Systems Biology (Methods in Molecular Biology)

The time differential equations are:

dC 2

dt

¼k 8 notPC 2 ðtÞþk 9 CPðtÞþk 6 MðtÞ

dCP

dt

¼k 8 notPC 2 ðtÞk 9 CPðtÞk 3 CPðtÞYðtÞ

dM

dt

¼k 5 notPMðtÞk 6 MðtÞþðk 4 primeþk 4 MðtÞ^2 ÞpMðtÞ

dpM

dt

¼k 5 notPMðtÞðk 4 primeþk 4 MðtÞ^2 ÞpMðtÞþk 3 CPðtÞYðtÞ

dY

dt

¼k 1 aak 2 YðtÞk 3 CPðtÞYðtÞ

dY P

dt

¼k 6 MðtÞk 7 YPðtÞ

ð 17 Þ

wheretis the time andki, the rate constant for stepi(i¼1,..., 9).

aa means amino acids. There are six time-dependent variables: the

concentrations of cdc2 (C2), cdc2-P (CP), preMPF¼P-cyclin-

cdc2-P (pM), active MPF¼P-cyclin-cdc2 (M), cyclin (Y), and

cyclin-P (YP). Active MPF is described by the function F([M]). The

equation where active MPF is described is given by the function

Mthat is equal to (k 4 prime+k 4 M)^2 , wherek 4 primeis the rate

constant when [active MPF]¼0 andk4 is the rate constant when

[active MPF]¼[CT], where [CT]¼total cdc2. Tyson assumesk 4

k 4 prime. Related data are reported in Table1.

The graphic plot is shown in Fig.1.

Table 1

Data value used in the numerical solution

Parameters Value

k1aa 0.015 min^1

k2 0 min^1

k3 200 min^1

k4 10–1000 min^1

k4prime 0.018 min^1

k5notP 0

k6 0.1–10 min^1

k7 0.6 min^1

k8notP k9 (10^6 )

k9 k6 (10^3 )

78 Rodolfo Guzzi et al.