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BIOMD0000000627 - Winter2017 - Brain Energy Metabolism with PPP

 

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Reference Publication
Publication ID: 10.1177/0271678X1769...
Felix Winter1,2, Catrin Bludszuweit-Philipp1 and Olaf Wolkenhauer2,3
Mathematical analysis of the influence of brain metabolism on the BOLD signal in Alzheimer's disease
Journal of Cerebral Blood Flow & Metabolism
1ASD Advanced Simulation and Design GmbH, Rostock, Germany 2Department of Systems Biology and Bioinformatics, Rostock University, Rostock, Germany 3Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, Stellenbosch, South Africa  [more]
Model
Original Model: BIOMD0000000627.origin
Submitter: Felix Winter
Submission ID: MODEL1603240000
Submission Date: 24 Mar 2016 20:58:10 UTC
Last Modification Date: 07 Apr 2017 17:55:35 UTC
Creation Date: 30 Jul 2013 11:50:11 UTC
Encoders:  Vijayalakshmi Chelliah
   Felix Winter
set #1
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
set #2
bqmodel:isDerivedFrom BioModels Database Cloutier2009 - Brain Energy Metabolism
BioModels Database Aubert2005 - Interaction between astrocytes and neurons on energy metabolism
DOI 10.1007/978-1-4613-1161-4
set #3
bqbiol:occursIn Brenda Tissue Ontology brain
set #4
bqbiol:hasPart Gene Ontology oxidative phosphorylation
Gene Ontology tricarboxylic acid cycle
Gene Ontology glycolytic process
Gene Ontology pentose-phosphate shunt
set #5
bqbiol:hasTaxon Taxonomy Homo sapiens
set #6
bqbiol:hasProperty Human Disease Ontology Alzheimer's disease
Notes
Winter2017 - Brain Energy Metabolism with PPP

This model is described in the article:

Felix Winter1,2, Catrin Bludszuweit-Philipp1 and Olaf Wolkenhauer2,3
Journal of Cerebral Blood Flow & Metabolism

Abstract:

Blood oxygen level-dependent functional magnetic resonance imaging (BOLD-fMRI) is a standard clinical tool for the detection of brain activation. In Alzheimer’s disease (AD), task-related and resting state fMRI have been used to detect brain dysfunction. It has been shown that the shape of the BOLD response is affected in early AD. To correctly interpret these changes, the mechanisms responsible for the observed behaviour need to be known. The parameters of the canonical hemodynamic response function (HRF) commonly used in the analysis of fMRI data have no direct biological interpretation and cannot be used to answer this question. We here present a model that allows relating AD-specific changes in the BOLD shape to changes in the underlying energy metabolism. According to our findings, the classic view that differences in the BOLD shape are only attributed to changes in strength and duration of the stimulus does not hold. Instead, peak height, peak timing and full width at half maximum are sensitive to changes in the reaction rate of several metabolic reactions. Our systems-theoretic approach allows the use of patient-specific clinical data to predict dementia- driven changes in the HRF, which can be used to improve the results of fMRI analyses in AD patients.

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: 10.1177/0271678X1769... Submission Date: 24 Mar 2016 20:58:10 UTC Last Modification Date: 07 Apr 2017 17:55:35 UTC Creation Date: 30 Jul 2013 11:50:11 UTC
Mathematical expressions
Reactions
HK_astrocytes (R01786) (HeinrichSchuster) PFK_neurons (R04779, R01070, R01015) PFK_astrocytes (R04779, R01070, R01015) PGK_neurons (R01061, R01512, R01518, R00658)
PGK_astrocytes (R01061, R01512, R01518, R00658) PK_neurons (R00200) PK_astrocytes (R00200) mitochondrial_respiration_neurons (n.a.)
mitochondrial_respiration_astrocytes (n.a.) GLC_exchange_extracellular_space_neurons (Aubert) GLC_exchange_extracellular_space_astrocytes (Aubert) GLC_exchange_capillary_ec (Aubert)
GLC_exchange_capillary_astrocytes (Aubert) LAC_exchange_ec_capillary LAC_exchange_neurons_ec LAC_exchange_astrocytes_ec
LAC_exchange_astrocytes_capillary O2_exchange_capillary_neurons O2_exchange_capillary_astrocytes O2_exchange_artery_capillary
GLC_exchange_artery_capillary LAC_exchange_capillary_artery CO2_exchange_capillary_artery Na+_exchange_neurons_extracellular_space (n.a.)
Na+_exchange_astrocytes_extracellular_space (n.a.) LEAK_Na_neurons (n.a.) LEAK_Na_astrocytes (n.a) Na+_exchange_extracellular_space_neurons (stimulation)
GLU_exchange_neurons_extracellular_space GLU_exchange_extracellular_space_astrocytes GLU_exchange_astrocytes_neurons inflow of dHb
outflow of dHb ATPase_neurons (n.a.) ATPase_astrocytes (n.a.) AK_neurons (R00127)
AK_astrocytes (R00127) CK_astrocytes (R01881) CK_neurons (R01881) LDH_astrocytes (R00703)
LDH_neurons (R00703) ZWF_astrocytes (R02736) ZWF_neurons (R02736) SOL_neurons (R02035)
SOL_astrocytes (R02035) GND_neurons (R01528) GND_astrocytes (R01528) RPE_neurons (R01529)
RPE_astrocytes (R01529) RKI_astrocytes (R01056) RKI_neurons (R01056) TKL-1_astrocytes (R01641)
TKL-1_neurons (R01641) TAL_astrocytes (R01827) TAL_neurons (R01827) TKL-2_astrocytes (R01830)
TKL-2_neurons (R01830) NADPH oxidase neurons (R07172) NADPH oxidase astrocytes (R07172) R5P sink_astrocytes (n.a.)
R5P sink_neurons (n.a.) PGI_astrocytes (R02740) (HS) HK_neurons (R01786) (HeinrichSchuster) PGI_neurons (R02740) (HS)
Rules
Assignment Rule (variable: E0) Assignment Rule (variable: BOLD signal) Assignment Rule (variable: Vmax_ce_GLC (wrt capillaries) (Aubert)) Assignment Rule (variable: Vmax_eg_GLC (wrt astrocytes) (Aubert) )
Assignment Rule (variable: Vmax_en_GLC (wrt neurons) (Aubert)) Assignment Rule (variable: Vmax_cg_GLC (wrt capillaries) (Aubert)) Assignment Rule (variable: Vmax_ec_LAC (wrt extracellular space) (Aubert)) Assignment Rule (variable: Vmax_gc_LAC (wrt astrocytes) (Aubert))
Assignment Rule (variable: Vmax_ge_LAC (wrt astrocytes) (Aubert)) Assignment Rule (variable: Vmax_ne_LAC (wrt neurons) (Aubert)) Assignment Rule (variable: PS_cap_astrocytes (wrt capillaries) (Aubert)) Assignment Rule (variable: PS_cap_neuron (wrt capillaries) (Aubert))
Assignment Rule (variable: f_CBF_dyn) Assignment Rule (variable: stimulus) Assignment Rule (variable: NAD_neurons) Assignment Rule (variable: NAD_astrocytes)
Assignment Rule (variable: Cr_neurons) Assignment Rule (variable: Cr_astrocytes) Assignment Rule (variable: F_in) Assignment Rule (variable: F_out)
Assignment Rule (variable: is_stimulated) Assignment Rule (variable: v_stim) Rate Rule (variable: venous balloon)  
Physical entities
Compartments Species
capillary O2 CO2 GLC
LAC dHb  
neurons GLC G6P ATP
F6P GAP NADH
PEP PYR LAC
O2 PCr Na+
GLU ADP AMP
Cr NAD G6L
P6G Ru5P X5P
R5P S7P E4P
NADPH NADP  
astrocytes GLC ATP G6P
F6P GAP NADH
PEP PYR LAC
O2 PCr Na+
GLU ADP AMP
Cr NAD G6L
P6G Ru5P X5P
R5P S7P E4P
NADP NADPH  
extracellular_space GLC LAC GLU
Na+    
venous balloon      
artery O2 CO2 GLC
LAC    
Global parameters
K_m_GLC K_m_G6P K_m_F6P_PGI K_m_F6P_PFK
K_I_ATP nH NADH_total_neurons NADH_total_astrocytes
NAD_neurons NAD_astrocytes ANP q_AK
K_m_ATP K_m_ADP K_m_O2 K_m_PYR
PCr_total Cr_neurons Cr_astrocytes Vmax_ATPase_neurons
Vmax_ATPase_astrocytes Vmax_ec_LAC (wrt extracellular space) F_0 delta_F
t_0 t_end t_1 F_in
F_out tau_v Hb.OP Sm_g
Sm_n k_pump K_m,Na-pump K_m_G6P_GLYS
delta_GLY K_m_GLY g_Na_neurons g_Na_astrocytes
Vm RT F vn_1
vn_2 t_stim_tp is_stimulated v_stim
R_Na_GLU V_eg_max_GLU K_m_GLU V_gn_max_GLU
delta_HK BOLD signal E0 K_m_ATP(ATPase)
NULL Vmax_ne_LAC (wrt extracellular space) PS_cap_astrocytes (wrt capillaries) PS_cap_neuron (wrt capillaries)
Vmax_eg_GLU (wrt extracellular space) K_T_GLC_ce (Aubert) Vmax_ce_GLC (wrt capillaries) (Aubert) Vmax_eg_GLC (wrt astrocytes) (Aubert)
K_T_GLC_eg (Aubert) K_T_GLC_en (Aubert) Vmax_en_GLC (wrt neurons) (Aubert) K_T_GLC_cg (Aubert)
Vmax_cg_GLC (wrt capillaries) (Aubert) Vmax_ec_LAC (wrt extracellular space) (Aubert) Vmax_gc_LAC (wrt astrocytes) (Aubert) Vmax_ge_LAC (wrt astrocytes) (Aubert)
Vmax_ne_LAC (wrt neurons) (Aubert) K_T_LAC_ne (Aubert) K_T_LAC_ge (Aubert) K_T_LAC_gc (Aubert)
K_T_LAC_ec (Aubert) PS_cap_astrocytes (wrt capillaries) (Aubert) PS_cap_neuron (wrt capillaries) (Aubert) K_O2 (Aubert)
nh_O2 (Aubert) Vmax_f_PGI (Cloutier) Vmax_r_PGI (Cloutier) Vmax_ce_GLC (Aubert)
Vmax_cg_GLC (Aubert) Vmax_eg_GLC (Aubert) Vmax_en_GLC (Aubert) sf
_PScap f_CBF_dyn stimulus Initial for O2
Initial for O2 Initial for dHb Initial for venous balloon Initial for E0
Initial for NADH_total_astrocytes Initial for NADH_total_neurons Initial for PCr_total Initial for Vmax_ce_GLC (Aubert)
Initial for Vmax_cg_GLC (Aubert) Initial for Vmax_en_GLC (Aubert) Initial for vn_1  
Reactions (64)
 
 HK_astrocytes (R01786) (HeinrichSchuster) [ATP] + [GLC] → [G6P] + [ADP];   {G6P}
 
 PFK_neurons (R04779, R01070, R01015) [F6P] + [ATP] → 2.0 × [GAP] + [ADP];  
 
 PFK_astrocytes (R04779, R01070, R01015) [F6P] + [ATP] → 2.0 × [GAP] + [ADP];  
 
 PGK_neurons (R01061, R01512, R01518, R00658) [GAP] + [ADP] + [NAD] → [NADH] + [PEP] + [ATP];  
 
 PGK_astrocytes (R01061, R01512, R01518, R00658) [GAP] + [ADP] + [NAD] → [NADH] + [PEP] + [ATP];  
 
 PK_neurons (R00200) [PEP] + [ADP] → [ATP] + [PYR];  
 
 PK_astrocytes (R00200) [PEP] + [ADP] → [ATP] + [PYR];  
 
 mitochondrial_respiration_neurons (n.a.) [PYR] + 3.0 × [O2] + [NADH] + 15.0 × [ADP] → 15.0 × [ATP] + 3.0 × [CO2] + [NAD];  
 
 mitochondrial_respiration_astrocytes (n.a.) [PYR] + 15.0 × [ADP] + 3.0 × [O2] + [NADH] → 15.0 × [ATP] + 3.0 × [CO2] + [NAD];  
 
 GLC_exchange_extracellular_space_neurons (Aubert) [GLC] → [GLC];  
 
 GLC_exchange_extracellular_space_astrocytes (Aubert) [GLC] → [GLC];  
 
 GLC_exchange_capillary_ec (Aubert) [GLC] → [GLC];  
 
 GLC_exchange_capillary_astrocytes (Aubert) [GLC] → [GLC];  
 
 LAC_exchange_ec_capillary [LAC] → [LAC];  
 
 LAC_exchange_neurons_ec [LAC] → [LAC];  
 
 LAC_exchange_astrocytes_ec [LAC] → [LAC];  
 
 LAC_exchange_astrocytes_capillary [LAC] → [LAC];  
 
 O2_exchange_capillary_neurons [O2] → [O2];  
 
 O2_exchange_capillary_astrocytes [O2] → [O2];  
 
 O2_exchange_artery_capillary [O2] → [O2];  
 
 GLC_exchange_artery_capillary [GLC] → [GLC];  
 
 LAC_exchange_capillary_artery [LAC] → [LAC];  
 
 CO2_exchange_capillary_artery [CO2] → [CO2];  
 
 Na+_exchange_neurons_extracellular_space (n.a.) [ATP] + 3.0 × [Na+] → [ADP];  
 
 Na+_exchange_astrocytes_extracellular_space (n.a.) [ATP] + 3.0 × [Na+] → [ADP];  
 
 LEAK_Na_neurons (n.a.) [Na+] → [Na+];  
 
 LEAK_Na_astrocytes (n.a) [Na+] → [Na+];  
 
 Na+_exchange_extracellular_space_neurons (stimulation) [Na+] → [Na+];  
 
 GLU_exchange_neurons_extracellular_space [GLU] → [GLU];  
 
 GLU_exchange_extracellular_space_astrocytes [GLU] → [GLU] + [Na+];  
 
 GLU_exchange_astrocytes_neurons [GLU] + [ATP] → [GLU] + [ADP];  
 
 inflow of dHb  → [dHb];   {O2} , {O2}
 
 outflow of dHb [dHb] → ;  
 
 ATPase_neurons (n.a.) [ATP] → [ADP];  
 
 ATPase_astrocytes (n.a.) [ATP] → [ADP];  
 
 AK_neurons (R00127) 2.0 × [ADP] ↔ [ATP] + [AMP];  
 
 AK_astrocytes (R00127) 2.0 × [ADP] ↔ [ATP] + [AMP];  
 
 CK_astrocytes (R01881) [ADP] + [PCr] ↔ [ATP] + [Cr];  
 
 CK_neurons (R01881) [PCr] + [ADP] ↔ [ATP] + [Cr];  
 
 LDH_astrocytes (R00703) [PYR] + [NADH] ↔ [LAC] + [NAD];  
 
 LDH_neurons (R00703) [PYR] + [NADH] ↔ [LAC] + [NAD];  
 
 ZWF_astrocytes (R02736) [G6P] + [NADP] → [G6L] + [NADPH];  
 
 ZWF_neurons (R02736) [G6P] + [NADP] → [G6L] + [NADPH];  
 
 SOL_neurons (R02035) [G6L] → [P6G];  
 
 SOL_astrocytes (R02035) [G6L] → [P6G];  
 
 GND_neurons (R01528) [P6G] + [NADP] ↔ [Ru5P] + [NADPH];  
 
 GND_astrocytes (R01528) [P6G] + [NADP] → [Ru5P] + [NADPH];  
 
 RPE_neurons (R01529) [Ru5P] ↔ [X5P];  
 
 RPE_astrocytes (R01529) [Ru5P] ↔ [X5P];  
 
 RKI_astrocytes (R01056) [Ru5P] ↔ [R5P];  
 
 RKI_neurons (R01056) [Ru5P] ↔ [R5P];  
 
 TKL-1_astrocytes (R01641) [X5P] + [R5P] → [GAP] + [S7P];  
 
 TKL-1_neurons (R01641) [X5P] + [R5P] → [GAP] + [S7P];  
 
 TAL_astrocytes (R01827) [GAP] + [S7P] ↔ [F6P] + [E4P];  
 
 TAL_neurons (R01827) [GAP] + [S7P] ↔ [F6P] + [E4P];  
 
 TKL-2_astrocytes (R01830) [F6P] + [GAP] → [X5P] + [E4P];  
 
 TKL-2_neurons (R01830) [F6P] + [GAP] → [X5P] + [E4P];  
 
 NADPH oxidase neurons (R07172) [NADPH] → [NADP];  
 
 NADPH oxidase astrocytes (R07172) [NADPH] → [NADP];  
 
 R5P sink_astrocytes (n.a.) [R5P] → ;  
 
 R5P sink_neurons (n.a.) [R5P] → ;  
 
 PGI_astrocytes (R02740) (HS) [G6P] ↔ [F6P];  
 
 HK_neurons (R01786) (HeinrichSchuster) [ATP] + [GLC] → [G6P] + [ADP];   {G6P}
 
 PGI_neurons (R02740) (HS) [G6P] ↔ [F6P];  
 
Rules (23)
 
 Assignment Rule (name: E0) E0 = 1-(2*Metabolite_1-Metabolite_123)/(O2_artery/artery)
 
 Assignment Rule (name: BOLD_signal) BOLD signal = Compartment_9*7*(1-dHb/compartment_1/Metabolite_9)+2*(1-dHb/compartment_1/Metabolite_9)/(venous_balloon/Compartment_9)+(2*ModelValue_54-0.2)*(1-venous_balloon/Compartment_9)
 
 Assignment Rule (name: Vmax_ce_GLC__wrt_capillaries___Aubert) Vmax_ce_GLC (wrt capillaries) (Aubert) = ModelValue_83*compartment_4/compartment_1
 
 Assignment Rule (name: Vmax_eg_GLC__wrt_astrocytes___Aubert_) Vmax_eg_GLC (wrt astrocytes) (Aubert)  = Vmax_eg_GLC__Aubert_*compartment_3/compartment_4
 
 Assignment Rule (name: Vmax_en_GLC__wrt_neurons___Aubert) Vmax_en_GLC (wrt neurons) (Aubert) = ModelValue_86*compartment_2/compartment_4
 
 Assignment Rule (name: Vmax_cg_GLC__wrt_capillaries___Aubert) Vmax_cg_GLC (wrt capillaries) (Aubert) = ModelValue_84*compartment_3/compartment_1
 
 Assignment Rule (name: Vmax_ec_LAC__wrt_extracellular_space___Aubert) Vmax_ec_LAC (wrt extracellular space) (Aubert) = 0.00783*_sf
 
 Assignment Rule (name: Vmax_gc_LAC__wrt_astrocytes___Aubert) Vmax_gc_LAC (wrt astrocytes) (Aubert) = 0.0058*_sf
 
 Assignment Rule (name: Vmax_ge_LAC__wrt_astrocytes___Aubert) Vmax_ge_LAC (wrt astrocytes) (Aubert) = 0.076*_sf
 
 Assignment Rule (name: Vmax_ne_LAC__wrt_neurons___Aubert) Vmax_ne_LAC (wrt neurons) (Aubert) = 0.29*_sf
 
 Assignment Rule (name: PS_cap_astrocytes__wrt_capillaries___Aubert) PS_cap_astrocytes (wrt capillaries) (Aubert) = 0.414*0.25*compartment_3/compartment_1
 
 Assignment Rule (name: PS_cap_neuron__wrt_capillaries___Aubert) PS_cap_neuron (wrt capillaries) (Aubert) = _PScap*0.45*compartment_2/compartment_1
 
 Assignment Rule (name: f_CBF_dyn) f_CBF_dyn = 1+delta_F*(1/(1+exp((-4.59186)*(time-((t_0+t_1)-3))))-1/(1+exp((-4.59186)*(time-(t_0+t_1+t_end+3)))))
 
 Assignment Rule (name: stimulus) stimulus = ModelValue_43+vn_2_tp*(time-t_0)/t_stim_tp*exp((-(time-t_0))/t_stim_tp)
 
 Assignment Rule (name: parameter_9) NAD_neurons = ModelValue_6-species_11/compartment_2
 
 Assignment Rule (name: parameter_10) NAD_astrocytes = ModelValue_7-species_13/compartment_3
 
 Assignment Rule (name: parameter_20) Cr_neurons = ModelValue_16-species_21/compartment_2
 
 Assignment Rule (name: parameter_21) Cr_astrocytes = ModelValue_16-species_22/compartment_3
 
 Assignment Rule (name: F_in) F_in = F_0*f_CBF_dyn
 
 Assignment Rule (name: F_out) F_out = F_0*((venous_balloon/Compartment_9)^(1/0.5)+(venous_balloon/Compartment_9)^((-1)/2)*tau_v/Compartment_9*F_in)/(1+F_0*(venous_balloon/Compartment_9)^((-1)/2)*tau_v/Compartment_9)
 
 Assignment Rule (name: is_stimulated) is_stimulated = piecewise(0, (time <= 200) || (time >= (t_0+t_end)), 1)
 
 Assignment Rule (name: v_stim) v_stim = is_stimulated*stimulus
 
 Rate Rule (name: venous_balloon) d [ venous balloon] / d t= F_in-F_out
 
Functions (20)
 
 vdHb_in [1] lambda(F_in, O2_a, O2_c, F_in*(O2_a-(2*O2_c-O2_a)))
 
 vdHb_out lambda(F_out, dHb, V_v, F_out*dHb/V_v)
 
 vATPase lambda(VmaxATPase, ATP, Km_ATP, VmaxATPase*ATP/(ATP+Km_ATP))
 
 vPK lambda(k_PK, PEP, ADP, k_PK*PEP*ADP)
 
 vPGK lambda(k_PGK, GAP, ADP, NAD, NADH, k_PGK*GAP*ADP*NAD/NADH)
 
 vPFK lambda(k_PFK, ATP, K_I_ATP, nH, F6P, K_m_F6P, k_PFK*ATP*(1+(ATP/K_I_ATP)^nH)^(-1)*F6P/(F6P+K_m_F6P))
 
 facilitated transport (inkl. Volume) lambda(Vmax, S, K, P, Volume, Vmax*(S/(S+K)-P/(P+K))*Volume)
 
 vGLU_eg (inkl. Volumes) lambda(Vmax_GLU, GLU_e, K_m_GLU, Volume, Vmax_GLU*GLU_e/(GLU_e+K_m_GLU)*Volume)
 
 vGLU_gn (inkl. Volume) lambda(Vmax_GLU, GLU_g, K_m_GLU, ATP_g, K_m_ATP, Volume, Vmax_GLU*GLU_g/(GLU_g+K_m_GLU)*ATP_g/(ATP_g+K_m_ATP)*Volume)
 
 vGLU_ne (inkl. Volume) lambda(vSTIM, ratio_Na_GLU, GLU_n, Km_GLU, Volume, vSTIM*ratio_Na_GLU*GLU_n/(GLU_n+Km_GLU)*Volume)
 
 vStim (with volume) lambda(vstim, Volume, vstim*Volume)
 
 modular rate law for two substrates, two products lambda(Vmax, K_S1, K_S2, S1, S2, P1, P2, Keq, K_P1, K_P2, Vmax*1/(K_S1*K_S2)*(S1*S2-P1*P2/Keq)/(((1+S1/K_S1)*(1+S2/K_S2)+(1+P1/K_P1)*(1+P2/K_P2))-1))
 
 modular rate law for one substrate, one product lambda(Vmax, K_S1, S1, P1, Keq, K_P1, Vmax*1/K_S1*(S1-P1/Keq)/((1+S1/K_S1+1+P1/K_P1)-1))
 
 Blood flow contribution inkl. volume lambda(F_in, V_c, Volume, Substrate, Product, 2*F_in/V_c*(Substrate-Product)*Volume)
 
 O2 transport function inkl. volume lambda(PScap, Volume, KO2, HbOP, O2_source, nh, O2_destination, Volume1, PScap/Volume*(KO2*(HbOP/O2_source-1)^((-1)/nh)-O2_destination)*Volume1)
 
 vLEAK_Na inkl. Volume lambda(Sm, gNA, Volume, F, RT, Na_e, Na, Vm, Volume1, Sm*gNA/(Volume*F)*(RT/F*ln(Na_e/Na)-Vm)*Volume1)
 
 vPUMP volume dependent lambda(Sm, Volume, k_pump, ATP, Na, Km_pump, Sm/Volume*k_pump*ATP*Na*(1+ATP/Km_pump)^(-1))
 
 vHK (HS) lambda(k_HK, ATP, G6P, K_I_G6P, k_HK*ATP*(1+G6P/K_I_G6P)^(-1))
 
 facilitated transport (inkl. Volume) (scaled) lambda(Vmax, sf, S, K, P, Volume, Vmax*sf*(S/(S+K)-P/(P+K))*Volume)
 
 vMITO2 (inkl. Volumes) lambda(v_max_mito, PYR, K_m_PYR, ADP, K_m_ADP, O2, K_m_O2, alpha, ATP, beta, Volume, v_max_mito*PYR/(PYR+K_m_PYR)*ADP/(ADP+K_m_ADP)*O2/(O2+K_m_O2)*(1-1/(1+exp((-alpha)*(ATP/ADP-beta))))*Volume)
 
 capillary Spatial dimensions: 3.0  Compartment size: 0.0055
 
 O2
Compartment: capillary
Initial amount: 0.040323291746644
 
 CO2
Compartment: capillary
Initial amount: 0.0121467082533562
 
 GLC
Compartment: capillary
Initial amount: 0.0253903826849856
 
 LAC
Compartment: capillary
Initial amount: 0.00188912996259375
 
 dHb
Compartment: capillary
Initial amount: 2.62913971209081E-4
 
 neurons Spatial dimensions: 3.0  Compartment size: 0.45
 
 GLC
Compartment: neurons
Initial amount: 0.513125204430911
 
 G6P
Compartment: neurons
Initial amount: 0.0506867341754652
 
 ATP
Compartment: neurons
Initial amount: 1.01756735100076
 
 F6P
Compartment: neurons
Initial amount: 0.0207718119329183
 
 GAP
Compartment: neurons
Initial amount: 4.84856903277021E-4
 
 NADH
Compartment: neurons
Initial amount: 0.00736369051750214
 
 PEP
Compartment: neurons
Initial amount: 0.00137130155845014
 
 PYR
Compartment: neurons
Initial amount: 0.05894677979576
 
 LAC
Compartment: neurons
Initial amount: 0.631465311475557
 
 O2
Compartment: neurons
Initial amount: 0.0134379352275963
 
 PCr
Compartment: neurons
Initial amount: 0.648285185366582
 
 Na+
Compartment: neurons
Initial amount: 6.98905574867159
 
 GLU
Compartment: neurons
Initial amount: 1.35000000000001
 
 ADP
Compartment: neurons
Initial amount: 0.0502819665719672
 
 AMP
Compartment: neurons
Initial amount: 0.00270068242727579
 
 Cr
Compartment: neurons
Initial amount: 1.60171481463342
 
 NAD
Compartment: neurons
Initial amount: 0.0916363094824979
 
 G6L
Compartment: neurons
Initial amount: 1.35054620762897E-6
 
 P6G
Compartment: neurons
Initial amount: 0.00129746785673949
 
 Ru5P
Compartment: neurons
Initial amount: 3.03470299804797E-4
 
 X5P
Compartment: neurons
Initial amount: 0.00930686571830458
 
 R5P
Compartment: neurons
Initial amount: 1.21527766162824E-5
 
 S7P
Compartment: neurons
Initial amount: 0.519857938505835
 
 E4P
Compartment: neurons
Initial amount: 0.00293045545188872
 
 NADPH
Compartment: neurons
Initial amount: 0.13105170046902
 
 NADP
Compartment: neurons
Initial amount: 9.96586007623714E-10
 
 astrocytes Spatial dimensions: 3.0  Compartment size: 0.25
 
 GLC
Compartment: astrocytes
Initial amount: 0.28506553827656
 
 ATP
Compartment: astrocytes
Initial amount: 0.453875749582273
 
 G6P
Compartment: astrocytes
Initial amount: 0.0170326696107673
 
 F6P
Compartment: astrocytes
Initial amount: 0.00698016362763041
 
 GAP
Compartment: astrocytes
Initial amount: 5.51039449892962E-4
 
 NADH
Compartment: astrocytes
Initial amount: 0.014484722086168
 
 PEP
Compartment: astrocytes
Initial amount: 2.31197219260613E-4
 
 PYR
Compartment: astrocytes
Initial amount: 0.0391626309395164
 
 LAC
Compartment: astrocytes
Initial amount: 0.341202758724066
 
 O2
Compartment: astrocytes
Initial amount: 0.0114703177351059
 
 PCr
Compartment: astrocytes
Initial amount: 0.0943080249454476
 
 Na+
Compartment: astrocytes
Initial amount: 4.00737645868716
 
 GLU
Compartment: astrocytes
Initial amount: 0.0
 
 ADP
Compartment: astrocytes
Initial amount: 0.111239857216292
 
 AMP
Compartment: astrocytes
Initial amount: 0.0296343932014343
 
 Cr
Compartment: astrocytes
Initial amount: 1.15569197505455
 
 NAD
Compartment: astrocytes
Initial amount: 0.040515277913832
 
 G6L
Compartment: astrocytes
Initial amount: 7.49440003798258E-7
 
 P6G
Compartment: astrocytes
Initial amount: 4.50905835212361E-4
 
 Ru5P
Compartment: astrocytes
Initial amount: 1.68586812670336E-4
 
 X5P
Compartment: astrocytes
Initial amount: 0.00517018155675064
 
 R5P
Compartment: astrocytes
Initial amount: 6.5024908937442E-6
 
 S7P
Compartment: astrocytes
Initial amount: 0.0691726529321511
 
 E4P
Compartment: astrocytes
Initial amount: 0.00142484578792443
 
 NADP
Compartment: astrocytes
Initial amount: 6.89248119909569E-10
 
 NADPH
Compartment: astrocytes
Initial amount: 0.0728065001051474
 
 extracellular_space Spatial dimensions: 3.0  Compartment size: 0.2
 
 GLC
Compartment: extracellular_space
Initial amount: 0.228060016230605
 
 LAC
Compartment: extracellular_space
Initial amount: 0.269553776630414
 
 GLU
Compartment: extracellular_space
Initial amount: 0.0
 
 Na+
Compartment: extracellular_space
Initial amount: 30.0
Constant
 
 venous balloon Spatial dimensions: 3.0  Compartment size: 0.0237
 artery Spatial dimensions: 3.0  Compartment size: 0.0055
 
 O2
Compartment: artery
Initial amount: 0.0458700000000001
Constant
 
 CO2
Compartment: artery
Initial amount: 0.00660000000000004
Constant
 
 GLC
Compartment: artery
Initial amount: 0.0264000000000002
Constant
 
 LAC
Compartment: artery
Initial amount: 0.0017215
Constant
 
Global Parameters (103)
 
 K_m_GLC
Value: 0.105
Constant
 
 K_m_G6P
Value: 0.5
Constant
 
 K_m_F6P_PGI
Value: 0.06
Constant
 
 K_m_F6P_PFK
Value: 0.18
Constant
 
 K_I_ATP
Value: 1.0
Constant
 
 nH
Value: 4.0
Constant
 
 NADH_total_neurons
Value: 0.22
Constant
 
 NADH_total_astrocytes
Value: 0.22
Constant
 
  NAD_neurons
Value: 0.20363624329444
 
  NAD_astrocytes
Value: 0.162061111655328
 
 ANP
Value: 2.379
Constant
 
 q_AK
Value: 0.92
Constant
 
 K_m_ATP
Value: 0.01532
Constant
 
 K_m_ADP
Value: 0.00107
Constant
 
 K_m_O2
Value: 0.0029658
Constant
 
 K_m_PYR
Value: 0.0632
Constant
 
 PCr_total
Value: 5.0
Constant
 
  Cr_neurons
Value: 3.55936625474093
 
  Cr_astrocytes
Value: 4.62276790021821
 
 Vmax_ATPase_neurons
Value: 0.04889
Constant
 
 Vmax_ATPase_astrocytes
Value: 0.035657
Constant
 
 Vmax_ec_LAC (wrt extracellular space)
Value: 0.0325
Constant
 
 F_0
Value: 0.012
Constant
 
 delta_F
Value: 0.42
Constant
 
 t_0
Value: 200.0
Constant
 
 t_end
Value: 40.0
Constant
 
 t_1
Value: 2.0
Constant
 
  F_in
Value: 0.012
 
  F_out
Value: 0.012
 
 tau_v
Value: 35.0
Constant
 
 Hb.OP
Value: 8.6
Constant
 
 Sm_g
Value: 10500.0
Constant
 
 Sm_n
Value: 40500.0
Constant
 
 k_pump
Value: 3.17E-7
Constant
 
 K_m,Na-pump
Value: 0.4243
Constant
 
 K_m_G6P_GLYS
Value: 0.5
Constant
 
 delta_GLY
Value: 62.0
Constant
 
 K_m_GLY
Value: 1.0
Constant
 
 g_Na_neurons
Value: 0.0039
Constant
 
 g_Na_astrocytes
Value: 0.00325
Constant
 
 Vm
Value: -70.0
Constant
 
 RT
Value: 2577340.0
Constant
 
 F
Value: 96500.0
Constant
 
 vn_1
Value: 0.041
Constant
 
 vn_2
Value: 1.44
Constant
 
 t_stim_tp
Value: 2.0
Constant
 
  is_stimulated  
 
  v_stim  
 
 R_Na_GLU
Value: 0.075
Constant
 
 V_eg_max_GLU
Value: 0.0208
Constant
 
 K_m_GLU
Value: 0.05
Constant
 
 V_gn_max_GLU
Value: 0.3
Constant
 
 delta_HK
Value: 0.6
Constant
 
  BOLD signal  
 
  E0
Value: 0.241844702566212
 
 K_m_ATP(ATPase)
Value: 0.001
Constant
 
 NULL
Constant
 
 Vmax_ne_LAC (wrt extracellular space)
Value: 0.44505
Constant
 
 PS_cap_astrocytes (wrt capillaries)
Value: 11.16181818
Constant
 
 PS_cap_neuron (wrt capillaries)
Value: 18.01636363
Constant
 
 Vmax_eg_GLU (wrt extracellular space)
Value: 0.026
Constant
 
 K_T_GLC_ce (Aubert)
Value: 9.0
Constant
 
  Vmax_ce_GLC (wrt capillaries) (Aubert)
Value: 4.29090909090909
 
  Vmax_eg_GLC (wrt astrocytes) (Aubert)
Value: 1275.0
 
 K_T_GLC_eg (Aubert)
Value: 9.0
Constant
 
 K_T_GLC_en (Aubert)
Value: 9.0
Constant
 
  Vmax_en_GLC (wrt neurons) (Aubert)
Value: 11767.5
 
 K_T_GLC_cg (Aubert)
Value: 9.0
Constant
 
  Vmax_cg_GLC (wrt capillaries) (Aubert)
Value: 0.422727272727273
 
  Vmax_ec_LAC (wrt extracellular space) (Aubert)
Value: 0.0058725
 
  Vmax_gc_LAC (wrt astrocytes) (Aubert)
Value: 0.00435
 
  Vmax_ge_LAC (wrt astrocytes) (Aubert)
Value: 0.057
 
  Vmax_ne_LAC (wrt neurons) (Aubert)
Value: 0.2175
 
 K_T_LAC_ne (Aubert)
Value: 0.5
Constant
 
 K_T_LAC_ge (Aubert)
Value: 0.5
Constant
 
 K_T_LAC_gc (Aubert)
Value: 0.5
Constant
 
 K_T_LAC_ec (Aubert)
Value: 0.5
Constant
 
  PS_cap_astrocytes (wrt capillaries) (Aubert)
Value: 4.70454545454546
 
  PS_cap_neuron (wrt capillaries) (Aubert)
Value: 40.5
 
 K_O2 (Aubert)
Value: 0.0361
Constant
 
 nh_O2 (Aubert)
Value: 2.73
Constant
 
 Vmax_f_PGI (Cloutier)
Value: 0.5
Constant
 
 Vmax_r_PGI (Cloutier)
Value: 0.45
Constant
 
 Vmax_ce_GLC (Aubert)
Value: 0.118
Constant
 
 Vmax_cg_GLC (Aubert)
Value: 0.0093
Constant
 
 Vmax_eg_GLC (Aubert)
Value: 1020.0
Constant
 
 Vmax_en_GLC (Aubert)
Value: 5230.0
Constant
 
 sf
Value: 0.75
Constant
 
 _PScap
Value: 1.1
Constant
 
  f_CBF_dyn
Value: 1.0
 
  stimulus
Value: -3.87088868421524E45
 
 Initial for O2
Value: 8.34000000000002
Constant
 
 Initial for O2
Value: 7.33150759029891
Constant
 
 Initial for dHb
Value: 0.0478025402198328
Constant
 
 Initial for venous balloon
Value: 0.0237
Constant
 
 Initial for E0
Value: 0.241844702566212
Constant
 
 Initial for NADH_total_astrocytes
Value: 0.22
Constant
 
 Initial for NADH_total_neurons
Value: 0.22
Constant
 
 Initial for PCr_total
Value: 5.0
Constant
 
 Initial for Vmax_ce_GLC (Aubert)
Value: 0.118
Constant
 
 Initial for Vmax_cg_GLC (Aubert)
Value: 0.0093
Constant
 
 Initial for Vmax_en_GLC (Aubert)
Value: 5230.0
Constant
 
 Initial for vn_1
Value: 0.041
Constant
 
HK_astrocytes (R01786) (HeinrichSchuster) (2)
 
   k_HK
Value: 0.01
Constant
 
   K_I_G6P
Value: 0.02
Constant
 
PFK_neurons (R04779, R01070, R01015) (2)
 
   k_PFK
Value: 0.44
Constant
 
   K_m_F6P
Value: 0.18
Constant
 
PFK_astrocytes (R04779, R01070, R01015) (2)
 
   k_PFK
Value: 0.2
Constant
 
   K_m_F6P
Value: 0.18
Constant
 
PGK_neurons (R01061, R01512, R01518, R00658) (1)
 
   k_PGK
Value: 10.0
Constant
 
PGK_astrocytes (R01061, R01512, R01518, R00658) (1)
 
   k_PGK
Value: 3.0
Constant
 
PK_neurons (R00200) (1)
 
   k_PK
Value: 44.0
Constant
 
PK_astrocytes (R00200) (1)
 
   k_PK
Value: 20.0
Constant
 
mitochondrial_respiration_neurons (n.a.) (3)
 
   v_max_mito
Value: 0.1
Constant
 
   alpha
Value: 5.0
Constant
 
   beta
Value: 20.0
Constant
 
mitochondrial_respiration_astrocytes (n.a.) (3)
 
   v_max_mito
Value: 0.01
Constant
 
   alpha
Value: 5.0
Constant
 
   beta
Value: 20.0
Constant
 
O2_exchange_capillary_astrocytes (1)
 
   PScap
Value: 10.0
Constant
 
LEAK_Na_astrocytes (n.a) (1)
 
   gNA
Value: 0.0039
Constant
 
ATPase_neurons (n.a.) (1)
 
   VmaxATPase
Value: 0.07
Constant
 
ATPase_astrocytes (n.a.) (1)
 
   VmaxATPase
Value: 0.035
Constant
 
AK_neurons (R00127) (2)
 
   k1
Value: 1000.0
Constant
 
   k2
Value: 920.0
Constant
 
AK_astrocytes (R00127) (2)
 
   k1
Value: 1000.0
Constant
 
   k2
Value: 920.0
Constant
 
CK_astrocytes (R01881) (2)
 
   k1
Value: 0.5
Constant
 
   k2
Value: 0.01
Constant
 
CK_neurons (R01881) (2)
 
   k1
Value: 0.5
Constant
 
   k2
Value: 0.01
Constant
 
LDH_astrocytes (R00703) (2)
 
   k1
Value: 780.0
Constant
 
   k2
Value: 32.0
Constant
 
LDH_neurons (R00703) (2)
 
   k1
Value: 2000.0
Constant
 
   k2
Value: 15.0
Constant
 
ZWF_astrocytes (R02736) (6)
 
   Vmax
Value: 0.29057
Constant
 
   K_S1
Value: 6.91392E-5
Constant
 
   K_S2
Value: 1.31616E-5
Constant
 
   Keq
Value: 22906.4
Constant
 
   K_P1
Value: 0.0180932
Constant
 
   K_P2
Value: 5.0314E-4
Constant
 
ZWF_neurons (R02736) (6)
 
   Vmax
Value: 0.586458
Constant
 
   K_S1
Value: 6.91392E-5
Constant
 
   K_S2
Value: 1.31616E-5
Constant
 
   Keq
Value: 22906.4
Constant
 
   K_P1
Value: 0.0180932
Constant
 
   K_P2
Value: 5.0314E-4
Constant
 
SOL_neurons (R02035) (4)
 
   Vmax
Value: 0.372782
Constant
 
   K_S1
Value: 0.0180932
Constant
 
   Keq
Value: 531174.0
Constant
 
   K_P1
Value: 2.28618
Constant
 
SOL_astrocytes (R02035) (4)
 
   Vmax
Value: 0.184701
Constant
 
   K_S1
Value: 0.0180932
Constant
 
   Keq
Value: 531174.0
Constant
 
   K_P1
Value: 2.28618
Constant
 
GND_neurons (R01528) (6)
 
   Vmax
Value: 2.65764
Constant
 
   K_S1
Value: 3.23421E-5
Constant
 
   K_S2
Value: 3.11043E-6
Constant
 
   Keq
Value: 4.0852E7
Constant
 
   K_P1
Value: 0.0537179
Constant
 
   K_P2
Value: 5.0314E-4
Constant
 
GND_astrocytes (R01528) (6)
 
   Vmax
Value: 1.31677
Constant
 
   K_S1
Value: 3.23421E-5
Constant
 
   K_S2
Value: 3.11043E-6
Constant
 
   Keq
Value: 4.0852E7
Constant
 
   K_P1
Value: 5.0314E-4
Constant
 
   K_P2
Value: 0.0537179
Constant
 
RPE_neurons (R01529) (4)
 
   Vmax
Value: 0.0156605
Constant
 
   K_S1
Value: 0.0537179
Constant
 
   Keq
Value: 39.2574
Constant
 
   K_P1
Value: 0.603002
Constant
 
RPE_astrocytes (R01529) (4)
 
   Vmax
Value: 0.00775925
Constant
 
   K_S1
Value: 0.0537179
Constant
 
   Keq
Value: 39.2574
Constant
 
   K_P1
Value: 0.603002
Constant
 
RKI_astrocytes (R01056) (4)
 
   Vmax
Value: 8.21984E-4
Constant
 
   K_S1
Value: 0.0537179
Constant
 
   Keq
Value: 35.4534
Constant
 
   K_P1
Value: 0.778461
Constant
 
RKI_neurons (R01056) (4)
 
   Vmax
Value: 0.00165901
Constant
 
   K_S1
Value: 0.0537179
Constant
 
   Keq
Value: 35.4534
Constant
 
   K_P1
Value: 0.778461
Constant
 
TKL-1_astrocytes (R01641) (6)
 
   Vmax
Value: 2.44278E-4
Constant
 
   K_S1
Value: 1.73625E-4
Constant
 
   K_S2
Value: 5.85387E-4
Constant
 
   Keq
Value: 1652870.0
Constant
 
   K_P1
Value: 0.168333
Constant
 
   K_P2
Value: 0.192807
Constant
 
TKL-1_neurons (R01641) (6)
 
   Vmax
Value: 4.93027E-4
Constant
 
   K_S1
Value: 1.73625E-4
Constant
 
   K_S2
Value: 5.85387E-4
Constant
 
   Keq
Value: 1652870.0
Constant
 
   K_P1
Value: 0.168333
Constant
 
   K_P2
Value: 0.192807
Constant
 
TAL_astrocytes (R01827) (6)
 
   Vmax
Value: 0.0080394
Constant
 
   K_S1
Value: 0.168333
Constant
 
   K_S2
Value: 0.192807
Constant
 
   Keq
Value: 0.323922
Constant
 
   K_P1
Value: 0.0799745
Constant
 
   K_P2
Value: 0.109681
Constant
 
TAL_neurons (R01827) (6)
 
   Vmax
Value: 0.0162259
Constant
 
   K_S1
Value: 0.168333
Constant
 
   K_S2
Value: 0.192807
Constant
 
   Keq
Value: 0.323922
Constant
 
   K_P1
Value: 0.0799745
Constant
 
   K_P2
Value: 0.109681
Constant
 
TKL-2_astrocytes (R01830) (6)
 
   Vmax
Value: 1.37124E-4
Constant
 
   K_S1
Value: 0.0799745
Constant
 
   K_S2
Value: 0.168333
Constant
 
   Keq
Value: 0.0777764
Constant
 
   K_P1
Value: 0.603002
Constant
 
   K_P2
Value: 0.109681
Constant
 
TKL-2_neurons (R01830) (6)
 
   Vmax
Value: 2.76758E-4
Constant
 
   K_S1
Value: 0.0799745
Constant
 
   K_S2
Value: 0.168333
Constant
 
   Keq
Value: 0.0777764
Constant
 
   K_P1
Value: 0.603002
Constant
 
   K_P2
Value: 0.109681
Constant
 
NADPH oxidase neurons (R07172) (1)
 
   k1
Value: 4.23283E-4
Constant
 
NADPH oxidase astrocytes (R07172) (1)
 
   k1
Value: 2.09722E-4
Constant
 
R5P sink_neurons (n.a.) (1)
 
   k1
Constant
 
PGI_astrocytes (R02740) (HS) (2)
 
   k1
Value: 931.69
Constant
 
   k2
Value: 2273.32
Constant
 
HK_neurons (R01786) (HeinrichSchuster) (2)
 
   k_HK
Value: 0.022
Constant
 
   K_I_G6P
Value: 0.02
Constant
 
PGI_neurons (R02740) (HS) (2)
 
   k1
Value: 931.69
Constant
 
   k2
Value: 2273.32
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000627

Curator's comment: (updated: 13 Mar 2017 12:24:25 GMT)

Figure 3 of the reference publication has been reproduced here. The model was simulated using Copasi, and the plots were generated using Gnuplot.

To import the SBML model in Copasi without any issues, the latest development version (atleast Build 144) is needed.

The SED-ML and Copasi file to reproduce the above figure can be accessed from the below link.

Additional file(s)
  • Copasi file::
    This Copasi file with the simulation settings can be used to reproduce the curation result (Fig 3) by opening the file in Copasi.
  • Simulation experiment description (SED-ML)::
    This SED-ML file allows you to reproduce the curation result (Fig 3), for example,
    by loading it into SED-ML Web Tools (http://sysbioapps.dyndns.org/SED-ML_Web_Tools/).
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