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BME 100L01 Modeling cellular and molecular systems
Spring 2010
Homework 8.
1) In general, the inputoutput characteristics of transcriptional control can be
quantitatively described by the foldchange function (F), defined as the ratio of the
transcription rate in the presence of the transcription factor to that in the absence of the
transcription factor:
1
2
1
1
n
n
aA
F
,
where 1)
A
is the concentration of the transcription factor, 2)
n
is the effective Hill
coefficient, and 3)
a
1
>
a
2
for activators and
a
1
<
a
2
for repressors.
(a) Use nM as the concentration unit, what units should
a
1
and
a
2
have?
(b) For
n
= 1 (no cooperativity in binding), derive the logarithmic sensitivity as function
of
A
. Recall:
ln
ln
F
s
A
by definition.
(c) For
n = 1
. Plot
F
vs
A
on both linearlinear and loglog plots for
a
1
= 0.01,
a
2
= 0.001,
0.1, 1 over the range
A
= 11000nM. Plot corresponding
s
vs
A
on linearlog plots (i.e.
use log scale in the Xaxis and linear scale in the Yaxis).
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 Spring '07
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