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Model Mathematics

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Component: environment

Component: Casp8

J_f0 = k_f0 Casp8Bid J_Casp8 = (- u) Casp8 J_0 = k_10 Casp8 Bid - (k_00 Casp8Bid) r_20NO = k_20NO FeLnNO Casp8 \frac{d}{d time} (Casp8) = (- J_0) + J_f0 + J_Casp8 - r_19NO - r_20NO \frac{d}{d time} (Casp8Bid) = J_0 - J_f0

Component: Apaf_1

J_Apaf_1 = P_Apaf_1 - (u Apaf_1) J_1 = k_11 Cytc Apaf_1 - (k_01 CytcApaf_1) \frac{d}{d time} (Apaf_1) = (- J_1) + J_Apaf_1

Component: CytcApaf_1

J_1b = k_11b {CytcApaf_1}^{p} - (k_01b Apop) \frac{d}{d time} (CytcApaf_1) = J_1 - (7 J_1b)

Component: Cytc

J_Cytc = (- u) Cytc PTPC_act = PTPC_0 - PTPC \frac{d}{d time} (Cytc) = (J_14 - J_1) + J_Cytc + k_1 PTPC_act Cytc_mito

Component: Cytc_mito

J_Cytc_mito = P_Cytc_mito - (u Cytc_mito) J_14 = k14 Bax_2 Cytc_mito \frac{d}{d time} (Cytc_mito) = (- J_14) + J_Cytc_mito

Component: Bax_2

J_Bax_2 = (- u) Bax_2 \frac{d}{d time} (Bax_2) = J_12b + J_Bax_2

Component: tBid_mito

J_tBid_mito = (- u) tBid_mito J_12a = k12a tBid_mito Bax \frac{d}{d time} (tBid_mito) = (J_11 - J_12a) + J_tBid_mito

Component: tBid

J_11 = k11 tBid J_tBid = (- u) tBid \frac{d}{d time} (tBid) = (J_f0 + J_f8 - J_11) + J_12b + J_tBid

Component: tBidBax

J_tBidBax = (- u) tBidBax J_12b = k12b tBidBax Bax \frac{d}{d time} (tBidBax) = (J_12a - J_12b) + J_tBidBax

Component: Bax

P_Bax = P_oBax (1 + \frac{{p53}^{4}}{{p53}^{4} + {p53_thresh}^{4}}) J_Bax = P_Bax - (u_Bax Bax) J_13 = k13 Bcl_2 Bax \frac{d}{d time} (Bax) = (- J_12a - J_12b - J_13) + J_Bax

Component: Bcl_2

P_Bcl_2 = \frac{P_oBcl_2 {p53_thresh}^{4}}{{p53}^{4} + {p53_thresh}^{4}} J_9 = k_19 Casp3 Bcl_2 - (k_09 Casp3Bcl_2) J_Bcl_2 = P_Bcl_2 - (u_Bcl_2 Bcl_2) \frac{d}{d time} (Bcl_2) = (- J_9 - J_13) + J_Bcl_2

Component: Casp3Bcl_2

J_f9 = k_f9 Casp3Bcl_2 \frac{d}{d time} (Casp3Bcl_2) = J_9 - J_f9

Component: Casp3Bid

J_8 = k_18 Casp3 Bid - (k_08 Casp3Bid) J_f8 = k_f8 Casp3Bid \frac{d}{d time} (Casp3Bid) = J_8 - J_f8

Component: Bid

J_Bid = P_Bid - (u Bid) \frac{d}{d time} (Bid) = (- J_0 - J_8) + J_Bid

Component: Casp3

J_Casp3 = (- u) Casp3 J_7 = k_17 Casp3 IAP - (k_07 Casp3IAP) \frac{d}{d time} (Casp3IAP) = J_7 \frac{d}{d time} (Casp3) = ((J_f6 + J_f6b - J_7 - J_8) + J_f8 - J_9) + J_f9 + J_Casp3 - r_22NO

Component: Apop

\frac{d}{d time} (Apop) = (J_1b - J_2) + J_4b

Component: Pro9

J_Pro9 = P_Pro9 - (u Pro9) J_2 = k_12 Apop Pro9 - (k_02 ApopPro9) J_3 = k_13 ApopPro9 Pro9 - (k_03 ApopPro9_2) \frac{d}{d time} (Pro9) = (- J_2 - J_3) + J_Pro9 \frac{d}{d time} (ApopPro9) = J_2 - J_3

Component: ApopPro9_2

J_f3 = k_f3 ApopPro9_2 \frac{d}{d time} (ApopPro9_2) = J_3 - J_f3

Component: ApopCasp9_2Pro3

J_6b = k_16b ApopCasp9_2 Pro3 - (k_06b ApopCasp9_2Pro3) J_f6b = k_f6b ApopCasp9_2Pro3 \frac{d}{d time} (ApopCasp9_2Pro3) = J_6b - J_f6b

Component: Casp9Pro3

J_f6 = k_f6 Casp9Pro3 \frac{d}{d time} (Casp9Pro3) = J_6 - J_f6

Component: Pro3

J_6 = k_16 Casp9 Pro3 - (k_06 Casp9Pro3) J_Pro3 = P_Pro3 - (u Pro3) \frac{d}{d time} (Pro3) = (- J_6 - J_6b) + J_Pro3

Component: IAP

J_5 = k_15 Casp9 IAP - (k_05 Casp9IAP) J_5b = k_15b ApopCasp9 IAP - (k_05b ApopCasp9IAP) J_5c = k_15c ApopCasp9_2 IAP - (k_05c ApopCasp9_2IAP) J_IAP = P_IAP - (u IAP) \frac{d}{d time} (Casp9IAP) = J_5 \frac{d}{d time} (ApopCasp9IAP) = J_5b \frac{d}{d time} (ApopCasp9_2IAP) = J_5c \frac{d}{d time} (IAP) = (- J_5 - J_5b - J_5c - J_7) + J_IAP

Component: ApopCasp9

J_4 = k_14 ApopCasp9_2 - (k_04 ApopCasp9 Casp9) J_4b = k_14b ApopCasp9 - (k_04b Apop Casp9) \frac{d}{d time} (ApopCasp9) = J_4 - J_4b - J_5b

Component: Casp9

J_Casp9 = (- u) Casp9 \frac{d}{d time} (Casp9) = (J_4 + J_4b - J_5 - J_6) + J_f6 + J_Casp9 - r_21NO

Component: ApopCasp9_2

\frac{d}{d time} (ApopCasp9_2) = (J_f3 - J_4 - J_5c - J_6b) + J_f6b

Component: NO

r_1NO = k_1NO r_4NO = k_4NO NO O_2m r_12aNO = k_12aNO {NO}^{2} O_2 r_12bNOp = k_12bNOp NO_2 NO r_12bNOm = k_12bNOm N2O3 r_14NO = k_14NO GSNO r_15NO = k_15NO CcOX NO r_16NO = k_16NO FeLn NO \frac{d}{d time} (NO) = (r_1NO - r_4NO - (2 r_12aNO) - r_12bNOp) + r_12bNOm + r_14NO - r_15NO - r_16NO \frac{d}{d time} (CcOX) = - r_15NO \frac{d}{d time} (NO_2) = (2 r_12aNO - r_12bNOp) + r_12bNOm

Component: O_2m

r_2NO = k_2NO r_5NO = k_5NO SOD O_2m r_10NO = k_10NO {GSNO}^{2} O_2m \frac{d}{d time} (O_2m) = r_2NO - r_4NO - r_5NO - r_10NO

Component: ONOO_m

r_6NO = k_6NO ONOO_m GSH r_7NO = k_7NO ONOO_m GPX r_8NO = k_8NO ONOO_m CO_2 r_9NO = k_9NO ONOO_m Cyt_c r_18NO = k_18NO ONOO_m PTPC \frac{d}{d time} (ONOO_m) = r_4NO - r_6NO - r_7NO - r_8NO - r_9NO - r_18NO

Component: GSH

GSSG = \frac{GSH_0 - GSH - GSNO}{2} r_11NO = k_11NO N2O3 GSH r_m = \frac{v_m GSSG}{k_m + GSSG} r_17NO = k_17NO FeLnNO GSH \frac{d}{d time} (GSH) = (- r_6NO - r_11NO) + 2 r_m - r_17NO

Component: GSNO

\frac{d}{d time} (GSNO) = ((r_6NO - (2 r_10NO)) + r_11NO - r_14NO) + r_17NO

Component: N2O3

r_13NO = k_13NO N2O3 \frac{d}{d time} (N2O3) = (- r_11NO) + r_12bNOp - r_12bNOm - r_13NO - r_19NO

Component: FeLn

r_21NO = k_21NO FeLnNO Casp9 r_22NO = k_22NO FeLnNO Casp3 \frac{d}{d time} (FeLn) = (- r_16NO) + r_17NO + r_20NO + r_21NO + r_22NO \frac{d}{d time} (FeLnNO) = r_16NO - r_17NO - r_20NO - r_21NO - r_22NO

Component: PTPC

r_19NO = k_19NO N2O3 Casp8 \frac{d}{d time} (PTPC) = - r_19NO

Component: model_constant

Source: Derived from workspace Bagci 2008 at changeset 219d126f6f27.

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