Announcements Mid-Term Test next Tuesday in class! (Oct. 7 th, 9:30-11am, Rm 136LLP) Will cover all of classes Lec 1-10 plus (qualitatively) on Lec 11– Lec 11: The difference between Hook’s Law, FJC, WLC; Prions (what they are, why unique, why Nobel Prize) (Today is Lec 12) Go over: Lecture notes (on Web). Make sure you can do all problems on Homework. Reading: Chpt 1 of Berg; Scientific American Article on Molecular Biol. Of Cell. The exam: Some qualitative questions (Explain the structure of DNA; explain why the Central Dogma of Molecular Biology has been modified recently and explain why RNA has played a role in this.) Know how many k B T’s are in ATP and how many pN-nm (and why there is a range). Some quantitative questions:  G,  H,  S. Boltzmann Distribution.

Questions related from Last Time

Simple, but excellent Videos about Prions

Simple, but excellent Videos about Prions

Two Models of DNA (simple) Freely Jointed Chain (FJC) & (more complicated) Worm-like Chain (WLC) Idealized FJC: Realistic Chain: FJC: Head in one direction for length b, then turn in any direction for length b. [b= Kuhn length = ½ P, where P= Persistence Length] WLC: Have a correlation length FJC: Completely straight, unstretchable. No thermal fluctuations away from straight line are allowed The polymer can only disorder at the joints between segments FJC: Can think of DNA as a random walk in 3-D.

Today’s Topic: AFM 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. Force Mode: Worm Like Chain model of Protein Folding (as well as DNA)

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

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? How to determine? Bend a cantilever (in z-direction): ½ kz 2 ½ k B T = ½ kz 2 (z 2 is the mean square deflection of the cantilever caused by thermal vibrations) What is k? Stiffer material? h, w, L go up or down? z 2 = k B T/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 ∆z, F: 1 pN - nN) Say, typical: 1 N/m = 1nN/nm: 1 nN causes deviation of 1 nm 1 nN usually really large  0.01 N/m = 10 pN/nm: 1 pN would cause a deviation of 1 nm) Can measure an Angstrom or less!! k = 0.25Ewh 3 /L 3, where E = modulus of Elasticity (how stiff the material is).

AFM — Force y= &nid= &id= Force – one place

Reversible Unfolding of Individual Titin Immunoglobulin Domains by AFM, Science, M. Reif, H. Gaub, 1997 Reversible Unfolding by AFM Pulling on Titin Gold Simple model: Upon reaching a certain force (peaks, e.g. 1), the abrupt unfolding of a (Titin) domain lengthens the polypeptide by 28 to 29 nm and reduces the force (troughs) to that of the value predicted by the force extension curve of the enlarged polypeptide (2). Start on next domain. As it’s pulling, polymer behaves like WLC. Why does curve look like it does? Why non-linear? Why repeat? Does repeat tell you anything about polymer?

Class evaluation 1. What was the most interesting thing you learned in class today? 2. What are you confused about? 3. Related to today’s subject, what would you like to know more about? 4. Any helpful comments. Answer, and turn in at the end of class.