程序代写案例-113B -
时间:2021-03-14
Chem 113B - Final
1) A particle of charge q is constraint to move in the xy-plane on the circumference
of a semi-circle of radius r between  .
a) Find its energy eigenvalues and eigenstates. (10 points)
b) A constant electric field E is applied along the y-axis (=). Find the
change in energy to second order in E.
Hint: sin  sin  = [(cos (−) – cos(+)]/2
sin  cos  = [(sin (+) + sin(−)]/2 (10 points)
c) The electric field is oscillating in time with frequency . Which
transitions are allowed and what is the transition rate between the ground
state and the first excited state? (20 points)
2) To monitor the activity of many neurons in a live animal, genetically encoded
voltage indicators (GEVI) have been developed in the past 10 years. The first
generation of GEVI used mutants of light sensitive ionic channels (that retain the
light sensitivity but lost the ionic conductivity property). One of these mutants is
QuasAr2 which fluorescent properties are shown in Fig.1d. This mutant switches
states quickly upon a change in voltage across the membrane and its fluorescence
doubles upon a change of 100mV across the membrane, properties essential to
monitor an action potential in a single neuron. Its main drawback is a low
brightness which impairs the detection of voltage changes when compared with
background fluorescence. To overcome this drawback, QuasAr2 was fused with
fluorescent proteins (FP), that act as fluorescent donors. The FRET efficiency
between the FP (here Citrine) and QuasAr2 depends on the protonation status of
QuasAr2 (see Fig.a,b). FRET is negligible when the voltage across the membrane
is negative (cell resting state), it becomes non-negligible when the membrane
potential is positive (during an action potential).
In the following we shall investigate the properties of QuasAr2 and its fusion with
Citrine.



a) Complete the table shown in Fig.1d. (10 points)
b) What is the signal to background ratio when a single QuasAr2 is excited and
background is due to Raman scattering from the water molecules (assume a
Raman cross-section of 10-29 cm2 and an excitation volume of 1m3). Compare
with the signal to background ratio when single citrine is excited (10 points)
c) Fig.1c displays the probability (in log scale) of observing an emitted photon at
a given time after excitation. From the QY of citrine () and the red curve
estimate the fluorescence lifetime F and spontaneous lifetime s of the
emission state. When citrine is fused to QuasAr2 (in its protonated form)
estimate the fluorescence lifetime F of citrine (blue curve) and the FRET
efficiency between citrine and QuasAr2. (10 points)
d) Compute the change in the fluorescence power emitted by a single citrine-
QuasAr2 construct illuminated with a 300 W/cm2 beam at 516nm upon cell
depolarization, assuming no-FRET in the deprotonated form of QuasAr2. (10
points)
e) Assuming that 10% of the emitted photons are detected how many photons are
detected from a single citrine-QuasAr2 construct as in (d) during an action
potential which depolarizes the cell during 1 msec? What is the signal to noise
ratio? Can a single citrine-QuasAr2 molecule detect an action potential (hint:
compare the change in fluorescence upon depolarization to the noise)? (20
points)





















































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