Biochemical Reactions and Enzyme Kinetics - Introduction to Biomedical Engineering - page 484

1 2

Na 3 C

C

Na 3 CP

Na +

P

ATP

ADP

Inside

Outside Inside Outside

3 4

K +

Na +

Na 3 CP

K 2 CP

Inside Inside

Outside Outside

5 6

K 2 CP C

K +

P P

Inside

Inside Outside Outside

ATP

FIGURE 8.22 The six steps that characterize the Na-K pump.

Using the law of mass action, the Na-K pump is characterized by the following set of differ-
ential equations:

3

q Na i ¼ J Na D K

q

Na i q C i

2

3

q Na 3 C

Þ i ¼ K 2 q Na i q C i K 3 q Na 3 C

Þ i q ATP i ð

ð

q ATP i ¼ K K q Na 3 C

Þ i q ATP i

1 3 ð

q Na 3 CP

Þ i ¼ K 3 q Na 3 C

Þ i q ATP i K 4 q Na 3 CP ð ð Þ i

ð

ð 8 : 84 Þ

q Na 3 CP

Þ o ¼ K

q Na 3 CP

Þ i K

q Na 3 CP

4 ð 5 ð Þ o

ð

q Na o ¼ K 5 q Na 3 CP

Þ o J Na D ð

2
K o q C ð o

q C ð o ¼ K q Na 3 CP

Þ o K

q

5 ð 6

2
K o q C ð o

q K o ¼ J K D K q

6