An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements Catherine Lloyd Auckland Bioengineering Institute, The University of Auckland
Model Status This CellMl model runs in OpenCell to recreate the published results. The units are balanced. Thank you to the original author Mathieu Cloutier for his invaluable help in the final stages of model curation. We recommend the followin simulation conditions: a duration of 2500 seconds with a an increase in neuronal activity at 200 seconds.
Model Structure 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. model diagram Schematic diagram of the model for astrocyte-neuron metabolism The original paper reference is cited below: An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements, Mathieu Cloutier, Fiachra B. Bolger, John P. Lowry and Peter Wellstead, 2009, Journal of Computational Neuroscience , 27, 391-414. PubMed ID: 19396534
time NAn Vn_leak_Na Vn_stim 3 Vn_pump time GLCn V_en_GLC Vn_hk time G6Pn Vn_hk Vn_pgi time F6Pn Vn_pgi Vn_pfk time GAPn 2 Vn_pfk Vn_pgk time PEPn Vn_pgk Vn_pk time PYRn Vn_pk Vn_ldh Vn_mito time LACn Vn_ldh Vne_LAC time NADHn Vn_pgk Vn_ldh Vn_mito time ATPn Vn_pgk Vn_pk nOP Vn_mito Vn_ck Vn_hk Vn_pfk Vn_ATPase Vn_pump 1 dAMP_dATPn -1 time PCrn Vn_ck time O2n Vcn_O2 NAero Vn_mito time GLUn Vg_gs 1 Rng Vn_stim_GLU time NAg Vg_leak_Na 3 Veg_GLU 3 Vg_pump time GLCg Vcg_GLC Veg_GLC Vg_hk time G6Pg Vg_hk Vg_glyp Vg_pgi Vg_glys time F6Pg Vg_pgi Vg_pfk time GAPg 2 Vg_pfk Vg_pgk time PEPg Vg_pgk Vg_pk time PYRg Vg_pk Vg_ldh Vg_mito time LACg Vg_ldh Vge_LAC Vgc_LAC time NADHg Vg_pgk Vg_ldh Vg_mito time ATPg Vg_pgk Vg_pk nOP Vg_mito Vg_ck Vg_hk Vg_pfk Vg_ATPase Vg_pump Vg_gs 1 dAMP_dATPg -1 time PCrg Vg_ck time O2g Vcg_O2 NAero Vg_mito time GLYg Vg_glys Vg_glyp time GLUg Veg_GLU Vg_gs time GLCe Vce_GLC Veg_GLC 1 Reg V_en_GLC 1 Ren time LACe Vne_LAC 1 Ren Vge_LAC 1 Reg Vec_LAC time GLUe Vn_stim_GLU 1 Ren Veg_GLU 1 Reg time O2c Vc_O2 Vcn_O2 1 Rcn Vcg_O2 1 Rcg time GLCc Vc_GLC Vce_GLC 1 Rce Vcg_GLC 1 Rcg time LACc Vc_LAC Vec_LAC 1 Rce Vgc_LAC 1 Rcg time CO2c Vnc_CO2 1 Rcn Vgc_CO2 1 Rcg Vc_CO2 time Vv Fin_t Fout_t time dHb Fin_t O2a O2c Fout_t dHb Vv Vn_leak_Na Sm_n Vn gn_NA F RT F NAe NAn Vm Vn_pump Sm_n Vn kpump ATPn NAn 1 ATPn Km_pump -1 Vn_stim v_stim V_en_GLC Vm_en_GLC GLCe GLCe Km_en_GLC GLCn GLCn Km_en_GLC Vn_hk Vmax_n_hk ATPn GLCn GLCn Km_GLC 1 1 1 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 aATP_mito 1 ATPn ADPn 1 rATP_mito Vne_LAC Vmax_ne_LAC LACn LACn Km_ne_LAC LACe LACe Km_ne_LAC Vn_ATPase Vmax_n_ATPase ATPn ATPn 0.001 Vn_ck kfn_ck PCrn ADPn krn_ck CRn ATPn Vcn_O2 PScapn Vn Ko2 HbOP O2c 1.0 -1.0 nh_O2 O2n Vg_leak_Na Sm_g Vg gg_NA F RT F NAe NAg Vm Vg_pump Sm_g Vg kpump ATPg NAg 1 ATPg Km_pump -1 Veg_GLC KO1 Vm_eg_GLC GLCe GLCe Km_eg_GLC GLCg GLCg Km_eg_GLC Vcg_GLC Vm_cg_GLC GLCc GLCc Km_cg_GLC GLCg GLCg Km_cg_GLC Vg_hk Vmax_g_hk ATPg GLCg GLCg Km_GLC 1 1 1 aG6P_inh_hk 1 G6Pg G6P_inh_hk Vg_pgi Vmaxf_g_pgi G6Pg G6Pg Km_G6P Vmaxr_g_pgi F6Pg F6Pg Km_F6P_pgi 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 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_ATPase Vmax_g_ATPase ATPg ATPg 0.001 Vg_ck kfg_ck PCrg ADPg krg_ck CRg ATPg Vcg_O2 PScapg Vg Ko2 HbOP O2c 1.0 -1.0 nh_O2 O2g Vc_O2 2.0 Fin_t Vc O2a O2c Vc_GLC 2.0 Fin_t Vc GLCa GLCc Vce_GLC Vm_ce_GLC GLCc GLCc Km_ce_GLC GLCe GLCe Km_ce_GLC Vc_LAC 2.0 Fin_t Vc LACa LACc Vec_LAC Vm_ec_LAC LACe LACe Km_ec_LAC LACc LACc Km_ec_LAC Vnc_CO2 3.0 Vn_mito Vgc_CO2 3.0 Vg_mito Vn_stim_GLU Vn_stim R_GLU_NA KO2 GLUn GLUn Km_GLU Vg_gs Vmax_g_gs GLUg GLUg Km_GLU ATPg ATPg Km_ATP Veg_GLU Vmax_eg_GLU GLUe GLUe Km_GLU Vc_CO2 2.0 Fin_t Vc CO2c CO2a Vg_glys Vmax_glys G6Pg G6Pg Km_G6P_glys 1 1 1 aGLY_inh 1 GLYg GLY_inh Vg_glyp Vmax_glyp GLYg GLYg Km_GLY deltaVt_GLY deltaVt_GLY 1 stim delta_GLY KO3 1 1 1 sr_GLY time to to_GLY 1 unitstepSB2 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 Fout_t CBF0 Vv Vv0 2 tv Vv Vv0 -0.5 Fin_t Vv0 1 CBF0 tv Vv Vv0 -0.5 1 Vv0 NADn NADH_n_tot NADHn NADg NADH_g_tot NADHg CRn PCrn_tot PCrn CRg PCrg_tot PCrg ADPn ATPn 2 qak qak 2 4 qak ATPtot ATPn 1 ADPg ATPg 2 qak qak 2 4 qak ATPtot ATPg 1 u_n qak 2 4 qak ATPtot ATPn 1 u_g qak 2 4 qak ATPtot ATPg 1 dAMP_dATPn qak 2 qak ATPtot ATPn u_n 1 0.5 u_n dAMP_dATPg qak 2 qak ATPtot ATPg u_g 1 0.5 u_g AMPn ATPtot ATPn ADPn AMPg ATPtot ATPg ADPg BOLD Vv0 k1 k2 1 dHb dHb0 k2 k3 1 Vv Vv0 v_stim stim v1_n v2_n time to t_n_stim time to unitpulseSB t_n_stim unitpulseSB unitpulseSB 1 time to time to tend 0 unitstepSB 1 time tend to 0 0 unitstepSB2 1 time tend_GLY to to_GLY 0 0 Na(1+) exchange from neuron to the extracellular space Sodium pump from neuron to the extracellular space. Blood flow out of the capillary. Concentration of ADP in astrocyte during adenylate kinase equilibrium Oxygen exchange between the capillary and the neurons. Oxygen exchange between the capillary and the neurons. Rate of change in the intracellular concentration of glutamate in the astrocyte. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Rate of change in the concentration of glyceraldehyde 3-phosphate in the neuron. Glutamate exchange between the extracellular space and the astrocyte Glutamate exchange between the extracellular space and the astrocyte. Astrocytic metabolism of Lactate dehydrogenase Blood flow contribution to capillary O2 Mitochondrial oxidation of pyruvate Astrocytic metabolism of Lactate dehydrogenase Rate of change in the concentration of glucose-6-phosphate in the neuron. Glucose exchange between the extracellular space and astrocytes. Glucose exchange between the extracellular space and astrocytes. Neuronal metabolism of Creatine kinase Blood flow entering the capillary. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Sodium exchange from the astrocyte to the extracellular space. Sodium exchange from astrocyte to the extracellular space. Concentration of ADP in neuron during adenylate kinase equilibrium Oxygen exchange between capillary and astrocytes Oxygen exchange between capillary and astrocytes Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Phosphoglucose isomerase metabolism in the neuron Phosphoglucose isomerase metabolism in the neuron rate of change in the concentration of sodium in the astrocyte. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Phosphoglycerate kinase metabolism in the neuron Phosphoglycerate kinase metabolism in the neuron Rate of change in concentration of Phosphoenolpyruvate in the astrocyte. Blood flow entering the capillary. Rate of change in the concentration of phosphocreatine in the astrocyte. Rate of change in the concentration of fructose-6-phosphate in the neuron. Rate of change in change in concentration of phosphocreatine in the neuron. Metabolism of ATPase (excluding Na-ATPase) in the astrocyte. Rate of change in the concentration of glucose-6-phosphate in the astrocyte Rate of change in the concentration of sodium in the neuron. Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Rate of change in the concentration of Nicotinamide adenine dinucleotide (reduced) in neuron Neuronal metabolism of Mitochondrial oxidation of pyruvate Rate of change in the concentration of glucose in the neuron. Concentration of ADP in astrocyte during adenylate kinase equilibrium Lactate exchange between neuron and extracellular space Lactate exchange between neuron and extracellular space. Phosphoglycerate kinase metabolism in the neuron CO2 exchange between the astrocyte and capillary. Carbon Dioxide exchange between astrocyte and capillary. Rate of change in the concentration of oxygen in the capillary. Astrocytic metabolism of Phosphoglycerate kinase Rate of change in the concentration of Lactate in the capillary. Rate of change in change in concentration of phosphocreatine in the neuron. Rate of change in the concentration of Lactate in the neuron. Rate of change in the concentration of glucose-6-phosphate in the astrocyte Glutamate exchange between the extracellular space and the astrocyte. Blood flow entering the capillary. Rate of change in the concentration of glutamate in the extracellular space. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Rate of change in the concentration of Lactate in the neuron. Lactate exchange between the astrocyte and the capillary. Lactate exchange between the astrocyte and the capillary. Astrocytic metabolism of Pyruvate kinase Blood flow entering the capillary. Neuronal metabolism of Mitochondrial oxidation of pyruvate Rate of change of glycogen in the astrocyte. Neuronal metabolism of Mitochondrial oxidation of pyruvate rate of change in the concentration of Lactate in the astrocyte Rate of change in the concentration of adenosine triphosphate in the astrocyte. Blood flow entering the capillary. Rate of change in the concentration of glucose in the extracellular space. Phosphofructokinase metabolism in the neuron Phosphofructokinase metabolism in the neuron Blood flow entering the capillary. Rate of change in the concentration of Carbon Dioxide in a capillary in the brain. Rate of change in the concentration of oxygen in the capillary. Neuronal metabolism of Lactate dehydrogenase Sodium exchange from astrocyte to the extracellular space. Rate of change in the concentration of Lactate in the extracellular space. rate of change in the concentration of sodium in the astrocyte. Rate of change in concentration of glutamate in the neuron Rate of change in the concentration of glyceraldehyde-3-phosphate in the astrocyte. Metabolism of creatine kinase in the astrocyte Blood flow entering the capillary. Rate of change in the concentration of fructose-6-phosphate in the astrocyte Neuronal metabolism of Hexokinase Lactate exchange between extracellular space and capillary. Lactate exchange between extracellular space and capillaries. Rate of change in the concentration of glucose in the extracellular space. Neuronal metabolism of Hexokinase Neuronal metabolism of Creatine kinase Rate of change in the concentration of Lactate in the extracellular space. Rate of change in the intracellular concentration of glutamate in the astrocyte. Lactate exchange between the astrocyte and the capillary. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Rate of change in pyruvate in the astrocyte. Exchange of glucose from capillary to extracellular space. Glucose exchange between capillary and extracellular space. Rate of change in the concentration of glucose in the neuron. Neuronal metabolism of Lactate dehydrogenase Sodium pump from neuron to the extracellular space. Rate of change in concentration of Phosphoenolpyruvate in the astrocyte. glycogen synthase flow rate Neuronal Na inflow due to stimulation Neuronal metabolism of Lactate dehydrogenase Glutamate exchange between the extracellular space and the astrocyte. Lactate exchange between the astrocyte and the extracellular space. Lactate exchange between the astrocyte and the extracellular space. Mitochondrial oxidation of pyruvate Astrocytic metabolism of Pyruvate kinase Neuronal metabolism of Lactate dehydrogenase Rate of change in the concentration of Oxygen in the neuron. Mitochondrial oxidation of pyruvate Rate of change in the concentration of Nicotinamide adenine dinucleotide (reduced) in neuron Oxygen exchange between capillary and astrocytes Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Neuronal metabolism of Mitochondrial oxidation of pyruvate Mitochondrial oxidation of pyruvate Rate of change in the concentration of fructose-6-phosphate in the astrocyte Lactate entering the capillary Mitochondrial oxidation of pyruvate Rate of change in the concentration of glucose-6-phosphate in the astrocyte Neuronal metabolism of ATPase (excluding Na-ATPase) Neuronal metabolism of Hexokinase Neuronal metabolism of Mitochondrial oxidation of pyruvate Na(1+) leak from the extracellular space to the astrocyte. Sodium leak from the extracellular space to the astrocyte. Glucose exchange between the extracellular space and astrocytes. Rate of change in the concentration of glucose in the astrocyte. Metabolism of creatine kinase in the astrocyte rate of change in the concentration of sodium in the astrocyte. Concentration of ADP in neuron during adenylate kinase equilibrium Rate of change in the concentration of pyruvate in the neuron. Concentration of ADP in astrocyte during adenylate kinase equilibrium Rate of change in the concentration of phosphocreatine in the astrocyte. Pyruvate kinase metabolism in the Neuron Pyruvate kinase metabolism in the Neuron Concentration of ADP in astrocyte during adenylate kinase equilibrium Rate of change in pyruvate in the astrocyte. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Rate of change of glycogen in the astrocyte. Rate of change in the concentration of glucose-6-phosphate in the neuron. glycogen synthase flow rate Phosphoglucose isomerase metabolism in the neuron Rate of change in the concentration of glucose in the astrocyte. Rate of change in the conc of Nicotinamide adenine dinucleotide reduced in astrocyte. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Rate of change in the concentration of Nicotinamide adenine dinucleotide (reduced) in neuron Rate of change in the concentration of glucose in the extracellular space. Astrocytic metabolism of Pyruvate kinase Rate of change in the concentration of glucose in the capillary. Phosphoglycerate kinase metabolism in the neuron Rate of change in the concentration of Carbon Dioxide in a capillary in the brain. Oxygen exchange between the capillary and the neurons. Pyruvate kinase metabolism in the Neuron Rate of change in the concentration of glucose-6-phosphate in the neuron. Rate of change in the concentration of adenosine triphosphate in the astrocyte. Oxygen exchange between the capillary and the neurons. Lactate exchange between the astrocyte and the extracellular space. Glucose exchange between extracellular fluid and neurons. Exchange of glucose between the extracellular space and neurons. Astrocytic metabolism of Hexokinase Astrocytic metabolism of Lactate dehydrogenase Rate of change in the concentration of phosphocreatine in the astrocyte. Rate of change in concentration of glutamate in the neuron Rate of change in the concentration of oxygen in the capillary. Astrocytic metabolism of Lactate dehydrogenase Rate of change in the concentration of Oxygen in the astrocyte. Rate of change in the concentration of glucose in the capillary. Lactate exchange between extracellular space and capillaries. Phosphoglucose isomerase metabolism in the neuron Concentration of ADP in neuron during adenylate kinase equilibrium Neuronal Na inflow due to stimulation Neuronal metabolism of Creatine kinase Sodium pump from neuron to the extracellular space. Phosphofructokinase metabolism in the astrocyte Phosphofructokinase metabolism in the astrocyte Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Concentration of ADP in neuron during adenylate kinase equilibrium Rate of change in the concentration of Lactate in the extracellular space. rate of change in the concentration of Lactate in the astrocyte Concentration of ADP in neuron during adenylate kinase equilibrium Astrocytic metabolism of Phosphoglucose isomerase cloutier_2009 bdf15 0.000001 0.000001 2000 2500 rate of change in the concentration of Lactate in the astrocyte Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Neuronal metabolism of ATPase (excluding Na-ATPase) Rate of change in the concentration of Lactate in the capillary. Glucose exchange between the extracellular space and astrocytes. Rate of change in the concentration of glucose in the astrocyte. Astrocytic metabolism of Phosphoglycerate kinase Sodium exchange from astrocyte to the extracellular space. Glycogen phosphorylase flow rate in the astrocyte Phosphofructokinase metabolism in the astrocyte Rate of change in the concentration of Lactate in the capillary. Metabolism of ATPase (excluding Na-ATPase) in the astrocyte. Glucose exchange between capillary and astrocytes. Glucose exchange between capillary and astrocytes. Rate of change in the concentration of Nicotinamide adenine dinucleotide (reduced) in neuron CO2 exchange from neuron and capillary. Carbon Dioxide exchange between neuron and capillary Rate of change in the conc of Nicotinamide adenine dinucleotide reduced in astrocyte. Rate of change in the concentration of glucose in the capillary. Rate of change in the concentration of glyceraldehyde-3-phosphate in the astrocyte. Na(1+) leakage from the neuron to the extracellular space. Sodium leak from the neuron to the extracellular space. Phosphofructokinase metabolism in the neuron Rate of change in the concentration of glucose-6-phosphate in the astrocyte Rate of change in the concentration of fructose-6-phosphate in the astrocyte Glucose exchange between capillary and extracellular space. Glycogen phosphorylase flow rate in the astrocyte Rate of change in the concentration of Lactate in the extracellular space. Sodium leak from the neuron to the extracellular space. Glucose exchange between capillary and astrocytes. Rate of change in the concentration of Lactate in the neuron. Mitochondrial oxidation of pyruvate Phosphofructokinase metabolism in the neuron Glutamate exchange between the extracellular space and the astrocyte. Rate of change in the concentration of Oxygen in the astrocyte. Rate of change in the concentration of glyceraldehyde 3-phosphate in the neuron. Concentration of ADP in astrocyte during adenylate kinase equilibrium Phosphofructokinase metabolism in the neuron Rate of change in the concentration of Oxygen in the astrocyte. Rate of change in the concentration of Oxygen in the neuron. Rate of change in the concentration of oxygen in the capillary. Rate of change in concentration of phosphoenolpyruvate in the neuron. Rate of change in the concentration of glutamate in the extracellular space. Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Astrocytic metabolism of Phosphoglucose isomerase Astrocytic metabolism of Phosphoglycerate kinase Carbon Dioxide exchange between astrocyte and capillary. Rate of change in the concentration of sodium in the neuron. Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Sodium leak from the extracellular space to the astrocyte. Blood flow contribution to capillary O2 Pyruvate kinase metabolism in the Neuron Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Glycogen phosphorylase flow rate in the astrocyte Blood flow out of the capillary. Rate of change in the conc of Nicotinamide adenine dinucleotide reduced in astrocyte. Rate of change in the concentration of glucose in the capillary. rate of change in the concentration of Lactate in the astrocyte Lactate exchange between the astrocyte and the extracellular space. Glucose exchange between capillary and extracellular space. Lactate exchange between neuron and extracellular space. Rate of change in the concentration of glucose in the astrocyte. Metabolism of creatine kinase in the astrocyte Blood flow entering the capillary. Lactate entering the capillary Glucose exchange between capillary and astrocytes. Rate of change in the concentration of pyruvate in the neuron. Oxygen exchange between capillary and astrocytes Rate of change in the concentration of fructose-6-phosphate in the neuron. Rate of change of glycogen in the astrocyte. Exchange of glucose between the extracellular space and neurons. Rate of change in concentration of phosphoenolpyruvate in the neuron. Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Pyruvate kinase metabolism in the Neuron Neuronal metabolism of Mitochondrial oxidation of pyruvate Rate of change in the concentration of adenosine triphosphate in the astrocyte. Rate of change in the conc of Nicotinamide adenine dinucleotide reduced in astrocyte. Blood flow out of the capillary. Astrocytic metabolism of Phosphoglycerate kinase Concentration of ADP in neuron during adenylate kinase equilibrium Rate of change in the concentration of Lactate in the capillary. Astrocytic metabolism of Hexokinase Astrocytic metabolism of Phosphoglucose isomerase Phosphofructokinase metabolism in the astrocyte Rate of change in the concentration of pyruvate in the neuron. glycogen synthase flow rate Astrocytic metabolism of Hexokinase Astrocytic metabolism of Hexokinase Lactate exchange between extracellular space and capillaries. Concentration of ADP in astrocyte during adenylate kinase equilibrium Rate of change in the concentration of adenosine triphosphate in the astrocyte. Rate of change in the concentration of adenosine triphosphate in the neuron of the brain. Rate of change in the concentration of Oxygen in the neuron. Rate of change in the concentration of sodium in the neuron. Rate of change in change in concentration of phosphocreatine in the neuron. Phosphofructokinase metabolism in the astrocyte Rate of change in pyruvate in the astrocyte. Astrocytic metabolism of Pyruvate kinase Exchange of glucose between the extracellular space and neurons. Rate of change in the concentration of fructose-6-phosphate in the neuron. Neuronal metabolism of Hexokinase Lactate exchange between the astrocyte and the capillary. Rate of change in the concentration of glucose in the extracellular space. Phosphoglycerate kinase metabolism in the neuron Lactate exchange between neuron and extracellular space. Rate of change in the concentration of oxygen in the capillary. Phosphoglycerate kinase metabolism in the neuron Astrocytic metabolism of Phosphoglycerate kinase Rate of change in the concentration of adenosine triphosphate in the astrocyte. Carbon Dioxide exchange between neuron and capillary Rate of change in the concentration of glucose in the neuron.