AFM Images

Bacteria

Mosquito eye

DNA molecules

http://www.afmhelp.com/index.php?option=com_content&view=article&id=51&Itemid=57

Today’s Topic: AFM(Next Time: FIONA)

• Experimental Approach via Atomic Force Microscopy• AFM: Can see Nanometer & Angstrom scale changes!• How you can see this: Hook’s Law• Imaging Mode, Force Mode.• To minimize noise, go to a higher frequency :

noise always goes like 1/f (f = frequency)• Force Mode: Worm Like Chain model of Protein Folding (and

DNA)

http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf

AFM—Imaging and/or Force

http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141

Ionic repulsion,bends tip

Imaging – ScanMuller,

Biochemistry, 2008

Measure (z-axis) distance,Or

Constant force (by altering distance with feedback)

http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf

AFM—Imaging and/or Force

http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141

Force – one place

http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141

*

* Regular resolution; Super-resolution, ~ 10 nm at somewhat greater expense (>$150k)

Diff. types of Microscopes(Diff. , techniques, diff. resolution)

MBC, Fig. 4-

1000x, 0.2 um 106x, 2 nm 20,000x 10 nm (3-D)

Or with CCD

TransmittedLight

Resolution of microscope ~/2, where is different for different techniques

Measuring forcesThe force is not measured directly, but calculated by measuring the deflection of the lever, and knowing the stiffness of the cantilever. Hook’s law gives F = -kz, where F is the force, k is the stiffness of the lever, (in Newtons/meter) and z is the distance the lever is bent.

http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf

Most AFM probes are made from silicon and/or silicon nitride (Si3N4) wafers using semiconductor-based etching processes.

Hook’s Law and AFM

http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141

Ionic repulsion,bends tip

Imaging—ScanForce– one place

Can measure Angstrom resolution – Nobel Prize, 1986

What determines how accurately you can measure?

If photodetector was on the moon, could you see infinitely small changes?

Brownian Noise & Equipartition Theorem

Each degree of freedom in Energy goes as x2 or v2 : has ½ kBT of energy.

A gas molecule at temperature T: Kinetic Energy: ½ mv2 : Has ½ kBT of energy

½ mv2 = ½ kT : v2 = kBT/m v = √kT/m : ~ 1000 mph!

If you have a spring at finite temperature:

Examples?

½ kx2 = ½ kBT

AFM CantileverHow small of a motion can you measure?

Bend a cantilever (in z-direction):½ kz2 = ½ kBT

(z2 is the mean square deflectionof the cantilever caused by thermal vibrations)

z2 = kBT/k = 0.64Å/√k at 22˚C (where k is in N/m)

Say, 1 N/m = 1 nN/nm: 1 nN causes deviation of 1 nm

1 nN really large for bio0.01 N/m = 10 pN/nm: 1 pN causes a deviation of 1 nm)

Can measure an Angstrom or less!!

k between 0.001 to 100 N/m (Huge range! Very useful for measuring large range ∆z: F from 1 pN - nN)

z

k= 0.25Ewh3/L3, where E = modulus of Elasticity (Non-trivial but based on F= kL) --see Joe Howard,

Mechanics of Motor Proteins…

What is k?

(E, how stiff the material is).

ΔX ~ (In1-In2) / (In1 + In2)

ΔY ~ (Out1-Out2) /(Out1+Out2)

N

P

N

P

In1 In2

Out1

Out2

POSITION

SIGNAL

Position sensitive detector (PSD)

Over a fairly wide range, it’s linear

Typically, probe radius varies from 5 to 20 nm

http://webserv.jcu.edu/chemistry/faculty/waner/research/AFM/tipconv.htm

If tip size is large, have to worry about distortions

Convolution

Convolution of tip and sample size

http://webserv.jcu.edu/chemistry/faculty/waner/research/AFM/tipconv.htm

Tobacco Mosaic Virus (TMV)

In truth, diameter of 180 Å. Due to finite tip size, w~ 350 A

Cross-correlation

Cross-correlation

Correlation functions

http://www.scholarpedia.org/article/1/f_noise

The End