matt_papers/canidacy_talk/canidacy_slides.tex

% temporary preamble

\documentclass{seminar}
\usepackage{color}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{epsf}

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

\title{A Coarse Grain 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


% 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}{Motivation}
\begin{itemize}

% make sure to come back and talk about the need for long time and length 
% scales

\item Drug diffusion

\item ripple phase

\item bilayer formation dynamics

\end{itemize}
\end{slide}


% Slide 3

\begin{slide}{Research Goals}
\begin{itemize}

\item 
To develop a coarse-grain simulation model with which to simulate
phospholipid bilayers.

\item To use the model to observe:

        \begin{itemize}
        
        \item Phospholipid properties with long length scales

                \begin{itemize}
                \item The ripple phase.
                \end{itemize}

        \item Long time scale dynamics of biological relevance
                
                \begin{itemize}
                \item Trans-membrane diffusion of drug molecules
                \end{itemize}
        \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}

\color{red}
!!!!!!!!!!!!!SSD image goes here.!!!!!!!!!!!!!!!!
\color{black}


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}

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

\color{red}
ICE SSD

ICE point Dipole
\color{black}

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}

\color{red}

Look at me, I'm a lipid.!!!!!!!!

YAY!!!!!!!!!!!!!!!!!!!!!
\color{black}

\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 and Final}

\color{red}
picture of initial

picture of final
\color{black}

\end{slide}


% Slide 14

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

\color{red}

GofR's baby

\color{black}

\end{slide}


% Slide 15

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

\color{red}
Cosine correlation functions
\color{black}

\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 and Final}

\color{red}
picture of initial

picture of final
\color{black}

\end{slide}


% Slide 18

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

\color{red}

GofR's baby

\color{black}

\end{slide}


% Slide 19

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

\color{red}
Cosine correlation functions
\color{black}

\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:	53
Committed:	Sun Jul 28 18:22:07 2002 UTC (22 years, 9 months ago) by mmeineke
Content type:	application/x-tex
File size:	8212 byte(s)
Log Message:	getting there. Most everything but the motivation slide has been filled out. Lacks only pictures and Diagrams.
#	Content
1	% temporary preamble
2
3	\documentclass{seminar}
4	\usepackage{color}
5	\usepackage{amsmath}
6	\usepackage{amssymb}
7	\usepackage{epsf}
8
9	% ----------------------
10	% \| Title \|
11	% ----------------------
12
13	\title{A Coarse Grain Model for Phospholipid MD Simulations}
14
15	\author{Matthew A. Meineke\\
16	Department of Chemistry and Biochemistry\\
17	University of Notre Dame\\
18	Notre Dame, Indiana 46556}
19
20	\date{\today}
21
22	%-------------------------------------------------------------------
23	% Begin Document
24
25	\begin{document}
26	\maketitle
27
28
29
30	% Slide 1
31	\begin{slide} {Talk Outline}
32	\begin{itemize}
33
34	\item Discussion of the research motivation and goals
35
36	\item Methodology
37
38	\item Discussion of current research and preliminary results
39
40	\item Future research
41
42	\end{itemize}
43	\end{slide}
44
45
46	% Slide 2
47
48	\begin{slide}{Motivation}
49	\begin{itemize}
50
51	% make sure to come back and talk about the need for long time and length
52	% scales
53
54	\item Drug diffusion
55
56	\item ripple phase
57
58	\item bilayer formation dynamics
59
60	\end{itemize}
61	\end{slide}
62
63
64	% Slide 3
65
66	\begin{slide}{Research Goals}
67	\begin{itemize}
68
69	\item
70	To develop a coarse-grain simulation model with which to simulate
71	phospholipid bilayers.
72
73	\item To use the model to observe:
74
75	\begin{itemize}
76
77	\item Phospholipid properties with long length scales
78
79	\begin{itemize}
80	\item The ripple phase.
81	\end{itemize}
82
83	\item Long time scale dynamics of biological relevance
84
85	\begin{itemize}
86	\item Trans-membrane diffusion of drug molecules
87	\end{itemize}
88	\end{itemize}
89	\end{itemize}
90	\end{slide}
91
92
93	% Slide 4
94
95	\begin{slide}{Length Scale Simplification}
96	\begin{itemize}
97
98	\item
99	Replace any charged interactions of the system with dipoles.
100
101	\begin{itemize}
102	\item Allows for computational scaling approximately by $N$ for
103	dipole-dipole interactions.
104	\item In contrast, the Ewald sum scales approximately by $N \log N$.
105	\end{itemize}
106
107	\item
108	Use unified models for the water and the lipid chain.
109
110	\begin{itemize}
111	\item Drastically reduces the number of atoms to simulate.
112	\item Number of water interactions alone reduced by $\frac{1}{3}$.
113	\end{itemize}
114	\end{itemize}
115	\end{slide}
116
117
118	% Slide 5
119
120	\begin{slide}{Time Scale Simplification}
121	\begin{itemize}
122
123	\item
124	No explicit hydrogens
125
126	\begin{itemize}
127	\item Hydrogen bond vibration is normally one of the fastest time
128	events in a simulation.
129	\end{itemize}
130
131	\item
132	Constrain all bonds to be of fixed length.
133
134	\begin{itemize}
135	\item As with the hydrogens, bond vibrations are the fastest motion in
136	a simulation
137	\end{itemize}
138
139	\item
140	Allows time steps of up to 3 fs with the current integrator.
141
142	\end{itemize}
143	\end{slide}
144
145
146	% Slide 6
147	\begin{slide}{Molecular Dynamics}
148
149	All of our simulations will be carried out using molecular
150	dynamics. This involves solving Newton's equations of motion using
151	the classical \emph{Hamiltonian} as follows:
152
153	\begin{equation}
154	H(\vec{q},\vec{p}) = T(\vec{p}) + V(\vec{q})
155	\end{equation}
156
157	Here $T(\vec{p})$ is the kinetic energy of the system which is a
158	function of momentum. In Cartesian space, $T(\vec{p})$ can be
159	written as:
160
161	\begin{equation}
162	T(\vec{p}) = \sum_{i=1}^{N} \sum_{\alpha = x,y,z} \frac{p^{2}_{i\alpha}}{2m_{i}}
163	\end{equation}
164
165	\end{slide}
166
167
168	% Slide 7
169	\begin{slide}{The Potential}
170
171	The main part of the simulation is then the calculation of forces from
172	the potential energy.
173
174	\begin{equation}
175	\vec{F}(\vec{q}) = - \nabla V(\vec{q})
176	\end{equation}
177
178	The potential itself is made of several parts.
179
180	\begin{equation}
181	V_{tot} =
182	\overbrace{V_{l} + V_{\theta} + V_{\omega}}^{\mbox{bonded}} +
183	\overbrace{V_{l\!j} + V_{d\!p} + V_{s\!s\!d}}^{\mbox{non-bonded}}
184	\end{equation}
185
186	Where the bond interactions $V_{l}$, $V_{\theta}$, and $V_{\omega}$ are
187	the bond, bend, and torsion potentials, and the non-bonded
188	interactions $V_{l\!j}$, $V_{d\!p}$, and $V_{s\!p}$ are the
189	lenard-jones, dipole-dipole, and sticky potential interactions.
190
191	\end{slide}
192
193
194	% Slide 8
195
196	\begin{slide}{Soft Sticky Dipole Model}
197
198	The Soft-Sticky model for water is a reduced model.
199
200	\begin{itemize}
201
202	\item
203	The model is represented by a single point mass at the water's center
204	of mass.
205
206	\item
207	The point mass contains a fixed dipole of 2.35 D pointing from the
208	oxygens toward the hydrogens.
209
210	\end{itemize}
211
212	\color{red}
213	!!!!!!!!!!!!!SSD image goes here.!!!!!!!!!!!!!!!!
214	\color{black}
215
216
217	It's potential is as follows:
218
219	\begin{equation}
220	V_{s\!s\!d} = V_{l\!j}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
221	+ V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
222	\end{equation}
223	\end{slide}
224
225
226	% Slide 9
227	\begin{slide}{Hydrogen Bonding in SSD}
228
229	It is important to note that SSD has a potential specifically to
230	recreate the hydrogen bonding network of water.
231
232	\color{red}
233	ICE SSD
234
235	ICE point Dipole
236	\color{black}
237
238	The importance of the hydrogen bond network is it's significant
239	contribution to the hydrophobic driving force of bilayer formation.
240	\end{slide}
241
242
243	% Slide 10
244
245	\begin{slide}{The Lipid Model}
246
247	To eliminate the need for charge-charge interactions, our lipid model
248	replaces the phospholipid head group with a single large head group
249	atom containing a freely oriented dipole. The tail is a simple alkane chain.
250
251	Lipid Properties:
252	\begin{itemize}
253	\item $\|\vec{\mu}_{\text{HEAD}}\| = 20.6\ \text{D}$
254	\item $m_{\text{HEAD}} = 196\ \text{amu}$
255	\item Tail atoms are unified CH, $\text{CH}_2$, and $\text{CH}_3$ atoms
256	\begin{itemize}
257	\item Alkane forcefield parameters taken from TraPPE
258	\end{itemize}
259	\end{itemize}
260
261	\end{slide}
262
263
264	% Slide 11
265
266	\begin{slide}{Lipid Model}
267
268	\color{red}
269
270	Look at me, I'm a lipid.!!!!!!!!
271
272	YAY!!!!!!!!!!!!!!!!!!!!!
273	\color{black}
274
275	\end{slide}
276
277
278	% Slide 12
279
280	\begin{slide}{Initial Runs: 25 Lipids in water}
281
282	\textbf{Simulation Parameters:}
283
284	\begin{itemize}
285
286	\item Starting Configuration:
287	\begin{itemize}
288	\item 25 lipid molecules arranged in a 5 x 5 square
289	\item square was surrounded by a sea of 1386 waters
290	\begin{itemize}
291	\item final water to lipid ratio was 55.4:1
292	\end{itemize}
293	\end{itemize}
294
295	\item Lipid had only a single saturated chain of 16 carbons
296
297	\item Box Size: 34.5 $\mbox{\AA}$ x 39.4 $\mbox{\AA}$ x 39.4 $\mbox{\AA}$
298
299	\item dt = 2.0 - 3.0 fs
300
301	\item T = 300 K
302
303	\item NVE ensemble
304
305	\item Periodic boundary conditions
306	\end{itemize}
307
308	\end{slide}
309
310
311	% Slide 13
312
313	\begin{slide}{5x5: Initial and Final}
314
315	\color{red}
316	picture of initial
317
318	picture of final
319	\color{black}
320
321	\end{slide}
322
323
324	% Slide 14
325
326	\begin{slide}{5x5: $g(r)$}
327
328	\color{red}
329
330	GofR's baby
331
332	\color{black}
333
334	\end{slide}
335
336
337	% Slide 15
338
339	\begin{slide}{5x5: $\cos$ correlations}
340
341	\color{red}
342	Cosine correlation functions
343	\color{black}
344
345	\end{slide}
346
347
348	% Slide 16
349
350	\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water}
351
352	\textbf{Simulation Parameters:}
353
354	\begin{itemize}
355
356	\item Starting Configuration:
357	\begin{itemize}
358	\item 50 lipid molecules arranged randomly in a rectangular box
359	\item The box was then filled with 1384 waters
360	\begin{itemize}
361	\item final water to lipid ratio was 27:1
362	\end{itemize}
363	\end{itemize}
364
365	\item Lipid had only a single saturated chain of 16 carbons
366
367	\item Box Size: 26.6 $\mbox{\AA}$ x 26.6 $\mbox{\AA}$ x 108.4 $\mbox{\AA}$
368
369	\item dt = 2.0 - 3.0 fs
370
371	\item T = 300 K
372
373	\item NVE ensemble
374
375	\item Periodic boundary conditions
376
377	\end{itemize}
378
379	\end{slide}
380
381
382	% Slide 17
383
384	\begin{slide}{R-50: Initial and Final}
385
386	\color{red}
387	picture of initial
388
389	picture of final
390	\color{black}
391
392	\end{slide}
393
394
395	% Slide 18
396
397	\begin{slide}{R-50: $g(r)$}
398
399	\color{red}
400
401	GofR's baby
402
403	\color{black}
404
405	\end{slide}
406
407
408	% Slide 19
409
410	\begin{slide}{R-50: $\cos$ correlations}
411
412	\color{red}
413	Cosine correlation functions
414	\color{black}
415
416	\end{slide}
417
418
419	% Slide 20
420
421	\begin{slide}{Future Directions}
422
423	\begin{itemize}
424
425	\item
426	Simulation of a lipid with 2 chains, or perhaps expand the current
427	unified chain atoms to take up greater steric bulk.
428
429	\item
430	Incorporate constant pressure and constant temperature into the ensemble.
431
432	\item
433	Parrellize the code.
434
435	\end{itemize}
436	\end{slide}
437
438
439	% Slide 21
440
441	\begin{slide}{Acknowledgements}
442
443	\begin{itemize}
444
445	\item Dr. J. Daniel Gezelter
446	\item Christopher Fennel
447	\item Charles Vardeman
448	\item Teng Lin
449
450	\end{itemize}
451
452	Funding by:
453	\begin{itemize}
454	\item Dreyfus New Faculty Award
455	\end{itemize}
456
457	\end{slide}
458
459
460
461
462
463
464
465
466	%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
467
468	\end{document}