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

Mechanical Functions of Proteins

Forces naturally arise in cells

and can also be substrates (ATPase)

products (myosin)signals (integrin)of cellular processes

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

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)

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.

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

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

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

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

• 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)

• 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.

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

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)

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

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)

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

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

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.

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 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

Ubiquitin

Fatemeh Araghi, Timothy Isgro, Marcos Sotomayor

Monoubiquitylation versus multi-ubiquitylation

• 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

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

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

Pulling Dimer• SMD (v=0.4 A/ps k=7 kcal/mol A^2) constant P• Two monomers separate.