ECE 416 Homework 5
Due: Friday, April 5th
THIS WEEK: Office hours moved to 5pm on April 4th.
“Fluorescence, FRET, and Fluorescence Polarization”
I.
Fluorescence
Fluorescent tags are a commonly used probe to find and track
biological molecules. Two new tags, “Guillermitium-236” (G-236)
and “Briandolinium-32” (B-32) have just been created and need to
be characterized.
We can start with G-236. The Jablonski diagram is provided here:
We first need to characterize its emission characteristic. We have
a laser (at 633 nm, = 0.1 nm, 1 mm2 spot size, 30mW output
power) that will serve as an excitation source.
Q1: How much power (in Joules) is needed to excite one
electron of a G-236 molecule to an excited state?
Q2: Calculate the Photon Flux (𝜙) and Irradiance of the laser.
Q3: Calculate the Intensity of the laser.
We create a .79 molar solution of the G-236 particles and place it
into a cuvette (depth of 1 cm). To measure the absorbance
coefficient, we measure the laser intensity after it passes through
the cuvette at 5 different wavelengths. The laser cavity can be
tuned to provide different output wavelengths at an identical initial
intensity of 20,000
𝑊
𝑚2
.
λ (nm) Intensity (W/m^2)
350
19937
352
19910
354
19890
356
19860
358
19937
Q4: Calculate the absorbance coefficient at each wavelength,
in units of (M-1 meter-1). To limit absorption, which
wavelength(s) should we use?
After investigating the absorbance of G-236, you realize you
never calculated the fluorescence lifetime. To measure the
lifetime, you first shine your laser incident on the cuvette and
measure the resulting light from the particles by placing an
emission filter in front of your detector. The filter ensures that the
only light reaching your detector is from your particles. After a
short time, you block your laser and record the resulting output
light, paying special attention to the decay profile.
Q5: Given the plot below, what is the lifetime of a G-236
particle?
Normalized Intensity
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
14
16
Time (ns)
Q6: If the quantum yield of a G-236 particle is 80%, what is
knot-fluoro?
While these new particles are useful, they are hard to fabricate
and use in your system. To simplify your work, you decide to
purchase fluorescent beads from a commercial vendor. There are
many choices, so now you need to find a pair of beads that
together can:
1- Absorb light near 350 nm
2- Emit light at 600 nm
Q7: Using this website, explore different dye pairs to find an
appropriate solution that fits our requirements as above. Try
and find a pair that produces as low background noise as
possible, meaning the spectral output of the first dye does
not overlap much with the spectral output of the second dye.
There may be more than one solution, please show a
screenshot of your chosen dyes, clearly showing the
excitation and emission spectra.
http://www.mcb.arizona.edu/ipc/spectra_page.htm
II.
FRET
FRET is often used as a “molecular ruler” to indirectly observe
biological events that are otherwise extremely difficult to quantify.
We want to use this technique to observe a DNA polymerase
replicate a piece of DNA. But before we do that, we first need to
calculate the Forster Radius of two fluorescence-emitting
proteins, Cyan-Fluorescent Protein (CFP) and Yellow-Fluorescent
Protein (YFP) to see if they will suit our needs.
Q8: Calculate the Forster Radius for this pair of tags using:
1
R0 = (8.8 ∗ 10−5 ∗ 𝑛−4 ∗ 𝑘 2 ∗ 𝑄𝑌 ∗ 𝐽(𝜆) ∗ 4 ∗ 10−45 )^( )
6
Assume k^2 = 2/3, we are imaging in water as our media, QYD =
70%. To find J(λ), find the overlapping area with these two curves
using the data below. Hint - For simplicity, I adjusted the data
such that integration is easily calculated. I added the 4*10^-45
scaling factor to correct for the simplification.
wavelength
(nm)
CFP Emission (Rel Int.) YFP Excitation (Rel Int.)
430
0
0
440
0.1
0.1
450
0.4
0.2
460
0.7
0.3
470
1
0.4
480
0.7
0.4
490
500
510
520
530
540
0.7
0.4
0.3
0.2
0.1
0
0.8
1
0.6
0.3
0.1
0
Q9: Calculate Efficiency for this pair of dyes, where R ranges
from 0 to 250 Angstroms. Plot the Efficiency (y) vs. R
(Angstroms) (x).
Now that we better understand our dyes and have verified they
are sufficient to observe this biological event, we can utilize them
to observe a DNA polymerase replicate a piece of ssDNA.
Imagine this situation: We have a piece of single stranded DNA
attached to a CFP dye at its 5’ end, its 3’ end free in solution. The
CFP is attached to the substrate surface with a simple linker. A
picture is included below.
We introduce a YFP labeled DNA Polymerase molecule in this
sample and observe the FRET output. DNA Pol. replicates ssDNA
from 3’->5’directionally, so it will preferentially attach to our DNA
strand. Once completed processing the strand, it will release from
the now dsDNA and diffuse away. The approximate output
intensity of the CFP over time is as follows:
Q10: Using what you now know about the CFP tag from the
plot above, draw a similar plot of approximate output
intensity (Y) vs time (X) plot for the YFP tag. Label key points
in the signal.
Sometimes the CFP will attach to the 3’ end, while the DNA is still
attached to the substrate at the 5’ end.
Q11: Draw the approximate output intensity (Y) vs time (X)
for this new situation from the perspective of the YFP tag.
III. Fluorescence Polarization
One application of fluorescence polarization assays is to
determine if a person will react to a particular antigen.
A friend that recently got sick when eating a meal full of peanuts
has asked us to see if they are allergic to peanuts, or if this was
caused by something else. When someone that is allergic to
peanuts comes into contact with the peanut allergen, their
immune system overreacts and produces an excess of histamine,
which most notably leads to constriction of the airways. IgE
(Immunoglobulin-E, an antibody in the immune system, MW ~200
kDa) is one of the major components in this histamine pathway.
To start, we labeled the “peanut allergy” protein (Mol. Weight =
~20 kDA) with a fluorescent tag. After placing the protein solution
into a transparent cuvette, we performed a FP measurement
(illuminating it with a polarized laser) by measuring the intensity of
fluorescence emission through polarizing filters oriented parallel
or perpendicular to the polarization of the laser:
Fparallel = .5, and Fanti-parallel =.3
Q12: Calculate the Polarization (P) and the molecule rotation
time (φ) for this molecule, given P0 = .5, and a lifetime of 10
nanoseconds. Assuming we performed our experiments in
room temperature (20 deg. C) and in water as our media (η =
1 kg * s-1m-1), what is the molecular volume (V – units =
m^3/mol) of our labeled allergy protein?
If a person is allergic to peanuts, IgE will bind with the
fluorescently-tagged protein, changing the response of the
fluorescent tags. To test our system, we add our own IgE to the
solution and incubate it for some time to allow for binding.
Afterwards we perform a polarization measurement again and
record these results:
Fparallel = 0.54 and Fanti-parallel = 0.30
Q13: You are not allergic to peanuts. Does the data confirm
this? Calculate P and Φ and provide your reasoning. (It may
help to do the following question as well..)
Q14: We now add the IgE from our friend to a new solution of
identically labeled allergens and collect these measurements
once again. Are they allergic to peanuts? Again, provide your
reasoning.
Fparallel = 0.95 and Fanti-parallel = 0.05