Biomedical Engineering Reference
In-Depth Information
The initial reaction rate (
v
≈
v
+
at
p
,
q
≈
0) obeys the general equation below with two
variables:
V
+
v
=
(14.4)
KK
a
KK
⎛
⎞
1
+
mA
+
mB
+
sA
mB
⎜
⎟
⎝
b
ab
⎠
where
V
+
is the maximal rate of forward reaction;
K
mA
,
K
mB
are the Michaelis constants
(which refer to the respective equilibriums of
A
+
EB
↔
EAB
and
B
+
EA
↔
EAB
for a
pseudo-equilibrium binding mechanism);
K
sA
describes the dissociation of
A
+
E
↔
EA
;
a
and
b
are the concentrations of substrates
A
and
B
, respectively.
Bi-substrate reactions follow one of the specific binding mechanisms, for example
random, sequential or ping-pong. The scheme below describes the equilibrium random
binding of
A
and
B
to
E
as:
+↔
E
A
;
EA E
+↔
B
;
EB EA
+↔
B
EAB EB
;
+↔
A
EAB EAB
;
→++
E
P
Q
(14.5)
where the rate of the reaction depends on
a
and
b
in accordance with Equation 14.4.
Sequential binding follows a different pattern:
E
+↔
A
EA EA B
;
+↔
EAB EAB
;
→+
E Q
(14.6)
where
A
does not dissociate from
EAB
. This results in
K
mA
= 0 considering a pseudo-
equilibrium binding mechanism. Description of a ping-pong reaction requires two sequential
steady state steps:
E
+↔ →+
A
EA
P
EX EX
;
+↔
B
EXB
→+
E Q
(14.7)
This model results in
K
sA
·K
mB
= 0 at
p
and
q
= 0.
Evaluation of parameters of a bisubstrate reaction is relatively complex and can be done
using three different approaches. In the first approach, the concentration of one substrate is
kept constant and included into the apparent values of
V
app
and
K
m,app
. Two separate plots of
v
as a function of
a
(
b
= constant) and
b
(
a
= constant) permit evaluation of all coefficients in
Equation 14.4. In the second approach, a 3D regression analysis can be performed to obtain
a
v
-surface dependent on both
a
and
b
. The third approach requires a fixed ratio between the
two substrates,
b =
γ
·a
, to transform the two-variable Equation 14.4 to a function with only
one variable,
a
.
V
v
=
(14.8)
1
⎛
K
⎞
1
KK
1
+
K
+
mB
+
sA
mB
⎜
⎟
mA
2
a
⎝
g
⎠
a
g
allows calculation of the constants in Equation 14.8.
Parameters of all functions discussed here can be calculated by regression fitting on a com-
puter, which is a routine procedure in modern science.
Lipases are a family of enzymes which catalyze cleavage of ester bonds between organic
alcohols and fatty acids (Lowe, 2002; Reis
et al
., 2009 ). They have distinctive structural
characteristics responsible for different kinetic behavior. For example, human pancreatic
lipase (hPL) (Reis
et al
., 2009), Candida antarctica lipase A (CALA) (Ericsson
et al
., 2007 )
Analysis of
v
data for two or more
γ
Search WWH ::
Custom Search