Adventures in nanoscale mechanics

Peter M. Hoffmann

Department of Physics & Astronomy

Wayne State University

What’s so special about the nanoscale?

Nano tech nol o gy

Noun, From the Greek, for “give me money for

funding”.

Silicon

What is so special about the nanoscale? Breakdown of continuum picture

Energy transduction and Conversion:

chemical-electrostatic-mechanical-thermal

Rob Philips, Steven Quake, Physics Today May 2006

What is so special about the nanoscale? Convergence of energy scales

What is so special about the nanoscale? Can see onset of collaborative effects which lead to long times

scales

Fast

Slow

Nanosystem examples • Nanoconfined liquids • Single biomolecules • Molecular machines

(Nano)Confined liquids- Why? • Biology:

• Biomolecular structure, • biochemical processes, • thermal reservoir, thermal noise (molecular machines) • Interactions with biological surfaces • Origin of Life

• Nanoscience: • Local order creation – influence on self-assembly • Flow through narrow channels, nanofluidics • Nanotribology • Colloid science • Phase transformations on surfaces • Wetting

•Oil & gas extraction

Water, water everywhere: The crowded cell

David Goodsell: “The machinery of life”

Water and Life • All known life relies on water • Solvent for biologically important molecules • Determines structure of macromolecules (hydrophilic, hydrophobic)

• Drives self-assembly, protein folding etc. • Transport medium, dissolves ions • Thermal reservoir & source of thermal noise

Geology, 2005

Water in porous rock, oil recovery

What happens when you squeeze a liquid to just a few nanometers?

Measuring mechanics at the nanoscale: The Atomic Force Microscope (AFM)

What kind of forces could we expect at the nanoscale (molecules) ? ..and how could we measure such forces ? Need: ‘Back-of-the-envelope’ calculation

Energy of a weak bond ≈ 0.1 eV ≈ 10-20 J

Length of a bond: a few Angstrom = 0.1 nm = 10-10 m

Work to break a bond = Energy of bond = Force x Distance, Therefore: Force = Energy/Length of bond ≈ 10-20J/10-10m = 10-10 N = 100 pN

Stiffness of ‘spring’ of bond: Hooke’s law: F = - k x Therefore: k ≈ 10-10 N/(10-10 m) = 1 N/m!

13

Homebuilt AFM

Measurement procedure

Oscillate at small amplitude: 0.05-0.2 nm

Move at low speed: 0.2 - 1.8 nm/s

Measure amplitude & phase

Our measurements: Probing dynamics

Measure amplitude & phase

Stiffness & damping

Mechanical relaxation time: low for liquid, high for solid

R

h

RtR

h

2 Å/s = 1 ft/50yrs

8 Å/s

14 Å/s

Silicon

What is so special about the nanoscale?

Breakdown of continuum picture

• When liquid is confined, motion is restricted to quasi 2D

• For liquid to move out of the way, many molecules have to move collectively.

A simple argument…

N

Np

p

2

1

2

11

molecules47

1

10

0

14

0

N

sp

s

N

N

Collective dynamics gives long relaxation times

What is so special about the nanoscale? Can see onset of collaborative effects which lead to long times

scales

Fast

Slow

Water, compressed at 0.2 nm/s

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

0.00E+00 1.00E-09 2.00E-09 3.00E-09 4.00E-09 5.00E-09

Vis

cosi

ty (

Pa

s)

Tip-surface separation (m)

Water, compressed at 1.4 nm/s

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

1.60E-03

0.00E+00 1.00E-09 2.00E-09 3.00E-09 4.00E-09 5.00E-09

Vis

cosi

ty (

Pa

s)

Tip-surface separation (m)

Changing gear….

1.75 m A few cm

X 100

20 microns

1000x

0.2-20 nm 1000 X

AFM: Pulling Molecules

EA DG ki

k0

Measurable Parameters:

Activation barrier height, E*

Position of activation barrier, x*

Shape of potential around Eb

Change in free energy/depth of energy well, DG

Stiffness of bond/ curvature of energy, ki

Off-rate at zero force, k0

Diffusion, friction, metastable states

Dissipated work, Wdis

Eb

Wdiss

x*

Polymer linker

(PEG)

27

Single molecule

Protein Interactions

Mechanics, dynamics and regulation of biological macromolecules and

molecular assemblies

28

Single molecule

0 20 40 60 80 100 120

-200

0

200

400

600

p

N)

distance(nm)

x*

Umax

Effect of applied force: Lowering of activation barrier

29

Single molecule

0 200 400 600 8000

10

20

30

40

50

0 200 400 600 8000

10

20

30

40

50

0 200 400 600 8000

10

20

30

40

50

0 200 400 600 8000

10

20

30

40

50

0 200 400 600 8000

20

40

60

0 200 400 600 8000

20

40

60

0 200 400 600 8000

10

20

30

40

50

0 200 400 600 8000

20

40

60

80

Monte-Carlo simulations of rupture events – Which tail is it?

Multiple bonding ? Heterogeneous bonding?

-500 0 500 1000 1500 2000 25000.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

pN

-1

Unibinding force (pN)

0 500 1000 1500 2000 2500 30000.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

pN

-1

Unbinding force (pN)

a b

Figure X1: AFM measurements of binding between TIMP1 (Fig. a) and TIMP 2 (Fig. b) on live cells expressing MT1-MMP (inset

to Fig. b). Fig. a shows predominantly non-specific binding (maximum probability for zero force) of TIMP1, while b shows strong

affinity of TIMP2 to MT1-MMP (most probable force ~500 pN). Inset a: Control: Binding probability for TIMP2 on cells without

MMP (EV) and with MMP (GPI) shows that about 60-70% of binding events are specific. For TIMP1 no significant difference is

observed.

Single protein force measurements on live cancer cells

A new instrument • Olympus IX-81 Fluorescence

microscope w. epifluorescence, TIRF, phase, DIC, lasers: 405, 488, 561, 640 nm, two cameras, one very high resolution, dual view

• Bruker Catalyst AFM w. peak force

imaging, perfusion capability, EasyAlign setup etc.

Force (recognition) imaging of (PS + LBP) membranes using a cantilever functionalized with

MEMO-linker molecules and αLBP antibodies.

Roes S et al. J. Biol. Chem. 2006;281:2757-2763

©2006 by American Society for Biochemistry and Molecular Biology

Total Internal Reflection Fluorescence (TIRF)

Single molecule

Single myosin, imaged with TIRF:

When a molecule becomes a machine

Fastest AFM in the World: Toshio Ando, Kanazawa University, Japan

~ 100 nm

150 ms/frame

What is so special about the nanoscale?

(4) Predominance of thermal noise

Feynman’s Ratchet

The ratchet, the reset, and the second law

Needs a reset step...

... powered by a supply of energy ... and an asymmetric energy landscape.

Hill 1938, Frog muscle

-5

0

5

10

15

20

25

0 1 2 3 4 5 6

Speed v

Simulation of damped diffusion on an oscillatory tilting sawtooth potential (stochastic differential equation, Markov process)

Do actual molecular machines really work like this?

Conclusions and Acknowledgments • AFM is a versatile tool to measure nanomechanical properties of nanosystems

• Liquids deviate strongly from bulk behavior when nanoconfined :

• Ordering • Divergence of relaxation time scales • Altered viscoelastic behavior • New, surprisingly complex phenomena

• AFM is a useful tool for single-molecule studies on live cells and can be combined

with optical methods. Acknowledgments: My students: Shah Khan, Venkatesh Subba-Rao, Essa Mayyas, George Matei, Ed Kramkowski, David Wilson, Anwesha Sakar. Post-docs: Shivprasad Patil, Mircea Pantea. Funding: NSF-DMR 0804283, WSU Nano@Wayne

45