Introduction and applications

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.

DNA Structure: will resist twisting

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

Compaction & Stretching & Rotation is critical for DNA.Compaction:

1 meter long DNA must be fit inside of a nucleus, ~5-10 m long.

Every time DNA needs to be expressed, it needs to unwind.(Has basic and clinical implications)

DNA PackagingIn 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.

Keq = 0.9; H3K56Ac increases open fraction 4x

http://www.youtube.com/watch?v=9kQpYdCnU14

Histones can be acetylated to make nucleosomes less stable (We can study what forces hold them together via Magnetic Traps

John Van Noort

Twisting of DNA is importantFluoroquinones as anti-cancer agents

https://www.youtube.com/watch?v=IkKZ_gxAOXI

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.

https://www.youtube.com/watch?feature=player_detailpage&v=IkKZ_gxAOXI

DNA is naturally super-coiled: crucial for activity.

DNA in our bodies are supercoiled

6 turns taken out for every 100 turns: Supercoiled

Superhelicity = -0.06.

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=2 Tw=0

Wr=0 Wr=2Example: Phone Cord:

Linking Number = Twist + WritheLk = Tw + Wr

Ex: Hold DNA out straight so that it has no Writhe, add of take out twist, then let fold up (Twist goes into Writhe).

Why is DNA is negatively supercoiled?

Positively supercoiled

• Helps unwind DNA– makes it easier to uncoil, separate strands. (Enzymes which do this called Topoisomerases.)

Makes DNA more stable

What about archea, some that lives in hot springs?

Yellowstone: Archea

http://www.ucmp.berkeley.edu/archaea/archaea.html

• Helps with compaction of DNA.

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.

Magnetic Tweezers and DNA

More sophisticated experiments: 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

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.

U = - . B : U ~ -B2.Δ

F = - U (Force is always the slope of the energy)

How stiff is DNA, longitudinally, laterally?Magnetic Trap movie

(Web-browser: ADN.SWF) Measureforce.3g2 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

Magnetic Traps: Attachment of Probe

Antibody

Antibody-ligand

Using Brownian noise.To know F, you might need to know size of

magnetic field and bead’s susceptibilityF = 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]

Diffraction rings

ZZ

Focal point

Magnetic Traps: Measuring DNA extension

Can get like 10 nm resolution (with visible or IR (500-1000 nm light!)

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.

Do not need to characterize the magnetic field nor the bead susceptibility. Just use Brownian motion.

Equipartition theorem:

Derive the Force vs. side-ways motion.

F = kB T l

< x2 >

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 get 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 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.