// Created by libAntimony v2.8.0
model *Cloutier2009_BrainEnergyMetabolism()

  // Compartments and Species:
  compartment Astrocytes, Capillaries, Extracellular_space, Neurons;
  species $NAg in Astrocytes, $GLCg in Astrocytes, $G6Pg in Astrocytes, $F6Pg in Astrocytes;
  species $GAPg in Astrocytes, $PEPg in Astrocytes, $PYRg in Astrocytes, $LACg in Astrocytes;
  species $NADHg in Astrocytes, $ATPg in Astrocytes, $PCrg in Astrocytes;
  species $O2g in Astrocytes, $GLYg in Astrocytes, $GLUg in Astrocytes, $NADg in Astrocytes;
  species $NADH_g_tot in Astrocytes, $ADPg in Astrocytes, $CRg in Astrocytes;
  species $PCrg_tot in Astrocytes, $AMPg in Astrocytes, $O2c in Capillaries;
  species $GLCc in Capillaries, $LACc in Capillaries, $CO2c in Capillaries;
  species $GLCe in Extracellular_space, $LACe in Extracellular_space, $GLUe in Extracellular_space;
  species $NAe in Extracellular_space, $O2a in Extracellular_space, $CO2a in Extracellular_space;
  species $GLCa in Extracellular_space, $LACa in Extracellular_space, $NAn_ in Neurons;
  species $GLCn in Neurons, $G6Pn in Neurons, $F6Pn in Neurons, $GAPn in Neurons;
  species $PEPn in Neurons, $PYRn in Neurons, $LACn in Neurons, $NADHn in Neurons;
  species $ATPn in Neurons, $PCrn in Neurons, $O2n in Neurons, $GLUn in Neurons;
  species $ADPn in Neurons, $CRn in Neurons, $PCrn_tot in Neurons, $NADn in Neurons;
  species $NADH_n_tot in Neurons, $AMPn in Neurons;

  // Assignment Rules:
  Vg_leak_Na := Sm_g/Vg*(gg_NA/F)*(RT/F*ln(NAe/NAg) - Vm);
  Veg_GLU := Vmax_eg_GLU*(GLUe/(GLUe + Km_GLU));
  Vg_pump := Sm_g/Vg*kpump*ATPg*NAg*(1 + ATPg/Km_pump)^-1;
  Vcg_GLC := Vm_cg_GLC*(GLCc/(GLCc + Km_cg_GLC) - GLCg/(GLCg + Km_cg_GLC));
  Veg_GLC := KO1*Vm_eg_GLC*(GLCe/(GLCe + Km_eg_GLC) - GLCg/(GLCg + Km_eg_GLC));
  Vg_hk := Vmax_g_hk*ATPg*(GLCg/(GLCg + Km_GLC))*(1 - 1/(1 + exp(-aG6P_inh_hk*1*(G6Pg - G6P_inh_hk))));
  Vg_glyp := Vmax_glyp*(GLYg/(GLYg + Km_GLY))*deltaVt_GLY;
  Vg_pgi := Vmaxf_g_pgi*(G6Pg/(G6Pg + Km_G6P)) - Vmaxr_g_pgi*(F6Pg/(F6Pg + Km_F6P_pgi));
  Vg_glys := Vmax_glys*(G6Pg/(G6Pg + Km_G6P_glys))*(1 - 1/(1 + exp(-aGLY_inh*1*(GLYg - GLY_inh))));
  Vg_pfk := kg_pfk*ATPg*(F6Pg/(F6Pg + Km_F6P_pfk))*(1 + (ATPg/Ki_ATP)^nH)^-1;
  Vg_pgk := kg_pgk*GAPg*ADPg*(NADg/NADHg);
  Vg_pk := kg_pk*PEPg*ADPg;
  Vg_ldh := kfg_ldh*PYRg*NADHg - krg_ldh*LACg*NADg;
  Vg_mito := Vmax_g_mito*(O2g/(O2g + Km_O2))*(ADPg/(ADPg + Km_ADP))*(PYRg/(PYRg + Km_PYR))*(1 - 1/(1 + exp(1*-aATP_mito*(ATPg/ADPg - 1*rATP_mito))));
  Vge_LAC := Vmax_ge_LAC*(LACg/(LACg + Km_ge_LAC) - LACe/(LACe + Km_ge_LAC));
  Vgc_LAC := Vmax_gc_LAC*(LACg/(LACg + Km_gc_LAC) - LACc/(LACc + Km_gc_LAC));
  Vg_ck := kfg_ck*PCrg*ADPg - krg_ck*CRg*ATPg;
  Vg_ATPase := Vmax_g_ATPase*(ATPg/(ATPg + 0.001));
  Vg_gs := Vmax_g_gs*(GLUg/(GLUg + Km_GLU))*(ATPg/(ATPg + Km_ATP));
  dAMP_dATPg := (qak/2 + qak*(ATPtot/(ATPg*u_g^(1/2)))) - (1 + 0.5*u_g^(1/2));
  Vcg_O2 := PScapg/Vg*(Ko2*(HbOP/O2c - 1)^(-1/nh_O2_model_parameters) - O2g);
  NADg := NADH_g_tot - NADHg;
  ADPg := ATPg/2*(-qak + (qak^2 + 4*qak*(ATPtot/ATPg - 1))^(1/2));
  CRg := PCrg_tot - PCrg;
  AMPg := ATPtot - (ATPg + ADPg);
  Vc_O2 := 2*(Fin_t/Vc)*(O2a - O2c);
  Vcn_O2 := PScapn/Vn*(Ko2*(HbOP/O2c - 1)^(-1/nh_O2_Vcn_O2) - O2n);
  Vc_GLC := 2*(Fin_t/Vc)*(GLCa - GLCc);
  Vce_GLC := Vm_ce_GLC*(GLCc/(GLCc + Km_ce_GLC) - GLCe/(GLCe + Km_ce_GLC));
  Vc_LAC := 2*(Fin_t/Vc)*(LACa - LACc);
  Vec_LAC := Vm_ec_LAC*(LACe/(LACe + Km_ec_LAC) - LACc/(LACc + Km_ec_LAC));
  Vnc_CO2 := 3*Vn_mito;
  Vgc_CO2 := 3*Vg_mito;
  Vc_CO2 := 2*(Fin_t/Vc)*(CO2c - CO2a);
  V_en_GLC := Vm_en_GLC*(GLCe/(GLCe + Km_en_GLC) - GLCn/(GLCn + Km_en_GLC));
  Vne_LAC := Vmax_ne_LAC*(LACn/(LACn + Km_ne_LAC) - LACe/(LACe + Km_ne_LAC));
  Vn_stim_GLU := Vn_stim*R_GLU_NA*KO2*(GLUn/(GLUn + Km_GLU));
  Vn_leak_Na := Sm_n/Vn*(gn_NA/F)*(RT/F*ln(NAe/NAn_) - Vm);
  Vn_stim := v_stim;
  Vn_pump := Sm_n/Vn*kpump*ATPn*NAn_*(1 + ATPn/Km_pump)^-1;
  Vn_hk := Vmax_n_hk*ATPn*(GLCn/(GLCn + Km_GLC))*(1 - 1/(1 + exp(-aG6P_inh_hk*1*(G6Pn - G6P_inh_hk))));
  Vn_pgi := Vmaxf_n_pgi*(G6Pn/(G6Pn + Km_G6P)) - Vmaxr_n_pgi*(F6Pn/(F6Pn + Km_F6P_pgi));
  Vn_pfk := kn_pfk*ATPn*(F6Pn/(F6Pn + Km_F6P_pfk))*(1 + (ATPn/Ki_ATP)^nH)^-1;
  Vn_pgk := kn_pgk*GAPn*ADPn*(NADn/NADHn);
  Vn_pk := kn_pk*PEPn*ADPn;
  Vn_ldh := kfn_ldh*PYRn*NADHn - krn_ldh*LACn*NADn;
  Vn_mito := Vmax_n_mito*(O2n/(O2n + Km_O2))*(ADPn/(ADPn + Km_ADP))*(PYRn/(PYRn + Km_PYR))*(1 - 1/(1 + exp(-aATP_mito*1*(ATPn/ADPn - 1*rATP_mito))));
  Vn_ck := kfn_ck*PCrn*ADPn - krn_ck*CRn*ATPn;
  Vn_ATPase := Vmax_n_ATPase*(ATPn/(ATPn + 0.001));
  dAMP_dATPn := (qak/2 + qak*(ATPtot/(ATPn*u_n^(1/2)))) - (1 + 0.5*u_n^(1/2));
  ADPn := ATPn/2*(-qak + (qak^2 + 4*qak*(ATPtot/ATPn - 1))^(1/2));
  CRn := PCrn_tot - PCrn;
  NADn := NADH_n_tot - NADHn;
  AMPn := ATPtot - (ATPn + ADPn);
  u_n := qak^2 + 4*qak*(ATPtot/ATPn - 1);
  u_g := qak^2 + 4*qak*(ATPtot/ATPg - 1);
  Fin_t := CBF0_Fin_t + (stim*CBF0_Fin_t*deltaf*(1/(1 + exp(1*-sr*(time - ((to + t1) - 3))))) - stim*CBF0_Fin_t*deltaf*(1/(1 + exp(1*-sr*(time - (to + tend + t1 + 3))))));
  Fout_t := CBF0_model_parameters*(((Vv/Vv0)^2 + tv*(Vv/Vv0)^-0.5*(Fin_t/Vv0))/(1 + CBF0_model_parameters*tv*(Vv/Vv0)^-0.5*(1/Vv0)));
  v_stim := stim*(v1_n + v2_n*((time - to)/t_n_stim)*exp(-((time - to)*(unitpulseSB/t_n_stim))))*unitpulseSB;
  deltaVt_GLY := 1 + stim*delta_GLY*KO3*(1/(1 + exp(1*-sr_GLY*(time - (to + to_GLY)))))*(1 - unitstepSB2);
  unitstepSB2 := piecewise(1, time - (tend_GLY + to + to_GLY) >= 0, 0);
  BOLD := Vv0*((k1 + k2)*(1 - dHb/dHb0) - (k2 + k3)*(1 - Vv/Vv0));
  unitpulseSB := piecewise(1, time >= to && time <= to + tend, 0);
  unitstepSB := piecewise(1, time - (tend + to) >= 0, 0);

  // Rate Rules:
  NAg' = (Vg_leak_Na + 3*Veg_GLU) - 3*Vg_pump;
  GLCg' = (Vcg_GLC + Veg_GLC) - Vg_hk;
  G6Pg' = (Vg_hk + Vg_glyp) - (Vg_pgi + Vg_glys);
  F6Pg' = Vg_pgi - Vg_pfk;
  GAPg' = 2*Vg_pfk - Vg_pgk;
  PEPg' = Vg_pgk - Vg_pk;
  PYRg' = Vg_pk - (Vg_ldh + Vg_mito);
  LACg' = Vg_ldh - (Vge_LAC + Vgc_LAC);
  NADHg' = Vg_pgk - (Vg_ldh + Vg_mito);
  ATPg' = ((Vg_pgk + Vg_pk + nOP*Vg_mito + Vg_ck) - (Vg_hk + Vg_pfk + Vg_ATPase + Vg_pump + Vg_gs))*(1 - dAMP_dATPg)^-1;
  PCrg' = -Vg_ck;
  O2g' = Vcg_O2 - NAero*Vg_mito;
  GLYg' = Vg_glys - Vg_glyp;
  GLUg' = Veg_GLU - Vg_gs;
  O2c' = Vc_O2 - (Vcn_O2*(1/Rcn) + Vcg_O2*(1/Rcg));
  GLCc' = Vc_GLC - (Vce_GLC*(1/Rce) + Vcg_GLC*(1/Rcg));
  LACc' = Vc_LAC + Vec_LAC*(1/Rce) + Vgc_LAC*(1/Rcg);
  CO2c' = (Vnc_CO2*(1/Rcn) + Vgc_CO2*(1/Rcg)) - Vc_CO2;
  GLCe' = Vce_GLC - (Veg_GLC*(1/Reg) + V_en_GLC*(1/Ren));
  LACe' = (Vne_LAC*(1/Ren) + Vge_LAC*(1/Reg)) - Vec_LAC;
  GLUe' = Vn_stim_GLU*(1/Ren) - Veg_GLU*(1/Reg);
  NAn_' = (Vn_leak_Na + Vn_stim) - 3*Vn_pump;
  GLCn' = V_en_GLC - Vn_hk;
  G6Pn' = Vn_hk - Vn_pgi;
  F6Pn' = Vn_pgi - Vn_pfk;
  GAPn' = 2*Vn_pfk - Vn_pgk;
  PEPn' = Vn_pgk - Vn_pk;
  PYRn' = Vn_pk - (Vn_ldh + Vn_mito);
  LACn' = Vn_ldh - Vne_LAC;
  NADHn' = Vn_pgk - (Vn_ldh + Vn_mito);
  ATPn' = ((Vn_pgk + Vn_pk + nOP*Vn_mito + Vn_ck) - (Vn_hk + Vn_pfk + Vn_ATPase + Vn_pump))*(1 - dAMP_dATPn)^-1;
  PCrn' = -Vn_ck;
  O2n' = Vcn_O2 - NAero*Vn_mito;
  GLUn' = Vg_gs*(1/Rng) - Vn_stim_GLU;
  Vv' = Fin_t - Fout_t;
  dHb' = Fin_t*(O2a - O2c) - Fout_t*(dHb/Vv);

  // Species initializations:
  NAg = 13.36;
  GLCg = 0.1656;
  G6Pg = 0.7326;
  F6Pg = 0.1116;
  GAPg = 0.0698;
  PEPg = 0.0254;
  PYRg = 0.1711;
  LACg = 0.4651;
  NADHg = 0.0445;
  ATPg = 2.24;
  PCrg = 4.6817;
  O2g = 0.1589;
  GLYg = 2.5;
  GLUg = 0;
  NADH_g_tot = 0.22;
  PCrg_tot = 5;
  O2c = 7.4201;
  GLCc = 4.6401;
  LACc = 0.3251;
  CO2c = 2.12;
  GLCe = 0.3339;
  LACe = 0.3986;
  GLUe = 0;
  NAe = 150;
  O2a = 8.34;
  CO2a = 1.2;
  GLCa = 4.8;
  LACa = 0.313;
  NAn_ = 15.533;
  GLCn = 0.2633;
  G6Pn = 0.7275;
  F6Pn = 0.1091;
  GAPn = 0.0418;
  PEPn = 0.0037;
  PYRn = 0.0388;
  LACn = 0.3856;
  NADHn = 0.0319;
  ATPn = 2.2592;
  PCrn = 4.2529;
  O2n = 0.0975;
  GLUn = 3;
  PCrn_tot = 5;
  NADH_n_tot = 0.22;

  // Compartment initializations:
  Astrocytes = 1;
  Capillaries = 1;
  Extracellular_space = 1;
  Neurons = 1;

  // Variable initializations:
  nOP = 15;
  NAero = 3;
  qak = 0.92;
  ATPtot = 2.379;
  Rcn = 0.01222;
  Rcg = 0.022;
  Rce = 0.0275;
  Reg = 0.8;
  Ren = 0.444444444444444;
  Rng = 1.8;
  Vv = 0.0237;
  dHb = 0.0218;
  Sm_n = 40500;
  Vn = 0.45;
  gn_NA = 0.0039;
  F = 96500;
  RT = 2577340;
  Vm = -70;
  kpump = 3.17e-007;
  Km_pump = 0.4243;
  Vm_en_GLC = 0.50417;
  Km_en_GLC = 5.32;
  Vmax_n_hk = 0.0513;
  Km_GLC = 0.105;
  aG6P_inh_hk = 20;
  G6P_inh_hk = 0.6;
  Vmaxf_n_pgi = 0.5;
  Km_G6P = 0.5;
  Vmaxr_n_pgi = 0.45;
  Km_F6P_pgi = 0.06;
  kn_pfk = 0.55783;
  Km_F6P_pfk = 0.18;
  Ki_ATP = 0.7595;
  nH = 4;
  kn_pgk = 0.4287;
  kn_pk = 28.6;
  kfn_ldh = 5.3;
  krn_ldh = 0.1046;
  Vmax_n_mito = 0.05557;
  Km_O2 = 0.0029658;
  Km_ADP = 0.00107;
  Km_PYR = 0.0632;
  aATP_mito = 5;
  rATP_mito = 20;
  Vmax_ne_LAC = 0.1978;
  Km_ne_LAC = 0.09314;
  Vmax_n_ATPase = 0.04889;
  kfn_ck = 0.0524681;
  krn_ck = 0.015;
  PScapn = 0.2202;
  Ko2 = 0.089733;
  HbOP = 8.6;
  nh_O2_Vcn_O2 = 2.7;
  Sm_g = 10500;
  Vg = 0.25;
  gg_NA = 0.00325;
  KO1 = 1;
  Vm_eg_GLC = 0.038089;
  Km_eg_GLC = 3.53;
  Vm_cg_GLC = 0.0098394;
  Km_cg_GLC = 9.92;
  Vmax_g_hk = 0.050461;
  Vmaxf_g_pgi = 0.5;
  Vmaxr_g_pgi = 0.45;
  kg_pfk = 0.403;
  kg_pgk = 0.2514;
  kg_pk = 2.73;
  kfg_ldh = 6.2613;
  krg_ldh = 0.54682;
  Vmax_g_mito = 0.008454;
  Vmax_ge_LAC = 0.086124;
  Km_ge_LAC = 0.22163;
  Vmax_gc_LAC = 0.00021856;
  Km_gc_LAC = 0.12862;
  Vmax_g_ATPase = 0.035657;
  kfg_ck = 0.0243;
  krg_ck = 0.02073;
  PScapg = 0.2457;
  nh_O2_model_parameters = 2.7;
  Vc = 0.0055;
  Vm_ce_GLC = 0.0489;
  Km_ce_GLC = 8.4568;
  Vm_ec_LAC = 0.0325;
  Km_ec_LAC = 0.764818;
  R_GLU_NA = 0.075;
  KO2 = 1;
  Km_GLU = 0.05;
  Vmax_g_gs = 0.3;
  Km_ATP = 0.01532;
  Vmax_eg_GLU = 0.0208;
  Vmax_glys = 0.0001528;
  Km_G6P_glys = 0.5;
  aGLY_inh = 20;
  GLY_inh = 4.2;
  Vmax_glyp = 4.922e-005;
  Km_GLY = 1;
  stim = 1;
  delta_GLY = 62;
  KO3 = 1;
  sr_GLY = 4;
  to = 200;
  to_GLY = 83;
  CBF0_Fin_t = 0.012;
  deltaf = 0.42;
  sr = 4.59186;
  t1 = 2;
  tend = 300;
  CBF0_model_parameters = 0.012;
  Vv0 = 0.0236;
  tv = 35;
  k1 = 2.22;
  k2 = 0.46;
  dHb0 = 0.064;
  k3 = 0.43;
  v1_n = 0.041;
  v2_n = 2.55;
  t_n_stim = 2;
  tend_GLY = 440;

  // Other declarations:
  var Vg_leak_Na, Veg_GLU, Vg_pump, Vcg_GLC, Veg_GLC, Vg_hk, Vg_glyp, Vg_pgi;
  var Vg_glys, Vg_pfk, Vg_pgk, Vg_pk, Vg_ldh, Vg_mito, Vge_LAC, Vgc_LAC, Vg_ck;
  var Vg_ATPase, Vg_gs, dAMP_dATPg, Vcg_O2, Vc_O2, Vcn_O2, Vc_GLC, Vce_GLC;
  var Vc_LAC, Vec_LAC, Vnc_CO2, Vgc_CO2, Vc_CO2, V_en_GLC, Vne_LAC, Vn_stim_GLU;
  var Vn_leak_Na, Vn_stim, Vn_pump, Vn_hk, Vn_pgi, Vn_pfk, Vn_pgk, Vn_pk;
  var Vn_ldh, Vn_mito, Vn_ck, Vn_ATPase, dAMP_dATPn, u_n, u_g, Vv, Fin_t;
  var Fout_t, dHb, v_stim, deltaVt_GLY, unitstepSB2, BOLD, unitpulseSB, unitstepSB;
  const Astrocytes, Capillaries, Extracellular_space, Neurons, nOP, NAero;
  const qak, ATPtot, Rcn, Rcg, Rce, Reg, Ren, Rng, Sm_n, Vn, gn_NA, F, RT;
  const Vm, kpump, Km_pump, Vm_en_GLC, Km_en_GLC, Vmax_n_hk, Km_GLC, aG6P_inh_hk;
  const G6P_inh_hk, Vmaxf_n_pgi, Km_G6P, Vmaxr_n_pgi, Km_F6P_pgi, kn_pfk;
  const Km_F6P_pfk, Ki_ATP, nH, kn_pgk, kn_pk, kfn_ldh, krn_ldh, Vmax_n_mito;
  const Km_O2, Km_ADP, Km_PYR, aATP_mito, rATP_mito, Vmax_ne_LAC, Km_ne_LAC;
  const Vmax_n_ATPase, kfn_ck, krn_ck, PScapn, Ko2, HbOP, nh_O2_Vcn_O2, Sm_g;
  const Vg, gg_NA, KO1, Vm_eg_GLC, Km_eg_GLC, Vm_cg_GLC, Km_cg_GLC, Vmax_g_hk;
  const Vmaxf_g_pgi, Vmaxr_g_pgi, kg_pfk, kg_pgk, kg_pk, kfg_ldh, krg_ldh;
  const Vmax_g_mito, Vmax_ge_LAC, Km_ge_LAC, Vmax_gc_LAC, Km_gc_LAC, Vmax_g_ATPase;
  const kfg_ck, krg_ck, PScapg, nh_O2_model_parameters, Vc, Vm_ce_GLC, Km_ce_GLC;
  const Vm_ec_LAC, Km_ec_LAC, R_GLU_NA, KO2, Km_GLU, Vmax_g_gs, Km_ATP, Vmax_eg_GLU;
  const Vmax_glys, Km_G6P_glys, aGLY_inh, GLY_inh, Vmax_glyp, Km_GLY, stim;
  const delta_GLY, KO3, sr_GLY, to, to_GLY, CBF0_Fin_t, deltaf, sr, t1, tend;
  const CBF0_model_parameters, Vv0, tv, k1, k2, dHb0, k3, v1_n, v2_n, t_n_stim;
  const tend_GLY;

  // Display Names:
  Extracellular_space is "Extracellular space";
  nh_O2_Vcn_O2 is "nh_O2";
  nh_O2_model_parameters is "nh_O2_2";
  CBF0_Fin_t is "CBF0";
  CBF0_model_parameters is "CBF0_2";
end