Introduction and applications
MT is a single molecule biophysics tools.
As a s.m. technique, can resolve heterogeneity.
“MT”
1. No HW assigned.
2. Quiz today
3. 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.
Quiz #3 on Chapter 3 of ECB
Catabolic reactions
1.____________________
break down food molecules through oxidative pathways and
Anabolic reactions
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
lower
state.
the concentrations of the
3.The free-energy change for a reaction, ΔG, depends on _______________________,
molecules
less
_________________and
it must be __________
than zero for a reaction to proceed
spontaneously.
reduction A
4. A chemical process where there is a net gain of electrons is called ___________.
oxidation
chemical process where there is a net loss of electrons is called __________.
the entropy
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.
KM , Michalis-Menten constant
_______________________________
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
coupled reaction
other useful molecule. ________________
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
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
Watch as a function of protein which interacts with DNA
(polymerases, topoisomerases), as a function of
chromatin: look for bending, twisting.
DNA Structure
• Right-hand helix
• One turn: 3.4 nm,
~10.5 bp
Molecular Cell Biology, Lodish
• Twist angle
between bps θ=36
polymers
Wikipedia
2nm
DNA
DNA will resist twisting
Magnetic Traps: Measuring twist
DNA twisting
s
Twisting leads to
motion in x-y plane
Antibody-ligand
Antibody
(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
Magnetic Traps: Measuring DNA stretch
Diffraction rings
Focal point
Z
Z
Magnetic Trap movie (ADN.SWF)
Microscopy
How to attach DNA: to glass; to paramagnetic bead
Set-up of Experimental system
Detect nanometer displacements with visible light
N
S
Video camera CCD
Experimental
Set-up
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? (1/2)kBT
(1/2)kBT
What is average velocity?
For monotonic gas, what is average translational kinetic energy: (3/2)kBT
http://en.wikipedia.org/wiki/Equipartition_theorem
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=kl
Note: Uvert. disp = ½ kl2
Ux displacement = ½ k(l2+x2)
Therefore, same k applies to x .
½ (F/ l) < x2 > = ½ kBT
T. Strick et al., J. Stat. Phys., 93, 648-672, 1998
kB T l
F = < x2 >
Force measurements- raw data
Measure < x2 >, l
and have F!
Measure z,
measure x
kB Tl
F=
< x2 >
Find F by
formula.
Example: Take l = 7.8 mm
(4.04 pN-nm)(7800nm)/
5772 nm = 0.097 pN
At higher F, smaller x;
so does z.
Z=l
Lambda DNA = 48 kbp = 15 mm
X
T. Strick et al., J. Stat. Phys., 93, 648-672, 1998
At low extension, with length
doubling, x ~ 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!
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.