Chemistry Reference
In-Depth Information
of tubulin (i.e., tubulin polymerization), even at low paclitaxel concentrations. At
high concentrations, however, the enhanced tubulin polymerization will be unable
to inhibit the responses to paclitaxel. Therefore, the reduced survival dependent on
paclitaxel concentrations (i.e., event
B
) becomes dominant and the efficacy of
paclitaxel becomes more apparent.
6.5.6 Response of Melanoma Cells to the DDMC/PTX Complex
By contrast, the responses of melanoma cells to the DDMC/PTX complex are much
more specific without event
A
. Of note, low concentrations of the DDMC/PTX
complex markedly inhibited the increase in number of melanoma cells, with a linear
negative correlation between paclitaxel concentration [E]
0
and survival rate. This
means that there is no resistance of melanoma cells to DDMC/PTX complex. In
other words, the relationship between the cell death (Cd) rate (Cd/d
t
) and tubulin
polymerization rate (d
p
/d
t
) will assume the following equation, as modified from
Cheng and Prusoff [
66
]:
Cd
=
d
t ¼ a
d
p=
d
t þC
1
(6.44)
where
a
is a constant and
C
1
is a device constant corresponding to
a >
0,
C
1
>
0.
The rate of tubulin polymerization
V ¼
d
p
/d
t
can also be expressed using a
Michaelis-Menten-derived S-shaped curve, as follows:
n
0
v ¼
κ
cat
½
E
0
½
S
(6.45)
0
½
S
þK
m
where
K
m
¼
Michaelis constant, [S]
0
¼
initial tubulin concentration and
n ¼
Hill
coefficient. In this case, because
n >
1, mutual interactions between numerous
points occur, which fit an S-shaped curve. The stability of the enzyme-substrate
complex is shown as 1/
K
m
, and is larger for DDMC/PTX than for paclitaxel alone,
corresponding to
0
K
m
.
½
S
The equation:
V ¼ κ
cat
½
E
0
(6.46)
can be substituted with the expression from (
6.45
), as follows:
Cd
=
d
t ¼ aκ
cat
½E
0
þC
1
(6.47)
and integrated into:
Cd
¼ aκ
cat
½
E
0
t þC
1
t
(6.48)
