Biology Reference
In-Depth Information
enzymes and hence
rate constant
, k (see Eq.
12.42
).
Rates
(usually denoted as v,
from velocity) and
rate constants
(denoted as k) are not the same but are related
to each other through Eq.
12.44
under the first-order kinetics conditions, i.e., in
the presence of enzymes in excess of their substrates:
¼
=
¼
v
d[S]
dt
k[S]
(12.44)
where [S] is the concentration of the substrate for an enzyme. As evident in
Eq.
12.44
, k can be defined as the v measured under condition where [S] is kept
at the unit concentration, i.e., [S]
1. The key idea behind Eq.
12.44
is that
v
depends on substrate concentration but k does not or that, under a constant
substrate concentration, v and k are quantitatively equivalent.
7. The kinetics of the X
th
RNA trajectory catalyzed by the (T
X
D
X
)complexis
determined by the Gibbs free energy levels (or the quantum states) of T
X
and
D
X
. The analysis of the TL vs. TR plots such as Fig.
12.6
indicates that
transcriptosomes
and
degradosomes
can exhibit at least five distinct turnover
rates, i.e., (1) slow decrease, (2) rapid decrease, (3) no change, (4) slow increase,
and (5) rapid increase. For example, in (a), Fig.
12.6
, during the first phase (i.e.,
0-5 min), TL decreases despite the fact that TR increases. This can be accounted
for only if we can assume that, during this phase, the rate of transcript degradation
(TD) decreases more than TR does. If each enzyme system has five conformational
(or quantum) states with free energy levels labeled as
¼
1, 0, 1, and 2 as in
Fig.
12.30b
, there are 25 possible conformational (or quantum) states for the
(T
X
D
X
) complex, each associated with a rate of change in TL given in parenthesis
as described in Table
12.11
. These 25 difference entries group into nine classes
as indicated by the nine dotted diagonal lines, and these lines are associated with
the relative frequencies of 1, 2, 3, 4, 5, 4, 3, 2, and 1. For example, the relative
frequencies of the occurrence of the (dTL/dt) classes,
n, d
1
,d
2
,d
3
,
and
d
4
(or
n, u
1
,
u
2
,u
3
,
and
u
4
) are 5, 4, 3, 2, and 1 (counting the number of cells along the
dotted lines). Thus, if all the possible couplings between the quantum states of
T and D have an equal probability of occurrence (as assumed in Table
12.11
),
RNA trajectories are five times more likely to remain unchanged, i.e., dTL/dt
¼
0
(or n), than to decrease (or increase) rapidly with dTL/dt
¼
2,
d4
(or
u4
). However,
the experimentally observed data (see Series 9 in Fig.
12.29a
) deviate from the
theoretically predicted behavior depicted as a red triangle. However, two interest-
ing features emerge. (1) Different metabolic pathways tend to show peak
frequencies located at different rate classes (see a in Fig.
12.29
), and (2) different
phases within a givenmetabolic pathway tend to showpeak frequencies at different
rate classes (see b and c in Fig.
12.29
). Thus, the possibility suggests itself that two
metabolic pathways that overlap in a two-dimensional frequency-rate class
(FR) plot such as Fig.
12.29a
may be distinguishable in three-dimensional fre-
quency-phase-rate class (FPR) plots such as Fig.
12.29b
, c and this may make the
FPR plots a sensitive tool for monitoring cell states in drug discovery research and
