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Model Mathematics

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Component: environment

Component: mass

\frac{d}{d time} (mass) = mass kg

Component: Cln2

\frac{d}{d time} (Cln2) = (ks_n2_+ ks_n2__SBF) mass - (kd_n2 Cln2)

Component: Clb5

\frac{d}{d time} (Clb5) = (ks_b5_+ ks_b5__MBF) mass + kd3_c1 C5P + kdi_b5 C5 + kd3_f6 F5P + kdi_f5 F5 - ((Vd_b5 + kas_b5 Sic1 + kas_f5 Cdc6) Clb5)

Component: Clb2

\frac{d}{d time} (Clb2) = (ks_b2_+ ks_b2__Mcm1) mass + kd3_c1 C2P + kdi_b2 C2 + kd3_f6 F2P + kdi_f2 F2 - ((Vd_b2 + kas_b2 Sic1 + kas_f2 Cdc6) Clb2)

Component: Sic1

\frac{d}{d time} (Sic1) = ks_c1_+ ks_c1__Swi5 + (Vd_b2 + kdi_b2) C2 + (Vd_b5 + kdi_b5) C5 + kpp_c1 Cdc14 Sic1P - ((kas_b2 Clb2 + kas_b5 Clb5 + Vkp_c1) Sic1)

Component: Sic1P

\frac{d}{d time} (Sic1P) = (Vkp_c1 Sic1 - ((kpp_c1 Cdc14 + kd3_c1) Sic1P)) + Vd_b2 C2P + Vd_b5 C5P

Component: C2

\frac{d}{d time} (C2) = kas_b2 Clb2 Sic1 + kpp_c1 Cdc14 C2P - ((kdi_b2 + Vd_b2 + Vkp_c1) C2)

Component: C5

\frac{d}{d time} (C5) = kas_b5 Clb5 Sic1 + kpp_c1 Cdc14 C5P - ((kdi_b5 + Vd_b5 + Vkp_c1) C5)

Component: C2P

\frac{d}{d time} (C2P) = Vkp_c1 C2 - ((kpp_c1 Cdc14 + kd3_c1 + Vd_b2) C2P)

Component: C5P

\frac{d}{d time} (C5P) = Vkp_c1 C5 - ((kpp_c1 Cdc14 + kd3_c1 + Vd_b5) C5P)

Component: Cdc6

\frac{d}{d time} (Cdc6) = ks_f6_+ ks_f6__Swi5 + ks_f6___SBF + (Vd_b2 + kdi_f2) F2 + (Vd_b5 + kdi_f5) F5 + kpp_f6 Cdc14 Cdc6P - ((kas_f2 Clb2 + kas_f5 Clb5 + Vkp_f6) Cdc6)

Component: Cdc6P

\frac{d}{d time} (Cdc6P) = (Vkp_f6 Cdc6 - ((kpp_f6 Cdc14 + kd3_f6) Cdc6P)) + Vd_b2 F2P + Vd_b5 F5P

Component: F2

\frac{d}{d time} (F2) = kas_f2 Clb2 Cdc6 + kpp_f6 Cdc14 F2P - ((kdi_f2 + Vd_b2 + Vkp_f6) F2)

Component: Pds1

\frac{d}{d time} (Pds1) = ks_pds_+ ks1_pds__SBF + ks2_pds__Mcm1 + kdi_esp PE - ((Vd_pds + kas_esp Esp1) Pds1)

Component: Esp1

\frac{d}{d time} (Esp1) = (- kas_esp) Pds1 Esp1 + (kdi_esp + Vd_pds) PE

Component: ORI

\frac{d}{d time} (ORI) = ks_ori (epsilon_ori_b5 Clb5 + epsilon_ori_b2 Clb2) - (kd_ori ORI)

Component: BUD

\frac{d}{d time} (BUD) = ks_bud (epsilon_bud_n2 Cln2 + epsilon_bud_n3 Cln3 + epsilon_bud_b5 Clb5) - (kd_bud BUD)

Component: SPN

\frac{d}{d time} (SPN) = \frac{ks_spn Clb2}{Jspn + Clb2} - (kd_spn SPN)

Component: G_sbf

G_sbf = \frac{2 Ji_sbf Va_sbf}{Vi_sbf + Ja_sbf Vi_sbf + Ji_sbf Va_sbf + \sqrt{{(Vi_sbf + Ja_sbf Vi_sbf + Ji_sbf Va_sbf - Va_sbf)}^{2} - (4 (Vi_sbf - Va_sbf) Ji_sbf Va_sbf)} - Va_sbf}

Component: G_mcm

G_mcm = \frac{2 Ji_mcm ka_mcm Clb2}{ki_mcm + Ja_mcm ki_mcm + Ji_mcm ka_mcm Clb2 + \sqrt{{(ki_mcm + Ja_mcm ki_mcm + Ji_mcm ka_mcm Clb2 - (ka_mcm Clb2))}^{2} - (4 (ki_mcm - (ka_mcm Clb2)) Ji_mcm ka_mcm Clb2)} - (ka_mcm Clb2)}

Component: SBF_MBF

SBF = MBF MBF = G_sbf

Component: Mcm1

Mcm1 = G_mcm

Component: Cln3

Cln3 = \frac{C0 Dn3 mass}{Jn3 + Dn3 mass}

Component: Bck2

Bck2 = B0 mass

Component: Clb5_T

Clb5_T = Clb5 + C5 + C5P + F5 + F5P

Component: Clb2_T

Clb2_T = Clb2 + C2 + C2P + F2 + F2P

Component: Sic1_T

Sic1_T = Sic1 + Sic1P + C2 + C2P + C5 + C5P

Component: F5

\frac{d}{d time} (F5) = kas_f5 Clb5 Cdc6 + kpp_f6 Cdc14 F5P - ((kdi_f5 + Vd_b5 + Vkp_f6) F5)

Component: F2P

\frac{d}{d time} (F2P) = Vkp_f6 F2 - ((kpp_f6 Cdc14 + kd3_f6 + Vd_b2) F2P)

Component: F5P

\frac{d}{d time} (F5P) = Vkp_f6 F5 - ((kpp_f6 Cdc14 + kd3_f6 + Vd_b5) F5P)

Component: Swi5_T

\frac{d}{d time} (Swi5_T) = ks_swi_+ ks_swi__Mcm1 - (kd_swi Swi5_T)

Component: Swi5

\frac{d}{d time} (Swi5) = ks_swi_+ ks_swi__Mcm1 + ka_swi Cdc14 (Swi5_T - Swi5) - ((kd_swi + ki_swi Clb2) Swi5)

Component: APC_P

\frac{d}{d time} (APC_P) = \frac{ka_apc Clb2 (1 - APC_P)}{Ja_apc + 1 - APC_P} - (\frac{ki_apc APC_P}{Ji_apc + APC_P})

Component: Cdc20_T

\frac{d}{d time} (Cdc20_T) = ks_20_+ ks_20__Mcm1 - (kd_20 Cdc20_T)

Component: Cdc20_A

\frac{d}{d time} (Cdc20_A) = (ka_20_+ ka_20__APC_P) (Cdc20_T - Cdc20_A) - ((kmad2 + kd_20) Cdc20_A)

Component: Cdh1_T

\frac{d}{d time} (Cdh1_T) = ks_cdh - (kd_cdh Cdh1_T)

Component: Cdh1

\frac{d}{d time} (Cdh1) = ks_cdh + \frac{Va_cdh (Cdh1_T - Cdh1)}{Ja_cdh + Cdh1_T - Cdh1} - (kd_cdh Cdh1 + \frac{Vi_cdh Cdh1}{Ji_cdh + Cdh1})

Component: Tem1

\frac{d}{d time} (Tem1) = \frac{klte1 (Tem1_T - Tem1)}{Ja_tem + Tem1_T - Tem1} - (\frac{kbub2 Tem1}{Ji_tem + Tem1})

Component: Cdc15

\frac{d}{d time} (Cdc15) = (ka_15_(Tem1_T - Tem1) + ka_15__Tem1 + ka_15___Cdc14) (Cdc15_T - Cdc15) - (ki_15 Cdc15)

Component: Cdc14_T

\frac{d}{d time} (Cdc14_T) = ks_14 - (kd_14 Cdc14_T)

Component: Cdc14

\frac{d}{d time} (Cdc14) = ks_14 + kd_net (RENT + RENTP) + kdi_rent RENT + kdi_rentp RENTP - (kd_14 Cdc14 + (kas_rent Net1 + kas_rentp Net1P) Cdc14)

Component: Net1_T

\frac{d}{d time} (Net1_T) = ks_net - (kd_net Net1_T)

Component: Cdc6_T

Cdc6_T = Cdc6 + Cdc6P + F2 + F2P + F5 + F5P

Component: CKI_T

CKI_T = Sic1_T + Cdc6_T

Component: RENTP

RENTP = Cdc14_T - (RENT + Cdc14)

Component: Net1P

Net1P = Net1_T + Cdc14 - (Net1 + Cdc14_T)

Component: PE

PE = Esp1_T - Esp1

Component: Vd_b5

Vd_b5 = kd_b5_+ kd_b5__Cdc20_A

Component: Vd_b2

Vd_b2 = kd_b2_+ kd_b2__Cdh1 + kd_b2p Cdc20_A

Component: Va_sbf

Va_sbf = ka_sbf (epsilon_sbf_n2 Cln2 + epsilon_sbf_n3 (Cln3 + Bck2) + epsilon_sbf_b5 Clb5)

Component: Vi_sbf

Vi_sbf = ki_sbf_+ ki_sbf__Clb2

Component: Vkp_c1

Vkp_c1 = kd1_c1 + \frac{kd2_c1 (epsilon_c1_n3 Cln3 + epsilon_c1_k2 Bck2 + epsilon_c1_n2 Cln2 + epsilon_c1_b5 Clb5 + epsilon_c1_b2 Clb2)}{Jd2_c1 + Sic1_T}

Component: Vkp_f6

Vkp_f6 = kd1_f6 + \frac{kd2_f6 (epsilon_f6_n3 Cln3 + epsilon_f6_k2 Bck2 + epsilon_f6_n2 Cln2 + epsilon_f6_b5 Clb5 + epsilon_f6_b2 Clb2)}{Jd2_f6 + Cdc6_T}

Component: Va_cdh

Va_cdh = ka_cdh_+ ka_cdh__Cdc14

Component: Vi_cdh

Vi_cdh = ki_cdh_+ ki_cdh__(epsilon_cdh_n3 Cln3 + epsilon_cdh_n2 Cln2 + epsilon_cdh_b5 Clb5 + epsilon_cdh_b2 Clb2)

Component: Vpp_net

Vpp_net = kpp_net_+ kpp_net__PPX

Component: Vkp_net

Vkp_net = (kkp_net_+ kkp_net__Cdc15) mass

Component: Net1

\frac{d}{d time} (Net1) = ks_net + kd_14 RENT + kdi_rent RENT + Vpp_net Net1P - (kd_net Net1 + kas_rent Cdc14 Net1 + Vkp_net Net1)

Component: RENT

\frac{d}{d time} (RENT) = kas_rent Cdc14 Net1 + Vpp_net RENTP - ((kd_14 + kd_net) RENT + kdi_rent RENT + Vkp_net RENT)

Component: PPX

\frac{d}{d time} (PPX) = ks_ppx - (Vd_ppx PPX)

Component: Vd_ppx

Vd_ppx = kd_ppx_+ \frac{kd_ppx__(J20_ppx + Cdc20_A) Jpds}{Jpds + Pds1}

Component: Vd_pds

Vd_pds = kd1_pds_+ kd2_pds__Cdc20_A + kd3_pds__Cdh1

Component: model_parameters

kmad2 = \{\begin{matrix} 8 if ORI > 1 \land SPN < 1 \\ 0.01 otherwise \end{matrix} kbub2 = \{\begin{matrix} 1 if ORI > 1 \land SPN < 1 \\ 0.2 otherwise \end{matrix} klte1 = \{\begin{matrix} 1 if SPN > 1 \land Clb2 > Kez \\ 0.1 otherwise \end{matrix}

Source: Derived from workspace Chen, Calzone, Csikasznagy, Cross, Novak, Tyson, 2004 at changeset edb741dbe5d9.

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Integrative Analysis of Cell Cycle Control in Budding Yeast