### k 2

```Today’s Topic (02/03/14)
How did 1st week of labs go?
Polarization assays—important for k2 and for
binding assays (Lab 2)
Fluorescence Polarization
Important for binding assays
Also important for k2.
1. Dyes have a transition absorption
dipole moment
If light is polarized in direction of
dipole,
, will absorb light; if
polarized perpendicular to light,
it won’t absorb it.
Signal proportional to sinQa, Qa is
angle between light vector and
dipole moment vector.
2. Once molecule is excited, then has
probability of emitting, via an emission
dipole moment, (which tends to be
aligned with the absorption dipole
moment).
The probability that it will make it
through the analyzer is sinQe, Qe is angle
between emission dipole vector and
analyzer.
Coordinate system
Excited fluorophores
How to measure FP
perpendicular (
Polarization
Anisotropy
(0 to 0.5)
(0 to 0.4)
parallel (
)
Polarization & Anisotropy: Just slightly different forms
Generally use Anisotropy because of simpler forms when time-dependent.
Also simpler when have multiple components:
A = SciAi where ci is the mole fraction of the ith component.
)
Polarization vs. Anisotropy
Denominators with P, A
Polarization
P defined by analogy
with dichroism ratio
Anisotropy
The denominator of Anisotropy
is simply the total light that
would be observed if no
polarizers were used. (Come in
along x-axis.)
Call Iz = I||
Call Iy = I
Non-polarized light
(along x-axis)
Break into Iz, Iy.
Call Ix = I
Ix+ Iy + Iz = 2 I + I||
Anisotropy is a more useful form for experimental data on complex systems
Generally use Anisotropy because of simpler forms when time-dependent.
Also simpler when have multiple components:
A = SciAi where ci is the mole fraction of the ith component.
Polarization
Can measure the average polarization (easiest),
Or the time-dependent (nanosecond lifetime) polarization (most informative)
http://www.lifetechnologies.com/us/en/home/references/
molecular-probes-the-handbook/technical-notes-andproduct-highlights/fluorescence-polarization-fp.html
FP set-up in a microscope
Anisotropy
Perrin equation (Perrin, 1926): A0/A=1+6Dt,
including the rotational diffusion coefficient
(D), fluorescence lifetime (t) and, more
significantly, the fundamental anisotropy (A0)
which varies according to wavelength
(Lakowicz, 1999; Weber & Shinitzky, 1970).
http://www.urmc.rochester.edu/imaging/research/tho
mas-foster/fluorescence-anisotropy.aspx
FP applied to binding
Competition monitored via FP
Homogeneous Assays, no labeling competitors
http://labs.fhcrc.org/hahn/Methods/biochem_meth/
beacon_fluorescence_guide.pdf
Competition monitored by FP
Competitive Binding monitored by FP
Anything that adds mass can be used
in FP: Homogeneous Assay
http://www.iss.com/resources/research/technical_notes/PC
1_FP.html
Examples
(from Life Technologies)
Examples of FP (in crystals)
GFP Crystals: Fluorescence
polarization of needle-shaped
GFP crystals revealed by false color. The
fluorescence of the crystals is strongly
polarized parallel to the needle axis. Hue
in this color image represents the
polarization orientation with maximum
fluorescence. Purified GFP extracted from
the jellyfish Aequorea was generously
provided by Osamu Shimomura and
crystals were prepared by Naoki Noda,
following the description given by Inoué
et al. (Inoue, S., O. Shimomura, M. Goda,
M. Shribak and P. T. Tran. 2002.
Fluorescence polarization of green
fluorescence protein. Proc Natl Acad Sci U
S A 99: 4272-7.)
http://openpolscope.org/pages/Fl
uorescence_Polarization.htm
Example of living cell FP
Septin-GFP constructs in MDCK Cell: Fluorescence
image of a living cell (MDCK) expressing septin
molecules linked to green fluorescent protein (GFP). The
image was recorded with the Fluorescence LC-PolScope
which reveals the polarized fluorescence of septin fibers
in false color. Each hue is associated with a different
orientation of the GFP dipoles, which in turn reflect the
fiber orientation, as septin-GFP molecules are locked
into the fiber assembly. The white color of the
fluorescence from the cytosol, on the other hand,
reveals the lack of a common alignment of septin-GFP
molecules suspended in the cytosol. Credit: Bradley
DeMay and Amy Gladfelter, Dartmouth College.
http://openpolscope.org/pages/
Fluorescence_Polarization.htm
Anisotropy and time-dependence
http://www.ursabioscience.com/technology/particle-probes
Anisotropy and time-dependence
For a spherical particle:
Rotational correlation time:
tc = 1/6Drot = Vhh/kBT
Where h = viscosity: Vh = hydrated molecular volume
A(t) = Ao exp(-t/tc)
Hydrated specific volume = 1g/ml
Hydrated volume = M/No
Roughly tc = 1 nsec for each 2,400 daltons of protein molecular weight
and for globular nucleic acids
k2 and Ro in FRET
1
E
1  ( R / R0 )6
Ro = 0.21( JqD n k
-4
2
)
1
6
in Angstroms
• J is the normalized spectral overlap of the donor emission (fD) and
acceptor absorption (eA) . Does donor emit where acceptor absorbs?
• qD is the quantum efficiency (or quantum yield) for donor emission
in the absence of acceptor (qD = number of photons emitted divided
by number of photons absorbed).
• n is the index of refraction (1.33 for water; 1.29 for many organic
molecules).
• k2 is a geometric factor related to the relative orientation of the
transition dipoles of the donor and acceptor and their relative
orientation in space. Very important; often set = 2/3.
k2 : Orientation Factor
The spatial relationship between the DONOR emission dipole moment and the
ACCEPTOR absorption dipole moment
y
qD
D
R
z
qDA q
A
A
(0< k2 >4)
k2 often = 2/3
x
where qDA is the angle between the donor and acceptor transition dipole
moments, qD (qA) is the angle between the donor (acceptor) transition dipole
moment and the R vector joining the two dyes.
k2 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
 k 2 is usually not known and is assumed to have a value of 2/3
(Randomized distribution)
 This assumption assumes D and A probes exhibit a high degree of rotational motion
Can measure whether donor & acceptor randomize by looking at polarization.
A range of k2 leads to range of E, Ro
The maximum range of k2 is given by
where Ad and Aa are the anisotropy of AF488 (donor) and AF568 (acceptor),
respectively.
Dale et al, Biophysical J. 1979
The End
Extra Slides
We briefly mentioned how Green Fluorescent
Protein (GFP) can be perfectly labeled in vivo
because it is placed in a cell by genetic means,
i.e. through DNA attached to another protein’s
DNA (like kinesin-GFP fusion, shown), and then
the DNA is transfected inside the cell. GFP now
comes in many colors.
Green Fluorescent Protein
GFP – genetically encoded dye (fluorescent protein)
(Motor) protein
GFP
Attach DNA for GFP onto end of DNA encoding for
protein. Get DNA inside cell and DNA process takes
over…perfectly
Came from Jelly Fish
Inserted in Tobacco (plant) & in Monkeys (animals)
Kinesin – GFP fusion
Lots of FP mutants—different colors
Genetically encoded  perfect specificity.
Different Fluorescent Proteins
Absorption
Fluorescence
mHoneydew, mBanana, mOrange, tdTomato, mTangerine, mStrawberry, mCherry
Shaner, Tsien, Nat. Bio., 2004
```