Introduction and applications

1. No HW assigned.2. Quiz today3. Bending & twisting rigidity of DNA

with Magnetic Traps.

“MT”

MT is a single molecule biophysics tools.As a s.m. technique, can resolve heterogeneity.

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.

Quiz #3 on Chapter 3 of ECB

1.____________________ 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. 2.Enzymes are catalysts that ______________ the free energy of the reaction’s transition state.3.The free-energy change for a reaction, ΔG, depends on _______________________, _________________and it must be __________ than zero for a reaction to proceed spontaneously.4. 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 __________.5.The measure of a system’s disorder is called ____________________ of the system. 6.This is the constant at which an enzyme is operating at half of its maximum speed. _______________________________7.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. ________________

Catabolic reactionsAnabolic reactions

lower

the concentrations of themolecules less

reductionoxidation

the entropy

KM , Michalis-Menten constant

coupled reaction

Magnetic Tweezers and DNA

Watch as a function of protein which interacts with DNA (polymerases, topoisomerases), as a function of

chromatin: look for bending, twisting.

Can be conveniently used to stretch and twist DNA.

• DNA tends to be stretched out if move magnet up.• DNA also tends to twist if twist magnets (since follows B).(either mechanically, or electrically move magnets)

Forces ranging from a few fN to nearly 100 pN: Huge Range

Dipole moment induced, and B. = x B = 0

U = - . B

F= ( . B) : U ~ -B2.

Δ

It is the gradient of the force, which determines the direction, the force is up. (i.e. where B is highest)

With Super-paramagnetic bead, no permanent dipole.

DNA Structure

Molecular Cell Biology, Lodish

Wikipedia

• Right-hand helix

• One turn: 3.4 nm, ~10.5 bp

• Twist angle between bps θ=36

2nm

polymers DNA

DNA will resist twisting

Magnetic Traps: Measuring twist

DNA twisting

Twisting leads to motion in x-y plane

Antibody

Antibody-ligand

(Reminder) Streptavidin (egg white) -Biotin

http://ambermd.org/tutorial/streptavidin/index.html

The tightest non-covalent bond known roughly ~100kTBiotin + SA ↔ Biotin-SA

Kassoc = [B-SA]/ [B][SA] = 1014M-1

The complex is also extremely stable over a wide range of temperature and pH.

http://faculty.washington.edu/stenkamp/stefanieweb/abstract.html

254 AA = 46 x 93 x 104 Å = 4 x 15kD =60kD

Diffraction rings

ZZ

Focal point

Magnetic Traps: Measuring DNA stretch

Magnetic Trap movie (ADN.SWF) How to attach DNA: to glass; to paramagnetic beadSet-up of Experimental system

Detect nanometer displacements with visible light

Experimental Set-up

N S

Mic

rosc

opy

Video camera CCD

Important Aside: Equipartition Theorem

(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.)

http://en.wikipedia.org/wiki/Equipartition_theorem

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: (3/2)kBT

(1/2)kBT(1/2)kBT

Average energy = (1/2)kBT for every variable which energy depends on quadratic,

e.g. if E x2, or E v2

Force measurement- Magnetic Pendulum

T. Strick et al., J. Stat. Phys., 93, 648-672, 1998

The DNA-bead system behaves like a small pendulum pulled to the vertical of its anchoring point & subjected to Brownian fluctuations

Each degree of freedom goes as x2 or v2 has ½kBT of energy. (HW coming week)

F = kB T l

< x2 >

Do not need to characterize the magnetic field nor the bead susceptibility, just use Brownian motion

Equipartition theorem

½ k < x2 > = ½ kBT

F = k l

½ (F/ l) < x2 > = ½ kBT

Note: Uvert. disp = ½ kl2

Ux displacement = ½ k(l2+x2)Therefore, same k applies to x .

Force measurements- raw data

T. Strick et al., J. Stat. Phys., 93, 648-672, 1998

F = kB Tl< x2 >

(4.04 pN-nm)(7800nm)/ 5772 nm = 0.097 pN

Measure < x2 >, l and have F!

At higher F, smaller x; so does z.

Example: Take l = 7.8 m

Lambda DNA = 48 kbp = 15 m

At low extension, with length doubling, x ~ const., F doubles.

At big extension (l: 12-14 m),x decrease, F ↑10x.

Spring constant gets bigger. Hard to stretch it when almost all stretched out!

Z = l

X

Measure z, measure x

Find F by formula.

Class evaluation1. 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.