]{ssd_ice.epsi}}}%
        \hspace{4mm}
        \subfigure[Stockmayer spheres relaxed on a diamond lattice]{%
                \mbox{\includegraphics[angle=-90,width=55mm]{dipole_ice.epsi}}}%
}

\end{center}
\end{figure}

\end{slide}


% Slide 10

\begin{slide}{The Lipid Model}

\begin{figure}
\begin{center}

\includegraphics[width=40mm,angle=-90]{lipidModel.epsi}

\end{center}
\end{figure}

\begin{equation}
V_{\mbox{lipid}} = \overbrace{%
        V_{\mbox{bend}}(\theta_{ijk}) + V_{\mbox{tors.}}(\phi_{ijkl})%
        }^{bonded}
        + \overbrace{%
        V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})%
        }^{non-bonded}
\end{equation}

\begin{itemize}
\item 
Tail forcefield parameters taken from TraPPE\footcite{Siepmann1998}
\end{itemize}

\end{slide}


% Slide 12

\begin{slide}{Initial Runs: 25 Lipids in water}

\begin{wrapfigure}{r}{60mm}
        
        \includegraphics[width=55mm]{5x5-initial.eps}

\end{wrapfigure}

\textbf{Simulation Parameters:}

\begin{itemize}

\item $N_{\mbox{lipids}} = 25$

\item $N_{\mbox{H}_{2}\mbox{O}} = 1386$

\item Water to lipid ratio of 55.4:1 or 70% wt.

\item Lipid had only a single saturated chain of 16 carbons

\item Box Size: 34.5~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$

\item T = 300 K

\item NVE ensemble

\item Periodic boundary conditions
\end{itemize}

\end{slide}

\begin{slide}{5x5: Final}


\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=75mm]{5x5-3.6ns.epsi}
\end{center}
\end{figure}

\begin{center}
The configuration at 3.6 ns.
\end{center}

\end{slide}


% Slide 14

\begin{slide}{5x5: Head to Head $g(r)$}

\begin{figure}
\begin{center}
\includegraphics[width=55mm,angle=-90]{all5x5-HEAD-HEAD.GofR.eps}
\end{center}
\end{figure}

\begin{equation}
g(r) = \frac{V}{N(N-1)}\langle \sum_{i} \sum_{j \neq i} \delta(|\mathbf{r} 
        - \mathbf{r}_{ij}|) \rangle
\end{equation}


\end{slide}

\begin{slide}{5x5: Head to Water $g(r)$}


\begin{figure}
\begin{center}
\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-X.GofR.eps}
\end{center}
\end{figure}

\end{slide}


% Slide 15

\begin{slide}{5x5: Head to Head $\cos$ correlation}

\begin{figure}
\begin{center}
\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-HEAD.cosCorr.eps}
\end{center}
\end{figure}

\end{slide}

\begin{slide}{5x5: Head to Water $\cos$ correlation}

\begin{figure}
\begin{center}
\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-X.cosCorr.eps}
\end{center}
\end{figure}

\end{slide}


% Slide 16

\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water}

\begin{wrapfigure}{r}{40mm}

\includegraphics[angle=-90,width=35mm]{r50-initial.eps}

\end{wrapfigure}

\textbf{Simulation Parameters:}

\begin{itemize}

\item $N_{\mbox{lipids}} = 50$

\item $N_{\mbox{H}_{2}\mbox{O}} = 1384$

\item Water to lipid ratio of 27:1 or 54\% wt.

\item Lipid had only a single saturated chain of 16 carbons

\item Box Size: 26.6 $\mbox{\AA}$ x 26.6 $\mbox{\AA}$ x 108.4 $\mbox{\AA}$

\item T = 300 K

\item NVE ensemble

\item Periodic boundary conditions

\end{itemize}

\end{slide}

\begin{slide}{R-50: Final}


\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=110mm]{r50_1.3ns.epsi}
\end{center}
\end{figure}

\begin{center}
The configuration at 1.3 ns
\end{center}

\end{slide}


% Slide 18

\begin{slide}{R-50: Head to Head $g(r)$}


\begin{figure}
\begin{center}
\includegraphics[width=70mm,angle=-90]{r50-HEAD-HEAD.GofR.eps}
\end{center}
\end{figure}

\end{slide}


\begin{slide}{R-50: Head to Water $g(r)$}


\begin{figure}
\begin{center}
\includegraphics[width=70mm,angle=-90]{r50-HEAD-X.GofR.eps}
\end{center}
\end{figure}

\end{slide}


% Slide 19

\begin{slide}{R-50: Head to Head $\cos$ correlation}


\begin{figure}
\begin{center}
\includegraphics[width=70mm,angle=-90]{r50-HEAD-HEAD.cosCorr.eps}
\end{center}
\end{figure}

\end{slide}

\begin{slide}{R-50: Head to Water $\cos$ correlation}

\begin{figure}
\begin{center}
\includegraphics[width=70mm,angle=-90]{r50-HEAD-X.cosCorr.eps}
\end{center}
\end{figure}

\end{slide}


% Slide 20

\begin{slide}{Future Directions}

\begin{itemize}

\item
Simulation of a lipid with 2 chains, or perhaps expand the current
unified chain atoms to take up greater steric bulk.

\item
Incorporate constant pressure and constant temperature into the ensemble.
\begin{itemize}
        \item Start initial configuration in the gas phase, and
        compress the system to STP.
\end{itemize}

\item
Parallelize the code.

\item
Explore and map the phase diagram for our model.

\item
Observe how modification of our model might affect the phase diagram.

\item
Add biologicaly interesting molecules to the system and observe
transport properties.

\end{itemize}
\end{slide}


% Slide 21

\begin{slide}{Acknowledgements}

\begin{itemize}

\item Dr. J. Daniel Gezelter
\item Christopher Fennell
\item Charles Vardeman
\item Teng Lin
\item Megan Sprauge
\item Patrick Conforti
\item Dan Combest

\end{itemize}

Funding by:
\begin{itemize}
\item NSF
\end{itemize}

\end{slide}


%%%%%%%%%%%%%%%%%%%%%%%%%% Auxillary Slides %%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Sticky Potential I}

\begin{equation}
V_{s\!p}(\mathbf{r}_{i\!j},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) =
        v^{\circ}[s(r_{ij})w_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},
                \boldsymbol{\Omega}_{j})
        +
        s'(r_{ij})w^{x}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},
                \boldsymbol{\Omega}_{j})]
\end{equation}
where
\begin{equation}
w_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) =
        \sin\theta_{ij} \sin 2\theta_{ij} \cos 2\phi_{ij}
        + \sin \theta_{ji} \sin 2\theta_{ji} \cos 2\phi_{ji}
\end{equation}
and $w^{x}_{ij}$ is a correction function for when $\theta_{ij}$ is
$0^{\circ}$ or $180^{\circ}$. Its form is:
\begin{equation}
\begin{split}
w^{x}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) &=
        (\cos\theta_{ij}-0.6)^2(\cos\theta_{ij} + 0.8)^2 \\
        &\phantom{=} + (\cos\theta_{ji}-0.6)^2(\cos\theta_{ji} + 0.8)^2 - 2w^{\circ}
\end{split}
\end{equation}


\end{slide}


%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}
Revision:	109
Committed:	Fri Sep 13 16:22:46 2002 UTC (22 years ago) by mmeineke
Content type:	application/x-tex
File size:	15784 byte(s)
Log Message:	added a bunch of igures
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148
149			\special{!userdict begin /bop-hook {gsave
150	mmeineke	64	1.0 1.0 1.0 setrgbcolor clippath fill
151	mmeineke	63	grestore} def end
152			}
153
154			% And here we are...
155
156			\setcounter{slide}{-1}
157			%\includeonly{slide10}
158
159
160	mmeineke	64	% setup the jurabib style
161	mmeineke	63
162	mmeineke	64	\renewcommand{\jbbtasep}{; } % bta = between two authors sep
163			\renewcommand{\jbbfsasep}{; } % bfsa = between first and second author sep
164			\renewcommand{\jbbstasep}{; } % bsta = between second and third author sep
165			%\renewcommand{\bibansep}{. } % seperator after name
166	mmeineke	63
167	mmeineke	64	\renewcommand{\bibtfont}{\textit} % change book title to italics
168			\renewcommand{\bibjtfont}{\textit} % change journal title to italics
169			\renewcommand{\bibapifont}[1]{} % gets rid of the article title in citation
170	mmeineke	63
171
172	mmeineke	69	\renewcommand{\theslidefootnote}{\arabic{footnote}}
173	mmeineke	64
174
175
176	mmeineke	49	% ----------------------
177			% \| Title \|
178			% ----------------------
179
180	mmeineke	62	\title{A Mezzoscale Model for Phospholipid MD Simulations}
181	mmeineke	49
182			\author{Matthew A. Meineke\\
183	mmeineke	63	Department of Chemistry and Biochemistry\\
184	mmeineke	49	University of Notre Dame\\
185			Notre Dame, Indiana 46556}
186
187			\date{\today}
188
189			%-------------------------------------------------------------------
190			% Begin Document
191
192			\begin{document}
193	mmeineke	62
194	mmeineke	63	%\maketitle
195	mmeineke	49
196
197
198	mmeineke	62
199
200	mmeineke	63	\nobibliography{canidacy_slides}
201			\bibliographystyle{jurabib}
202	mmeineke	62
203	mmeineke	63
204			% Slide 0 Title slide
205			\begin{slide}
206			\begin{center}
207			\bfseries
208			\fontsize{24pt}{30pt}\selectfont \color{Black}
209	mmeineke	109	A Mesoscale Model for Phospholipid Simulations \par
210	mmeineke	63	\fontsize{16pt}{20pt}\selectfont \color{Green3}
211			Matthew A. Meineke\par
212			\fontsize{12pt}{15pt}\selectfont \color{Purple2}
213	mmeineke	80	Department of Chemistry and Biochemistry \par
214	mmeineke	63	University of Notre Dame \par
215			Notre Dame, IN 46556 \par
216			\fontsize{12pt}{15pt}\selectfont \color{Red} \date{today} \par
217			\end{center}
218			\end{slide}
219
220	mmeineke	64
221	mmeineke	49	% Slide 1
222	mmeineke	64	\begin{slide} {\LARGE Talk Outline}
223	mmeineke	49	\begin{itemize}
224
225			\item Discussion of the research motivation and goals
226
227			\item Methodology
228
229			\item Discussion of current research and preliminary results
230
231			\item Future research
232
233			\end{itemize}
234			\end{slide}
235
236
237			% Slide 2
238
239	mmeineke	63	\begin{slide}
240	mmeineke	62
241	mmeineke	64	\centerline{\LARGE Motivation A: Long Length Scales}
242
243	mmeineke	63	\begin{wrapfigure}{r}{60mm}
244	mmeineke	62
245	mmeineke	63	\epsfxsize=45mm
246			\epsfbox{ripple.epsi}
247	mmeineke	62
248	mmeineke	63	\end{wrapfigure}
249	mmeineke	62
250	mmeineke	63	\mbox{}
251	mmeineke	62	Ripple phase:
252			\begin{itemize}
253
254	mmeineke	63	\item
255	mmeineke	62	The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel
256			to fluid phase.
257
258	mmeineke	63	\item
259	mmeineke	64	Periodicity of 100 - 200 $\mbox{\AA}$\footcite{Cevc87}
260	mmeineke	62
261	mmeineke	64	\item
262			Current simulations have box sizes ranging from 50 - 100 $\mbox{\AA}$
263			on a side.\footcite{Venable93}\footcite{Heller93}
264
265	mmeineke	62	\end{itemize}
266	mmeineke	64	\vspace{10mm}
267	mmeineke	62	\end{slide}
268
269
270	mmeineke	64	\begin{slide}{\LARGE Motivation B: Long Time Scales}
271	mmeineke	62
272	mmeineke	64	\begin{itemize}
273	mmeineke	62
274	mmeineke	64	\item
275	mmeineke	80	Drug Diffusion
276	mmeineke	64	\begin{itemize}
277			\item
278	mmeineke	80	Some drug molecules may spend appreciable amounts of time in the
279	mmeineke	64	membrane
280	mmeineke	62
281	mmeineke	64	\item
282	mmeineke	80	Long time scale dynamics are need to observe and characterize their
283	mmeineke	64	actions
284			\end{itemize}
285	mmeineke	62
286	mmeineke	64	\item
287			Bilayer Formation Dynamics
288			\begin{itemize}
289			\item
290	mmeineke	109	Current lipid simulations indicate\footcite{Marrink01}:
291			\begin{itemize}
292			\item Aggregation can happen as quickly as 200 ps
293
294			\item Bilayers can take up to 20 ns to form completely
295			\end{itemize}
296
297	mmeineke	64	\end{itemize}
298			\end{itemize}
299			\end{slide}
300	mmeineke	54
301
302	mmeineke	64	% Slide 4
303	mmeineke	49
304	mmeineke	64	\begin{slide}{\LARGE Length Scale Simplification I}
305	mmeineke	49
306
307	mmeineke	109	Replace charge distriibutions of the system with dipoles.
308	mmeineke	49
309	mmeineke	64	\begin{itemize}
310			\item Allows for computational scaling approximately by $N$ for
311			dipole-dipole interactions.
312			\begin{itemize}
313			\item Relatively short range, $\frac{1}{r^3}$, interactions allow
314			the application of computational simplification algorithms,
315			ie. neighbor lists.
316			\end{itemize}
317
318			\item In contrast, the Ewald sum, needed for calculating charge - charge
319			interactions, scales approximately by $N \log N$.
320	mmeineke	49	\end{itemize}
321	mmeineke	109
322			\begin{equation}
323			V^{\text{dp}}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},
324			\boldsymbol{\Omega}_{j}) = \frac{1}{4\pi\epsilon_{0}} \biggl[
325			\frac{\boldsymbol{\mu}_{i} \cdot \boldsymbol{\mu}_{j}}{r^{3}_{ij}}
326			-
327			\frac{3(\boldsymbol{\mu}_i \cdot \mathbf{r}_{ij}) %
328			(\boldsymbol{\mu}_j \cdot \mathbf{r}_{ij}) }
329			{r^{5}_{ij}} \biggr]
330			\end{equation}
331
332			\begin{center}
333			\vspace{4mm}
334			vs.
335			\end{center}
336
337			\begin{equation}
338			V^{\text{ch}}_{ij}(\mathbf{r}_{ij}) = \frac{q_{i}q_{j}}%
339			{4\pi\epsilon_{0} r_{ij}}
340			\end{equation}
341
342	mmeineke	49	\end{slide}
343
344	mmeineke	64	\begin{slide}{\LARGE Length Scale Simplification II}
345	mmeineke	49
346	mmeineke	64	Use unified models for the water and the lipid chain.
347	mmeineke	49
348			\begin{itemize}
349	mmeineke	64	\item
350	mmeineke	69	Drastically reduces the number of atoms and interactions to simulate.
351	mmeineke	49
352	mmeineke	64	\end{itemize}
353	mmeineke	49
354
355	mmeineke	69
356	mmeineke	65	\begin{figure}
357	mmeineke	69	%\epsfxsize=30mm
358			%\leavevmode
359			\begin{center}
360			\includegraphics[width=50mm,angle=-90]{reduction.epsi}
361			\end{center}
362	mmeineke	65	\end{figure}
363	mmeineke	64
364	mmeineke	69
365	mmeineke	49	\end{slide}
366
367
368			% Slide 5
369
370			\begin{slide}{Time Scale Simplification}
371			\begin{itemize}
372			\item
373			Constrain all bonds to be of fixed length.
374
375	mmeineke	63	\begin{itemize}
376	mmeineke	69	\item bond vibrations are the fastest motion in
377	mmeineke	63	a simulation
378			\end{itemize}
379	mmeineke	49
380			\item
381	mmeineke	69	Allows time steps of up to 3 fs with the current integrator. In
382	mmeineke	109	contrast, a time step of 1 fs is usually required for energy conservation.
383	mmeineke	49
384			\end{itemize}
385			\end{slide}
386
387	mmeineke	51	% Slide 8
388	mmeineke	49
389	mmeineke	69	\begin{slide}{Soft Sticky Dipole Model\footcite{Liu96}}
390	mmeineke	49
391	mmeineke	69	\begin{figure}
392			\begin{center}
393			\includegraphics[width=40mm]{ssd.epsi}
394			\end{center}
395			\end{figure}
396	mmeineke	49
397
398	mmeineke	52	It's potential is as follows:
399
400			\begin{equation}
401	mmeineke	69	V_{s\!s\!d} = V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
402	mmeineke	63	+ V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
403	mmeineke	52	\end{equation}
404			\end{slide}
405
406
407			% Slide 9
408			\begin{slide}{Hydrogen Bonding in SSD}
409
410	mmeineke	69	The SSD model's $V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})$ recreates
411			the hydrogen bonding network of water.
412	mmeineke	52
413	mmeineke	54
414	mmeineke	69	\begin{figure}
415			\begin{center}
416			\mbox{%
417			\subfigure[SSD relaxed on a diamond lattice]{%
418			\mbox{\includegraphics[angle=-90,width=55mm]{ssd_ice.epsi}}}%
419			\hspace{4mm}
420			\subfigure[Stockmayer spheres relaxed on a diamond lattice]{%
421			\mbox{\includegraphics[angle=-90,width=55mm]{dipole_ice.epsi}}}%
422			}
423	mmeineke	52
424	mmeineke	69	\end{center}
425			\end{figure}
426	mmeineke	52
427			\end{slide}
428
429
430			% Slide 10
431
432			\begin{slide}{The Lipid Model}
433
434	mmeineke	78	\begin{figure}
435			\begin{center}
436	mmeineke	53
437	mmeineke	78	\includegraphics[width=40mm,angle=-90]{lipidModel.epsi}
438
439			\end{center}
440			\end{figure}
441
442			\begin{equation}
443			V_{\mbox{lipid}} = \overbrace{%
444			V_{\mbox{bend}}(\theta_{ijk}) + V_{\mbox{tors.}}(\phi_{ijkl})%
445			}^{bonded}
446			+ \overbrace{%
447			V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})%
448			}^{non-bonded}
449			\end{equation}
450
451	mmeineke	53	\begin{itemize}
452	mmeineke	78	\item
453			Tail forcefield parameters taken from TraPPE\footcite{Siepmann1998}
454	mmeineke	53	\end{itemize}
455
456			\end{slide}
457
458
459
460			% Slide 12
461	mmeineke	52
462			\begin{slide}{Initial Runs: 25 Lipids in water}
463
464	mmeineke	76	\begin{wrapfigure}{r}{60mm}
465
466			\includegraphics[width=55mm]{5x5-initial.eps}
467
468			\end{wrapfigure}
469
470	mmeineke	53	\textbf{Simulation Parameters:}
471	mmeineke	52
472	mmeineke	53	\begin{itemize}
473
474	mmeineke	76	\item $N_{\mbox{lipids}} = 25$
475	mmeineke	53
476	mmeineke	76	\item $N_{\mbox{H}_{2}\mbox{O}} = 1386$
477
478	mmeineke	109	\item Water to lipid ratio of 55.4:1 or 70% wt.
479	mmeineke	76
480	mmeineke	53	\item Lipid had only a single saturated chain of 16 carbons
481
482	mmeineke	76	\item Box Size: 34.5~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$
483	mmeineke	53
484			\item T = 300 K
485
486			\item NVE ensemble
487
488			\item Periodic boundary conditions
489			\end{itemize}
490
491	mmeineke	52	\end{slide}
492
493	mmeineke	76	\begin{slide}{5x5: Final}
494	mmeineke	52
495
496	mmeineke	76	\begin{figure}
497	mmeineke	54	\begin{center}
498	mmeineke	87	\includegraphics[angle=-90,width=75mm]{5x5-3.6ns.epsi}
499	mmeineke	76	\end{center}
500	mmeineke	54	\end{figure}
501	mmeineke	52
502	mmeineke	54	\begin{center}
503	mmeineke	109	The configuration at 3.6 ns.
504	mmeineke	54	\end{center}
505
506			\end{slide}
507
508
509	mmeineke	53	% Slide 14
510	mmeineke	52
511	mmeineke	87	\begin{slide}{5x5: Head to Head $g(r)$}
512	mmeineke	52
513	mmeineke	54	\begin{figure}
514	mmeineke	87	\begin{center}
515			\includegraphics[width=55mm,angle=-90]{all5x5-HEAD-HEAD.GofR.eps}
516			\end{center}
517	mmeineke	54	\end{figure}
518	mmeineke	52
519	mmeineke	87	\begin{equation}
520	mmeineke	109	g(r) = \frac{V}{N(N-1)}\langle \sum_{i} \sum_{j \neq i} \delta(\|\mathbf{r}
521			- \mathbf{r}_{ij}\|) \rangle
522	mmeineke	87	\end{equation}
523	mmeineke	52
524	mmeineke	76
525	mmeineke	54	\end{slide}
526	mmeineke	52
527	mmeineke	87	\begin{slide}{5x5: Head to Water $g(r)$}
528	mmeineke	54
529	mmeineke	76
530	mmeineke	54	\begin{figure}
531	mmeineke	87	\begin{center}
532			\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-X.GofR.eps}
533			\end{center}
534	mmeineke	54	\end{figure}
535
536	mmeineke	52	\end{slide}
537
538
539	mmeineke	53	% Slide 15
540	mmeineke	52
541	mmeineke	87	\begin{slide}{5x5: Head to Head $\cos$ correlation}
542	mmeineke	52
543	mmeineke	54	\begin{figure}
544	mmeineke	87	\begin{center}
545			\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-HEAD.cosCorr.eps}
546			\end{center}
547	mmeineke	54	\end{figure}
548	mmeineke	52
549			\end{slide}
550
551	mmeineke	87	\begin{slide}{5x5: Head to Water $\cos$ correlation}
552	mmeineke	52
553	mmeineke	54	\begin{figure}
554	mmeineke	87	\begin{center}
555			\includegraphics[width=70mm,angle=-90]{all5x5-HEAD-X.cosCorr.eps}
556			\end{center}
557	mmeineke	54	\end{figure}
558
559			\end{slide}
560
561
562	mmeineke	53	% Slide 16
563	mmeineke	52
564	mmeineke	53	\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water}
565	mmeineke	52
566	mmeineke	79	\begin{wrapfigure}{r}{40mm}
567	mmeineke	78
568	mmeineke	79	\includegraphics[angle=-90,width=35mm]{r50-initial.eps}
569
570			\end{wrapfigure}
571
572	mmeineke	53	\textbf{Simulation Parameters:}
573	mmeineke	52
574	mmeineke	53	\begin{itemize}
575
576	mmeineke	79	\item $N_{\mbox{lipids}} = 50$
577	mmeineke	53
578	mmeineke	79	\item $N_{\mbox{H}_{2}\mbox{O}} = 1384$
579
580	mmeineke	109	\item Water to lipid ratio of 27:1 or 54\% wt.
581	mmeineke	79
582	mmeineke	53	\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	mmeineke	63	\item Periodic boundary conditions
591	mmeineke	53
592			\end{itemize}
593
594	mmeineke	52	\end{slide}
595
596	mmeineke	79	\begin{slide}{R-50: Final}
597	mmeineke	52
598
599	mmeineke	76	\begin{figure}
600	mmeineke	54	\begin{center}
601	mmeineke	87	\includegraphics[angle=-90,width=110mm]{r50_1.3ns.epsi}
602	mmeineke	76	\end{center}
603	mmeineke	54	\end{figure}
604	mmeineke	52
605	mmeineke	54	\begin{center}
606	mmeineke	109	The configuration at 1.3 ns
607	mmeineke	54	\end{center}
608
609			\end{slide}
610
611
612	mmeineke	53	% Slide 18
613	mmeineke	52
614	mmeineke	87	\begin{slide}{R-50: Head to Head $g(r)$}
615	mmeineke	52
616
617	mmeineke	54	\begin{figure}
618	mmeineke	87	\begin{center}
619			\includegraphics[width=70mm,angle=-90]{r50-HEAD-HEAD.GofR.eps}
620			\end{center}
621	mmeineke	54	\end{figure}
622	mmeineke	52
623	mmeineke	54	\end{slide}
624	mmeineke	52
625	mmeineke	54
626	mmeineke	87	\begin{slide}{R-50: Head to Water $g(r)$}
627	mmeineke	54
628
629			\begin{figure}
630	mmeineke	87	\begin{center}
631			\includegraphics[width=70mm,angle=-90]{r50-HEAD-X.GofR.eps}
632			\end{center}
633	mmeineke	54	\end{figure}
634
635	mmeineke	52	\end{slide}
636
637
638	mmeineke	53	% Slide 19
639	mmeineke	52
640	mmeineke	87	\begin{slide}{R-50: Head to Head $\cos$ correlation}
641	mmeineke	52
642
643	mmeineke	54	\begin{figure}
644	mmeineke	87	\begin{center}
645			\includegraphics[width=70mm,angle=-90]{r50-HEAD-HEAD.cosCorr.eps}
646			\end{center}
647	mmeineke	54	\end{figure}
648
649	mmeineke	52	\end{slide}
650
651	mmeineke	87	\begin{slide}{R-50: Head to Water $\cos$ correlation}
652	mmeineke	52
653	mmeineke	54	\begin{figure}
654	mmeineke	87	\begin{center}
655			\includegraphics[width=70mm,angle=-90]{r50-HEAD-X.cosCorr.eps}
656			\end{center}
657	mmeineke	54	\end{figure}
658
659			\end{slide}
660
661
662	mmeineke	53	% Slide 20
663	mmeineke	52
664			\begin{slide}{Future Directions}
665
666	mmeineke	53	\begin{itemize}
667	mmeineke	52
668	mmeineke	63	\item
669	mmeineke	53	Simulation of a lipid with 2 chains, or perhaps expand the current
670			unified chain atoms to take up greater steric bulk.
671
672	mmeineke	63	\item
673	mmeineke	53	Incorporate constant pressure and constant temperature into the ensemble.
674	mmeineke	80	\begin{itemize}
675			\item Start initial configuration in the gas phase, and
676			compress the system to STP.
677			\end{itemize}
678	mmeineke	109
679	mmeineke	53	\item
680	mmeineke	80	Parallelize the code.
681	mmeineke	53
682	mmeineke	109	\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	mmeineke	53	\end{itemize}
693	mmeineke	52	\end{slide}
694
695
696	mmeineke	53	% Slide 21
697	mmeineke	52
698			\begin{slide}{Acknowledgements}
699
700	mmeineke	53	\begin{itemize}
701	mmeineke	52
702	mmeineke	53	\item Dr. J. Daniel Gezelter
703	mmeineke	80	\item Christopher Fennell
704	mmeineke	53	\item Charles Vardeman
705			\item Teng Lin
706	mmeineke	64	\item Megan Sprauge
707			\item Patrick Conforti
708			\item Dan Combest
709	mmeineke	52
710	mmeineke	53	\end{itemize}
711
712			Funding by:
713			\begin{itemize}
714	mmeineke	80	\item NSF
715	mmeineke	53	\end{itemize}
716
717	mmeineke	52	\end{slide}
718
719
720	mmeineke	109	%%%%%%%%%%%%%%%%%%%%%%%%%% Auxillary Slides %%%%%%%%%%%%%%%%%%%%%%%%
721	mmeineke	52
722	mmeineke	109	\begin{slide}{Sticky Potential I}
723	mmeineke	52
724	mmeineke	109	\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	mmeineke	52
748
749	mmeineke	109	\end{slide}
750	mmeineke	52
751
752	mmeineke	109
753
754
755	mmeineke	49	%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
756
757			\end{document}