AFM Images Bacteria DNA molecules Mosquito eye 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)
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) http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141
AFM—Imaging and/or Force Force – one place http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141
Super-resolution, ~ 10 nm at somewhat greater expense (>$150k) * * Regular resolution; Super-resolution, ~ 10 nm at somewhat greater expense (>$150k) http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141
Diff. types of Microscopes (Diff. l, techniques, diff. resolution) MBC, Fig. 4- Or with CCD 1000x, 0.2 um 106x, 2 nm 20,000x 10 nm (3-D) Transmitted Light Resolution of microscope ~l/2, where l is different for different techniques
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 http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&ckey=1774141&nid=-33986.0.02&id=1774141
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
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 0.001 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 bio0.01 N/m = 10 pN/nm: 1 pN causes a deviation of 1 nm) Can measure an Angstrom or less!!
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
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 http://webserv.jcu.edu/chemistry/faculty/waner/research/AFM/tipconv.htm
Convolution of tip and sample size Tobacco Mosaic Virus (TMV) In truth, diameter of 180 Å. Due to finite tip size, w~ 350 A http://webserv.jcu.edu/chemistry/faculty/waner/research/AFM/tipconv.htm
Correlation functions Cross-correlation Cross-correlation http://www.scholarpedia.org/article/1/f_noise
The End