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during this time interval, their frequency of distribution would be expected to be
proportional to the magnitude of the angle
α
associated with the vector spanning
the time intervals involved,
i.e.
, 6
◦
for Mechanisms 1, 3, 5, and 7, and 84
◦
for
Mechanisms 2, 4, 6 and 8. The theoretically predicted distributions of the mecha-
nisms based on the angular sizes are given in the 9
th
row in Table 12.1. Compar-
ing Rows 8 and 9, it is clear that all of the 8 mechanisms occur with frequencies
different from those expected on the basis of random distributions, except Mecha-
nism 5, as evidenced by the fact that the associated
p
-values are all less than 0.001
except that associated with Mechanism 5.
In 2002, Gorospe and her group measured for the first time the
TL
and
TR
data for about 2,000 genes from non-small cell human lung carcinoma H1299 [8]
and found that
TL
could increase or decrease without any changes in
TR
(see
Groups
IV
and
V
in Table 1 of [8]), from which they concluded that transcript
degradation played a critical role in determining mRNA levels. The first genome-
wide measurements of
TL
and
TR
in budding yeast
S. cerevisiae
were reported by
Garcia-Martinez
et al.
[10], whose results also indicated that there were no
1-to-1
correlation between
TL
and
TR
. However, neither of these publications included
any mathematical equation relating
TL, TR,
and
TD
. One of the main objectives
of this paper is to fill this gap in our knowledge and use the derived equation
to analyze the
TL
and
TR
data of functionally well-defined groups of mRNAs in
order to investigate the possible functional roles of mRNA levels in cell biology.
For this purpose, we chose the glycolytic and respiratory mRNA molecules for a
detailed analysis because the biochemistry of glycolysis and respiration (leading
to oxidative phosphorylation) and their antagonistic interactions are well known
in
S. cerevisiae
during glucose-galsctose shift [2, 7, 15, 16, 18].
The unicellular organism
S. cerevisiae
(also known as budding yeast, baker's
yeast, or wine yeast) has the capacity to metabolize glucose and galactose but
prefers the former as the carbon and energy sources when both nutrients are
present in its environment. In the presence of glucose, the organism turns on
those genes coding for the enzymes needed to convert glucose to ethanol (which
phenomenon is known as
glucose induction
) and turns off those genes needed for
galactose metabolism (which phenomenon is known as
glucose repression
)[2,
7, 15, 16, 18]. The detailed molecular mechanisms underlying these phenomena
(called
diauxic shift
) are incompletely understood at present and are under inten-
sive studies [11, 25, 31]. When glucose is depleted,
S. cerevisiae
increases its rate
of metabolism of ethanol to produce ATP via the Krebs cycle and mitochondrial
respiration [11, 25]. This metabolic control is exerted by reversing the glucose re-
pression of the genes encoding the enzymes required for respiration (
i.e.
, oxidative
phosphorylation) - the process referred to as
glucose de-repression
[11].
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