steered molecular dynamics klaus introduction and … · why steered molecular dynamics? ... k t p...
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Why Steered Molecular Dynamics?
- Accelerates processes to simulation time scales (ns)-Yields explanations of biopolymer mechanics
- Complements Atomic Force Microscopy- Finds underlying unbinding potentials
- Generates and tests Hypotheses
Steered Molecular DynamicsIntroduction and Examples
Rosemary Braun
Barry Isralewitz
Hui LuJustinGullingsrud
DorinaKosztin
SergeiIzrailev
FerencMolnar
biotin
avidin
KlausSchulten
Acknowledgements:Fernandez group, Mayo C.; Vogel group, U. WashingtonNIH, NSF, Carver Trust
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Mechanical Functions of Proteins
Forces naturally arise in cells
and can also be substrates (ATPase)
products (myosin)signals (integrin)of cellular processes
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Atomic Force Microscopy Experimentsof Ligand Unbinding
Biotin
avidin biotin
AFM
Displacement of AFM tip
Forc
e
Florin et al., Science 264:415 (1994)
Chemical structure of biotin
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NIH Resource for Macromolecular Modeling and BioinformaticsTheoretical Biophysics Group, Beckman Institute, UIUC
Atomic Force Microscopy Experimentsof Ligand Unbinding
Biotin
avidin biotin
AFM
Displacement of AFM tip
Forc
e
Florin et al., Science 264:415 (1994)
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Pulling Biotin out of Avidin
Molecular dynamics study of unbinding of the avidin-biotin complex. Sergei Izrailev,Sergey Stepaniants, Manel Balsera, Yoshi Oono, and Klaus Schulten. BiophysicalJournal, 72:1568-1581, 1997.
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NIH Resource for Macromolecular Modeling and BioinformaticsTheoretical Biophysics Group, Beckman Institute, UIUC
SMD of Biotin Unbinding: What We Learnedbiotin slips out in steps, guided by amino acid side groups, watermolecules act as lubricant, MD overestimates extrusion force
Israilev et al., Biophys. J., 72, 1568-1581 (1997)http://www.ks.uiuc.edu
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AFM range
Current SMD range
Target simulation range
SMD dataAFM data
Extrapolation of AFM data
Force-pulling velocity relationship
Force-extension curve
AFM regime
eδ(F) >> 1τAFM ~ 2τDδ-2(F)eδ(F)
SMD regime
eδ(F) << 1τSMD ~ 2τD|δ(F)|-1
Quantitative ComparisonBridging the gap between SMD and AFM experiments
δ(F) = β [ΔU – F(b-a)]
Schematic potentials
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Rupture/Unfolding Force F0and its Distribution
Israilev et al., Biophys. J., 72, 1568-1581 (1997)Balsera et al., Biophys. J., 73, 1281-1287 (1997)
τ(F0) = 1 ms time of measurement => F0 rupture/unfolding force
Distribution of rupture/unfolding force
κ = δ2(F)/2τDkv
the best fit suggests apotential barrier ofΔU = 20 kcal/mol
stationary force applied (pN)
burs
t tim
e (p
s)
determination of barrier height basedon mean first passage time
400 600 800 1000 1200
1200
0
400
0
800
( )]1)(exp[)( )(00 0 −
−−Δ−−= −Δ− abFUB
eeabTk
UabFFp ββκββκ
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Distribution of the Barrier Crossing Time
The fraction N(t) that has not crossed the barrier can be expressed through solvingthe Smoluchowski diffusion equation (linear model potential):
Or approximated by double exponential (general potential): N(t) = [t1 exp(-t/t1) – t2 exp(-t/t2)]/(t1-t2), Nadler & Schulten, JCP., 82, 151-160 (1985)
Multiple runs with same forceof 750 pN
Barrier crossing times of18 SMD simulations
Theoretical prediction ofthe barrier crossing times
NIH Resource for Macromolecular Modeling and BioinformaticsTheoretical Biophysics Group, Beckman Institute, UIUC
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• Retinal deep in bacterio-opsin binding cleft• How does it get in?• Use batch mode interactive steered molecular dynamics to pull retinal out of cleft, find possible binding path
• 10 path segments, 3 attempts each• Choose best attempt at 9 pointsduring pull• Found path through membrane,and electrostatically attractiveentrance window
NIH Resource for Macromolecular Modeling and BioinformaticsTheoretical Biophysics Group, Beckman Institute, UIUC
Interactive ModelingBinding path of retinal to bacterio-opsin (1)
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• Retinal deep in bacterio-opsin binding cleft• How does it get in?• Use batch mode interactive steered molecular dynamics to pull retinal out of cleft, find possible binding path
NIH Resource for Macromolecular Modeling and BioinformaticsTheoretical Biophysics Group, Beckman Institute, UIUC
Interactive ModelingBinding path of retinal to bacterio-opsin
Binding pathway ofretinal to bacterio-opsin: A predictionby moleculardynamicssimulations. BarryIsralewitz, SergeiIzrailev, and KlausSchulten. BiophysicalJournal , 73:2972-2979, 1997.
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Stepwise Unbinding of Retinal from bR
Isralewitz et al., Biophys. J., 73, 2972-2979 (1997)NIH Resource for Macromolecular Modeling and BioinformaticsTheoretical Biophysics Group, Beckman Institute, UIUC
Retinal’sexit andentrance“door”attractsitsaldehydegroup
protein conformationunaffected
waterneededtoshieldlys –retinalinteract.
http://www.ks.uiuc.edu
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UserNAMD
(HHS Secretary Thompson)
0
20
40
60
80
100
120
0 4 8 12 16 20processors
NAMD 2.5new cluster
NAMD 2.5
NAMD 2.4
old cluster GlpF IMD Benchmark:
• 4210 atoms
• 3295 fixed atoms
• 10A cutoff, no PME
• Limited by network latency
Interactive Molecular Dynamics
steps per second (more is better)
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J. Stone, J. Gullingsrud, K. Schulten, and P. Grayson.A System for Interactive Molecular Dynamics Simulation.2001 ACM Symposium on Interactive 3D Graphics,pp.191-194, ACM SIGGRAPHP. Grayson, E. Tajkhorshid, and K. Schulten.Biophysical J, 83: 36 (2003)
Interactive Molecular DynamicsVMD NAMD
• Any PC/Workstation• Supports 3D force-feedback devices forinteraction
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Is there any chance to discountthe irreversible work? Yes!
WG ≤ΔThermodynamics:Calculation of the free energyprofile of sugar transport fromSMD simulations by Jarzynski’sidentity
displacement
applied force
Quantitative Analysis of Substrate Permeation
Jensen et al, PNAS 99: 6731-6736 (2002)
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Free energy calculation from steered moleculardynamics simulations using Jarzynski's equality. S.Park, F. Khalili-Araghi, E. Tajkhorshid, and K. Schulten.Journal of Chemical Physics , 119:3559-3566, 2003
Free Energy of Stretched Alpha-Helix (Deca-alanin)
TkWTkG BB ee // −Δ− =Jarzynski (1997):
WG ≤ΔThermodynamics:
Calculating potentials of mean force from steeredmolcular dynamics simulations. S. Park and K.Schulten. Journal of Chemical Physics , 120: 5946-5961, 2004
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Ankyrin Repeats: Springs in theInner Ear
Mammalian Inner Ear(from SensoryTransduction, G. L. Fain).
Cuticular plate,stereocilia and
kinocilium in haircells (from SensoryTransduction, G. L.
Fain)
Tip Links (Kachar et al.,
2000)
Hair bundle (D.P. Corey)
Marcos Sotomayor
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Tip Links (Kacharet al., 2000; CoreyLab)
Hair bundle (Assadand Corey, from SensoryTransduction, G. L. Fain).
340,000 atom simulation of 24 repeat ankyrin
Inner Ear Mechanism
NAMD: 128 processors NCSA teragrid
water bath• 340,000 atoms including explicitwater molecules
• CHARMM27 force-field• Periodic boundary conditions• Steered MD (25-75 pN)• PME for full electrostatic calculation• Teragrid benchmark: 0.7 day/ns on
128 Itanium 1.5GHz processors.
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Tip Links (Kacharet al., 2000; CoreyLab)
Hair bundle (Assadand Corey, from SensoryTransduction, G. L. Fain).
340,000 atom simulation of 24 repeat ankyrin
Inner Ear Mechanism
NAMD: 128 processors NCSA teragrid
water bath
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340,000 atom simulation of 24 repeat ankyrin
Inner Ear Mechanism
Tip Links (Kacharet al., 2000; CoreyLab)
Hair bundle (Assadand Corey, from SensoryTransduction, G. L. Fain).
NAMD: 128 processors NCSA teragrid
water bath
Non-entropic, nearly indistructable molecular spring
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Ubiquitin
Fatemeh Araghi, Timothy Isgro, Marcos Sotomayor
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Monoubiquitylation versus multi-ubiquitylation
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• SMD simulation, with constant velocity
• Box of water 70x240x70 A ~81K atoms
• smd velocity 0.4 A/ps• smd spring constant 7 kcal/mol A^2
First peak when the first beta strand is stretched out
First SMD Simulation
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Ubiquitin Unfolding IFo
rce
(pN
)
extension (Å)
cv-0.02 Å/psK6F4
L69
Q2
L69L67
S65
E64 water
Q2
Q2
F4
F4
K6
K6
E64
E64
S65
S65
L67
L67
L69
L69
N-term fixed 0 Å, 1 ps
14 Å, 700ps
15 Å, 813ps
Mu Gao
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Ubiquitin Unfolding II
Time (ps)
Ext
ensi
on (
Å) cf-500pN
K48 fixed
H68V70
R72
Q40R42L43I44
F45
K48
L50
H68
H68
H68
V70
V70
V70
R72
R72
R72
Q40
Q40
Q40
R42
R42
R42
L43
L43
L43
I44
I44
I44
F45
F45
F45
K48
K48
K48
L50
L50
L50
0 Å, 1 ps 9 Å, 60 ps
17 Å, 320 ps
19 Å, 340 psMu Gao
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Pulling Dimer• SMD (v=0.4 A/ps k=7 kcal/mol A^2) constant P• Two monomers separate.