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Table 12.10A Planck's radiation law-like equation (BRE) is obeyed by (1) blackbody radiation; (2) single-molecule enzymic activity of cholesterol oxidase,
whole-cell RAN metabolism measured as (3) distances between transcription rate trajectories a and (4) distances between transcript level trajectories b ; and
(5) protein stability data. The numerical values of the BRE parameters for Processes 3 and 4 are the averages of 17-18 metabolic pathways (listed in the
legend to Fig. 12.26a ) with standard deviations as indicated
y = a(Ax + B) 5 /(e b/(Ax + B)
1)
Process
a
b
A
B
a/b
y
x
10 15
10 13
10 2
1. Blackbody
radiation
5
4.8
1
0
1.04
Spectral
intensity
Wavelength
10 5
10 2
10 3
Waiting time c
2. Single-molecule
enzymic turnover
times
3.5
2.0
1
0
1.75
Frequency of
occurrences
10 8
10 6
3. Distances between
transcription rate
trajectories in
budding yeast e
(n = 17)
(3.2
2.3)
51
9.5
1.41
0.26
2.41
0.36
6.27
(8.8 8.9) 10 8
1.7 10 7
4. Distances between
RNA trajectories
in budding yeast e
(n = 18)
50 11.6
2.23 1.45
3.21 1.67
Frequency of
occurrences
Phenotypic similarity
classes d
1.8 10 10
6.0 10 7
5. Protein stability
D G, i.e., the Gibbs
free changes
accompanying
protein
denaturation
a Transcription rates (TRs) were measured at six time points from budding yeast after glucose-galactose shift and plotted against time to generate one TR
trajectory for each gene. The similarity between a pair of TR trajectories was quantified as the Euclidean distance between the two trajectories
b Transcript levels (TLs) were measured at the same time points as TRs producing one TL trajectory for each gene. The distances between pairs of TL
trajectories were calculated as described in Footnote a
c The time it takes for an enzyme to be thermally activated to perform simple catalysis
d Different classes of the similarities between all possible pairs of RNA trajectories belonging to a pathway
e Undergoing glucose-galactose shift
300
14
18
Frequency
of the
occurrence
of D G
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