collective brownian motors - experiments and models

Collective Brownian Motors - Experiments and ModelsErin Craig, Heiner LinkeUniversity of Oregon

Ann Arbor, June 12 2007

Load force

-

+

J. Bader et al,PNAS 96, 13165 (1999)

Ajdari and Prost, C.R. Acad. Sci. Paris II 315, 1635 (1992)

Non-equilibrium+ Asymmetry+ Thermal fluctuations= Transport

Brownian motorsexample: flashing ratchet

ON

OFF

ON

Brownian motors: overview of projects

Experimental ratchets:

Collective Brownian motors: modeling and experimental planning

Computational models of biological molecular motors:

Information feedback Coupled particle ratchet Polymer motor

Self-propelled droplets Quantum ratchets

1D kinesin model 3D myosin V model

Efficient thermoelectrics

e

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Self-propelled fluids

Droplet of liquid nitrogen (77 K) onmachined brass surface (300 K).

Filmed at 500 frames per second

15 mm

Slow motion

QuickTime™ and aMicrosoft Video 1 decompressorare needed to see this picture.

Film boiling (Leidenfrost effect)

Vapor layer separates solid and liquid (≈ 10 - 100 µm).

Film boiling point: Water ≈ 200 - 300 °C

Ethanol ≈ 120 °C R134a ≈ 22 °C

0.3 mm

1.5 mm

Film boiling (Leidenfrost effect)

0.3 mm

1.5 mm

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H. Linke et. al., PRL 96, 154502 (2006).More movies: darkwing.uoregon.edu/~linke/dropletmovies









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How to get flux or work out of a thermal system?Open-loop strategy:ex: Brownian ratchet

Closed-loop (feedback) strategy:ex: Maxwell’s demon

• Directionality: spatial asymmetry• Energy input: turning potential on/off

• Directionality: information feedback• Energy input:

collecting informationopen/closing door








Both systems produce net flux w/o applying macroscopic forces directly to particles and w/o violating the 2nd Law of Thermodynamics.








• Do closed-loop strategies always out perform open-loop strategies?

• Fundamental limitations on output of information feedback strategy?

• Experimental realization?

Information feedback in thermal ratchets:

For a system of N particles,

€

ft()=1N Fxi( )i

N∑ , is av e rage

force particles w ou ld fee l if potentia l ONß If

€

f t()≥0, turn potential ONß If

€

f t()<0, turn potential OFF

F. J. Cao et. al., PRL 93, 040603 (2004).

V(x)

x

aL

L

Information feedback in thermal ratchets:

F. J. Cao et. al., PRL 93, 040603 (2004).

optimal periodic switching

V(x)

x

aL

L

Time delay in feedback implementation:

t1 = delay due to computational time(If a measurement is taken at time t, the feedback based on this measurement will occur at

time t + t1.)

t2 = delay due to measurement time(If a measurement is taken at time t, the next measurement will be taken at time t + t2.)

Time delay in feedback implementation:

• Original scheme: higher current than optimal periodic switching• Delay t1 reduces current because high fluctuations reduce relevance of delayed information

• Original scheme worse than periodic switching• For some values of t1, system settles into steady state that reproduces optimal periodic flashing.

Large N (more deterministic):

Small N (high fluctuations):

0

1

2

3

4

0 0.02 0.04 0.06 0.08 0.1

N=1N=10N=100N=316N=1000N=3162N=10,000N=100,000N=1,000,000

t1t1 / (L

2/D)

0

0.1

0.2

0.3

0 0.02 0.04 0.06 0.08 0.1

t1 / (L

2/D)

E. Craig et. al., to submit (2007).

Time delay in feedback, N=106:

-1

0

1

0 0.1 0.2 0.3 0.4 0.5At / (L

2/D)

0

1

A

0

1

A

b)

-1

0

1

0 0.1 0.2 0.3 0.4 0.5At / (L

2/D)

0

1

a)

0

1

D

A

α( )t

t1 = 0.02 L2/D; t2 = 0 t1 = 0.09 L2/D; t2 = 0


Time delay in feedback, N=106:

-1

0

1

0 0.1 0.2 0.3 0.4 0.5At / (L

2/D)

0

1

A

0

1

A

b)

-1

0

1

0 0.1 0.2 0.3 0.4 0.5At / (L

2/D)

0

1

a)

0

1

D

A

α( )t

t1 = 0.02 L2/D; t2 = 0 t1 = 0.09 L2/D; t2 = 0


0

0.2

0.4

0 0.05 0.1 0.15 0.2At

1 / (L

2/D)

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2

t1 / (L

2/D)

a)

b)

= t1

= t1/2

a

b

Time delay in electrostatic experiment:

Simulated time delay:Experimental time delay:

V(x)for anegativelychargedparticle

+

_Inter Digitated Electrode Array (IDEA): Manufacturedusing lithography to deposit platinum electrodes on toa silicon substrate.

Expose, Readout Image to Computer

Locate Particles Decide voltage Actuate Voltage

Next Exposure

Actuate Voltage(from previous image)

t2

t1









e

E. Craig et. al., PRE, 2006

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Artificial single-molecule motor

M. Downton

Average velocity peaks at L ≈ 5 , independent of polymer length N.

Ratchet period L ()

Vel

ocity

(L/

L

ton = toff = 20

M. Downton et. al.,Phys. Rev. E 73, 011909 (2006)

Stall force is proportional to polymer length

Fstall ≈ 1kT/

= 0.04 pNfor 100 nm

≈ pN for 5 nm

L = 5

Sta

ll fo

rce

(kT

/

M. Downton et. al.,Phys. Rev. E 73, 011909 (2006)

Experiment in progress

1 µm

Brian Long, UOJonas Tegenfeldt, Lund

• cycle time ≈ 20 ms ≈ 50 Hz• expected speed ≈ 1 µm/s

10 µm

• High resolution images of DNA• Response to voltage, background drift

• Future: analysis of conformations, fluctuations, trajectories

Brian Long, UOJonas Tegenfeldt, Lund

Experiment in progress

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Myosin V: hand-over-hand walking molecular motor

A. R. Dunn, J. A. Spudich, Nature SMB 14, 246 (2007).

• Processive motor involved in vesicle and organelle transport• Two part step: lever arm rotation followed by diffusive search?



A. Yildiz,..., P. Selvin,Science 300, 2061 (2003).

Myosin V mechanochemical cycle

K.I.

Ska

u, R

.B. H

oyle

, M.S

. Tur

ner,

BP

J 91

, 247

5 (2

006)

.M

. Rie

f.,...

,J. S

pudi

ch, P

NA

S 9

7, 9

482

(200

0).

• Conformational change• Internal coordination• Brownian diffusion

ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP


ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP

Conformational change creates strain K

.I. S

kau,

R.B

. Hoy

le, M

.S. T

urne

r, B

PJ

91, 2

475

(200

6).

M. R

ief.,

...,J

. Spu

dich

, PN

AS

97,

948

2 (2

000)

.



ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP

Conformational change creates strain

Strain-dependent coordination of chemical cycle K

.I. S

kau,

R.B

. Hoy

le, M

.S. T

urne

r, B

PJ

91, 2

475

(200

6).

M. R

ief.,

...,J

. Spu

dich

, PN

AS

97,

948

2 (2

000)

.



ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP


Release of strain

K.I.

Ska

u, R

.B. H

oyle

, M.S

. Tur

ner,

BP

J 91

, 247

5 (2

006)

.M

. Rie

f.,...

,J. S

pudi

ch, P

NA

S 9

7, 9

482

(200

0).


Strain-dependent coordination of chemical cycle

ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP

Diffusion



Release of strain

K.I.

Ska

u, R

.B. H

oyle

, M.S

. Tur

ner,

BP

J 91

, 247

5 (2

006)

.M

. Rie

f.,...

,J. S

pudi

ch, P

NA

S 9

7, 9

482

(200

0).


Strain-dependent coordination of chemical cycle

Myosin V: 3D model

pair of IQ motifstreated as rigid element

flexibility at joints

hinge between neck domains

myosin head

harmonic rotation about state-dependent equilibrium angle

neckdomain

Myosin V 3D model: elasticity of neck domains

Neck domain:• 3 rigid segments • flexibility at joints

M. Terrak et. el., PNAS 102, 12718 (2005).M. Doi and S. F. Edwards, “The Theory of Polymer dynamics”, (1986).

Bending energy of semiflexible filaments:

r´3

r1 r´1

r´2r2

r3

r0 r´0

A

i

j

kr0

Myosin V 3D model: rotational states

Post-stroke:Pre-stroke:

ADP-boundEmpty

ATP-bound

B

x

zy

r1

ADP.Pi-bound

A

y

x

z

r1

y

x

r1

“Bird’s eye” view:

Myosin V 3D model: mechanical cycle

ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP


ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP

r1 r´1

A B

I


ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP

r1 r´1

A B

I

r1

r´1

A A

II


ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP

r1 r´1

A B

I

r1

r´1

A A

II

r´1

A

III

ATP ADP ADP

ATP

ADP·Pi

ADP

ADPADP

ADP

4. 5.

1.

2.

3.

ATP

PiADP

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Myosin V 3D model: inputs and outputs

fext

Model Parameters: • Binding sites• Neck domain length• Drag coefficients• Transition rates • Neck domain persistence length• Equilibrium angles• Rotational stiffness • Neck domains: free swivel?

Myosin V 3D model: inputs and outputs

fext

Model Parameters: • Binding sites• Neck domain length• Drag coefficients• Transition rates • Neck domain persistence length• Equilibrium angles• Rotational stiffness • Neck domains: free swivel?

Experimentally measured behavior: • Average step size• Substep (“prestroke”) size, ATP dependence• Step trajectories, cargo• Step trajectories, individual heads• Profile of step average, cargo• Profile of step average, heads• correlation of z-position with steps• correlation of x and z variance with steps• non-Gaussian fluctuations (failed steps?)• positional distribution of detached head• load dependence of velocity and dwell times• Mechanical processivity (steps per contact) • Kinetic processivity (1 step per ATP)• Stepping vs. neck length• Characteristics of backsteps under load

fext

• Mechanics of stepping: what happens during one-head-bound state?

• Role of strain in coordinated walking?

• Backwards steps under load: processive walking?

• Mechanism behind distribution of step sizes for different neck lengths?

Mechanistic model can demonstrate which physical assumptions are consistent with known data. This can help address...

Funding:NSF CAREER, NSF-GK12, NSF IGERT, ONR, Army, Australian Research Council, ONR-Global.

UO Linke lab:

PhD students:Erin CraigEric HoffmanBen LopezBrian LongNate KuwadaPreeti ManiJason Matthews

PostdocAnn Persson

UgradsAdam CaccavanoMike TaorminaTyler HennonSteve BattazzoBenji Aleman (Berkeley)Laura Melling (UCSB)Corey Dow (UCSC)

Collaborations:

Lars Samuelson, Henrik Nilsson, Linus Fröberg (Lund, Sweden)

Martin Zuckermann, Mike Plischke, Matthew Downton, Nancy Forde (Simon Fraser University, B.C.)

Dek Woolfson (Bristol, U.K.)

Tammy Humphrey, Paul Curmi (Sydney)

collective brownian motors - experiments and models

Documents

openloop strategy

feedback implementation

unknowninfo feedback

potential onoff directionality

thermal ratchets

thermal system

spatial asymmetry energy

openloop strategies