You are here: Home / Exposures / Csikasz-Nagy, Battogtokh, Chen, Novak, Tyson, 2006 / Analysis of a generic model of eukaryotic cell-cycle regulation: budding yeast taken from the original model code

Model Mathematics

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Component: environment

Component: CycA

\frac{d}{d time} (CycA) = k_dissa Tri_A + V_di Tri_A + V_sa - (V_da CycA) - (k_assa CKI CycA)

Component: CycB

\frac{d}{d time} (CycB) = ((V_sb - (V_db CycB)) + V_25 pB - (V_wee CycB) - (k_assb CycB CKI)) + k_dissb BCKI + V_di BCKI

Component: CycE

\frac{d}{d time} (CycE) = k_disse Tri_E + V_di Tri_E + V_se - (V_de CycE) - (k_asse CKI CycE)

Component: CycD

CycD = CycD_0 mass

Component: Cdc20_A

\frac{d}{d time} (Cdc20_A) = \frac{k_a20 APCP Cdc20_i}{J_a20 + Cdc20_i} - (\frac{Cdc20_A k_i20}{J_i20 + Cdc20_A}) - (Cdc20_A k_d20)

Component: Cdc20_i

\frac{d}{d time} (Cdc20_i) = \frac{k_s20p + k_s20pp {CycB}^{n20}}{{J_20}^{n20} + {CycB}^{n20}} + \frac{Cdc20_A k_i20}{J_i20 + Cdc20_A} - (k_d20 Cdc20_i) - (\frac{k_a20 APCP Cdc20_i}{J_a20 + Cdc20_i})

Component: APC

APC = \frac{APC_T - APCP}{1}

Component: APCP

\frac{d}{d time} (APCP) = \frac{k_aie CycB APC}{J_aie + APC} - (\frac{k_iie APCP}{J_iie + APCP})

Component: pB

\frac{d}{d time} (pB) = (V_wee CycB - (V_db pB) - (k_assb pB CKI)) + k_dissb pBCKI + V_di pBCKI - (V_25 pB)

Component: BCKI

\frac{d}{d time} (BCKI) = (k_assb CycB CKI - (k_dissb BCKI)) + V_25 pBCKI - (V_wee BCKI) - (V_db BCKI) - (V_di BCKI)

Component: pBCKI

\frac{d}{d time} (pBCKI) = (k_assb pB CKI - (k_dissb pBCKI) - (V_25 pBCKI)) + V_wee BCKI - (V_db pBCKI) - (V_di pBCKI)

Component: Tri_A

\frac{d}{d time} (Tri_A) = k_assa CKI CycA - (k_dissa Tri_A) - (V_di Tri_A) - (V_da Tri_A)

Component: Tri_E

\frac{d}{d time} (Tri_E) = k_asse CKI CycE - (k_disse Tri_E) - (V_di Tri_E) - (V_de Tri_E)

Component: CKI

\frac{d}{d time} (CKI) = ((((- k_assb) CycB CKI + k_dissb BCKI - (k_assb pB CKI)) + k_dissb pBCKI + V_db BCKI + V_db pBCKI + V_si - (V_di CKI) - (k_assa CKI CycA)) + k_dissa Tri_A + V_da Tri_A - (k_asse CKI CycE)) + k_disse Tri_E + V_de Tri_E

Component: Cdh1_i

Cdh1_i = \frac{Cdh1_T - Cdh1}{1}

Component: Cdh1

\frac{d}{d time} (Cdh1) = \frac{Cdh1_i V_ah1}{J_ah1 + Cdh1_i} - (\frac{Cdh1 V_ih1}{J_ih1 + Cdh1})

Component: mass

\frac{d}{d time} (mass) = mu mass (1 - (\frac{mass}{maxmass}))

Component: V_atf

V_atf = k_atfp + k_atfapp CycA + k_atfepp CycE + k_atfdpp CycD

Component: V_itf

V_itf = k_itfp + k_itfapp CycA + k_itfbpp CycB

Component: TF_E

TF_E = \frac{2 V_atf J_itf}{(V_itf - V_atf) + J_atf V_itf + J_itf V_atf + \sqrt{{((V_itf - V_atf) + J_atf V_itf + J_itf V_atf)}^{2} - (4 (V_itf - V_atf) J_itf V_atf)}}

Component: V_de

V_de = k_dep + k_deepp CycE + k_deapp CycA + k_debpp CycB

Component: V_da

V_da = k_dap + (k_dapp + k_dappp) Cdc20_A + k_dappp Cdc20_i

Component: TF_I

Cdc14 = Cdc20_A TF_I = \frac{2 k_afi Cdc14 J_ifi}{(k_ifip + k_ifibpp CycB - (k_afi Cdc14)) + J_afi (k_ifip + k_ifibpp CycB) + J_ifi k_afi Cdc14 + \sqrt{{((k_ifip + k_ifibpp CycB - (k_afi Cdc14)) + J_afi (k_ifip + k_ifibpp CycB) + J_ifi k_afi Cdc14)}^{2} - (4 (k_ifip + k_ifibpp CycB - (k_afi Cdc14)) J_ifi k_afi Cdc14)}}

Component: V_ah1

V_ah1 = k_ah1p + k_ah1pp Cdc14

Component: V_ih1

V_ih1 = k_ih1p + k_ih1app CycA + k_ih1bpp CycB + k_ih1epp CycE + k_ih1dpp CycD

Component: V_si

V_si = k_sip + k_sipp TF_I

Component: V_di

V_di = \frac{k_dip + k_diapp CycA + k_dibpp CycB + k_diepp CycE + k_didpp CycD}{1 + k_14di Cdc14}

Component: preMPF

preMPF = pB + BCKI

Component: CycBT

CycBT = CycB + pB + BCKI + pBCKI

Component: CycAT

CycAT = CycA + Tri_A

Component: CycET

CycET = CycE + Tri_E

Component: Tri_B

Tri_B = BCKI + pBCKI

Component: CKIT

CKIT = CKI + BCKI + pBCKI + Tri_A + Tri_E

Component: Cdc20_T

Cdc20_T = Cdc20_i + Cdc20_A

Component: TF_B

TF_B = \frac{2 k_afb CycB J_ifb}{(k_ifb - (k_afb CycB)) + J_afb k_ifb + J_ifb k_afb CycB + \sqrt{{((k_ifb - (k_afb CycB)) + J_afb k_ifb + J_ifb k_afb CycB)}^{2} - (4 (k_ifb - (k_afb CycB)) k_afb CycB J_ifb)}}

Component: V_sb

V_sb = mass (k_sbp + k_sbpp TF_B)

Component: V_sa

V_sa = mass (k_sap + k_sapp TF_E)

Component: V_se

V_se = mass (k_sep + k_sepp TF_E)

Component: V_db

V_db = k_dbp + k_dbhpp Cdh1 + k_dbcpp Cdc20_A

Component: Wee1

Wee1 = \frac{2 (k_aweep + k_aweepp Cdc14) J_iwee}{(k_iweep + k_iweepp CycB - (k_aweep + k_aweepp Cdc14)) + J_awee (k_iweep + k_iweepp CycB) + J_iwee (k_aweep + k_aweepp Cdc14) + \sqrt{{((k_iweep + k_iweepp CycB - (k_aweep + k_aweepp Cdc14)) + J_awee (k_iweep + k_iweepp CycB) + J_iwee (k_aweep + k_aweepp Cdc14))}^{2} - (4 (k_iweep + k_iweepp CycB - (k_aweep + k_aweepp Cdc14)) (k_aweep + k_aweepp Cdc14) J_iwee)}}

Component: V_wee

V_wee = k_weep + k_weepp Wee1

Component: Cdc25

Cdc25 = \frac{2 (k_a25p + k_a25pp CycB) J_i25}{(k_i25p + k_i25pp Cdc14 - (k_a25p + k_a25pp CycB)) + J_a25 (k_i25p + k_i25pp Cdc14) + (k_a25p + k_a25pp CycB) J_i25 + \sqrt{{((k_i25p + k_i25pp Cdc14 - (k_a25p + k_a25pp CycB)) + J_a25 (k_i25p + k_i25pp Cdc14) + (k_a25p + k_a25pp CycB) J_i25)}^{2} - (4 (k_i25p + k_i25pp Cdc14 - (k_a25p + k_a25pp CycB)) (k_a25p + k_a25pp CycB) J_i25)}}

Component: V_25

V_25 = k_25p + k_25pp Cdc25

Component: kinetic_parameters

Source: Derived from workspace Csilkasz-Nagy 2006 at changeset 1dd4d0a48cec.

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