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Model Mathematics

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Component: environment

Component: Clb2

\frac{d}{d time} (Clb2) = \frac{ks_clb (epsilon + Mcm_a) M}{1 + \frac{M}{Jm}} + kmih PClb2 + kdiss Trim + (kd_sic + kd_sic_1 Cln + kd_sic_2 Clb2) Trim - ((kd_clb_1 + kd_clb_2 Cdh1_a + kd_clb_3 Cdc20_a) Clb2 + kswe Clb2 + kass Sic1 Clb2)

Component: PClb2

\frac{d}{d time} (PClb2) = kswe Clb2 + kdiss PTrim + (kd_sic + kd_sic_1 Cln + kd_sic_2 Clb2) PTrim - ((kd_clb_1 + kd_clb_2 Cdh1_a + kd_clb_3 Cdc20_a) PClb2 + kmih PClb2 + kass Sic1 PClb2)

Component: Trim

\frac{d}{d time} (Trim) = kass Sic1 Clb2 + kmih PTrim - (kdiss Trim + (kd_sic + kd_sic_1 Cln + kd_sic_2 Clb2) Trim + (kd_clb_1 + kd_clb_2 Cdh1_a + kd_clb_3 Cdc20_a) Trim + kswe Trim)

Component: PTrim

\frac{d}{d time} (PTrim) = kswe Trim + kass Sic1 PClb2 - (kdiss PTrim + (kd_sic + kd_sic_1 Cln + kd_sic_2 Clb2) PTrim + (kd_clb_1 + kd_clb_2 Cdh1_a + kd_clb_3 Cdc20_a) PTrim + kmih PTrim)

Component: Mcm_a

\frac{d}{d time} (Mcm_a) = \frac{(- ki_mcm) Mcm_a}{Ji_mcm + Mcm_a} + \frac{ka_mcm Mcm Clb2}{Ja_mcm + Mcm}

Component: Sic1

\frac{d}{d time} (Sic1) = ks_sic + kdiss (PTrim + Trim) + (kd_clb_1 + kd_clb_2 Cdh1_a + kd_clb_3 Cdc20_a) (PTrim + Trim) - ((kd_sic + kd_sic_1 Cln + kd_sic_2 Clb2) Sic1 + kass Sic1 (Clb2 + PClb2))

Component: Mih1_a

\frac{d}{d time} (Mih1_a) = \frac{(- Vi_mih) Mih1_a}{Ji_mih + Mih1_a} + \frac{Va_mih Clb2 Mih1}{Ja_mih + Mih1}

Component: IE_a

\frac{d}{d time} (IE_a) = \frac{(- ki_ie) IE_a}{Ji_ie + IE_a} + \frac{ka_ie Clb2 IE}{Ja_ie + IE}

Component: Cdc20_a

\frac{d}{d time} (Cdc20_a) = \frac{ka_cdc20 IE_a Cdc20}{Ja_cdc20 + Cdc20} - (\frac{ki_cdc20 Cdc20_a}{Ji_cdc20 + Cdc20_a} + kd_cdc20 Cdc20_a)

Component: Cdc20

\frac{d}{d time} (Cdc20) = ks_cdc20_1 + \frac{ks_cdc20_2 {Clb2}^{4}}{{Js_cdc20}^{4} + {Clb2}^{4}} + \frac{ki_cdc20 Cdc20_a}{Ji_cdc20 + Cdc20_a} - (\frac{ka_cdc20 IE_a Cdc20}{Ja_cdc20 + Cdc20} + kd_cdc20 Cdc20)

Component: Cdh1_a

\frac{d}{d time} (Cdh1_a) = \frac{(- (ki_cdh Clb2 + ki_cdh_1 Cln)) Cdh1_a}{Ji_cdh + Cdh1_a} + \frac{(ka_cdh_1 + ka_cdh_2 Cdc20_a) Cdh1}{Ja_cdh + Cdh1}

Component: Cln

\frac{d}{d time} (Cln) = ks_cln SBF_a - (kd_cln Cln)

Component: SBF_a

\frac{d}{d time} (SBF_a) = \frac{(- (ki_sbf_1 + ki_sbf_2 Clb2)) SBF_a}{Ji_sbf + SBF_a} + \frac{(ka_sbf_1 M + ka_sbf_2 Cln) SBF}{Ja_sbf + SBF}

Component: Swe1

\frac{d}{d time} (Swe1) = ks_swe SBF_a + ks_sweC + khsl1r Swe1M + \frac{Va_wee PSwe1}{Ja_wee + PSwe1} - (khsl1 BUD Swe1 + \frac{Vi_wee Clb2 Swe1}{Ji_wee + Swe1} + kd_swe_1 Swe1)

Component: PSwe1

\frac{d}{d time} (PSwe1) = khsl1r PSwe1M + \frac{Vi_wee Swe1 Clb2}{Ji_wee + Swe1} - (khsl1 BUD PSwe1 + \frac{Va_wee PSwe1}{Ja_wee + PSwe1} + kd_swe_1 PSwe1)

Component: Swe1M

\frac{d}{d time} (Swe1M) = khsl1 BUD Swe1 + \frac{Va_wee PSwe1M}{Ja_wee + PSwe1M} - (khsl1r Swe1M + \frac{Vi_wee Clb2 Swe1M}{Ji_wee + Swe1M} + kd_swe_1 Swe1M)

Component: PSwe1M

\frac{d}{d time} (PSwe1M) = khsl1 BUD PSwe1 + \frac{Vi_wee Clb2 Swe1M}{Ji_wee + Swe1M} - (khsl1r PSwe1M + \frac{Va_wee PSwe1M}{Ja_wee + PSwe1M} + kd_swe_2 PSwe1M)

Component: BE

\frac{d}{d time} (BE) = ks_bud Cln - (kd_bud BE)

Component: M

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

Component: IE

IE = IE_total - IE_a

Component: Cdh1

Cdh1 = Cdh1_total - Cdh1_a

Component: Mih1

Mih1 = Mih1_total - Mih1_a

Component: Mcm

Mcm = Mcm_total - Mcm_a

Component: SBF

SBF = SBF_total - SBF_a

Component: Swe1_total

Swe1_total = Swe1 + PSwe1 + Swe1M + PSwe1M

Component: BUD

BUD = \{\begin{matrix} 0 if BE ≦ 0.6 \land Clb2 < 0.2 \\ 1 otherwise \end{matrix}

Component: kinetic_parameters

kmih = kmih_1 Mih1_a + kmih_2 Mih1 kswe = kswe_1 Swe1 + kswe_2 Swe1M + kswe_3 PSwe1

Source: Derived from workspace Ciliberto, Novak, Tyson, 2003 at changeset 58d58f539f22.

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Mathematical Model of the Morphogenesis Checkpoint in Budding Yeast