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

3. Compaction & Stretching & Rotation is critical for DNA.
1 meter long DNA must be fit inside of a nucleus, ~5-10 mm long.
Every time DNA needs to be expressed, it needs to unwind.
(Has basic and clinical implications)

4. DNA Packaging In Eukaryotic DNA, packaged into nucleosomes: about 2 loops around 4 histone proteins, making about 10 nm “disks”. Disks must be removed when DNA is active.
Histones can be acetylated to make nucleosomes less stable
(We can study what forces hold them together via Magnetic Traps
Keq = 0.9; H3K56Ac increases open fraction 4x
John Van Noort

5. Twisting of DNA is important
Fluoroquinones as anti-cancer agents

6. DNA is naturally super-coiled: crucial for activity.
For every 100 turns, take out 6 and re-seal up. Why?
Answer: makes DNA easier to unwind.
It turns out to be critical for DNA, RNA polymerase…
Body has created tons of proteins to control this.
Topoisomerases: Many drugs operate through interference with the topoisomerases. The broad-spectrum fluoroquinolone antibiotics act by disrupting the function of bacterial type II topoisomerases. Some chemotherapy drugs called topoisomerase inhibitors work by interfering with mammalian-type eukaryotic topoisomerases in cancer cells., helicases, gyrases.

7. DNA in our bodies are supercoiled
6 turns taken out for every 100 turns: Supercoiled Superhelicity = Sometimes goes into Twist, sometimes Writhe
Tw: # of times the two strands wrap around each other
Wr: # of times C crosses itself.
Charvin, Contemporary Physics,2004
Tw= Tw=0
Wr= Wr=2
Linking Number = Twist + Writhe
Lk = Tw + Wr
Example: Phone Cord:
Ex: Hold DNA out straight so that it has no Writhe, add of take out twist, then let fold up (Twist goes into Writhe).

8. Why is DNA is negatively supercoiled?
Helps with compaction of DNA.
Helps unwind DNA– makes it easier to uncoil, separate strands. (Enzymes which do this called Topoisomerases.)
What about archea, some that lives in hot springs?
Yellowstone: Archea
Positively supercoiled
Makes DNA more stable

9. How to Measuring DNA Flexibility (Bending & Twisting) Magnetic Traps
Magnetic Field produces both a force (stretch) and a torque on magnet.
Earth’s magnet field: produces a torque to make a dipole compass.
Two magnets produce a force: stick together, or repel.
MT uses both force and torque to pull and twist a little magnetic dipole attached to end of DNA.
To quantify: need Equipartition Theorem, Brownian Noise
Worm Like Chain– model for extended biopolymer -- DNA (later look at AFM. 

10. Magnetic Tweezers and DNA
Can be conveniently used to stretch and twist DNA.
With Super-paramagnetic bead, no permanent dipole.
Dipole moment induced, and m a B. t = m x B = 0
U = - m . B : U ~ -moB2. Δ
F = - U (Force is always the slope of the energy)
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
More sophisticated experiments: Watch as a function of protein which interacts with DNA (polymerases, topoisomerases), as a function of chromatin: look for bending, twisting.

11. How stiff is DNA, longitudinally, laterally
How stiff is DNA, longitudinally, laterally? Magnetic Trap movie (Web-browser: ADN.SWF) Measureforce.3g2
How to attach DNA: to glass; to paramagnetic bead
Set-up of Experimental system
Detect nanometer displacements with visible light N S
Microscopy
Video camera CCD
Experimental Set-up

12. Magnetic Traps: Attachment of Probe
Antibody-ligand
Antibody

13. Using Brownian noise. To know F, you might need to know size of magnetic field and bead’s susceptibility F = kx Know F, measure x, get k.
Difficult.
Instead, analysis of bead’s Brownian motion.
DNA-bead system acts like a small pendulum
pulled vertically (z) from it’s anchoring point,
subject to Brownian fluctuations (x,y).
[Mag Traps.x y motion.force.swf]

14. Magnetic Traps: Measuring DNA extension
Diffraction rings Z
Focal point
Can get like 10 nm resolution
(with visible or IR ( nm light!)

15. 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.
Derive the Force vs. side-ways motion.
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
F =
kB T l
< x2 >
T. Strick et al., J. Stat. Phys., 93, , 1998

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

17. Answer, and turn in at the end of class.
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.