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 Mezzoscale Model for Phospholipid MD Simulations  \par
    \fontsize{16pt}{20pt}\selectfont \color{Green3}
     Matthew A. Meineke\par
    \fontsize{12pt}{15pt}\selectfont \color{Purple2}
    Department of Chemistry and Biochemisty \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} {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}


%\epsfbox{ripple.epsi}
%\begin{floatingfigure}{0.45\linewidth}
%  \incffig{ripple.epsi}
%\end{floatingfigure}


\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{Berne90}

\end{itemize}
\vspace{30mm}
\end{slide}


\begin{slide}{Motivation}

There is a strong need in phospholipid bilayer simulations for the
capability to simulate both long time and length scales. Consider the
following:

\begin{itemize}

\item Drug diffusion
        \begin{itemize}
        \item Some drug molecules may spend an appreciable time in the
        membrane. Long time scale dynamics are needed to observe and
        characterize their actions.
        \end{itemize}

\item Ripple phase
        \begin{itemize}
        \item Between the bilayer gel and fluid phase there exists a ripple
        phase. This phase has a period of about 100 - 200 $\mbox{\AA}$.
        \end{itemize}

\item Bilayer formation dynamics
        \begin{itemize}
        \item Initial simulations show that bilayers can take upwards of
        20 ns to form completely.
        \end{itemize}

\end{itemize}
\end{slide}


% Slide 4

\begin{slide}{Length Scale Simplification}
\begin{itemize}

\item
Replace any charged interactions of the system with dipoles.

        \begin{itemize}
        \item Allows for computational scaling approximately by $N$ for
              dipole-dipole interactions.
        \item In contrast, the Ewald sum scales approximately by $N \log N$.
        \end{itemize}

\item
Use unified models for the water and the lipid chain.

        \begin{itemize}
        \item Drastically reduces the number of atoms to simulate.
        \item Number of water interactions alone reduced by $\frac{1}{3}$.
        \end{itemize}
\end{itemize}
\end{slide}


% Slide 5

\begin{slide}{Time Scale Simplification}
\begin{itemize}

\item
No explicit hydrogens

        \begin{itemize}
        \item Hydrogen bond vibration is normally one of the fastest time
                events in a simulation.
        \end{itemize}

\item
Constrain all bonds to be of fixed length.

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

\item
Allows time steps of up to 3 fs with the current integrator.

\end{itemize}
\end{slide}


% Slide 6
\begin{slide}{Molecular Dynamics}

All of our simulations will be carried out using molecular
dynamics. This involves solving Newton's equations of motion using
the classical \emph{Hamiltonian} as follows:

\begin{equation}
H(\vec{q},\vec{p}) = T(\vec{p}) + V(\vec{q})
\end{equation}

Here $T(\vec{p})$ is the kinetic energy of the system which is a
function of momentum. In Cartesian space, $T(\vec{p})$ can be
written as:

\begin{equation}
T(\vec{p}) = \sum_{i=1}^{N} \sum_{\alpha = x,y,z} \frac{p^{2}_{i\alpha}}{2m_{i}}
\end{equation}

\end{slide}


% Slide 7
\begin{slide}{The Potential}

The main part of the simulation is then the calculation of forces from
the potential energy.

\begin{equation}
\vec{F}(\vec{q}) = - \nabla V(\vec{q})
\end{equation}

The potential itself is made of several parts.

\begin{equation}
V_{tot} =
\overbrace{V_{l} + V_{\theta} + V_{\omega}}^{\mbox{bonded}} +
\overbrace{V_{l\!j} + V_{d\!p} + V_{s\!s\!d}}^{\mbox{non-bonded}}
\end{equation}

Where the bond interactions $V_{l}$, $V_{\theta}$, and $V_{\omega}$ are
the bond, bend, and torsion potentials, and the non-bonded
interactions $V_{l\!j}$, $V_{d\!p}$, and $V_{s\!p}$ are the
lenard-jones, dipole-dipole, and sticky potential interactions.

\end{slide}


% Slide 8

\begin{slide}{Soft Sticky Dipole Model}

The Soft-Sticky model for water is a reduced model.

\begin{itemize}

\item
The model is represented by a single point mass at the water's center
of mass.

\item
The point mass contains a fixed dipole of 2.35 D pointing from the
oxygens toward the hydrogens.

\end{itemize}

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 8b

\begin{slide}{SSD Diagram}

\begin{center}
\begin{figure}
\epsfxsize=50mm
\epsfbox{ssd.epsi}
\end{figure}
\end{center}

A Diagram of the SSD model.
\end{slide}

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

It is important to note that SSD has a potential specifically to
recreate the hydrogen bonding network of water.


ICE SSD

ICE point Dipole


The importance of the hydrogen bond network is it's significant
contribution to the hydrophobic driving force of bilayer formation.
\end{slide}


% Slide 10

\begin{slide}{The Lipid Model}

To eliminate the need for charge-charge interactions, our lipid model
replaces the phospholipid head group with a single large head group
atom containing a freely oriented dipole. The tail is a simple alkane chain.

Lipid Properties:
\begin{itemize}
\item $|\vec{\mu}_{\text{HEAD}}| = 20.6\ \text{D}$
\item $m_{\text{HEAD}} = 196\ \text{amu}$
\item Tail atoms are unified CH, $\text{CH}_2$, and $\text{CH}_3$ atoms
        \begin{itemize}
        \item Alkane forcefield parameters taken from TraPPE
        \end{itemize}
\end{itemize}

\end{slide}


% Slide 11

\begin{slide}{Lipid Model}


\end{slide}


% Slide 12

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

\textbf{Simulation Parameters:}

\begin{itemize}

\item Starting Configuration:
        \begin{itemize}
        \item 25 lipid molecules arranged in a 5 x 5 square
        \item square was surrounded by a sea of 1386  waters
                \begin{itemize}
                \item final water to lipid ratio was 55.4:1
                \end{itemize}
        \end{itemize}

\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 dt = 2.0 - 3.0 fs

\item T = 300 K

\item NVE ensemble

\item Periodic boundary conditions
\end{itemize}

\end{slide}


% Slide 13

\begin{slide}{5x5: Initial}

\begin{center}
\begin{figure}
\epsfxsize=50mm
\epsfbox{5x5-initial.eps}
\end{figure}
\end{center}

The initial configuration

\end{slide}

\begin{slide}{5x5: Final}

\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{5x5-1.7ns.eps}
\end{figure}
\end{center}

The final configuration at 1.7 ns.

\end{slide}


% Slide 14

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

\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{all5x5-HEAD-HEAD-gr.eps}
\end{figure}
\end{center}


\end{slide}

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

\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{all5x5-HEAD-X-gr.eps}
\end{figure}
\end{center}


\end{slide}


% Slide 15

\begin{slide}{5x5: $\cos$ correlations}

\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{all5x5-HEAD-HEAD-cr.eps}
\end{figure}
\end{center}

\end{slide}

\begin{slide}{5x5: $\cos$ correlations}

\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{all5x5-HEAD-X-cr.eps}
\end{figure}
\end{center}

\end{slide}


% Slide 16

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

\textbf{Simulation Parameters:}

\begin{itemize}

\item Starting Configuration:
        \begin{itemize}
        \item 50 lipid molecules arranged randomly in a rectangular box
        \item The box was then filled with 1384 waters
                \begin{itemize}
                \item final water to lipid ratio was 27:1
                \end{itemize}
        \end{itemize}

\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 dt = 2.0 - 3.0 fs

\item T = 300 K

\item NVE ensemble

\item Periodic boundary conditions

\end{itemize}

\end{slide}


% Slide 17

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

\begin{center}
\begin{figure}
\epsfxsize=100mm
\epsfbox{r50-initial.eps}
\end{figure}
\end{center}

The initial configuration

\end{slide}

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

\begin{center}
\begin{figure}
\epsfxsize=100mm
\epsfbox{r50-521ps.eps}
\end{figure}
\end{center}

The fianl configuration at 521 ps

\end{slide}


% Slide 18

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


\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{r50-HEAD-HEAD-gr.eps}
\end{figure}
\end{center}

\end{slide}


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


\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{r50-HEAD-X-gr.eps}
\end{figure}
\end{center}

\end{slide}


% Slide 19

\begin{slide}{R-50: $\cos$ correlations}


\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{r50-HEAD-HEAD-cr.eps}
\end{figure}
\end{center}

\end{slide}

\begin{slide}{R-50: $\cos$ correlations}


\begin{center}
\begin{figure}
\epsfxsize=60mm
\epsfbox{r50-HEAD-X-cr.eps}
\end{figure}
\end{center}

\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.

\item
Parrellize the code.

\end{itemize}
\end{slide}


% Slide 21

\begin{slide}{Acknowledgements}

\begin{itemize}

\item Dr. J. Daniel Gezelter
\item Christopher Fennel
\item Charles Vardeman
\item Teng Lin

\end{itemize}

Funding by:
\begin{itemize}
\item Dreyfus New Faculty Award
\end{itemize}

\end{slide}


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

\end{document}
Revision:	63
Committed:	Wed Aug 7 19:09:03 2002 UTC (22 years, 1 month ago) by mmeineke
Content type:	application/x-tex
File size:	15099 byte(s)
Log Message:	switched in Chuck's magic slide enviroment
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163	mmeineke	49	% ----------------------
164			% \| Title \|
165			% ----------------------
166
167	mmeineke	62	\title{A Mezzoscale Model for Phospholipid MD Simulations}
168	mmeineke	49
169			\author{Matthew A. Meineke\\
170	mmeineke	63	Department of Chemistry and Biochemistry\\
171	mmeineke	49	University of Notre Dame\\
172			Notre Dame, Indiana 46556}
173
174			\date{\today}
175
176			%-------------------------------------------------------------------
177			% Begin Document
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179			\begin{document}
180	mmeineke	62
181	mmeineke	63	%\maketitle
182	mmeineke	49
183
184
185	mmeineke	62
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187	mmeineke	63	\nobibliography{canidacy_slides}
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189	mmeineke	62
190	mmeineke	63
191			% Slide 0 Title slide
192			\begin{slide}
193			\begin{center}
194			\bfseries
195			\fontsize{24pt}{30pt}\selectfont \color{Black}
196			A Mezzoscale Model for Phospholipid MD Simulations \par
197			\fontsize{16pt}{20pt}\selectfont \color{Green3}
198			Matthew A. Meineke\par
199			\fontsize{12pt}{15pt}\selectfont \color{Purple2}
200			Department of Chemistry and Biochemisty \par
201			University of Notre Dame \par
202			Notre Dame, IN 46556 \par
203			\fontsize{12pt}{15pt}\selectfont \color{Red} \date{today} \par
204			\end{center}
205			\end{slide}
206
207	mmeineke	49	% Slide 1
208			\begin{slide} {Talk Outline}
209			\begin{itemize}
210
211			\item Discussion of the research motivation and goals
212
213			\item Methodology
214
215			\item Discussion of current research and preliminary results
216
217			\item Future research
218
219			\end{itemize}
220			\end{slide}
221
222
223			% Slide 2
224
225	mmeineke	63	\begin{slide}
226	mmeineke	62
227	mmeineke	63	\centerline{\LARGE Motivation A:
228			Long Length Scales}
229			\begin{wrapfigure}{r}{60mm}
230	mmeineke	62
231	mmeineke	63	\epsfxsize=45mm
232			\epsfbox{ripple.epsi}
233	mmeineke	62
234	mmeineke	63	\end{wrapfigure}
235	mmeineke	62
236
237
238	mmeineke	63
239			%\epsfbox{ripple.epsi}
240			%\begin{floatingfigure}{0.45\linewidth}
241			% \incffig{ripple.epsi}
242			%\end{floatingfigure}
243
244
245
246			\mbox{}
247	mmeineke	62	Ripple phase:
248			\begin{itemize}
249
250	mmeineke	63	\item
251	mmeineke	62	The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel
252			to fluid phase.
253
254	mmeineke	63	\item
255			Periodicity of 100 - 200 $\mbox{\AA}$\footcite{Berne90}
256	mmeineke	62
257			\end{itemize}
258	mmeineke	63	\vspace{30mm}
259	mmeineke	62	\end{slide}
260
261
262
263
264
265
266	mmeineke	49	\begin{slide}{Motivation}
267	mmeineke	54
268			There is a strong need in phospholipid bilayer simulations for the
269			capability to simulate both long time and length scales. Consider the
270			following:
271
272	mmeineke	49	\begin{itemize}
273
274			\item Drug diffusion
275	mmeineke	63	\begin{itemize}
276			\item Some drug molecules may spend an appreciable time in the
277			membrane. Long time scale dynamics are needed to observe and
278			characterize their actions.
279			\end{itemize}
280	mmeineke	49
281	mmeineke	54	\item Ripple phase
282	mmeineke	63	\begin{itemize}
283			\item Between the bilayer gel and fluid phase there exists a ripple
284			phase. This phase has a period of about 100 - 200 $\mbox{\AA}$.
285			\end{itemize}
286	mmeineke	49
287	mmeineke	54	\item Bilayer formation dynamics
288	mmeineke	63	\begin{itemize}
289			\item Initial simulations show that bilayers can take upwards of
290			20 ns to form completely.
291			\end{itemize}
292	mmeineke	49
293			\end{itemize}
294			\end{slide}
295
296
297			% Slide 4
298
299			\begin{slide}{Length Scale Simplification}
300			\begin{itemize}
301
302	mmeineke	63	\item
303	mmeineke	49	Replace any charged interactions of the system with dipoles.
304
305	mmeineke	63	\begin{itemize}
306			\item Allows for computational scaling approximately by $N$ for
307			dipole-dipole interactions.
308			\item In contrast, the Ewald sum scales approximately by $N \log N$.
309			\end{itemize}
310	mmeineke	49
311			\item
312			Use unified models for the water and the lipid chain.
313
314	mmeineke	63	\begin{itemize}
315			\item Drastically reduces the number of atoms to simulate.
316			\item Number of water interactions alone reduced by $\frac{1}{3}$.
317			\end{itemize}
318	mmeineke	49	\end{itemize}
319			\end{slide}
320
321
322			% Slide 5
323
324			\begin{slide}{Time Scale Simplification}
325			\begin{itemize}
326
327			\item
328			No explicit hydrogens
329
330	mmeineke	63	\begin{itemize}
331			\item Hydrogen bond vibration is normally one of the fastest time
332			events in a simulation.
333			\end{itemize}
334	mmeineke	49
335			\item
336			Constrain all bonds to be of fixed length.
337
338	mmeineke	63	\begin{itemize}
339			\item As with the hydrogens, bond vibrations are the fastest motion in
340			a simulation
341			\end{itemize}
342	mmeineke	49
343			\item
344			Allows time steps of up to 3 fs with the current integrator.
345
346			\end{itemize}
347			\end{slide}
348
349
350			% Slide 6
351			\begin{slide}{Molecular Dynamics}
352
353	mmeineke	53	All of our simulations will be carried out using molecular
354			dynamics. This involves solving Newton's equations of motion using
355	mmeineke	49	the classical \emph{Hamiltonian} as follows:
356
357			\begin{equation}
358			H(\vec{q},\vec{p}) = T(\vec{p}) + V(\vec{q})
359			\end{equation}
360
361			Here $T(\vec{p})$ is the kinetic energy of the system which is a
362	mmeineke	53	function of momentum. In Cartesian space, $T(\vec{p})$ can be
363	mmeineke	49	written as:
364
365			\begin{equation}
366			T(\vec{p}) = \sum_{i=1}^{N} \sum_{\alpha = x,y,z} \frac{p^{2}_{i\alpha}}{2m_{i}}
367			\end{equation}
368
369			\end{slide}
370
371
372			% Slide 7
373			\begin{slide}{The Potential}
374
375			The main part of the simulation is then the calculation of forces from
376			the potential energy.
377
378			\begin{equation}
379			\vec{F}(\vec{q}) = - \nabla V(\vec{q})
380			\end{equation}
381
382			The potential itself is made of several parts.
383
384			\begin{equation}
385	mmeineke	63	V_{tot} =
386	mmeineke	49	\overbrace{V_{l} + V_{\theta} + V_{\omega}}^{\mbox{bonded}} +
387			\overbrace{V_{l\!j} + V_{d\!p} + V_{s\!s\!d}}^{\mbox{non-bonded}}
388			\end{equation}
389
390			Where the bond interactions $V_{l}$, $V_{\theta}$, and $V_{\omega}$ are
391			the bond, bend, and torsion potentials, and the non-bonded
392	mmeineke	51	interactions $V_{l\!j}$, $V_{d\!p}$, and $V_{s\!p}$ are the
393			lenard-jones, dipole-dipole, and sticky potential interactions.
394	mmeineke	49
395			\end{slide}
396
397
398	mmeineke	51	% Slide 8
399	mmeineke	49
400	mmeineke	51	\begin{slide}{Soft Sticky Dipole Model}
401	mmeineke	49
402	mmeineke	52	The Soft-Sticky model for water is a reduced model.
403	mmeineke	49
404	mmeineke	52	\begin{itemize}
405	mmeineke	49
406	mmeineke	63	\item
407	mmeineke	52	The model is represented by a single point mass at the water's center
408			of mass.
409	mmeineke	49
410	mmeineke	63	\item
411	mmeineke	52	The point mass contains a fixed dipole of 2.35 D pointing from the
412	mmeineke	53	oxygens toward the hydrogens.
413	mmeineke	51
414	mmeineke	52	\end{itemize}
415	mmeineke	51
416	mmeineke	52	It's potential is as follows:
417
418			\begin{equation}
419			V_{s\!s\!d} = V_{l\!j}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
420	mmeineke	63	+ V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
421	mmeineke	52	\end{equation}
422			\end{slide}
423
424	mmeineke	54	% Slide 8b
425	mmeineke	52
426	mmeineke	54	\begin{slide}{SSD Diagram}
427
428			\begin{center}
429			\begin{figure}
430			\epsfxsize=50mm
431			\epsfbox{ssd.epsi}
432			\end{figure}
433			\end{center}
434
435			A Diagram of the SSD model.
436			\end{slide}
437
438	mmeineke	52	% Slide 9
439			\begin{slide}{Hydrogen Bonding in SSD}
440
441			It is important to note that SSD has a potential specifically to
442	mmeineke	53	recreate the hydrogen bonding network of water.
443	mmeineke	52
444	mmeineke	54
445	mmeineke	52	ICE SSD
446
447			ICE point Dipole
448
449	mmeineke	54
450	mmeineke	53	The importance of the hydrogen bond network is it's significant
451	mmeineke	52	contribution to the hydrophobic driving force of bilayer formation.
452			\end{slide}
453
454
455			% Slide 10
456
457			\begin{slide}{The Lipid Model}
458
459	mmeineke	53	To eliminate the need for charge-charge interactions, our lipid model
460			replaces the phospholipid head group with a single large head group
461			atom containing a freely oriented dipole. The tail is a simple alkane chain.
462
463			Lipid Properties:
464			\begin{itemize}
465			\item $\|\vec{\mu}_{\text{HEAD}}\| = 20.6\ \text{D}$
466			\item $m_{\text{HEAD}} = 196\ \text{amu}$
467			\item Tail atoms are unified CH, $\text{CH}_2$, and $\text{CH}_3$ atoms
468	mmeineke	63	\begin{itemize}
469			\item Alkane forcefield parameters taken from TraPPE
470			\end{itemize}
471	mmeineke	53	\end{itemize}
472
473			\end{slide}
474
475
476			% Slide 11
477
478			\begin{slide}{Lipid Model}
479
480	mmeineke	52
481	mmeineke	63
482	mmeineke	52	\end{slide}
483
484
485	mmeineke	53	% Slide 12
486	mmeineke	52
487			\begin{slide}{Initial Runs: 25 Lipids in water}
488
489	mmeineke	53	\textbf{Simulation Parameters:}
490	mmeineke	52
491	mmeineke	53	\begin{itemize}
492
493			\item Starting Configuration:
494	mmeineke	63	\begin{itemize}
495			\item 25 lipid molecules arranged in a 5 x 5 square
496			\item square was surrounded by a sea of 1386 waters
497			\begin{itemize}
498			\item final water to lipid ratio was 55.4:1
499			\end{itemize}
500			\end{itemize}
501	mmeineke	53
502			\item Lipid had only a single saturated chain of 16 carbons
503
504			\item Box Size: 34.5 $\mbox{\AA}$ x 39.4 $\mbox{\AA}$ x 39.4 $\mbox{\AA}$
505
506			\item dt = 2.0 - 3.0 fs
507
508			\item T = 300 K
509
510			\item NVE ensemble
511
512			\item Periodic boundary conditions
513			\end{itemize}
514
515	mmeineke	52	\end{slide}
516
517
518	mmeineke	53	% Slide 13
519	mmeineke	52
520	mmeineke	54	\begin{slide}{5x5: Initial}
521	mmeineke	52
522	mmeineke	54	\begin{center}
523			\begin{figure}
524			\epsfxsize=50mm
525			\epsfbox{5x5-initial.eps}
526			\end{figure}
527			\end{center}
528	mmeineke	52
529	mmeineke	54	The initial configuration
530	mmeineke	52
531			\end{slide}
532
533	mmeineke	54	\begin{slide}{5x5: Final}
534	mmeineke	52
535	mmeineke	54	\begin{center}
536			\begin{figure}
537			\epsfxsize=60mm
538			\epsfbox{5x5-1.7ns.eps}
539			\end{figure}
540			\end{center}
541
542			The final configuration at 1.7 ns.
543
544			\end{slide}
545
546
547	mmeineke	53	% Slide 14
548	mmeineke	52
549			\begin{slide}{5x5: $g(r)$}
550
551	mmeineke	54	\begin{center}
552			\begin{figure}
553			\epsfxsize=60mm
554			\epsfbox{all5x5-HEAD-HEAD-gr.eps}
555			\end{figure}
556			\end{center}
557	mmeineke	52
558
559	mmeineke	54	\end{slide}
560	mmeineke	52
561	mmeineke	54	\begin{slide}{5x5: $g(r)$}
562
563			\begin{center}
564			\begin{figure}
565			\epsfxsize=60mm
566			\epsfbox{all5x5-HEAD-X-gr.eps}
567			\end{figure}
568			\end{center}
569
570
571	mmeineke	52	\end{slide}
572
573
574	mmeineke	53	% Slide 15
575	mmeineke	52
576			\begin{slide}{5x5: $\cos$ correlations}
577
578	mmeineke	54	\begin{center}
579			\begin{figure}
580			\epsfxsize=60mm
581			\epsfbox{all5x5-HEAD-HEAD-cr.eps}
582			\end{figure}
583			\end{center}
584	mmeineke	52
585			\end{slide}
586
587	mmeineke	54	\begin{slide}{5x5: $\cos$ correlations}
588	mmeineke	52
589	mmeineke	54	\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	mmeineke	53	% Slide 16
600	mmeineke	52
601	mmeineke	53	\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water}
602	mmeineke	52
603	mmeineke	53	\textbf{Simulation Parameters:}
604	mmeineke	52
605	mmeineke	53	\begin{itemize}
606
607			\item Starting Configuration:
608	mmeineke	63	\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	mmeineke	53
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	mmeineke	63	\item Periodic boundary conditions
627	mmeineke	53
628			\end{itemize}
629
630	mmeineke	52	\end{slide}
631
632
633	mmeineke	53	% Slide 17
634	mmeineke	52
635	mmeineke	54	\begin{slide}{R-50: Initial}
636	mmeineke	52
637	mmeineke	54	\begin{center}
638			\begin{figure}
639			\epsfxsize=100mm
640			\epsfbox{r50-initial.eps}
641			\end{figure}
642			\end{center}
643	mmeineke	52
644	mmeineke	54	The initial configuration
645	mmeineke	52
646			\end{slide}
647
648	mmeineke	54	\begin{slide}{R-50: Final}
649	mmeineke	52
650	mmeineke	54	\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	mmeineke	53	% Slide 18
663	mmeineke	52
664			\begin{slide}{R-50: $g(r)$}
665
666
667	mmeineke	54	\begin{center}
668			\begin{figure}
669			\epsfxsize=60mm
670			\epsfbox{r50-HEAD-HEAD-gr.eps}
671			\end{figure}
672			\end{center}
673	mmeineke	52
674	mmeineke	54	\end{slide}
675	mmeineke	52
676	mmeineke	54
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	mmeineke	52	\end{slide}
688
689
690	mmeineke	53	% Slide 19
691	mmeineke	52
692			\begin{slide}{R-50: $\cos$ correlations}
693
694
695	mmeineke	54	\begin{center}
696			\begin{figure}
697			\epsfxsize=60mm
698			\epsfbox{r50-HEAD-HEAD-cr.eps}
699			\end{figure}
700			\end{center}
701
702	mmeineke	52	\end{slide}
703
704	mmeineke	54	\begin{slide}{R-50: $\cos$ correlations}
705	mmeineke	52
706	mmeineke	54
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	mmeineke	53	% Slide 20
718	mmeineke	52
719			\begin{slide}{Future Directions}
720
721	mmeineke	53	\begin{itemize}
722	mmeineke	52
723	mmeineke	63	\item
724	mmeineke	53	Simulation of a lipid with 2 chains, or perhaps expand the current
725			unified chain atoms to take up greater steric bulk.
726
727	mmeineke	63	\item
728	mmeineke	53	Incorporate constant pressure and constant temperature into the ensemble.
729
730			\item
731			Parrellize the code.
732
733			\end{itemize}
734	mmeineke	52	\end{slide}
735
736
737	mmeineke	53	% Slide 21
738	mmeineke	52
739			\begin{slide}{Acknowledgements}
740
741	mmeineke	53	\begin{itemize}
742	mmeineke	52
743	mmeineke	53	\item Dr. J. Daniel Gezelter
744			\item Christopher Fennel
745			\item Charles Vardeman
746			\item Teng Lin
747	mmeineke	52
748	mmeineke	53	\end{itemize}
749
750			Funding by:
751			\begin{itemize}
752			\item Dreyfus New Faculty Award
753			\end{itemize}
754
755	mmeineke	52	\end{slide}
756
757
758
759
760
761
762
763
764	mmeineke	49	%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
765
766			\end{document}