AFM Images Bacteria Mosquito eye DNA molecules t&view=article&id=51&Itemid=57

Today’s Topic: AFM ( You will get a demo via Jaya) 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)

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

AFM—Imaging and/or Force y= &nid= &id= Force – one place

eng&ckey= &nid= &id= * * Regular resolution; Super-resolution, ~ 10 nm at somewhat greater expense (>$150k)

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. Most AFM probes are made from silicon and/or silicon nitride (Si 3 N 4 ) wafers using semiconductor-based etching processes. Hook’s Law and AFM y= &nid= &id= Ionic repulsion, bends tip Imaging—Scan Force– 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 x 2 or v 2 : has ½ k B T of energy. A gas molecule at temperature T: Kinetic Energy: ½ mv 2 : Has ½ k B T of energy ½ mv 2 = ½ kT :  v 2 = k B T/m  v = √kT/m : ~ 1000 mph! If you have a spring at finite temperature: Examples? ½ kx 2 = ½ k B T

AFM Cantilever How small of a motion can you measure? Bend a cantilever (in z-direction): ½ kz 2 = ½ k B T (z 2 is the mean square deflection of the cantilever caused by thermal vibrations) z 2 = k B T/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 bio  0.01 N/m = 10 pN/nm: 1 pN causes a deviation of 1 nm) Can measure an Angstrom or less!! k between to 100 N/m (Huge range! Very useful for measuring large range ∆z: F from 1 pN - nN) z k= 0.25Ewh 3 /L 3, 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 ~ (In 1 -In 2 ) / (In 1 + In 2 ) ΔY ~ (Out 1 -Out 2 ) /(Out 1 +Out 2 ) N P N P In 1 In 2 Out 1 Out 2 POSITION SIGNAL Position sensitive detector (PSD) Over a fairly wide range, it’s linear

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

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

Correlation functions Auto-correlation If they’re the probe and sample is same shape. Cross-correlation if probe and sample are different shapes.

The End