Today’s take-home lessons(i.e. what you should be able to answer at end of lecture)

FRET – why it’s useful, R-6 dependence; R0 (3-7 nm), very convenient.

1. Homework assigned #6 due next Monday, 4/12 in class.2. Next Monday 4/12: Klaus Schulten birds and

magnetotaxis.3. Next Wednesday 4/14: VMD (computer analysis)

Today’s Announcements

1. Two models of DNA: A ________________________model assumes that DNA chains are completely straight, unstretchable. No thermal fluctuations away from straight line are allowed. The polymer can only disorder at the joints between segments. A ______________________model assumes that DNA chains have a correlation length called the persistence length.

3. Resolution of a microscope is (classically) limited by Heisenberg uncertainty principle and is equal to __________________.

Quiz

2. DNA has both twist and writhe. What is the twist and writhe number in the follow graph?

Left:_______ ________, Center: ____ _________,Right: _____ _________

Freely jointed chain (FJC)

Worm-like chain (WLC)

Tw = 0, Wr = 0

Tw = 2, Wr = 0Tw = 0, Wr = 2

λ/2 N.A

5. There are three families of motor proteins called: _______ ______ and _______.6. List two advantages of two-photon microscopy: ______________________ and ______________________________.

4. If you excite a fluorescent molecule with light of a certain wavelength, the molecule will emit light at a ______________ wavelength.longer

Kinesin, Myosin, Dynein Low light scattering

Inherent z-resolution (or confocality)

FRET

FRET: measuring conformational changes of single biomolecules

The distance interactions between green and red light bulbs can be used to deduce the shape of the scissors during the function.

FRET useful for 20-80Å

FRET is so useful because Ro (2-8 nm) is often ideal

Bigger Ro (>8 nm) can use FIONA-type techniques

Reminder: Fluorescence properties.

Abso

rptio

n

WavelengthFluorescence

Stokes Shift (10-100 nm)

Excitation from lowest ground state to excited states (fsec).Relaxation to lowest excitation singlet state (psec).Transition to multiple ground states (nsec).

Lifetimes and Quantum Yields

Lifetime (d): exp(-/d): 1-100nsec

d = 1/k

Quantum yield() : krad/ (krad +knon-rad)

[how much of excited-state energy goes into light vs. heat]

d, k

Fluorescence Resonance Energy Transfer (FRET)

EnergyTransfer

Donor Acceptor

Dipole-dipole Distant-dependentEnergy transfer

AD

R0AD

D A

R (Å)0 25 50 75 100

0.0

0.2

0.4

0.6

0.8

1.0

E

Ro 50 Å

60 )/(1

1

RRE

Spectroscopic Ruler for measuring nm-scale distances, binding

Time

Time

Look at relative amounts of green & red

Derivation of 1/R6

60 )/(1

1

RRE

knon-distance = knd = kf + kheat

EnergyTransfer

Donor Acceptor

kET

E.T. = kET/(kET + knd)

E.T. = 1/(1 + knd/kET)

How is kET dependent on R?knd

E.T. = 1/(1 + 1/kETD)

E.T. = function (kET, knd)

Classically: How is kET dependent on R?

Classically: E.T. goes like R-6 , Depends on Ro

How does electric field go like?

Far-field:

Near-field: 1/R3 (d << )

1/R2

Dipole emitting: Energy = U =

So light absorbed goes like:

peE = pe/R3 (E = electric field)

Dipole absorption:Probability that absorbing molecule (dipole) absorbs the light paE

E.T. = 1/(1 + 1/kETD)

E.T. = 1/(1 + (R6/Ro6))

paE x peE = papeE2 = pepa/R6

E.T. = 1/(1 + knd/kET)

Quantum MechanicallyDetermine Hamiltonian (Energy) of Interaction.

By Fermi’s Golden Rule, rate goes like H2.

Dipoles interacting:

Dipolar Interaction depends on R3:

E.T. = H2 = R6

Terms in Ro

61

2421.0 nJqRo D in Angstroms

where J is the normalized spectral overlap of the donor emission (fD) and acceptor absorption (A)

(Draw out a() and fd() and show how you calculate J.)

Donor Emission

http://mekentosj.com/science/fret/

Donor Emission

http://mekentosj.com/science/fret/

Acceptor Emission

Acceptor Emission

Spectral Overlap terms

http://mekentosj.com/science/fret/

Spectral Overlap between Donor & Acceptor Emission

For CFP and YFP, Ro, or Förster radius, is 49-52Å.

(J)

With a measureable E.T. signal

http://mekentosj.com/science/fret/

E.T. leads to decrease in Donor Emission & Increase in Acceptor Emission

How to measure Energy TransferDonor intensity decrease, donor lifetime decrease, acceptor

increase.

E.T. by increase in acceptor fluorescence and compare it to residual donor emission. Need to compare one sample at two and also measure their quantum yields.

E.T. by changes in donor.Need to compare two samples, d-only, and D-A.

Where are the donor’s intensity, and excited state lifetime in the presence of acceptor, and ________ are the same but without the acceptor.

AD

R0AD

D A

Time

Time

Orientation Factor

where DA is the angle between the donor and acceptor transition dipole moments, D (A) is the angle between the donor (acceptor) transition dipole moment and the R vector joining the two dyes.

2 ranges from 0 if all angles are 90°, to 4 if all angles are 0°, and equals 2/3 if the donor and acceptor rapidly and completely rotate during the donor excited state lifetime.

x

y

z

D

AR A

DDA

This assumption assumes D and A probes exhibit a high degree of rotational motion

2 is usually not known and is assumed to have a value of 2/3 (Randomized distribution)

The spatial relationship between the DONOR emission dipole moment and the ACCEPTOR absorption dipole moment

(0< 2 >4)2 often = 2/3

Orientation of transition moments of cyanine fluorophores terminally attached to double-stranded DNA.

Iqbal A et al. PNAS 2008;105:11176-11181

Simulation of the dependence of calculated efficiency of energy transfer between Cy3 and Cy5 terminally attached to duplex DNA as a function of the length of the helix.

Iqbal A et al. PNAS 2008;105:11176-11181

Efficiency of energy transfer for Cy3, Cy5-labeled DNA duplexes as a function of duplex length.

Iqbal A et al. PNAS 2008;105:11176-11181Orientation Effect observed, verified!

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.