Introduction and applications Bending & twisting rigidity of DNA - - PowerPoint PPT Presentation

Introduction and applications

Bending & twisting rigidity of DNA with Magnetic Traps.

What we will learn today Magnetic Traps

Tuesday: DNA: Want to twist it and compact it.

• -Essential for life. (1m à 5µm; supercoiled)

Measure via Magnetic Tweezers: apply range of

forces

• -Put a little magnetic particle on end of

DNA: Pull & Twist it with magnets. Measure DNA twist and stretch via microscope. Tell how stiff it is.

• DNA does NOT act like a Hookian Spring—

(F ≠ -kx) acts like a Worm-Like Chain (WLC).

• DNA twisted like Right-handed Helix—makes

difference if you over- or under-wind it.

Magnetic particle

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.

(either mechanically, or electrically move magnets) Forces ranging from a few fN to nearly 100 pN: Huge Range Dipole moment induced, and µ α B. τ = µ 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 = E = - µ . B : µ is proportional to B: U ~ -µοB2. Δ F = - U (Force is always the slope of the energy) What is force, energy? What is Torque?

• DNA also tends to twist if twist magnets (since µ follows B).

(either mechanically, or electrically move magnets)

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

(Web-browser, Safari: 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

N S

Microscopy

Video camera CCD

Measureforce.3g2

Diffraction rings Z Z

Focal point

Magnetic Traps: Measuring DNA extension

Z: Can get like 10 nm resolution (with visible or IR (500-1000 nm light!) Move objectives up/down at calibrated steps (~ 100 nm over several microns). Use as a reference for actual experiment. Find the (x, y) center to determine the location within 1 nm! (in 1 second) X,Y,Z are then used with

• bjective fixed

and something is changing Z. 1-5 µm bead Can go to ~10,000 Hz!

To know F, you need to know size of magnetic field (B) and bead’s susceptibility µο F = kx Know F, measure x, get k.

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]

How to measure Force?

Ideas? U = - µ . B : U ~ -µοB2 Δ F = - U (Force is always the slope of the energy)

Instead, use Brownian noise.

Difficult.

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]

How to measure Force?

Using Brownian noise of bead motion.

Force measurement- Magnetic Pendulum

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

Looks like regular pendulum with force not equal to gravitational force but due to magnetic force.

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

Looks just like a pendulum acting under the force of gravity!

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

< δx2 >

½ k < δx2 > = ½ kBT F = k l ½ (F/ l) < δx2 > = ½ kBT

Note: Uvert. disp = ½ kl2 Uδx displacement = ½ k(l2+δx2) Therefore, same k applies to δx .

Force measurements- raw data

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

F = kB TL < δx2 >

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

Measure < δx2 >, L and get F

At higher F, smaller δx; so does δz. Example: Take L = 7.8 µm Lambda DNA = 48 kbp = 15 µm At low extension, with length doubling, δx ~ const., F doubles. At big extension (L: 12-14 µm), Δx decrease, F ↑10x. Spring constant gets bigger. Hard to stretch it when almost all stretched out!

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.