Introduction and applications

1. Introduction and applications MT is a single molecule biophysics tools. As a s.m. technique, can resolve heterogeneity. magnetic tweezers “MT” • No HW assigned. • Quiz today • Bending & twisting rigidity of DNA with Magnetic Traps. Many slides came from Laura Finzi at Emory University. Some came from Majid Minary-Jolandan, grad. student at UIUC. Others from Carlos Bustamante at UC Berkeley. Helpful comments from David Bensimon.

2. Catabolic reactions • ____________________break down food molecules through oxidative pathways and release energy. __________________ generate the many complex molecules needed by the cell, and they require an energy input. • Enzymes are catalysts that ______________ the free energy of the reaction’s transition state. • The free-energy change for a reaction, ΔG, depends on _______________________, _________________and it must be __________ than zero for a reaction to proceed spontaneously. • A chemical process where there is a net gain of electrons is called ___________. A chemical process where there is a net loss of electrons is called __________. • The measure of a system’s disorder is called ____________________ of the system. • This is the constant at which an enzyme is operating at half of its maximum speed. _______________________________ • What is the name of the reaction in which an energetically favorable reaction is used to drive an energetically unfavorable one that produces an activated carrier molecule or some other useful molecule. ________________ Anabolic reactions lower Quiz #3 on Chapter 3 of ECB the concentrations of the molecules less reduction oxidation the entropy KM , Michalis-Menten constant coupled reaction

3. Magnetic Tweezers and DNA Can be conveniently used to stretch and twist DNA. With Super-paramagnetic bead, no permanent dipole. Watch as a function of protein which interacts with DNA (polymerases, topoisomerases), as a function of chromatin: look for bending, twisting. Dipole moment induced, and ma B. t = m x B = 0 U = - m. B F= (m. B) : U ~ -mB2. Δ It is the gradient of the force, which determines the direction, the force is up. (i.e. where B is highest) • DNA tends to be stretched out if move magnet up. • DNA also tends to twist if twist magnets • (since m follows B). • (either mechanically, or electrically move magnets) Forces ranging from a few fN to nearly 100 pN: Huge Range

4. polymers DNA DNA Structure • Right-hand helix • One turn: 3.4 nm, ~10.5 bp • Twist angle between bps θ=36 Molecular Cell Biology, Lodish Wikipedia 2nm DNA will resist twisting

5. DNA twisting s Magnetic Traps: Measuring twist Twisting leads to motion in x-y plane Antibody-ligand Antibody

6. (Reminder) Streptavidin (egg white) -Biotin The tightest non-covalent bond known roughly ~100kT Biotin + SA ↔ Biotin-SA Kassoc = [B-SA]/ [B][SA] = 1014M-1 The complex is also extremely stable over a wide range of temperature and pH. 254 AA = 46 x 93 x 104 Å = 4 x 15kD =60kD http://faculty.washington.edu/stenkamp/stefanieweb/abstract.html http://ambermd.org/tutorial/streptavidin/index.html

7. Focal point Z Z Magnetic Traps: Measuring DNA stretch Diffraction rings

8. N S Microscopy Video camera CCD Magnetic Trap movie (ADN.SWF) How to attach DNA: to glass; to paramagnetic bead Set-up of Experimental system Detect nanometer displacements with visible light Experimental Set-up

9. Important Aside: Equipartition Theorem Average energy = (1/2)kBT for every variable which energy depends on quadratic, e.g. if E a x2, or E a v2 (In classical statistical mechanics), the equipartition theorem is a general formula that relates the temperature of a system with its average energies. In thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy in the translational motion of a molecule should equal the average kinetic energy in its rotational motion. Note: There are quantum corrections (such at very low temperatures). (But in biophysics, don’t have to worry about.) For example: Simple Harmonic Oscillator at temperature T. What is average displacement? What is average velocity? For monotonic gas, what is average translational kinetic energy: (1/2)kBT (1/2)kBT (3/2)kBT http://en.wikipedia.org/wiki/Equipartition_theorem

10. kB T l F = < x2 > Force measurement- Magnetic Pendulum The DNA-bead system behaves like a small pendulum pulled to the vertical of its anchoring point & subjected to Brownian fluctuations Do not need to characterize the magnetic field nor the bead susceptibility, just use Brownian motion Equipartition theorem Each degree of freedom goes as x2 or v2 has ½kBT of energy. (HW coming week) ½ k < x2> = ½ kBT F = k l Note: Uvert. disp = ½ kl2 Udx displacement = ½ k(l2+dx2) Therefore, same k applies to dx . ½ (F/ l) < x2> = ½ kBT T. Strick et al., J. Stat. Phys., 93, 648-672, 1998

11. Force measurements- raw data kB Tl F = < x2 > Measure < x2 >, l and have F! Measure z, measure dx Find F by formula. Example: Take l = 7.8 mm (4.04 pN-nm)(7800nm)/ 5772 nm = 0.097 pN At higher F, smaller dx; so does dz. Z = l Lambda DNA = 48 kbp = 15 mm At low extension, with length doubling, dx ~ const., F doubles. At big extension (l: 12-14 mm), Dx decrease, F ↑10x. Spring constant gets bigger. Hard to stretch it when almost all stretched out! X T. Strick et al., J. Stat. Phys., 93, 648-672, 1998

12. 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.