Model Mathematics

kplus_z = bz + cz cyclin_CDK_active kminus_z = az kplus_w = bw + cw cyclin_CDK_active kminus_w = aw kplus_i = bi + ci cyclin_CDK_active kminus_i = ai

\frac{d}{d time} (cyclin) = k1 + k4 cyclin_CDK_inactive - (k3 cyclin CDK) - ((k2 + k2u APC) cyclin)

\frac{d}{d time} (cyclin_CDK_inactive) = k3 cyclin CDK + k6 cyclin_CDK_active + wee1 cyclin_CDK_active 1 - (k4 cyclin_CDK_inactive) - (k5 cyclin_CDK_inactive) - (Cdc25_2P cyclin_CDK_inactive 1)

\frac{d}{d time} (cyclin_CDK_active) = (k5 cyclin_CDK_inactive + Cdc25_2P cyclin_CDK_inactive 1 - (k6 cyclin_CDK_active) - (wee1 cyclin_CDK_active 1) - ((k7 + k7u APC) cyclin_CDK_active) - (k14 cyclin_CDK_active CKI)) + k15 cyclin_CDK_CKI + (k16 + k16u APC) cyclin_CDK_CKI_P

\frac{d}{d time} (Cdc25) = k8 + kminus_z Cdc25_P - (kplus_z Cdc25) - (k9 Cdc25)

\frac{d}{d time} (Cdc25_P) = kplus_z (Cdc25 - Cdc25_P) + kminus_z (Cdc25_2P - Cdc25_P) - (k9 Cdc25_P)

\frac{d}{d time} (Cdc25_2P) = kplus_z Cdc25_P - (kminus_z Cdc25_2P) - (k9 Cdc25_2P)

\frac{d}{d time} (wee1) = k10 + kminus_w wee1_P - (kplus_w wee1) - (k11 wee1)

\frac{d}{d time} (wee1_P) = kplus_w wee1 - (kminus_w wee1_P) - (k11 wee1_P)

h_x = \frac{{cyclin_CDK_active}^{2}}{a^{2} + {cyclin_CDK_active}^{2}} \frac{d}{d time} (APC) = \frac{h_x - APC}{tau}

\frac{d}{d time} (CKI) = (k12 - (k13 CKI) - (k14 cyclin_CDK_active CKI)) + k15 cyclin_CDK_CKI

\frac{d}{d time} (cyclin_CDK_CKI) = (k14 cyclin_CDK_active CKI - (k15 cyclin_CDK_CKI)) + kminus_i cyclin_CDK_CKI_P - (kplus_i cyclin_CDK_CKI)

\frac{d}{d time} (cyclin_CDK_CKI_P) = kplus_i cyclin_CDK_CKI - (kminus_i cyclin_CDK_CKI_P) - ((k16 + k16u APC) cyclin_CDK_CKI_P)

CDK = \frac{CDK_T - cyclin_CDK_active - cyclin_CDK_inactive - cyclin_CDK_CKI - cyclin_CDK_CKI_P}{CDK_T}

cyclin_T = cyclin + cyclin_CDK_active + cyclin_CDK_inactive