Molecular Dynamics
Arjan van der Vaart
vandervaart@asu.edu
PSF346
Center for Biological Physics
Department of Chemistry and Biochemistry
Arizona State University
Molecular Dynamics (MD):
1. Atoms are classical point-masses that move in a physical potential
Bonded terms
Bonds
kb(r–r0)2
Angles
ka(–0)2
Dihedrals
kd[1+cos(n–0)]
Non-bonded terms
Improper
Dihedrals
ki(–0)2
Electrostatics
van der
Waals
– +

(q1q2)/(r)
E[(rm/r)12–(rm/r)6]
2. The potential is fitted to experiments and quantum mechanical
calculations
3. The potential is transferable
4. Atoms are propagated by classical (Newtonian) dynamics
What can you do with MD?
What can you do with MD?
1. Obtain data that is normally measured by experiments
a. thermodynamic data (by using statistical mechanics)
b. kinetic data (by using statistical mechanics)
2. Obtain data that cannot be measured by experiments
a. very high spatial and time resolution data
b. certain energies, correlation functions, etc.
c. decomposition of energies
Example
Let’s look at a MD simulation of salt in liquid water
http://www.public.asu.edu/~avanderv/nacl.tar.gz
Questions
1. Do you see order, chaos, or something in between?
2. What kind of motions do you see?
3. Are there any differences in the time scales of the
motions (what type of motions occur frequently/rarely,
how long do the motions last)
4. Are there differences in the structure of water around
the positively and negatively charged ions?
5. What kind of interactions forms the water with itself?
How stable (long lasting) are these?
6. Could such detailed information be obtained from
experiments?
Computer simulations can:
1. provide quantitative data
2. provide qualitative data
3. provide experimentally
verifiable data
4. help predict properties
Thus:
Computer simulations can
complement experiments
by providing data that is
hard to obtain experimentally
The
question my research addresses is:
How do conformational changes work?
The
question my research addresses is:
How do conformational changes work?
Conformational change = The change in shape of
a biomolecule upon
binding other molecules
Maltose-binding protein
Proc. Natl. Acad. Sci. USA 100 12700 (2003)
Oxygen transport by
hemoglobin
Protein Data Bank
www.rcsb.org
Membrane fusion by hemagglutinin of
influenza virus
Nature Struct. Biol. 8 653 (2001)
QuickTime™ and a
GI F decompressor
are needed to see this picture.
ATP hydrolysis by F1-ATPase
Nature 386 299 (1997)
Conformational changes are crucial for the functioning of many proteins
1. transport proteins
e.g. maltose-binding protein
2. kinases
e.g. Src tyrosine kinase
3. molecular motors
e.g. FOF1-ATPase
4. etc. etc.
The
question my research addresses is:
How do conformational changes work?
-) How are they triggered/induced
-) How are they propagated
-) What are their pathways
-) What is their function
Timescales of Conformational Motion
protein domain motion
unwinding of DNA helix
protein folding
10-15
10-12
10-9
10-6
10-3
1
molecular dynamics large system
molecular dynamics small system
Need to “speed up” simulations: apply biases
103 s
grey
black
Alanine dipeptide
–
–
O
–
–

O
–

–
120
–
CH3–C–N—C—C–N–CH3
H
CH3
H
12.0
C7eq
L
0
9.0
6.0
R
C7ax
-120
3.0
0.0
-120
0

120
∆=0.0005Å
∆=0.00001Å
∆=0.0005Å
∆=0.00001Å
PF=0.0005Å
PF=0.0003Å
PF=0.0004Å
PF=0.0002Å
PF=0.001Å
PB=0.001Å
PF=0.001Å
PB=0.000Å
Artifacts
Energy
Rmsd
Trajectories
GroEL:
 Helps proteins fold
 2 rings stacked back to back;
each with a central cavity
“trans” cavity (closed state):
volume = 85,000 Å3, hydrophobic cavity lining
“cis” cavit y (open state):
volume = 175,000 Å3, hydrophilic cavity lining
Rings switch between closed and open state;
this is driven by ATP binding/hydrolysis
GroEL: helps proteins fold
H
H
I
closed
open
Sigler et. al. Nature 371 578 (1994), Nature 388 741 (1997)
I
GroEL Cycle
GroES
7 ATP
7 ADP
cis
trans
Closed
(t)
Unfolded
Open
(r’’)
=
Intermediate
(r’)
Folded
How does this help protein folding?
Key notion: Protein folding in vivo is complicated, due
to molecular crowding
1. provides a water-like, shielded environment,
preventing aggregation
2. might there be a second effect?
MD trajectory of opening motion of GroEL in presence
of unfolded protein (rhodanese)
http://www.public.asu.edu/~avanderv/groel.tar.gz
1.
2.
3.
4.
What is GroEL, what the protein?
Is the entire GroEL present, or only a part (and which)?
Describe what happens to GroEL
Describe what happens to rhodanese
More difficult:
1. Characterize the binding of the part of rhodanese that
is tightly bound. What type of contacts are important?
2. Compare this binding to experimental studies (pdb
databank entry 1DKD). What is similar, what is different?
(e.g. type of contacts, orientation, type of interactions)