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Model Mathematics

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Component: environment

Component: Cln2

\frac{d}{d time} (Cln2) = mass (ks_n2 + ks_n2_SBF) - (kd_n2 Cln2)

Component: Clb2_T

\frac{d}{d time} (Clb2_T) = mass (ks_b2 + ks_b2_Mcm1) - (Vd_b2 Clb2_T) Vd_b2 = kd_b2 (Hct1_T - Hct1) + kd_b2_Hct1 + kd_b2__Cdc20

Component: Clb2

Clb2 = Clb2_T - Clb2_Sic1

Component: Clb5

Clb5 = Clb5_T - Clb5_Sic1

Component: Sic1

Sic1 = Sic1_T - (Clb2_Sic1 + Clb5_Sic1)

Component: Clb5_T

\frac{d}{d time} (Clb5_T) = mass (ks_b5 + ks_b5_MBF) - (Vd_b5 Clb5_T) Vd_b5 = kd_b5 + kd_b5_Cdc20

Component: Bck2

Bck2 = Bck2_0 mass

Component: Cln3

Cln3 = \frac{Cln3_max Dn3 mass}{Jn3 + Dn3 mass}

Component: Sic1_T

\frac{d}{d time} (Sic1_T) = ks_c1 + ks_c1_Swi5 - (Sic1_T (kd1_c1 + \frac{Vd2_c1}{Jd2_c1 + Sic1_T}))

Component: Clb2_Sic1

\frac{d}{d time} (Clb2_Sic1) = kas_b2 Clb2 Sic1 - (Clb2_Sic1 (kdi_b2 + Vd_b2 + kd1_c1 + \frac{Vd2_c1}{Jd2_c1 + Sic1_T}))

Component: Clb5_Sic1

\frac{d}{d time} (Clb5_Sic1) = kas_b5 Clb5 Sic1 - (Clb5_Sic1 (kdi_b5 + Vd_b5 + kd1_c1 + \frac{Vd2_c1}{Jd2_c1 + Sic1_T}))

Component: Vd2_c1

Vd2_c1 = kd2_c1 (epsilonc1_n3 Cln3 + epsilonc1_k2 Bck2 + Cln2 + epsilonc1_b5 Clb5 + epsilonc1_b2 Clb2)

Component: Cdc20_T

\frac{d}{d time} (Cdc20_T) = ks_20 + ks_20_Clb2 - (kd_20 Cdc20_T)

Component: Cdc20

\frac{d}{d time} (Cdc20) = ka_20 (Cdc20_T - Cdc20) - (Cdc20 (Vi_20 + kd_20)) Vi_20 = \{\begin{matrix} ki_20_if ORI \geq 1 \\ ki_20 if SPN \geq 1 \\ 0.1 otherwise \end{matrix}

Component: Hct1

\frac{d}{d time} (Hct1) = \frac{(ka_t1 + ka_t1_Cdc20) (Hct1_T - Hct1)}{Ja_t1 + Hct1_T - Hct1} - (\frac{Vi_t1 Hct1}{Ji_t1 + Hct1}) Vi_t1 = ki_t1 + ki_t1_(Cln3 + epsiloni_t1_n2 Cln2 + epsiloni_t1_b5 Clb5 + epsiloni_t1_b2 Clb2)

Component: mass

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

Component: ORI

\frac{d}{d time} (ORI) = ks_ori (Clb5 + epsilonori_b2 Clb2) - (kd_ori ORI)

Component: BUD

\frac{d}{d time} (BUD) = ks_bud (Cln2 + Cln3 + epsilonbud_b5 Clb5) - (kd_bud BUD)

Component: SPN

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

Component: SBF

SBF = \frac{2 Va_sbf Ji_sbf}{(ki_sbf + ki_sbf_Clb2 + Va_sbf Ji_sbf + (ki_sbf + ki_sbf_Clb2) Ja_sbf - Va_sbf) + \sqrt{{(ki_sbf + ki_sbf_Clb2 + Va_sbf Ji_sbf + (ki_sbf + ki_sbf_Clb2) Ja_sbf - Va_sbf)}^{2} - (4 Va_sbf Ji_sbf (ki_sbf + ki_sbf_Clb2 - Va_sbf))}} Va_sbf = ka_sbf (Cln2 + epsilonsbf_n3 (Cln3 + Bck2) + epsilonsbf_b5 Clb5)

Component: MBF

MBF = SBF

Component: Mcm1

Mcm1 = \frac{2 ka_mcm Clb2 Ji_mcm}{(ki_mcm + ka_mcm Clb2 Ji_mcm + ki_mcm Ja_mcm - (ka_mcm Clb2)) + \sqrt{{(ki_mcm + ka_mcm Clb2 Ji_mcm + ki_mcm Ja_mcm - (ka_mcm Clb2))}^{2} - (4 (ki_mcm - (ka_mcm Clb2)) ka_mcm Clb2 Ji_mcm)}}

Component: Swi5

Swi5 = \frac{2 ka_swi Cdc20 Ji_swi}{(ki_swi + ki_swi_Clb2 + ka_swi Cdc20 Ji_swi + (ki_swi + ki_swi_Clb2) Ja_swi - (ka_swi Cdc20)) + \sqrt{{(ki_swi + ki_swi_Clb2 + ka_swi Cdc20 Ji_swi + (ki_swi + ki_swi_Clb2) Ja_swi - (ka_swi Cdc20))}^{2} - (4 (ki_swi + ki_swi_Clb2 - (ka_swi Cdc20)) ka_swi Cdc20 Ji_swi)}}

Component: parameters

Source: Derived from workspace Chen, Csikasz-Nagy, Gyorffy, Val, Novak, Tyson, 2000 at changeset 42ecf20937b3.

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Kinetic Analysis of a Molecular Model of the Budding Yeast Cell Cycle