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Model Mathematics

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Component: environment

Component: ERG

\frac{d}{d time} (ERG) = \frac{epsilon k_15}{1 + {(\frac{DRG}{J_15})}^{2}} - (k_16 ERG)

Component: DRG

\frac{d}{d time} (DRG) = epsilon (k_17_ERG + \frac{{(\frac{DRG}{J_17})}^{2} k_17}{1 + {(\frac{DRG}{J_17})}^{2}}) - (k_18 DRG)

Component: Kip1

\frac{d}{d time} (Kip1) = ((epsilon k_5 - (V_6 Kip1) - (k_24 CycD Kip1)) + k_24r CycD_Kip1 + k_10 CycD_Kip1 - (k_25 Kip1 (CycE + CycA))) + k_25r (CycE_Kip1 + CycA_Kip1) + V_8 CycE_Kip1 + k_30 Cdc20 CycA_Kip1

Component: CycA_Kip1

\frac{d}{d time} (CycA_Kip1) = k_25 CycA Kip1 - (k_25r CycA_Kip1) - (V_6 CycA_Kip1) - (k_30 Cdc20 CycA_Kip1)

Component: CycD_Kip1

\frac{d}{d time} (CycD_Kip1) = k_24 CycD Kip1 - (k_24r CycD_Kip1) - (V_6 CycD_Kip1) - (k_10 CycD_Kip1)

Component: CycE_Kip1

\frac{d}{d time} (CycE_Kip1) = k_25 CycE Kip1 - (k_25r CycE_Kip1) - (V_6 CycE_Kip1) - (V_8 CycE_Kip1)

Component: CycA

\frac{d}{d time} (CycA) = (epsilon k_29 E2FA mass - (k_30 Cdc20 CycA) - (k_25 CycA Kip1)) + k_25r CycA_Kip1 + V_6 CycA_Kip1

Component: CycB

\frac{d}{d time} (CycB) = epsilon (k_1_+ \frac{k_1 {(\frac{CycB}{J_1})}^{2}}{1 + {(\frac{CycB}{J_1})}^{2}}) - (V_2 CycB)

Component: CycE

CycE_T = CycE + CycE_Kip1 \frac{d}{d time} (CycE) = (epsilon (k_7_+ k_7 E2FA) - (V_8 CycE) - (k_25 CycE Kip1)) + k_25r CycE_Kip1 + V_6 CycE_Kip1

Component: CycD

CycD_T = CycD + CycD_Kip1 \frac{d}{d time} (CycD) = epsilon k_9 DRG + V_6 CycD_Kip1 + k_24r CycD_Kip1 - (k_24 CycD_Kip1) - (k_10 CycD)

Component: Cdc20

\frac{d}{d time} (Cdc20) = \frac{k_13 IEP (Cdc20_T - Cdc20)}{J_13 + Cdc20_T - Cdc20} - (\frac{Cdc20 k_14}{J_4 + Cdc20}) - (k_12 Cdc20)

Component: Cdc20_T

\frac{d}{d time} (Cdc20_T) = epsilon (k_11_+ k_11 CycB) - (k_12 Cdc20_T)

Component: IEP

\frac{d}{d time} (IEP) = \frac{k_31 CycB (1 - IEP)}{J_31 + 1 - IEP} - (\frac{k_32 PPX IEP}{J_32 + IEP})

Component: PPX

\frac{d}{d time} (PPX) = epsilon k_33 - (k_34 PPX)

Component: E2F

\frac{d}{d time} (E2F) = k_22 (E2FT - E2F) - ((k_23_+ k_23 (CycA + CycB)) E2F)

Component: Cdh1

\frac{d}{d time} (Cdh1) = \frac{(k_3_+ k_3 Cdc20) (1 - Cdh1)}{J_3 + 1 - Cdh1} - (\frac{Cdh1 V_4}{J_4 + Cdh1})

Component: GM

H = \{\begin{matrix} 0 if \frac{Rb_hypo}{Rb_T} > 0.8 \\ 1 otherwise \end{matrix} \frac{d}{d time} (GM) = k_27 mass H - (k_28 GM)

Component: mass

\frac{d}{d time} (mass) = epsilon mu GM

Component: PP1_A

PP1_A = \frac{PP1_T}{1 + K_21 (phi_E (CycE + CycA) + phi_B CycB)}

Component: Rb_hypo

Rb_hypo = \frac{Rb_T}{1 + \frac{k_20 (lambda_D CycD_T + lambda_E CycE + lambda_A CycA + lambda_B CycB)}{k_19_(PP1_T - PP1_A) + k_19 PP1_A}}

Component: E2FA

E2FA = \frac{E2F (E2FT - E2F_Rb)}{E2FT}

Component: E2F_Rb

E2F_Rb = \frac{2 E2FT Rb_hypo}{E2FT + Rb_hypo + L + \sqrt{{(E2FT + Rb_hypo + L)}^{2} - (4 E2FT Rb_hypo)}}

Component: V_2

V_2 = k_2_(1 - Cdh1) + k_2 Cdh1 + k_2__Cdc20

Component: V_4

V_4 = k_4 (gamma_A CycA + gamma_B CycB)

Component: V_6

V_6 = k_6_+ k_6 (eta_E CycE + eta_A CycA + eta_B CycB)

Component: V_8

V_8 = \frac{k_8_k_8 (psi_E (CycE + CycA) + psi_B CycB) 1}{J_8 + CycE_T}

Component: L

L = \frac{k_26r}{k_26} + \frac{k_20}{k_26} (lambda_D CycD + lambda_E CycE + lambda_A CycA + lambda_B CycB)

Component: rate_constants

Component: dimensionless_constants

Source: Derived from workspace Novak, Tyson, 2004 at changeset cadfae101d9f.

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License: This work is licensed under a Creative Commons Attribution 3.0 Unported License.

A model for restriction point control of the mammalian cell cycle