BME 100L. Modeling Cellular and Molecular Systems
Fall 2009
Homework 3
Chapter 8. Problems 2, 4, 5, 7, 10, and 11
Due: 5pm
September 23
rd
(
reversed due date
)
Hints:
2.(a) Hydration reaction mechanism is
CO
2
+ E
k
1
k
1
ECO
2
ECO
2
+ H
2
O
k
2
E + HCO
3

+ H
+
]
[
]
][
[
'
2
2
1
2
1
ECO
E
CO
k
k
k
K
H
M
, V
max
= k
2
’[E]
0
[H
2
O] is combined with k
2
to form a new constant k
2
’ = k
2
[H
2
O]
The curve fitting of the data will provide the values of K
M
and V
max
.
(b) Dehydration reaction mechanism is
CO
2
+ E
k
1
ECO
2
ECO
2
+ H
2
O
E + HCO
3

+ H
+
k
2
k
2
]
[
]
][
[
'
'
2
3
2
2
1
ECO
E
HCO
k
k
k
K
DH
M
, V
max
= k
1
[E]
0
[H
+
] can be absorbed into k
2
to form a new constant k
2
’ = k
2
[H
2
O]
(c)
E + CO
2
+ H
2
O
complex
E + HCO
3

+ H
+
k
1
k
1
k
2
k
2
When the system is at equilibrium, both reversible reactions are at equilibrium.
Using the values of K
M
H
, K
M
DH
, k
2
’ and k
1
obtained from (a) and (b) to calculate the
overall equilibrium constant (K
eq
= [HCO
3

]
e
[H
+
]
e
/[CO
2
]
e
[H
2
O]
e
or
K
eq
= [HCO
3

]
e
[H
+
]
e
/[CO
2
]
e
.
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 Fall '07
 YUAN
 Numerical Analysis, Enzyme, vmax, new constant k2, ECO2

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