1. AFM Images Bacteria DNA molecules Mosquito eye

2. 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)

3. AFM—Imaging and/or Force
Muller,
Biochemistry, 2008
Ionic repulsion,
bends tip
Imaging – Scan
Measure (z-axis) distance, Or
Constant force (by altering distance with feedback)

4. AFM—Imaging and/or Force
Force – one place

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

6. Diff. types of Microscopes (Diff. l, techniques, diff. resolution)
MBC, Fig. 4-
Or with CCD
1000x, 0.2 um x, 2 nm ,000x 10 nm (3-D)
Transmitted
Light
Resolution of microscope ~l/2, where l is different for different techniques

7. Hook’s Law and AFM Imaging—Scan Force– one place Ionic repulsion,
bends tip
Most AFM probes are made from silicon and/or silicon nitride (Si3N4) wafers using semiconductor-based etching processes.
Measuring forces
The 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.
Can measure Angstrom resolution – Nobel Prize, 1986

8. 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.
Examples?
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:
½ kx2 = ½ kBT

9. AFM Cantilever How small of a motion can you measure?z
Bend a cantilever (in z-direction): ½ kz2 = ½ kBT
(z2 is the mean square deflection
of the cantilever caused by thermal vibrations)
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).
z2 = kBT/k = 0.64Å/√k at 22˚C (where k is in N/m)
k between to 100 N/m
(Huge range! Very useful for measuring large range ∆z: F from 1 pN - nN)
Say, 1 N/m = 1 nN/nm: 1 nN causes deviation of 1 nm
1 nN really large for bio0.01 N/m = 10 pN/nm: 1 pN causes a deviation of 1 nm)
Can measure an Angstrom or less!!

10. Position sensitive detector (PSD)
In1
In2
Out1
Out2
POSITION
SIGNAL
ΔX ~ (In1-In2) / (In1 + In2)
ΔY ~ (Out1-Out2) /(Out1+Out2)
Over a fairly wide range, it’s linear

11. have to worry about distortions
If tip size is large,
have to worry about distortions
Convolution
Typically, probe radius varies from 5 to 20 nm

12. Convolution of tip and sample size
Tobacco Mosaic Virus (TMV)
In truth, diameter of 180 Å.
Due to finite tip size, w~ 350 A

13. Correlation functions
Cross-correlation
Cross-correlation

14. The End