Model Mathematics

Component: environment

Component: NAn

ddtime NAn = Vn_leak_Na + Vn_stim - 3 Vn_pump

Component: GLCn

ddtime GLCn = V_en_GLC - Vn_hk

Component: G6Pn

ddtime G6Pn = Vn_hk - Vn_pgi

Component: F6Pn

ddtime F6Pn = Vn_pgi - Vn_pfk

Component: GAPn

ddtime GAPn = 2 Vn_pfk - Vn_pgk

Component: PEPn

ddtime PEPn = Vn_pgk - Vn_pk

Component: PYRn

ddtime PYRn = Vn_pk - Vn_ldh + Vn_mito

Component: LACn

ddtime LACn = Vn_ldh - Vne_LAC

Component: NADHn

ddtime NADHn = Vn_pgk - Vn_ldh + Vn_mito

Component: ATPn

ddtime ATPn = Vn_pgk + Vn_pk + nOP Vn_mito + Vn_ck - Vn_hk + Vn_pfk + Vn_ATPase + Vn_pump 1 - dAMP_dATPn -1

Component: PCrn

ddtime PCrn =- Vn_ck

Component: O2n

ddtime O2n = Vcn_O2 - NAero Vn_mito

Component: GLUn

ddtime GLUn = Vg_gs 1 Rng - Vn_stim_GLU

Component: NAg

ddtime NAg = Vg_leak_Na + 3 Veg_GLU - 3 Vg_pump

Component: GLCg

ddtime GLCg = Vcg_GLC + Veg_GLC - Vg_hk

Component: G6Pg

ddtime G6Pg = Vg_hk + Vg_glyp - Vg_pgi + Vg_glys

Component: F6Pg

ddtime F6Pg = Vg_pgi - Vg_pfk

Component: GAPg

ddtime GAPg = 2 Vg_pfk - Vg_pgk

Component: PEPg

ddtime PEPg = Vg_pgk - Vg_pk

Component: PYRg

ddtime PYRg = Vg_pk - Vg_ldh + Vg_mito

Component: LACg

ddtime LACg = Vg_ldh - Vge_LAC + Vgc_LAC

Component: NADHg

ddtime NADHg = Vg_pgk - Vg_ldh + Vg_mito

Component: ATPg

ddtime ATPg = Vg_pgk + Vg_pk + nOP Vg_mito + Vg_ck - Vg_hk + Vg_pfk + Vg_ATPase + Vg_pump + Vg_gs 1 - dAMP_dATPg -1

Component: PCrg

ddtime PCrg =- Vg_ck

Component: O2g

ddtime O2g = Vcg_O2 - NAero Vg_mito

Component: GLYg

ddtime GLYg = Vg_glys - Vg_glyp

Component: GLUg

ddtime GLUg = Veg_GLU - Vg_gs

Component: GLCe

ddtime GLCe = Vce_GLC - Veg_GLC 1 Reg + V_en_GLC 1 Ren

Component: LACe

ddtime LACe = Vne_LAC 1 Ren + Vge_LAC 1 Reg - Vec_LAC

Component: GLUe

ddtime GLUe = Vn_stim_GLU 1 Ren - Veg_GLU 1 Reg

Component: O2c

ddtime O2c = Vc_O2 - Vcn_O2 1 Rcn + Vcg_O2 1 Rcg

Component: GLCc

ddtime GLCc = Vc_GLC - Vce_GLC 1 Rce + Vcg_GLC 1 Rcg

Component: LACc

ddtimeLACc=Vc_LAC+Vec_LAC1Rce+Vgc_LAC1Rcg

Component: CO2c

ddtime CO2c = Vnc_CO2 1 Rcn + Vgc_CO2 1 Rcg - Vc_CO2

Component: Vv

ddtime Vv = Fin_t - Fout_t

Component: dHb

ddtime dHb = Fin_t O2a - O2c - Fout_t dHb Vv

Component: Vn_leak_Na

Vn_leak_Na=Sm_nVngn_NAFRTFlnNAeNAn-Vm

Component: Vn_pump

Vn_pump = Sm_n Vn kpump ATPn NAn 1 + ATPn Km_pump -1

Component: Vn_stim

Vn_stim = v_stim

Component: V_en_GLC

V_en_GLC = Vm_en_GLC GLCe GLCe + Km_en_GLC - GLCn GLCn + Km_en_GLC

Component: Vn_hk

Vn_hk = Vmax_n_hk ATPn GLCn GLCn + Km_GLC 1 - 1 1 +- aG6P_inh_hk 1 G6Pn - G6P_inh_hk

Component: Vn_pgi

Vn_pgi = Vmaxf_n_pgi G6Pn G6Pn + Km_G6P - Vmaxr_n_pgi F6Pn F6Pn + Km_F6P_pgi

Component: Vn_pfk

Vn_pfk = kn_pfk ATPn F6Pn F6Pn + Km_F6P_pfk 1 + ATPn Ki_ATP nH -1

Component: Vn_pgk

Vn_pgk = kn_pgk GAPn ADPn NADn NADHn

Component: Vn_pk

Vn_pk = kn_pk PEPn ADPn

Component: Vn_ldh

Vn_ldh = kfn_ldh PYRn NADHn - krn_ldh LACn NADn

Component: Vn_mito

Vn_mito=Vmax_n_mitoO2nO2n+Km_O2ADPnADPn+Km_ADPPYRnPYRn+Km_PYR1-11+-aATP_mito1ATPnADPn-1rATP_mito

Component: Vne_LAC

Vne_LAC=Vmax_ne_LACLACnLACn+Km_ne_LAC-LACeLACe+Km_ne_LAC

Component: Vn_ATPase

Vn_ATPase = Vmax_n_ATPase ATPn ATPn + 0.001

Component: Vn_ck

Vn_ck = kfn_ck PCrn ADPn - krn_ck CRn ATPn

Component: Vcn_O2

Vcn_O2 = PScapn Vn Ko2 HbOP O2c - 1.0 -1.0 nh_O2 - O2n

Component: Vg_leak_Na

Vg_leak_Na=Sm_gVggg_NAFRTFlnNAeNAg-Vm

Component: Vg_pump

Vg_pump=Sm_gVgkpumpATPgNAg1+ATPgKm_pump-1

Component: Veg_GLC

Veg_GLC = KO1 Vm_eg_GLC GLCe GLCe + Km_eg_GLC - GLCg GLCg + Km_eg_GLC

Component: Vcg_GLC

Vcg_GLC = Vm_cg_GLC GLCc GLCc + Km_cg_GLC - GLCg GLCg + Km_cg_GLC

Component: Vg_hk

Vg_hk = Vmax_g_hk ATPg GLCg GLCg + Km_GLC 1 - 1 1 +- aG6P_inh_hk 1 G6Pg - G6P_inh_hk

Component: Vg_pgi

Vg_pgi = Vmaxf_g_pgi G6Pg G6Pg + Km_G6P - Vmaxr_g_pgi F6Pg F6Pg + Km_F6P_pgi

Component: Vg_pfk

Vg_pfk = kg_pfk ATPg F6Pg F6Pg + Km_F6P_pfk 1 + ATPg Ki_ATP nH -1

Component: Vg_pgk

Vg_pgk = kg_pgk GAPg ADPg NADg NADHg

Component: Vg_pk

Vg_pk = kg_pk PEPg ADPg

Component: Vg_ldh

Vg_ldh = kfg_ldh PYRg NADHg - krg_ldh LACg NADg

Component: Vg_mito

Vg_mito=Vmax_g_mitoO2gO2g+Km_O2ADPgADPg+Km_ADPPYRgPYRg+Km_PYR1-11+1-aATP_mitoATPgADPg-1rATP_mito

Component: Vge_LAC

Vge_LAC=Vmax_ge_LACLACgLACg+Km_ge_LAC-LACeLACe+Km_ge_LAC

Component: Vgc_LAC

Vgc_LAC=Vmax_gc_LACLACgLACg+Km_gc_LAC-LACcLACc+Km_gc_LAC

Component: Vg_ATPase

Vg_ATPase = Vmax_g_ATPase ATPg ATPg + 0.001

Component: Vg_ck

Vg_ck = kfg_ck PCrg ADPg - krg_ck CRg ATPg

Component: Vcg_O2

Vcg_O2 = PScapg Vg Ko2 HbOP O2c - 1.0 -1.0 nh_O2 - O2g

Component: Vc_O2

Vc_O2 = 2.0 Fin_t Vc O2a - O2c

Component: Vc_GLC

Vc_GLC = 2.0 Fin_t Vc GLCa - GLCc

Component: Vce_GLC

Vce_GLC = Vm_ce_GLC GLCc GLCc + Km_ce_GLC - GLCe GLCe + Km_ce_GLC

Component: Vc_LAC

Vc_LAC = 2.0 Fin_t Vc LACa - LACc

Component: Vec_LAC

Vec_LAC = Vm_ec_LAC LACe LACe + Km_ec_LAC - LACc LACc + Km_ec_LAC

Component: Vnc_CO2

Vnc_CO2 = 3.0 Vn_mito

Component: Vgc_CO2

Vgc_CO2 = 3.0 Vg_mito

Component: Vn_stim_GLU

Vn_stim_GLU = Vn_stim R_GLU_NA KO2 GLUn GLUn + Km_GLU

Component: Vg_gs

Vg_gs=Vmax_g_gsGLUgGLUg+Km_GLUATPgATPg+Km_ATP

Component: Veg_GLU

Veg_GLU = Vmax_eg_GLU GLUe GLUe + Km_GLU

Component: Vc_CO2

Vc_CO2 = 2.0 Fin_t Vc CO2c - CO2a

Component: Vg_glys

Vg_glys = Vmax_glys G6Pg G6Pg + Km_G6P_glys 1 - 1 1 +- aGLY_inh 1 GLYg - GLY_inh

Component: Vg_glyp

Vg_glyp = Vmax_glyp GLYg GLYg + Km_GLY deltaVt_GLY deltaVt_GLY=1+stimdelta_GLYKO311+1-sr_GLYtime-to+to_GLY1-unitstepSB2

Component: Fin_t

Fin_t = CBF0 + stim CBF0 deltaf 1 1 + 1 - sr time - to + t1 - 3 - stim CBF0 deltaf 1 1 + 1 - sr time - to + tend + t1 + 3

Component: Fout_t

Fout_t=CBF0VvVv02+tvVvVv0-0.5Fin_tVv01+CBF0tvVvVv0-0.51Vv0

Component: NADn

NADn = NADH_n_tot - NADHn

Component: NADg

NADg = NADH_g_tot - NADHg

Component: CRn

CRn = PCrn_tot - PCrn

Component: CRg

CRg = PCrg_tot - PCrg

Component: ADPn

ADPn=ATPn2-qak+qak2+4qakATPtotATPn-1

Component: ADPg

ADPg=ATPg2-qak+qak2+4qakATPtotATPg-1

Component: u_n

u_n = qak 2 + 4 qak ATPtot ATPn - 1

Component: u_g

u_g = qak 2 + 4 qak ATPtot ATPg - 1

Component: dAMP_dATPn

dAMP_dATPn = qak 2 + qak ATPtot ATPn u_n - 1 + 0.5 u_n

Component: dAMP_dATPg

dAMP_dATPg = qak 2 + qak ATPtot ATPg u_g - 1 + 0.5 u_g

Component: AMPn

AMPn=ATPtot-ATPn+ADPn

Component: AMPg

AMPg=ATPtot-ATPg+ADPg

Component: BOLD

BOLD = Vv0 k1 + k2 1 - dHb dHb0 - k2 + k3 1 - Vv Vv0

Component: v_stim

v_stim=stimv1_n+v2_ntime-tot_n_stim-time-tounitpulseSBt_n_stimunitpulseSB unitpulseSB = 1 if time to time to + tend 0 otherwise

Component: unitstepSB

unitstepSB = 1 if time - tend + to 0 0 otherwise

Component: model_parameters

Component: unitstepSB2

unitstepSB2=1iftime-tend_GLY+to+to_GLY00otherwise