Cyclin Cdk1

Cdc25

IE APC

APC

P

Cdk1

Cyclin

PP Cdk1

Cyclin

P

P Cdc25

Wee1 Wee1 P

IE

Cdk1

OFF

ON

Goal: Develop a collection of differential equations to represent the abovesystem

Cyclin Cdk1

Cdc25

IE APC

APC

P

Cdk1

Cyclin

PP Cdk1

Cyclin

P

P Cdc25

Wee1 Wee1 P

IE

Cdk1

OFF

ON

Simple Law of Mass Action:

AA -> AA + Cyclin k1

Cyclin + Cdk1 -> MPF k3

k1

k3

AA -> AA + Cyclin k1

Cyclin + Cdk1 -> MPF k3

Cyclin Cdk1

Cdc25

IE APC

APC

P

Cdk1

Cyclin

PP Cdk1

Cyclin

P

P Cdc25

Wee1 Wee1 P

IE

Cdk1

OFF

ON

Mass Action with APC State-Dependent Rates:V21: APC is offV22: APC is on

V21,V22

V21,V22

Two rules for each form of cyclin:Cyclin + APCoff -> AA + APCoff V21 Cyclin + APCon -> AA +APCon V22 MPF + APCoff -> AA + Cdk + APCoff V21 MPF + APCon -> AA + Cdk + APCon V22PreMPF + APCoff -> AA + Cdk + APCoff V21 PreMPF + APCon -> AA + Cdk + APCon V22

Cyclin Cdk1

Cdc25

IE APC

APC

P

Cdk1

Cyclin

PP Cdk1

Cyclin

P

P Cdc25

Wee1 Wee1 P

IE

Cdk1

OFF

ON

Catalytic Reactions

ka,Ka

kb,Kbkd,Kdkc,Kc

ke,Ke

kf,Kf

kg,Kg kh,Kh

All of these reactions work the same way:Cdc25U + MPF -> Cdc25P + MPF ka,KaCdc25P + PPase -> Cdc25U + PPase kb,KbAPCoff + IEP -> APCon+IEP kc,Kc APCon + PPase -> APCoff + PPase kd,Kd Wee1U + MPF -> Wee1P + MPF ke,Ke Wee1P + PPase->Wee1U+PPase kf,Kf IEU+MPF->IEP+MPF kg,Kg IEP+PPase->IEU+PPase kh,Kh

Cyclin Cdk1

Cdc25

IE APC

APC

P

Cdk1

Cyclin

PP Cdk1

Cyclin

P

P Cdc25

Wee1 Wee1 P

IE

Cdk1

OFF

ON

The MPF/PreMPF Reactions

MPF + Wee1P -> PreMPF+Wee1P Vwee1 MPF +Wee1U -> PreMPF+Wee1U Vwee2 PreMPF+Cdc25P -> MPF +Cdc25P V252 PreMPF+Cdc25U -> MPF+Cdc25U V251

Figure 2 from Sible et al, Methods 41, 2007