1. AFM Images Bacteria Mosquito eye DNA molecules http://www.afmhelp.com/index.php?option=com_conten t&view=article&id=51&Itemid=57

2. 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)

3. 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&cke y=1774141&nid=-33986.0.02&id=1774141 Ionic repulsion, bends tip Imaging – Scan Muller, Biochemistry, 2008 Measure (z-axis) distance, Or Constant force (by altering distance with feedback)

4. 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&cke y=1774141&nid=-33986.0.02&id=1774141 Force – one place

5. 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)

6. 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. http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf 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 http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&cke y=1774141&nid=-33986.0.02&id=1774141 Ionic repulsion, bends tip Imaging—Scan Force– one place Can measure Angstrom resolution – Nobel Prize, 1986

7. 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

8. 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 0.001 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).

9. 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

10. 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

11. 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

12. Correlation functions http://www.scholarpedia.org/article/1/f_noise Auto-correlation If they’re the probe and sample is same shape. Cross-correlation if probe and sample are different shapes.

13. The End