Biology Reference
In-Depth Information
a)
b)
Average mRNA Levels
= Glycolys is; = Oxphos
V_S vs time Plots
= Glycolys is ; = Oxphos
50
1
45
0.9
40
0.8
35
0.7
30
0.6
25
0.5
20
0.4
15
0.3
10
0.2
5
0.1
0
0
0
200
400
600
800
1000
0
200
400
600
800
1000
Time (minute)
Time (minute)
Fig. 12.3. The time courses of the average changes in the transcript level (
TL
) and transcription rate
(
TR
) of 12-15 glycolytic (
) and 14 respiratory genes (
).
12.3.2.
Calibration of
TR
Data
Transcription rates of yeast genes at
t
0
were estimated by utilizing the genome-
wide mRNA decay half-lives reported by Wang
et al.
[32] The half-life data were
down-loaded from their web site (
http://www-genome.stanford.edu/turnover
).
The mathematical relation between transcription rate,
dn
s,i
/dt
,where
n
s,i
is the
number of the
i
th
mRNA molecules synthesized per cell during the time interval
dt
,andthe
mRNA
i
decay half-life, denoted by
t
2
,i
, can be derived based on the
following assumptions.
(i)
At
t
0
, budding yeast cells are at a steady state with respect to transcription
and transcript degradation. In other words, at
t
0
,
dn
S,i
/dt
=
dn
D,i
/dt
,
where
n
D,i
is the number of the
i
th
mRNA molecules per cell degraded
during the time interval
dt
.
The decay of the
i
th
mRNA molecules obeys a first-order rate law given
by
(ii)
−
dn
i
/dt
=
dn
D,i
/dt
=
k
D,i
[
mRNA
i
]
,
(12.1)
where
k
D,i
is the first-order degradation rate constant and [
mRNA
i
]is
the concentration of the
i
th
mRNA in the cell. Integrating Eq. (12.1) with
respect to time leads to
[
mRNA
i
]=[
mRNA
i
]
0
e
−k
D,i
t
,
(12.2)
where [
mRNA
i
]
0
is the
mRNA
i
abundance at
t
0
. Substituting the val-
ues, [
mRNA
i
]=[
mRNA
i
]
0
/
2 at
t
=
t
2
,i
, and solving the resulting
equation for
k
D,i
yields
k
D,i
=
ln2
t
2
,i
=
0
.
693
t
2
,i
.
(12.3)
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