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BIOMD0000000554 - Cloutier2009 - Brain Energy Metabolism

 

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Reference Publication
Publication ID: 19396534
Cloutier M, Bolger FB, Lowry JP, Wellstead P.
An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements.
J Comput Neurosci 2009 Dec; 27(3): 391-414
Hamilton Institute, National University of Ireland Maynooth, Maynooth, Ireland.  [more]
Model
Original Model: CellML logo
Submitter: Camille Laibe
Submission ID: MODEL1006230041
Submission Date: 23 Jun 2010 09:12:09 UTC
Last Modification Date: 20 Apr 2015 15:57:22 UTC
Creation Date: 25 Jun 2010 12:46:06 UTC
Encoders:  Catherine Lloyd
   Vijayalakshmi Chelliah
   Audald Lloret i Villas
set #1
bqmodel:isDerivedFrom BioModels Database Aubert2005 - Interaction between astrocytes and neurons on energy metabolism
PubMed 16260743
set #2
bqbiol:occursIn Brenda Tissue Ontology BTO:0000142
set #3
bqbiol:isVersionOf Gene Ontology generation of precursor metabolites and energy
set #4
bqbiol:hasTaxon Taxonomy Homo sapiens
Taxonomy Rattus norvegicus
Notes
Cloutier2009 - Brain Energy Metabolism


This model was taken from the  CellML repository  and automatically converted to SBML.  Following the submission the parameters are manually encoded and annotated as spices and global quantities by BioModels curators. 
 
The original model was:  Cloutier M, Bolger FB, Lowry JP, Wellstead P. (2009) - version=1.0 
The original CellML model was created by: 
Catherine Lloyd  
c.lloyd@auckland.ac.nz 
The University of Auckland 

This model is described in the article:

Cloutier M, Bolger FB, Lowry JP, Wellstead P.
J Comput Neurosci 2009 Dec; 27(3): 391-414

Abstract:

An integrative, systems approach to the modelling of brain energy metabolism is presented. Mechanisms such as glutamate cycling between neurons and astrocytes and glycogen storage in astrocytes have been implemented. A unique feature of the model is its calibration using in vivo data of brain glucose and lactate from freely moving rats under various stimuli. The model has been used to perform simulated perturbation experiments that show that glycogen breakdown in astrocytes is significantly activated during sensory (tail pinch) stimulation. This mechanism provides an additional input of energy substrate during high consumption phases. By way of validation, data from the perfusion of 50 microM propranolol in the rat brain was compared with the model outputs. Propranolol affects the glucose dynamics during stimulation, and this was accurately reproduced in the model by a reduction in the glycogen breakdown in astrocytes. The model's predictive capacity was verified by using data from a sensory stimulation (restraint) that was not used for model calibration. Finally, a sensitivity analysis was conducted on the model parameters, this showed that the control of energy metabolism and transport processes are critical in the metabolic behaviour of cerebral tissue.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Model
Publication ID: 19396534 Submission Date: 23 Jun 2010 09:12:09 UTC Last Modification Date: 20 Apr 2015 15:57:22 UTC Creation Date: 25 Jun 2010 12:46:06 UTC
Mathematical expressions
Rules
Assignment Rule (variable: V_en_GLC) Assignment Rule (variable: Vn_hk) Assignment Rule (variable: Vn_pgi) Assignment Rule (variable: NADg)
Assignment Rule (variable: ADPg) Assignment Rule (variable: CRg) Assignment Rule (variable: AMPg) Assignment Rule (variable: Vg_ck)
Assignment Rule (variable: ADPn) Assignment Rule (variable: CRn) Assignment Rule (variable: NADn) Assignment Rule (variable: AMPn)
Assignment Rule (variable: u_n) Assignment Rule (variable: u_g) Assignment Rule (variable: dAMP_dATPn) Assignment Rule (variable: dAMP_dATPg)
Assignment Rule (variable: Vn_leak_Na) Assignment Rule (variable: Vn_pump) Assignment Rule (variable: Vn_pfk) Assignment Rule (variable: Vn_pgk)
Assignment Rule (variable: Vn_pk) Assignment Rule (variable: Vn_ldh) Assignment Rule (variable: Vn_mito) Assignment Rule (variable: Vne_LAC)
Assignment Rule (variable: Vn_ATPase) Assignment Rule (variable: Vge_LAC) Assignment Rule (variable: Vn_ck) Assignment Rule (variable: Vcn_O2)
Assignment Rule (variable: Vg_leak_Na) Assignment Rule (variable: Vg_pump) Assignment Rule (variable: Veg_GLC) Assignment Rule (variable: Vcg_GLC)
Assignment Rule (variable: Vg_hk) Assignment Rule (variable: Vg_pgi) Assignment Rule (variable: Vg_pfk) Assignment Rule (variable: Vg_pgk)
Assignment Rule (variable: Vg_pk) Assignment Rule (variable: Vg_ldh) Assignment Rule (variable: Vg_mito) Assignment Rule (variable: Vgc_LAC)
Assignment Rule (variable: Vg_ATPase) Assignment Rule (variable: Vcg_O2) Assignment Rule (variable: Vce_GLC) Assignment Rule (variable: Vec_LAC)
Assignment Rule (variable: Vnc_CO2) Assignment Rule (variable: Vgc_CO2) Assignment Rule (variable: Vg_gs) Assignment Rule (variable: Veg_GLU)
Assignment Rule (variable: Vg_glys) Assignment Rule (variable: Fin_t) Assignment Rule (variable: Vc_O2) Assignment Rule (variable: Vc_GLC)
Assignment Rule (variable: Vc_LAC) Assignment Rule (variable: Vc_CO2) Assignment Rule (variable: Fout_t) Assignment Rule (variable: BOLD)
Assignment Rule (variable: unitpulseSB) Assignment Rule (variable: v_stim) Assignment Rule (variable: Vn_stim) Assignment Rule (variable: Vn_stim_GLU)
Assignment Rule (variable: unitstepSB) Assignment Rule (variable: unitstepSB2) Assignment Rule (variable: deltaVt_GLY) Assignment Rule (variable: Vg_glyp)
Rate Rule (variable: NAg) Rate Rule (variable: GLCg) Rate Rule (variable: G6Pg) Rate Rule (variable: F6Pg)
Rate Rule (variable: GAPg) Rate Rule (variable: PEPg) Rate Rule (variable: PYRg) Rate Rule (variable: LACg)
Rate Rule (variable: NADHg) Rate Rule (variable: ATPg) Rate Rule (variable: PCrg) Rate Rule (variable: O2g)
Rate Rule (variable: GLYg) Rate Rule (variable: GLUg) Rate Rule (variable: O2c) Rate Rule (variable: GLCc)
Rate Rule (variable: LACc) Rate Rule (variable: CO2c) Rate Rule (variable: GLCe) Rate Rule (variable: LACe)
Rate Rule (variable: GLUe) Rate Rule (variable: NAn) Rate Rule (variable: GLCn) Rate Rule (variable: G6Pn)
Rate Rule (variable: F6Pn) Rate Rule (variable: GAPn) Rate Rule (variable: PEPn) Rate Rule (variable: PYRn)
Rate Rule (variable: LACn) Rate Rule (variable: NADHn) Rate Rule (variable: ATPn) Rate Rule (variable: PCrn)
Rate Rule (variable: O2n) Rate Rule (variable: GLUn) Rate Rule (variable: Vv) Rate Rule (variable: dHb)
Physical entities
Compartments Species
Astrocytes NAg GLCg G6Pg
F6Pg GAPg PEPg
PYRg LACg NADHg
ATPg PCrg O2g
GLYg GLUg NADg
ADPg CRg NADH_g_tot
PCrg_tot AMPg  
Capillaries O2c GLCc LACc
CO2c    
Extracellular space GLCe LACe GLUe
NAe O2a CO2a
GLCa LACa  
Neurons NAn GLCn G6Pn
F6Pn GAPn PEPn
PYRn LACn NADHn
ATPn PCrn O2n
GLUn ADPn CRn
NADn NADH_n_tot PCrn_tot
AMPn    
Global parameters
u_n u_g dAMP_dATPn dAMP_dATPg
Vv dHb Vn_leak_Na gn_NA
Vn_pump Vn_stim V_en_GLC Km_en_GLC
Vm_en_GLC Vn_hk Vmax_n_hk Vn_pgi
Vmaxf_n_pgi Vmaxr_n_pgi Vn_pfk kn_pfk
Vn_pgk kn_pgk Vn_pk kn_pk
Vn_ldh kfn_ldh krn_ldh Vn_mito
Vmax_n_mito Vne_LAC Vmax_ne_LAC Km_ne_LAC
Vn_ATPase Vmax_n_ATPase Vn_ck krn_ck
kfn_ck Vcn_O2 nh_O2 PScapn
Vg_leak_Na gg_NA Vg_pump Veg_GLC
Km_eg_GLC Vm_eg_GLC Vcg_GLC Km_cg_GLC
Vm_cg_GLC Vg_hk Vmax_g_hk Vg_pgi
Vmaxf_g_pgi Vmaxr_g_pgi Vg_pfk kg_pfk
Vg_pgk kg_pgk Vg_pk kg_pk
Vg_ldh kfg_ldh krg_ldh Vg_mito
Vmax_g_mito Vge_LAC Vmax_ge_LAC Km_ge_LAC
Vgc_LAC Vmax_gc_LAC Km_gc_LAC Vg_ATPase
Vmax_g_ATPase Vg_ck krg_ck kfg_ck
Vcg_O2 PScapg Vc_O2 Vc_GLC
Vce_GLC Km_ce_GLC Vm_ce_GLC Vc_LAC
Vec_LAC Km_ec_LAC Vm_ec_LAC Vnc_CO2
Vgc_CO2 Vn_stim_GLU Vg_gs Vmax_g_gs
Veg_GLU Vmax_eg_GLU Vc_CO2 Vg_glys
Vmax_glys Km_G6P_glys Vg_glyp Vmax_glyp
Km_GLY deltaVt_GLY Fin_t CBF0
Fout_t BOLD v_stim unitpulseSB
unitstepSB Km_PYR Km_ATP Ki_ATP
Km_ADP Km_O2 Km_GLC Km_GLU
Km_G6P Km_F6P_pgi Km_F6P_pfk Km_pump
nh_O2_2 Ko2 kpump ATPtot
nH nOP NAero Rng
Reg Ren Rcn Rcg
Rce Sm_n Vm RT
F Vn G6P_inh_hk aG6P_inh_hk
rATP_mito aATP_mito HbOP Sm_g
Vg KO1 Vc R_GLU_NA
KO2 KO3 GLY_inh aGLY_inh
CBF0_2 Vv0 tv qak
k1 k2 k3 dHb0
stim to tend v1_n
v2_n t_n_stim sr t1
delta_GLY deltaf tend_GLY to_GLY
sr_GLY unitstepSB2    
Reactions (0)
Rules (100)
 
 Assignment Rule (name: V_en_GLC) V_en_GLC = Vm_en_GLC*(GLCe/(GLCe+Km_en_GLC)-GLCn/(GLCn+Km_en_GLC))
 
 Assignment Rule (name: Vn_hk) Vn_hk = Vmax_n_hk*ATPn*GLCn/(GLCn+Km_GLC)*(1-1/(1+exp((-aG6P_inh_hk)*1*(G6Pn-G6P_inh_hk))))
 
 Assignment Rule (name: Vn_pgi) Vn_pgi = Vmaxf_n_pgi*G6Pn/(G6Pn+Km_G6P)-Vmaxr_n_pgi*F6Pn/(F6Pn+Km_F6P_pgi)
 
 Assignment Rule (name: NADg) NADg = NADH_g_tot-NADHg
 
 Assignment Rule (name: ADPg) ADPg = ATPg/2*((-qak)+(qak^2+4*qak*(ATPtot/ATPg-1))^(1/2))
 
 Assignment Rule (name: CRg) CRg = PCrg_tot-PCrg
 
 Assignment Rule (name: AMPg) AMPg = ATPtot-(ATPg+ADPg)
 
 Assignment Rule (name: Vg_ck) Vg_ck = kfg_ck*PCrg*ADPg-krg_ck*CRg*ATPg
 
 Assignment Rule (name: ADPn) ADPn = ATPn/2*((-qak)+(qak^2+4*qak*(ATPtot/ATPn-1))^(1/2))
 
 Assignment Rule (name: CRn) CRn = PCrn_tot-PCrn
 
 Assignment Rule (name: NADn) NADn = NADH_n_tot-NADHn
 
 Assignment Rule (name: AMPn) AMPn = ATPtot-(ATPn+ADPn)
 
 Assignment Rule (name: u_n) u_n = qak^2+4*qak*(ATPtot/ATPn-1)
 
 Assignment Rule (name: u_g) u_g = qak^2+4*qak*(ATPtot/ATPg-1)
 
 Assignment Rule (name: dAMP_dATPn) dAMP_dATPn = (qak/2+qak*ATPtot/(ATPn*u_n^(1/2)))-(1+0.5*u_n^(1/2))
 
 Assignment Rule (name: dAMP_dATPg) dAMP_dATPg = (qak/2+qak*ATPtot/(ATPg*u_g^(1/2)))-(1+0.5*u_g^(1/2))
 
 Assignment Rule (name: Vn_leak_Na) Vn_leak_Na = Sm_n/Vn*gn_NA/F*(RT/F*ln(NAe/NAn)-Vm)
 
 Assignment Rule (name: Vn_pump) Vn_pump = Sm_n/Vn*kpump*ATPn*NAn*(1+ATPn/Km_pump)^(-1)
 
 Assignment Rule (name: Vn_pfk) Vn_pfk = kn_pfk*ATPn*F6Pn/(F6Pn+Km_F6P_pfk)*(1+(ATPn/Ki_ATP)^nH)^(-1)
 
 Assignment Rule (name: Vn_pgk) Vn_pgk = kn_pgk*GAPn*ADPn*NADn/NADHn
 
 Assignment Rule (name: Vn_pk) Vn_pk = kn_pk*PEPn*ADPn
 
 Assignment Rule (name: Vn_ldh) Vn_ldh = kfn_ldh*PYRn*NADHn-krn_ldh*LACn*NADn
 
 Assignment Rule (name: Vn_mito) 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))))
 
 Assignment Rule (name: Vne_LAC) Vne_LAC = Vmax_ne_LAC*(LACn/(LACn+Km_ne_LAC)-LACe/(LACe+Km_ne_LAC))
 
 Assignment Rule (name: Vn_ATPase) Vn_ATPase = Vmax_n_ATPase*ATPn/(ATPn+0.001)
 
 Assignment Rule (name: Vge_LAC) Vge_LAC = Vmax_ge_LAC*(LACg/(LACg+Km_ge_LAC)-LACe/(LACe+Km_ge_LAC))
 
 Assignment Rule (name: Vn_ck) Vn_ck = kfn_ck*PCrn*ADPn-krn_ck*CRn*ATPn
 
 Assignment Rule (name: Vcn_O2) Vcn_O2 = PScapn/Vn*(Ko2*(HbOP/O2c-1)^((-1)/nh_O2_Vcn_O2)-O2n)
 
 Assignment Rule (name: Vg_leak_Na) Vg_leak_Na = Sm_g/Vg*gg_NA/F*(RT/F*ln(NAe/NAg)-Vm)
 
 Assignment Rule (name: Vg_pump) Vg_pump = Sm_g/Vg*kpump*ATPg*NAg*(1+ATPg/Km_pump)^(-1)
 
 Assignment Rule (name: Veg_GLC) Veg_GLC = KO1*Vm_eg_GLC*(GLCe/(GLCe+Km_eg_GLC)-GLCg/(GLCg+Km_eg_GLC))
 
 Assignment Rule (name: Vcg_GLC) Vcg_GLC = Vm_cg_GLC*(GLCc/(GLCc+Km_cg_GLC)-GLCg/(GLCg+Km_cg_GLC))
 
 Assignment Rule (name: Vg_hk) Vg_hk = Vmax_g_hk*ATPg*GLCg/(GLCg+Km_GLC)*(1-1/(1+exp((-aG6P_inh_hk)*1*(G6Pg-G6P_inh_hk))))
 
 Assignment Rule (name: Vg_pgi) Vg_pgi = Vmaxf_g_pgi*G6Pg/(G6Pg+Km_G6P)-Vmaxr_g_pgi*F6Pg/(F6Pg+Km_F6P_pgi)
 
 Assignment Rule (name: Vg_pfk) Vg_pfk = kg_pfk*ATPg*F6Pg/(F6Pg+Km_F6P_pfk)*(1+(ATPg/Ki_ATP)^nH)^(-1)
 
 Assignment Rule (name: Vg_pgk) Vg_pgk = kg_pgk*GAPg*ADPg*NADg/NADHg
 
 Assignment Rule (name: Vg_pk) Vg_pk = kg_pk*PEPg*ADPg
 
 Assignment Rule (name: Vg_ldh) Vg_ldh = kfg_ldh*PYRg*NADHg-krg_ldh*LACg*NADg
 
 Assignment Rule (name: Vg_mito) 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))))
 
 Assignment Rule (name: Vgc_LAC) Vgc_LAC = Vmax_gc_LAC*(LACg/(LACg+Km_gc_LAC)-LACc/(LACc+Km_gc_LAC))
 
 Assignment Rule (name: Vg_ATPase) Vg_ATPase = Vmax_g_ATPase*ATPg/(ATPg+0.001)
 
 Assignment Rule (name: Vcg_O2) Vcg_O2 = PScapg/Vg*(Ko2*(HbOP/O2c-1)^((-1)/nh_O2_model_parameters)-O2g)
 
 Assignment Rule (name: Vce_GLC) Vce_GLC = Vm_ce_GLC*(GLCc/(GLCc+Km_ce_GLC)-GLCe/(GLCe+Km_ce_GLC))
 
 Assignment Rule (name: Vec_LAC) Vec_LAC = Vm_ec_LAC*(LACe/(LACe+Km_ec_LAC)-LACc/(LACc+Km_ec_LAC))
 
 Assignment Rule (name: Vnc_CO2) Vnc_CO2 = 3*Vn_mito
 
 Assignment Rule (name: Vgc_CO2) Vgc_CO2 = 3*Vg_mito
 
 Assignment Rule (name: Vg_gs) Vg_gs = Vmax_g_gs*GLUg/(GLUg+Km_GLU)*ATPg/(ATPg+Km_ATP)
 
 Assignment Rule (name: Veg_GLU) Veg_GLU = Vmax_eg_GLU*GLUe/(GLUe+Km_GLU)
 
 Assignment Rule (name: Vg_glys) Vg_glys = Vmax_glys*G6Pg/(G6Pg+Km_G6P_glys)*(1-1/(1+exp((-aGLY_inh)*1*(GLYg-GLY_inh))))
 
 Assignment Rule (name: Fin_t) 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)))))
 
 Assignment Rule (name: Vc_O2) Vc_O2 = 2*Fin_t/Vc*(O2a-O2c)
 
 Assignment Rule (name: Vc_GLC) Vc_GLC = 2*Fin_t/Vc*(GLCa-GLCc)
 
 Assignment Rule (name: Vc_LAC) Vc_LAC = 2*Fin_t/Vc*(LACa-LACc)
 
 Assignment Rule (name: Vc_CO2) Vc_CO2 = 2*Fin_t/Vc*(CO2c-CO2a)
 
 Assignment Rule (name: Fout_t) 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)
 
 Assignment Rule (name: BOLD) BOLD = Vv0*((k1+k2)*(1-dHb/dHb0)-(k2+k3)*(1-Vv/Vv0))
 
 Assignment Rule (name: unitpulseSB) unitpulseSB = piecewise(1, (time >= to) && (time <= (to+tend)), 0)
 
 Assignment Rule (name: v_stim) v_stim = stim*(v1_n+v2_n*(time-to)/t_n_stim*exp(-(time-to)*unitpulseSB/t_n_stim))*unitpulseSB
 
 Assignment Rule (name: Vn_stim) Vn_stim = v_stim
 
 Assignment Rule (name: Vn_stim_GLU) Vn_stim_GLU = Vn_stim*R_GLU_NA*KO2*GLUn/(GLUn+Km_GLU)
 
 Assignment Rule (name: unitstepSB) unitstepSB = piecewise(1, (time-(tend+to)) >= 0, 0)
 
 Assignment Rule (name: unitstepSB2) unitstepSB2 = piecewise(1, (time-(tend_GLY+to+to_GLY)) >= 0, 0)
 
 Assignment Rule (name: deltaVt_GLY) deltaVt_GLY = 1+stim*delta_GLY*KO3*1/(1+exp(1*(-sr_GLY)*(time-(to+to_GLY))))*(1-unitstepSB2)
 
 Assignment Rule (name: Vg_glyp) Vg_glyp = Vmax_glyp*GLYg/(GLYg+Km_GLY)*deltaVt_GLY
 
 Rate Rule (name: NAg) d [ NAg] / d t= (Vg_leak_Na+3*Veg_GLU)-3*Vg_pump
 
 Rate Rule (name: GLCg) d [ GLCg] / d t= (Vcg_GLC+Veg_GLC)-Vg_hk
 
 Rate Rule (name: G6Pg) d [ G6Pg] / d t= (Vg_hk+Vg_glyp)-(Vg_pgi+Vg_glys)
 
 Rate Rule (name: F6Pg) d [ F6Pg] / d t= Vg_pgi-Vg_pfk
 
 Rate Rule (name: GAPg) d [ GAPg] / d t= 2*Vg_pfk-Vg_pgk
 
 Rate Rule (name: PEPg) d [ PEPg] / d t= Vg_pgk-Vg_pk
 
 Rate Rule (name: PYRg) d [ PYRg] / d t= Vg_pk-(Vg_ldh+Vg_mito)
 
 Rate Rule (name: LACg) d [ LACg] / d t= Vg_ldh-(Vge_LAC+Vgc_LAC)
 
 Rate Rule (name: NADHg) d [ NADHg] / d t= Vg_pgk-(Vg_ldh+Vg_mito)
 
 Rate Rule (name: ATPg) d [ ATPg] / d t= ((Vg_pgk+Vg_pk+nOP*Vg_mito+Vg_ck)-(Vg_hk+Vg_pfk+Vg_ATPase+Vg_pump+Vg_gs))*(1-dAMP_dATPg)^(-1)
 
 Rate Rule (name: PCrg) d [ PCrg] / d t= -Vg_ck
 
 Rate Rule (name: O2g) d [ O2g] / d t= Vcg_O2-NAero*Vg_mito
 
 Rate Rule (name: GLYg) d [ GLYg] / d t= Vg_glys-Vg_glyp
 
 Rate Rule (name: GLUg) d [ GLUg] / d t= Veg_GLU-Vg_gs
 
 Rate Rule (name: O2c) d [ O2c] / d t= Vc_O2-(Vcn_O2*1/Rcn+Vcg_O2*1/Rcg)
 
 Rate Rule (name: GLCc) d [ GLCc] / d t= Vc_GLC-(Vce_GLC*1/Rce+Vcg_GLC*1/Rcg)
 
 Rate Rule (name: LACc) d [ LACc] / d t= Vc_LAC+Vec_LAC*1/Rce+Vgc_LAC*1/Rcg
 
 Rate Rule (name: CO2c) d [ CO2c] / d t= (Vnc_CO2*1/Rcn+Vgc_CO2*1/Rcg)-Vc_CO2
 
 Rate Rule (name: GLCe) d [ GLCe] / d t= Vce_GLC-(Veg_GLC*1/Reg+V_en_GLC*1/Ren)
 
 Rate Rule (name: LACe) d [ LACe] / d t= (Vne_LAC*1/Ren+Vge_LAC*1/Reg)-Vec_LAC
 
 Rate Rule (name: GLUe) d [ GLUe] / d t= Vn_stim_GLU*1/Ren-Veg_GLU*1/Reg
 
 Rate Rule (name: NAn) d [ NAn] / d t= (Vn_leak_Na+Vn_stim)-3*Vn_pump
 
 Rate Rule (name: GLCn) d [ GLCn] / d t= V_en_GLC-Vn_hk
 
 Rate Rule (name: G6Pn) d [ G6Pn] / d t= Vn_hk-Vn_pgi
 
 Rate Rule (name: F6Pn) d [ F6Pn] / d t= Vn_pgi-Vn_pfk
 
 Rate Rule (name: GAPn) d [ GAPn] / d t= 2*Vn_pfk-Vn_pgk
 
 Rate Rule (name: PEPn) d [ PEPn] / d t= Vn_pgk-Vn_pk
 
 Rate Rule (name: PYRn) d [ PYRn] / d t= Vn_pk-(Vn_ldh+Vn_mito)
 
 Rate Rule (name: LACn) d [ LACn] / d t= Vn_ldh-Vne_LAC
 
 Rate Rule (name: NADHn) d [ NADHn] / d t= Vn_pgk-(Vn_ldh+Vn_mito)
 
 Rate Rule (name: ATPn) d [ ATPn] / d t= ((Vn_pgk+Vn_pk+nOP*Vn_mito+Vn_ck)-(Vn_hk+Vn_pfk+Vn_ATPase+Vn_pump))*(1-dAMP_dATPn)^(-1)
 
 Rate Rule (name: PCrn) d [ PCrn] / d t= -Vn_ck
 
 Rate Rule (name: O2n) d [ O2n] / d t= Vcn_O2-NAero*Vn_mito
 
 Rate Rule (name: GLUn) d [ GLUn] / d t= Vg_gs*1/Rng-Vn_stim_GLU
 
 Rate Rule (name: Vv) d [ Vv] / d t= Fin_t-Fout_t
 
 Rate Rule (name: dHb) d [ dHb] / d t= Fin_t*(O2a-O2c)-Fout_t*dHb/Vv
 
 Astrocytes Spatial dimensions: 3.0  Compartment size: 1.0
 
 NAg
Compartment: Astrocytes
Initial concentration: 13.36
 
 GLCg
Compartment: Astrocytes
Initial concentration: 0.1656
 
 G6Pg
Compartment: Astrocytes
Initial concentration: 0.7326
 
 F6Pg
Compartment: Astrocytes
Initial concentration: 0.1116
 
 GAPg
Compartment: Astrocytes
Initial concentration: 0.0698
 
 PEPg
Compartment: Astrocytes
Initial concentration: 0.0254
 
 PYRg
Compartment: Astrocytes
Initial concentration: 0.1711
 
 LACg
Compartment: Astrocytes
Initial concentration: 0.4651
 
 NADHg
Compartment: Astrocytes
Initial concentration: 0.0445
 
 ATPg
Compartment: Astrocytes
Initial concentration: 2.24
 
 PCrg
Compartment: Astrocytes
Initial concentration: 4.6817
 
 O2g
Compartment: Astrocytes
Initial concentration: 0.1589
 
 GLYg
Compartment: Astrocytes
Initial concentration: 2.5
 
 GLUg
Compartment: Astrocytes
Initial concentration: 0.0
 
  NADg
Compartment: Astrocytes
Initial concentration: 0.1755
 
  ADPg
Compartment: Astrocytes
Initial concentration: 0.13070953832961
 
  CRg
Compartment: Astrocytes
Initial concentration: 0.318300000000001
 
 NADH_g_tot
Compartment: Astrocytes
Initial concentration: 0.22
Constant
 
 PCrg_tot
Compartment: Astrocytes
Initial concentration: 5.0
Constant
 
  AMPg
Compartment: Astrocytes
Initial concentration: 0.00829046167039005
 
 Capillaries Spatial dimensions: 3.0  Compartment size: 1.0
 
 O2c
Compartment: Capillaries
Initial concentration: 7.4201
 
 GLCc
Compartment: Capillaries
Initial concentration: 4.6401
 
 LACc
Compartment: Capillaries
Initial concentration: 0.3251
 
 CO2c
Compartment: Capillaries
Initial concentration: 2.12
 
 Extracellular space Spatial dimensions: 3.0  Compartment size: 1.0
 
 GLCe
Compartment: Extracellular space
Initial concentration: 0.3339
 
 LACe
Compartment: Extracellular space
Initial concentration: 0.3986
 
 GLUe
Compartment: Extracellular space
Initial concentration: 0.0
 
 NAe
Compartment: Extracellular space
Initial concentration: 150.0
Constant
 
 O2a
Compartment: Extracellular space
Initial concentration: 8.34
Constant
 
 CO2a
Compartment: Extracellular space
Initial concentration: 1.2
Constant
 
 GLCa
Compartment: Extracellular space
Initial concentration: 4.8
Constant
 
 LACa
Compartment: Extracellular space
Initial concentration: 0.313
Constant
 
 Neurons Spatial dimensions: 3.0  Compartment size: 1.0
 
 NAn
Compartment: Neurons
Initial concentration: 15.533
 
 GLCn
Compartment: Neurons
Initial concentration: 0.2633
 
 G6Pn
Compartment: Neurons
Initial concentration: 0.7275
 
 F6Pn
Compartment: Neurons
Initial concentration: 0.1091
 
 GAPn
Compartment: Neurons
Initial concentration: 0.0418
 
 PEPn
Compartment: Neurons
Initial concentration: 0.0037
 
 PYRn
Compartment: Neurons
Initial concentration: 0.0388
 
 LACn
Compartment: Neurons
Initial concentration: 0.3856
 
 NADHn
Compartment: Neurons
Initial concentration: 0.0319
 
 ATPn
Compartment: Neurons
Initial concentration: 2.2592
 
 PCrn
Compartment: Neurons
Initial concentration: 4.2529
 
 O2n
Compartment: Neurons
Initial concentration: 0.0975
 
 GLUn
Compartment: Neurons
Initial concentration: 3.0
 
  ADPn
Compartment: Neurons
Initial concentration: 0.113591983539553
 
  CRn
Compartment: Neurons
Initial concentration: 0.7471
 
  NADn
Compartment: Neurons
Initial concentration: 0.1881
 
 NADH_n_tot
Compartment: Neurons
Initial concentration: 0.22
Constant
 
 PCrn_tot
Compartment: Neurons
Initial concentration: 5.0
Constant
 
  AMPn
Compartment: Neurons
Initial concentration: 0.006208016460449
 
Global Parameters (174)
 
   u_n
Value: 1.04154164305949
 
   u_g
Value: 1.07475714285714
 
   dAMP_dATPn
Value: -0.101010798503538
 
   dAMP_dATPg
Value: -0.115857415908852
 
   Vv
Value: 0.0237
 
   dHb
Value: 0.0218
 
   Vn_leak_Na
Value: 0.474905958264092
 
   gn_NA
Value: 0.0039
Constant
 
   Vn_pump
Value: 0.158300842198194
 
   Vn_stim  
 
   V_en_GLC
Value: 0.00599865999248041
 
   Km_en_GLC
Value: 5.32
Constant
 
   Vm_en_GLC
Value: 0.50417
Constant
 
   Vn_hk
Value: 0.00600093047858717
 
   Vmax_n_hk
Value: 0.0513
Constant
 
   Vn_pgi
Value: 0.00600284722882977
 
   Vmaxf_n_pgi
Value: 0.5
Constant
 
   Vmaxr_n_pgi
Value: 0.45
Constant
 
   Vn_pfk
Value: 0.00599809710207478
 
   kn_pfk
Value: 0.55783
Constant
 
   Vn_pgk
Value: 0.012002606302138
 
   kn_pgk
Value: 0.4287
Constant
 
   Vn_pk
Value: 0.0120203036981555
 
   kn_pk
Value: 28.6
Constant
 
   Vn_ldh
Value: -0.001026864256
 
   kfn_ldh
Value: 5.3
Constant
 
   krn_ldh
Value: 0.1046
Constant
 
   Vn_mito
Value: 0.0129174754920542
 
   Vmax_n_mito
Value: 0.05557
Constant
 
   Vne_LAC
Value: -0.00101735054205471
 
   Vmax_ne_LAC
Value: 0.1978
Constant
 
   Km_ne_LAC
Value: 0.09314
Constant
 
   Vn_ATPase
Value: 0.0488683691708698
 
   Vmax_n_ATPase
Value: 0.04889
Constant
 
   Vn_ck
Value: 2.93701651940294E-5
 
   krn_ck
Value: 0.015
Constant
 
   kfn_ck
Value: 0.0524681
Constant
 
   Vcn_O2
Value: 0.0390504186958046
 
   nh_O2
Value: 2.7
Constant
 
   PScapn
Value: 0.2202
Constant
 
   Vg_leak_Na
Value: 0.190378997692294
 
   gg_NA
Value: 0.00325
Constant
 
   Vg_pump
Value: 0.0634531133946177
 
   Veg_GLC
Value: 0.00158470181577655
 
   Km_eg_GLC
Value: 3.53
Constant
 
   Vm_eg_GLC
Value: 0.038089
Constant
 
   Vcg_GLC
Value: 0.00297412147754264
 
   Km_cg_GLC
Value: 9.92
Constant
 
   Vm_cg_GLC
Value: 0.0098394
Constant
 
   Vg_hk
Value: 0.00455613617326311
 
   Vmax_g_hk
Value: 0.050461
Constant
 
   Vg_pgi
Value: 0.00451935700191414
 
   Vmaxf_g_pgi
Value: 0.5
Constant
 
   Vmaxr_g_pgi
Value: 0.45
Constant
 
   Vg_pfk
Value: 0.00450657384340637
 
   kg_pfk
Value: 0.403
Constant
 
   Vg_pgk
Value: 0.0090457605321121
 
   kg_pgk
Value: 0.2514
Constant
 
   Vg_pk
Value: 0.00906366080685179
 
   kg_pk
Value: 2.73
Constant
 
   Vg_ldh
Value: 0.003039015294
 
   kfg_ldh
Value: 6.2613
Constant
 
   krg_ldh
Value: 0.54682
Constant
 
   Vg_mito
Value: 0.0060112916441682
 
   Vmax_g_mito
Value: 0.008454
Constant
 
   Vge_LAC
Value: 0.00298013264659761
 
   Vmax_ge_LAC
Value: 0.086124
Constant
 
   Km_ge_LAC
Value: 0.22163
Constant
 
   Vgc_LAC
Value: 1.46095762940601E-5
 
   Vmax_gc_LAC
Value: 2.1856E-4
Constant
 
   Km_gc_LAC
Value: 0.12862
Constant
 
   Vg_ATPase
Value: 0.035641088799643
 
   Vmax_g_ATPase
Value: 0.035657
Constant
 
   Vg_ck
Value: 8.98869880248884E-5
 
   krg_ck
Value: 0.02073
Constant
 
   kfg_ck
Value: 0.0243
Constant
 
   Vcg_O2
Value: 0.0180867710645166
 
   PScapg
Value: 0.2457
Constant
 
   Vc_O2
Value: 4.01410909090909
 
   Vc_GLC
Value: 0.69774545454546
 
   Vce_GLC
Value: 0.0154673938740423
 
   Km_ce_GLC
Value: 8.4568
Constant
 
   Vm_ce_GLC
Value: 0.0489
Constant
 
   Vc_LAC
Value: -0.0528
 
   Vec_LAC
Value: 0.0014407850610198
 
   Km_ec_LAC
Value: 0.764818
Constant
 
   Vm_ec_LAC
Value: 0.0325
Constant
 
   Vnc_CO2
Value: 0.0387524264761627
 
   Vgc_CO2
Value: 0.0180338749325046
 
   Vn_stim_GLU  
 
   Vg_gs  
 
   Vmax_g_gs
Value: 0.3
Constant
 
   Veg_GLU  
 
   Vmax_eg_GLU
Value: 0.0208
Constant
 
   Vc_CO2
Value: 4.01454545454546
 
   Vg_glys
Value: 9.08171994158688E-5
 
   Vmax_glys
Value: 1.528E-4
Constant
 
   Km_G6P_glys
Value: 0.5
Constant
 
   Vg_glyp
Value: 3.51571428571429E-5
 
   Vmax_glyp
Value: 4.922E-5
Constant
 
   Km_GLY
Value: 1.0
Constant
 
   deltaVt_GLY
Value: 1.0
 
   Fin_t
Value: 0.012
 
   CBF0
Value: 0.012
Constant
 
   Fout_t
Value: 0.0120054326049026
 
   BOLD
Value: 0.04179315
 
   v_stim  
 
   unitpulseSB  
 
   unitstepSB  
 
   Km_PYR
Value: 0.0632
Constant
 
   Km_ATP
Value: 0.01532
Constant
 
   Ki_ATP
Value: 0.7595
Constant
 
   Km_ADP
Value: 0.00107
Constant
 
   Km_O2
Value: 0.0029658
Constant
 
   Km_GLC
Value: 0.105
Constant
 
   Km_GLU
Value: 0.05
Constant
 
   Km_G6P
Value: 0.5
Constant
 
   Km_F6P_pgi
Value: 0.06
Constant
 
   Km_F6P_pfk
Value: 0.18
Constant
 
   Km_pump
Value: 0.4243
Constant
 
   nh_O2_2
Value: 2.7
Constant
 
   Ko2
Value: 0.089733
Constant
 
   kpump
Value: 3.17E-7
Constant
 
   ATPtot
Value: 2.379
Constant
 
   nH
Value: 4.0
Constant
 
   nOP
Value: 15.0
Constant
 
   NAero
Value: 3.0
Constant
 
   Rng
Value: 1.8
Constant
 
   Reg
Value: 0.8
Constant
 
   Ren
Value: 0.444444444444444
Constant
 
   Rcn
Value: 0.01222
Constant
 
   Rcg
Value: 0.022
Constant
 
   Rce
Value: 0.0275
Constant
 
   Sm_n
Value: 40500.0
Constant
 
   Vm
Value: -70.0
Constant
 
   RT
Value: 2577340.0
Constant
 
   F
Value: 96500.0
Constant
 
   Vn
Value: 0.45
Constant
 
   G6P_inh_hk
Value: 0.6
Constant
 
   aG6P_inh_hk
Value: 20.0
Constant
 
   rATP_mito
Value: 20.0
Constant
 
   aATP_mito
Value: 5.0
Constant
 
   HbOP
Value: 8.6
Constant
 
   Sm_g
Value: 10500.0
Constant
 
   Vg
Value: 0.25
Constant
 
   KO1
Value: 1.0
Constant
 
   Vc
Value: 0.0055
Constant
 
   R_GLU_NA
Value: 0.075
Constant
 
   KO2
Value: 1.0
Constant
 
   KO3
Value: 1.0
Constant
 
   GLY_inh
Value: 4.2
Constant
 
   aGLY_inh
Value: 20.0
Constant
 
   CBF0_2
Value: 0.012
Constant
 
   Vv0
Value: 0.0236
Constant
 
   tv
Value: 35.0
Constant
 
   qak
Value: 0.92
Constant
 
   k1
Value: 2.22
Constant
 
   k2
Value: 0.46
Constant
 
   k3
Value: 0.43
Constant
 
   dHb0
Value: 0.064
Constant
 
   stim
Value: 1.0
Constant
 
   to
Value: 200.0
Constant
 
   tend
Value: 300.0
Constant
 
   v1_n
Value: 0.041
Constant
 
   v2_n
Value: 2.55
Constant
 
   t_n_stim
Value: 2.0
Constant
 
   sr
Value: 4.59186
Constant
 
   t1
Value: 2.0
Constant
 
   delta_GLY
Value: 62.0
Constant
 
   deltaf
Value: 0.42
Constant
 
   tend_GLY
Value: 440.0
Constant
 
   to_GLY
Value: 83.0
Constant
 
   sr_GLY
Value: 4.0
Constant
 
   unitstepSB2  
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000554

Curator's comment: (updated: 22 Oct 2014 18:38:51 BST)

Figures 2f and 2i of the reference publication have been reproduced here. Concentration of extracellular glucose and lactate are plotted over time. The profile moves along the x-axis depending on the neuronal stimulation start, strength and duration.

The simulation was done using Copasi v4.12 (Build 81) and the plots were generated using Gnuplot. The Copasi file of the model with simulation settings can be downloaded from the below link:

Additional file(s)
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