Computational singular perturbation analysis of brain lactate metabolism

Autoři: Dimitris G. Patsatzis aff001;  Efstathios-Al. Tingas aff001;  Dimitris A. Goussis aff004;  S. Mani Sarathy aff001
Působiště autorů: King Abdullah University of Science and Technology (KAUST), Clean Combustion Research Center (CCRC), Thuwal, Saudi Arabia aff001;  Department of Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens (NTUA), Athens, Greece aff002;  Perth College, University of the Highlands and Islands, Crieff Rd, Perth PH1 2NX, United Kingdom aff003;  Department of Mechanical Engineering, Khalifa University of Science, Technology and Research (KUSTAR), Abu Dhabi, United Arab Emirates aff004
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: 10.1371/journal.pone.0226094


Lactate in the brain is considered an important fuel and signalling molecule for neuronal activity, especially during neuronal activation. Whether lactate is shuttled from astrocytes to neurons or from neurons to astrocytes leads to the contradictory Astrocyte to Neuron Lactate Shuttle (ANLS) or Neuron to Astrocyte Lactate Shuttle (NALS) hypotheses, both of which are supported by extensive, but indirect, experimental evidence. This work explores the conditions favouring development of ANLS or NALS phenomenon on the basis of a model that can simulate both by employing the two parameter sets proposed by Simpson et al. (J Cereb. Blood Flow Metab., 27:1766, 2007) and Mangia et al. (J of Neurochemistry, 109:55, 2009). As most mathematical models governing brain metabolism processes, this model is multi-scale in character due to the wide range of time scales characterizing its dynamics. Therefore, we utilize the Computational Singular Perturbation (CSP) algorithm, which has been used extensively in multi-scale systems of reactive flows and biological systems, to identify components of the system that (i) generate the characteristic time scale and the fast/slow dynamics, (ii) participate to the expressions that approximate the surfaces of equilibria that develop in phase space and (iii) control the evolution of the process within the established surfaces of equilibria. It is shown that a decisive factor on whether the ANLS or NALS configuration will develop during neuronal activation is whether the lactate transport between astrocytes and interstitium contributes to the fast dynamics or not. When it does, lactate is mainly generated in astrocytes and the ANLS hypothesis is realised, while when it doesn’t, lactate is mainly generated in neurons and the NALS hypothesis is realised. This scenario was tested in exercise conditions.

Klíčová slova:

Algorithms – Astrocytes – Evolutionary rate – Glucose – Glucose metabolism – Neurons – Reactants – Reaction dynamics


1. Howarth C, Gleeson P, Attwell D. Updated energy budgets for neural computation in the neocortex and cerebellum. Journal of Cerebral Blood Flow & Metabolism. 2012;32(7):1222–32. doi: 10.1038/jcbfm.2012.35

2. Falkowska A, Gutowska I, Goschorska M, Nowacki P, Chlubek D, Baranowska-Bosiacka I. Energy metabolism of the brain, including the cooperation between astrocytes and neurons, especially in the context of glycogen metabolism. International journal of molecular sciences. 2015;16(11):25959–81. doi: 10.3390/ijms161125939 26528968

3. Mergenthaler P, Lindauer U, Dienel GA, Meisel A. Sugar for the brain: the role of glucose in physiological and pathological brain function. Trends in neurosciences. 2013;36(10):587–97. doi: 10.1016/j.tins.2013.07.001 23968694

4. Pellerin L, Magistretti PJ. Glutamate uptake into astrocytes stimulates aerobic glycolysis: a mechanism coupling neuronal activity to glucose utilization. Proceedings of the National Academy of Sciences. 1994;91(22):10625–10629. doi: 10.1073/pnas.91.22.10625

5. Pellerin L, Magistretti PJ. Sweet sixteen for ANLS. Journal of Cerebral Blood Flow & Metabolism. 2012;32(7):1152–1166. doi: 10.1038/jcbfm.2011.149

6. Bélanger M, Allaman I, Magistretti PJ. Brain energy metabolism: focus on astrocyte-neuron metabolic cooperation. Cell metabolism. 2011;14(6):724–738. doi: 10.1016/j.cmet.2011.08.016 22152301

7. Newington JT, Harris RA, Cumming RC. Reevaluating metabolism in Alzheimer’s disease from the perspective of the astrocyte-neuron lactate shuttle model. Journal of neurodegenerative diseases. 2013;2013. doi: 10.1155/2013/234572 26316984

8. DiNuzzo M, Mangia S, Maraviglia B, Giove F. Changes in glucose uptake rather than lactate shuttle take center stage in subserving neuroenergetics: evidence from mathematical modeling. Journal of Cerebral Blood Flow & Metabolism. 2010;30(3):586–602. doi: 10.1038/jcbfm.2009.232

9. Simpson IA, Carruthers A, Vannucci SJ. Supply and demand in cerebral energy metabolism: the role of nutrient transporters. J Cereb Blood Flow Metab. 2007;27(11):1766–91. doi: 10.1038/sj.jcbfm.9600521 17579656

10. Mangia S, Simpson IA, Vannucci SJ, Carruthers A. The in vivo neuron-to-astrocyte lactate shuttle in human brain: evidence from modeling of measured lactate levels during visual stimulation. Journal of Neurochemistry. 2009;109:55–62. doi: 10.1111/j.1471-4159.2009.06003.x 19393009

11. Dienel GA. Brain lactate metabolism: the discoveries and the controversies. Journal of Cerebral Blood Flow & Metabolism. 2012;32(7):1107–1138. doi: 10.1038/jcbfm.2011.175

12. Chih CP, Roberts EL Jr. Energy substrates for neurons during neural activity: a critical review of the astrocyte-neuron lactate shuttle hypothesis. Journal of Cerebral Blood Flow & Metabolism. 2003;23(11):1263–1281. doi: 10.1097/01.WCB.0000081369.51727.6F

13. Patel AB, Lai JC, Chowdhury GM, Hyder F, Rothman DL, Shulman RG, Behar KL. Direct evidence for activity-dependent glucose phosphorylation in neurons with implications for the astrocyte-to-neuron lactate shuttle. Proceedings of the National Academy of Sciences. 2014:201403576. doi: 10.1073/pnas.1403576111

14. Lundgaard I, Li B, Xie L, Kang H, Sanggaard S, Haswell JD, Sun W, Goldman S, Blekot S, Nielsen M, Takano T. Direct neuronal glucose uptake heralds activity-dependent increases in cerebral metabolism. Nature communications. 2015;6:6807. doi: 10.1038/ncomms7807 25904018

15. Diaz-Garcia CM, Mongeon R, Lahmann C, Koveal D, Zucker H, Yellen G. Neuronal stimulation triggers neuronal glycolysis and not lactate uptake. Cell metabolism. 2017;26(2):361–74. doi: 10.1016/j.cmet.2017.06.021 28768175

16. Herrero-Mendez A, Almeida A, Fernández E, Maestre C, Moncada S, Bolaños JP. The bioenergetic and antioxidant status of neurons is controlled by continuous degradation of a key glycolytic enzyme by APC/C–Cdh1. Nature cell biology. 2009;11(6):747–752. doi: 10.1038/ncb1881 19448625

17. Patel JR, Brewer GJ. Age-related changes in neuronal glucose uptake in response to glutamate and β-amyloid. Journal of neuroscience research. 2003;72(4):527–536. doi: 10.1002/jnr.10602 12704814

18. Porras OH, Loaiza A, Barros LF. Glutamate mediates acute glucose transport inhibition in hippocampal neurons. Journal of Neuroscience. 2004;24(43):9669–9673. doi: 10.1523/JNEUROSCI.1882-04.2004 15509754

19. Erecińska M, Nelson D, Chance B. Depolarization-induced changes in cellular energy production. Proc. of the National Academy of Sciences. 1991;88(17):7600–7604. doi: 10.1073/pnas.88.17.7600

20. Kauppinen RA, Nicholls DG. Synaptosomal bioenergetics: the role of glycolysis, pyruvate oxidation and responses to hypoglycaemia. European journal of biochemistry. 1986;158(1):159–165. doi: 10.1111/j.1432-1033.1986.tb09733.x 2874024

21. Kauppinen RA, Taipale HT, Komulainen H. Interrelationships Between Glucose Metabolism, Energy State, and the Cytosolic Free Calcium Concentration in Cortical Synjaptosomes from the Guinea Pig. Journal of neurochemistry. 1989;53(3):766–771. doi: 10.1111/j.1471-4159.1989.tb11771.x 2503588

22. Jolivet R, Coggan JS, Allaman I, Magistretti PJ. Multi-timescale modeling of activity-dependent metabolic coupling in the neuron-glia-vasculature ensemble. PLoS computational biology. 2015 Feb 26;11(2):e1004036. doi: 10.1371/journal.pcbi.1004036 25719367

23. Juaristi I, Contreras P, González-Sánchez P, Pérez-Liébana I, González-Moreno L, Pardo B, del Arco A, Satrústegui J. The response to stimulation in neurons and astrocytes. Neurochemical research. 2019, 31016552

24. Calì C, Tauffenberger A, Magistretti P. The strategic location of glycogen and lactate: from body energy reserve to brain plasticity. Frontiers in cellular neuroscience. 2019;13(82):1–7.

25. Wang Q, Hu Y, Wan J, Dong B, Sun J. Lactate: a novel signaling molecule in synaptic plasticity and drug addiction. BioEssays. 2019;41(8):1900008. doi: 10.1002/bies.201900008

26. Magistretti PJ, Allaman I. Lactate in the brain: from metabolic end-product to signalling molecule. Nature Reviews Neuroscience. 2018;19(4):235–249. doi: 10.1038/nrn.2018.19 29515192

27. Coggan JS, Keller D, Calì C, Lehväslaiho H, Markram H, Schürmann F, Magistretti PJ. Norepinephrine stimulates glycogenolysis in astrocytes to fuel neurons with lactate. PLOS Computational Biology. 2018;14(8):e1006392. doi: 10.1371/journal.pcbi.1006392 30161133

28. Barros LF, Joachim WD. Glucose and lactate supply to the synapse. Brain Research Reviews. 2010;63(1):149–159. doi: 10.1016/j.brainresrev.2009.10.002 19879896

29. Pellerin L, Bouzier-Sore AK, Aubert A, Serres S, Merle M, Costalat R, Magistretti PJ. Activity-dependent regulation of energy metabolism by astrocytes: an update. Glia. 2007;55(12):1251–1262. doi: 10.1002/glia.20528 17659524

30. Hyder F, Patel AB, Gjedde A, Rothman DL, Behar KL, Shulman RG. Neuronal–glial glucose oxidation and glutamatergic–GABAergic function. Journal of Cerebral Blood Flow & Metabolism. 2006;26(7):865–877. doi: 10.1038/sj.jcbfm.9600263

31. Jolivet R, Allaman I, Pellerin L, Magistretti PJ, Weber B. Comment on recent modeling studies of astrocyte-neuron metabolic interactions. Journal of Cerebral Blood Flow & Metabolism. 2010;30(12):1982–1986. doi: 10.1038/jcbfm.2010.132

32. Lundengård K, Cedersund G, Sten S, Leong F, Smedberg A, Elinder F, Engström M. Mechanistic mathematical modeling tests hypotheses of the neurovascular coupling in fMRI. PLOS Computational Biology. 2016;12(6):e1004971. doi: 10.1371/journal.pcbi.1004971 27310017

33. Rouach N, Koulakoff A, Abudara V, Willecke K, Giaume C. Astroglial metabolic networks sustain hippocampal synaptic transmission. American Association for the Advancement of Science. 2008;322(5907):1551–1555. doi: 10.1126/science.1164022

34. Kasischke KA, Vishwasrao HD, Fisher PJ, Zipfel WR, Webb WW. Neural activity triggers neuronal oxidative metabolism followed by astrocytic glycolysis. Science. 2004;305(5680):99–103. doi: 10.1126/science.1096485 15232110

35. Prichard J, Rothman D, Novotny E, Petroff O, Kuwabara T, Avison M, Howseman A, Hanstock C, Shulman R. Lactate rise detected by 1H NMR in human visual cortex during physiologic stimulation. Proceedings of the National Academy of Sciences of the United States of America. 1991;88(13):5829. doi: 10.1073/pnas.88.13.5829 2062861

36. Miyamoto K, Ishikura K, Kume K, Ohsawa M. Astrocyte-neuron lactate shuttle sensitizes nociceptive transmission in the spinal cord. Glia. 2019;67:27–36. doi: 10.1002/glia.23474 30430652

37. Mächler P, Wyss MT, Elsayed M, Stobart J, Gutierrez R, von Faber-Castell A, Kaelin V, Zuend M, San Martín A, Romero-Gómez I, Baeza-Lehnert F, Lengacher S, Schneider BL, Aebischer P, Magistretti PJ, Barros LF, Weber B. In vivo evidence for a lactate gradient from astrocytes to neurons. Cell Metabolism. 2016;23(1):94–102. doi: 10.1016/j.cmet.2015.10.010 26698914

38. Ruminot I, Schmälzle J, Leyton B, Barros LF, Deitmer JW. Tight coupling of astrocyte energy metabolism to synaptic activity revealed by genetically encoded FRET nanosensors in hippocampal tissue. Journal of Cerebral Blood Flow & Metabolism. 2019;39(3):513–523. doi: 10.1177/0271678X17737012

39. Liu L, MacKenzie KR, Putluri N, Maletić-Savatić M, Bellen HJ. The Glia-Neuron Lactate Shuttle and Elevated ROS Promote Lipid Synthesis in Neurons and Lipid Droplet Accumulation in Glia via APOE/D. Cell Metabolism. 2017;26(5):719–737. doi: 10.1016/j.cmet.2017.08.024 28965825

40. Cholet N, Pellerin L, Welker E, Lacombe P, Seylaz J, Magistretti PJ, Bonvento G. Local injection of antisense oligonucleotides targeted to the glial glutamate transporter GLAST decreases the metabolic response to somatosensory activation. Journal of Cerebral Blood Flow & Metabolism. 2001;21(4):404–412. doi: 10.1097/00004647-200104000-00009

41. Voutsinos-Porche B, Bonvento G, Tanaka K, Steiner P, Welker E, Chatton J-Y, Magistretti PJ, Pellerin L. Glial glutamate transporters mediate a functional metabolic crosstalk between neurons and astrocytes in the mouse developing cortex. Neuron. 2003;37(2):275–286. doi: 10.1016/s0896-6273(02)01170-4 12546822

42. Herard A-S, Dubois A, Escartin C, Tanaka K, Delzescaux T, Hantraye P, Bonvento G. Decreased metabolic response to visual stimulation in the superior colliculus of mice lacking the glial glutamate transporter GLT-1. European Journal of Neuroscience. 2005;22(7):1807–1811. doi: 10.1111/j.1460-9568.2005.04346.x 16197522

43. Chuquet J, Quilichini P, Nimchinsky EA, Buzsáki G. Predominant enhancement of glucose uptake in astrocytes versus neurons during activation of the somatosensory cortex. Journal of Neuroscience. 2010;30(45):15298–15303. doi: 10.1523/JNEUROSCI.0762-10.2010 21068334

44. Lin A-L, Fox PT, Hardies J, Duong TQ, Gao J-H. Nonlinear coupling between cerebral blood flow, oxygen consumption, and ATP production in human visual cortex. Proceedings of the National Academy of Sciences. 2010;107(418):8446–8451. doi: 10.1073/pnas.0909711107

45. Dienel GA. The “protected” glucose transport through the astrocytic endoplasmic reticulum is too slow to serve as a quantitatively-important highway for nutrient delivery. Journal of Neuroscience Research. 2019;97:854–862. doi: 10.1002/jnr.24432 31050047

46. Díaz-García CM, Yellen G. Neurons rely on glucose rather than astrocytic lactate during stimulation. Journal of Neuroscience Research. 2019;97:883–889. doi: 10.1002/jnr.24374 30575090

47. Dienel GA. Lack of appropriate stoichiometry: Strong evidence against an energetically important astrocyte–neuron lactate shuttle in brain. Journal of Neuroscience Research. 2017;95:2103–2125. doi: 10.1002/jnr.24015 28151548

48. Bak LK, Walls AB. CrossTalk opposing view: lack of evidence supporting an astrocyte-to-neuron lactate shuttle coupling neuronal activity to glucose utilisation in the brain. Journal of Physiology. 2018;596(3):351–353. doi: 10.1113/JP274945 29292507

49. Dienel GA. Lactate shuttling and lactate use as fuel after traumatic brain injury: metabolic considerations. Journal of Cerebral Blood Flow & Metabolism. 2014;34(11):1736–1748. doi: 10.1038/jcbfm.2014.153

50. Dienel GA. Fueling and imaging brain activation. JASN neuro. 2012;4(5):267–321.

51. Hertz L, Dienel GA. Lactate transport and transporters: general principles and functional roles in brain cells. Journal of neuroscience research. 2005;79(1-2):11–18. doi: 10.1002/jnr.20294 15586354

52. Hertz L. The astrocyte-neuron lactate shuttle: a challenge of a challenge. Journal of Cerebral Blood Flow & Metabolism. 2004;24(11):1241–1248. doi: 10.1097/00004647-200411000-00008

53. Hertz L, Dienel GA. Energy metabolism in the brain. International review of neurobiology. 2002;51:1–102. doi: 10.1016/s0074-7742(02)51003-5 12420357

54. Dienel GA, Hertz L. Glucose and lactate metabolism during brain activation. Journal of neuroscience research. 2001;66(5):824–838. doi: 10.1002/jnr.10079 11746408

55. Mangia S, Garreffa G, Bianciardi M, Giove F, Di Salle F, Maraviglia B. The aerobic brain: lactate decrease at the onset of neural activity. Neuroscience. 2003;118(1):7–10. doi: 10.1016/s0306-4522(02)00792-3 12676131

56. Maher F, Simpson IA. Modulation of expression of glucose transporters GLUT3 and GLUT1 by potassium and N-methyl-D-aspartate in cultured cerebellar granule neurons. Molecular and Cellular Neuroscience. 1994;5(4):369–375. doi: 10.1006/mcne.1994.1044 7804607

57. Castro MA, Pozo M, Cortés C, García MA, Concha II, Nualart F. Intracellular ascorbic acid inhibits transport of glucose by neurons, but not by astrocytes. Journal of neurochemistry. 2007;102(3):773–782. doi: 10.1111/j.1471-4159.2007.04631.x 17630983

58. Weisová P, Concannon CG, Devocelle M, Prehn JHM, Ward MW. Regulation of glucose transporter 3 surface expression by the AMP-activated protein kinase mediates tolerance to glutamate excitation in neurons. Journal of Neuroscience. 2009;29(9):2997–3008. doi: 10.1523/JNEUROSCI.0354-09.2009 19261894

59. Ferreira JM, Burnett AL, Rameau GA. Activity-dependent regulation of surface glucose transporter-3 Journal of Neuroscience. 2011;31(6):1991–1999. doi: 10.1523/JNEUROSCI.1850-09.2011 21307237

60. Almeida A, Almeida J, Bolaños JP, Moncada S. Different responses of astrocytes and neurons to nitric oxide: the role of glycolytically generated ATP in astrocyte protection. Proceedings of the National Academy of Sciences. 2001;98(26):15294–15299. doi: 10.1073/pnas.261560998

61. Dienel GA, Cruz NF. Astrocyte activation in working brain: energy supplied by minor substrates. Neurochemistry international. 2006;48(6-7):586–595. doi: 10.1016/j.neuint.2006.01.004 16513214

62. Gegg ME, Beltran B, Salas-Pino S, Bolanos JP, Clark JB, Moncada S, Heales SJR. Differential effect of nitric oxide on glutathione metabolism and mitochondrial function in astrocytes and neurones: implications for neuroprotection/neurodegeneration? Journal of neurochemistry. 2003;86(1):228–237. doi: 10.1046/j.1471-4159.2003.01821.x 12807442

63. Gjedde A, Marrett S. Glycolysis in neurons, not astrocytes, delays oxidative metabolism of human visual cortex during sustained checkerboard stimulation in vivo. Journal of Cerebral Blood Flow & Metabolism. 2001;21(12):1384–1392. doi: 10.1097/00004647-200112000-00002

64. Bak LK, Walls AB, Schousboe A, Ring A, Sonnewald U, Waagepetersen HS. Neuronal glucose but not lactate utilization is positively correlated with NMDA-induced neurotransmission and fluctuations in cytosolic Ca2+ levels. Journal of neurochemistry. 2009;109(1):87–93. doi: 10.1111/j.1471-4159.2009.05943.x 19393013

65. Cunnane S, Nugent S, Roy M, Courchesne-Loyer A, Croteau E, Tremblay S, Castellano A, Pifferi F, Bocti C, Paquet N and others. Brain fuel metabolism, aging, and Alzheimer’s disease. Nutrition. 2011;27(1):3–20. doi: 10.1016/j.nut.2010.07.021 21035308

66. Harris DL, Weston PJ, Harding JE. Lactate, rather than ketones, may provide alternative cerebral fuel in hypoglycaemic newborns. Archives of Disease in Childhood-Fetal and Neonatal Edition. 2015;100(2):F161–F164. doi: 10.1136/archdischild-2014-306435 25189167

67. Thudichum J. A. Treatise on the Chemical Constitution of the Brain. 1884. London: Bailliere, Tindall and Cox. 1962:262.

68. Himwich HE. Brain metabolism and cerebral disorders. Williams & Wilkins; 1951.

69. Itoh Y, Esaki T, Shimoji K, Cook M, Law MJ, Kaufman E, Sokoloff L. Dichloroacetate effects on glucose and lactate oxidation by neurons and astroglia in vitro and on glucose utilization by brain in vivo. Proceedings of the National Academy of Sciences. 2003;100(8):4879–84. doi: 10.1073/pnas.0831078100

70. Nakai T, Matsuo K, Kato C, Takehara Y, Isoda H, Moriya T, Okada T, Sakahara H. Post-stimulus response in hemodynamics observed by functional magnetic resonance imaging-Difference between the primary sensorimotor area and the supplementary motor area. Magnetic resonance imaging. 2000;18(10):1215–9. doi: 10.1016/s0730-725x(00)00217-4 11167041

71. Ances BM, Buerk DG, Greenberg JH, Detre JA. Temporal dynamics of the partial pressure of brain tissue oxygen during functional forepaw stimulation in rats. Neuroscience letters. 2001;306(1-2):106–10. doi: 10.1016/s0304-3940(01)01868-7 11403969

72. Fellows LK, Boutelle MG, Fillenz M. Physiological stimulation increases nonoxidative glucose metabolism in the brain of the freely moving rat. Journal of neurochemistry. 1993;60(4):1258–63. doi: 10.1111/j.1471-4159.1993.tb03285.x 8455025

73. Fray AE, Forsyth RJ, Boutelle MG, Fillenz M. The mechanisms controlling physiologically stimulated changes in rat brain glucose and lactate: a microdialysis study. The Journal of physiology. 1996;496(1):49–57. doi: 10.1113/jphysiol.1996.sp021664 8910195

74. Vega C, Martiel JL, Drouhault D, Burckhart MF, Coles JA. Uptake of locally applied deoxyglucose, glucose and lactate by axons and Schwann cells of rat vagus nerve. The Journal of physiology. 2003;546(2):551–64. doi: 10.1113/jphysiol.2002.029751 12527741

75. Kuhr WG, van den Berg CJ, Korf J. In vivo identification and quantitative evaluation of carrier-mediated transport of lactate at the cellular level in the striatum of conscious, freely moving rats. Journal of Cerebral Blood Flow & Metabolism. 1988;8(6):848–56. doi: 10.1038/jcbfm.1988.142

76. Hu Y, Wilson GS A temporary local energy pool coupled to neuronal activity: fluctuations of extracellular lactate levels in rat brain monitored with rapid-response enzyme-based sensor. Journal of neurochemistry. 1997;69(4):1484–90. doi: 10.1046/j.1471-4159.1997.69041484.x 9326277

77. Lebon V, Petersen KF, Cline GW, Shen J, Mason GF, Dufour S, Behar KL, Shulman GI, Rothman DL. Astroglial contribution to brain energy metabolism in humans revealed by 13C nuclear magnetic resonance spectroscopy: elucidation of the dominant pathway for neurotransmitter glutamate repletion and measurement of astrocytic oxidative metabolism. Journal of Neuroscience. 2002;22(5):1523–31. doi: 10.1523/JNEUROSCI.22-05-01523.2002 11880482

78. Buxton RB, Wong EC, Frank LR. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magnetic resonance in medicine. 1998;39(6):855–64. doi: 10.1002/mrm.1910390602 9621908

79. Gruetter R, Seaquist ER, Ugurbil K. A mathematical model of compartmentalized neurotransmitter metabolism in the human brain. American Journal of Physiology-Endocrinology And Metabolism. 2001;281(1):E100–12. doi: 10.1152/ajpendo.2001.281.1.E100 11404227

80. Aubert A, Costalat R, Valabrègue R. Modelling of the coupling between brain electrical activity and metabolism. Acta biotheoretica. 2001;49(4):301–26. doi: 10.1023/a:1014286728421 11804241

81. Aubert A, Costalat R. A model of the coupling between brain electrical activity, metabolism, and hemodynamics: application to the interpretation of functional neuroimaging. Neuroimage. 2002;17(3):1162–81. doi: 10.1006/nimg.2002.1224 12414257

82. Aubert A, Costalat R. Interaction between astrocytes and neurons studied using a mathematical model of compartmentalized energy metabolism. Journal of Cerebral Blood Flow & Metabolism. 2005; 25(11): 1476–90. doi: 10.1038/sj.jcbfm.9600144

83. Aubert A, Costalat R, Magistretti PJ, Pellerin L. Brain lactate kinetics: modeling evidence for neuronal lactate uptake upon activation. Proceedings of the National Academy of Sciences. 2005 Nov 8;102(45):16448–53. doi: 10.1073/pnas.0505427102

84. Aubert A, Pellerin L, Magistretti PJ, Costalat R. A coherent neurobiological framework for functional neuroimaging provided by a model integrating compartmentalized energy metabolism. Proceedings of the National Academy of Sciences. 2007 Mar 6;104(10):4188–93. doi: 10.1073/pnas.0605864104

85. Cloutier M, Bolger FB, Lowry JP, Wellstead P. An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements. Journal of computational neuroscience. 2009;27(3):391. doi: 10.1007/s10827-009-0152-8 19396534

86. Occhipinti R, Puchowicz MA, LaManna JC, Somersalo E, Calvetti D. Statistical analysis of metabolic pathways of brain metabolism at steady state. Annals of biomedical engineering. 2007;35(6):886–902. doi: 10.1007/s10439-007-9270-5 17385046

87. Occhipinti R, Somersalo E, Calvetti D. Astrocytes as the glucose shunt for glutamatergic neurons at high activity: an in silico study. Journal of neurophysiology. 2009;101(5):2528–38. doi: 10.1152/jn.90377.2008 18922953

88. Occhipinti R, Somersalo E, Calvetti D. Energetics of inhibition: insights with a computational model of the human GABAergic neuron–astrocyte cellular complex. Journal of Cerebral Blood Flow & Metabolism. 2010;30(11):1834–46. doi: 10.1038/jcbfm.2010.107

89. Calvetti D, Somersalo E. Menage a trois: the role of neurotransmitters in the energy metabolism of astrocytes, glutamatergic, and GABAergic neurons. Journal of Cerebral Blood Flow & Metabolism. 2012 Aug;32(8):1472–83. doi: 10.1038/jcbfm.2012.31

90. Blanchard S, Papadopoulo T, Bénar C-G, Voges N, Clerc M, Benali H, Warnking J, David O, Wendling F. Relationship between flow and metabolism in BOLD signals: insights from biophysical models. Brain topography, 2011 Nov 6;24(1):40–53 doi: 10.1007/s10548-010-0166-6 21057867

91. Winter F, Bludszuweit-Philipp C, Wolkenhauer O. Mathematical analysis of the influence of brain metabolism on the BOLD signal in Alzheimer’s disease. Journal of Cerebral Blood Flow & Metabolism, 2018;38(2):304–316 doi: 10.1177/0271678X17693024

92. Çakιr T, Alsan S, Saybaşιlι H, Akιn A, Ülgen K. Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia. Theoretical Biology and Medical Modelling, 2007 Dec 10;4(1):48–66 doi: 10.1186/1742-4682-4-48

93. Massucci FA, DiNuzzo M, Giove F, Maraviglia B, Castillo IP, Marinari E, De Martino A. Energy metabolism and glutamate-glutamine cycle in the brain: a stoichiometric modeling perspective. BMC systems biology, 2013;7(1):103–117 doi: 10.1186/1752-0509-7-103 24112710

94. DiNuzzo M, Giove F, Maraviglia B, Mangia S. Computational flux balance analysis predicts that stimulation of energy metabolism in astrocytes and their metabolic interactions with neurons depend on uptake of K+ rather than glutamate. Neurochemical research, 2016 Sep 14;42(1):202–216 doi: 10.1007/s11064-016-2048-0 27628293

95. Calvetti D, Somersalo E. Dynamic activation model for a glutamatergic neurovascular unit. Journal of theoretical biology, 2010 Dec 19;274(1):12–29 doi: 10.1016/j.jtbi.2010.12.007 21176783

96. Somersalo E, Cheng Y, Calvetti D. The metabolism of neurons and astrocytes through mathematical models Annals of biomedical engineering, 2012 Sep 22;40(11):2328–2344 doi: 10.1007/s10439-012-0643-z 23001357

97. Frenklach M. Modeling. In: Gardiner WC, editor. Combustion Chemistry. Springer-Verlag, New York; 1984. p. 423–454.

98. Vajda S, Valko P, Turanyi T Principal component analysis of kinetic models. International Journal of Chemical Kinetics. 1985;17(1):55–81. doi: 10.1002/kin.550170107

99. Lam S, Goussis D. The CSP method for simplifying kinetics. International Journal of Chemical Kinetics. 1994;26(4):461–486. doi: 10.1002/kin.550260408

100. Lam S, Goussis D. Understanding complex chemical kinetics with computational singular perturbation. In: Symposium (International) on Combustion. 1989;22:931–941.

101. Hadjinicolaou M, Goussis DA. Asymptotic solution of stiff PDEs with the CSP method: the reaction diffusion equation. SIAM J. Sci. Comp., 1999;20:781–819. doi: 10.1137/S1064827596303995

102. Prager J, Najm HN, Valorani M, Goussis DA. Structure of n-heptane/air triple flames in partially-premixed mixing layers. Combustion and Flame. 2011;158(11):2128–44. doi: 10.1016/j.combustflame.2011.03.017

103. Goussis DA, Valorani M. An efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems. Journal of Computational Physics. 2006;214(1):316–46. doi: 10.1016/

104. Neophytou MK, Goussis DA, Mastorakos E, Britter RE. The conceptual development of a simple scale-adaptive reactive pollutant dispersion model. Atmospheric Environment. 2005;39(15):2787–94. doi: 10.1016/j.atmosenv.2004.12.025

105. Kourdis PD, Goussis DA. Glycolysis in saccharomyces cerevisiae: algorithmic exploration of robustness and origin of oscillations. Mathematical biosciences. 2013;243(2):190–214. doi: 10.1016/j.mbs.2013.03.002 23517854

106. Surovtsova I, Simus N, Hübner K, Sahle S, Kummer U. Simplification of biochemical models: a general approach based on the analysis of the impact of individual species and reactions on the systems dynamics. BMC systems biology. 2012;6(1):14. doi: 10.1186/1752-0509-6-14 22390191

107. Samant A, Ogunnaike BA, Vlachos DG. A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks. BMC bioinformatics. 2007;8(1):175. doi: 10.1186/1471-2105-8-175 17524148

108. Patsatzis DG, Goussis DA. A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails. Mathematical biosciences. 2019;315:108220. doi: 10.1016/j.mbs.2019.108220 31255632

109. Patsatzis DG, Maris DT, Goussis DA. Asymptotic analysis of a target-mediated drug disposition model: algorithmic and traditional approaches. Bulletin of mathematical biology, 2016;78(6):1121–1161. doi: 10.1007/s11538-016-0176-y 27271122

110. Michalaki LI, Goussis DA. Asymptotic analysis of a TMDD model: when a reaction contributes to the destruction of its product. Journal of mathematical biology. 2018:1–35.

111. Fenichel N. Geometric singular perturbation theory for ordinary differential equations. Journal of differential equations. 1979;31(1):53–98. doi: 10.1016/0022-0396(79)90152-9

112. Kaper TJ. An introduction to geometric methods and dynamical systems theory for singular perturbation problems. In: Cronin J, Robert J, O’Malley E (eds) Analyzing multiscale phenomena using singular perturbation methods. Proceedings of symposia in applied mathematics. 1999;56(1):85–131.

113. Kuehn C. Multiple time scale dynamics. Springer; 2015.

114. Zagaris A, Kaper HG, Kaper TJ. Analysis of the computational singular perturbation reduction method for chemical kinetics. Journal of Nonlinear Science. 2004;14(1):59–91. doi: 10.1007/s00332-003-0582-9

115. Zagaris A, Kaper HG, Kaper TJ. Fast and slow dynamics for the computational singular perturbation method. Multiscale Modeling & Simulation. 2004;2(4):613–638. doi: 10.1137/040603577

116. Zagaris A, Kaper HG, Kaper TJ. Two perspectives on reduction of ordinary differential equations. Mathematische Nachrichten. 2005;278(12-13):1629–1642. doi: 10.1002/mana.200410328

117. Kaper HG, Kaper TJ, Zagaris A. Geometry of the computational singular perturbation method. Mathematical modelling of natural phenomena. 2015;10(3):16–30. doi: 10.1051/mmnp/201510303

118. Hek G. Geometric singular perturbation theory in biological practice. Journal of mathematical biology. 2010;60(3):347–386. doi: 10.1007/s00285-009-0266-7 19347340

119. Auger P, de La Parra RB, Poggiale J-C, Sánchez E, Sanz L. Aggregation methods in dynamical systems and applications in population and community dynamics. Physics of Life Reviews. 2008;5(2):79–105. doi: 10.1016/j.plrev.2008.02.001

120. Kosiuk I, Szmolyan P. Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle. Journal of mathematical biology. 2016;72(5):1337–1368. doi: 10.1007/s00285-015-0905-0 26100376

121. Popović N, Marr C, Swain PS. A geometric analysis of fast-slow models for stochastic gene expression. Journal of mathematical biology. 2016;72(1-2):87–122. doi: 10.1007/s00285-015-0876-1 25833185

122. Vanselow A, Wieczorek S, Feudel U. When very slow is too fast-collapse of a predator-prey system. Journal of theoretical biology. 2019;479:64–72. doi: 10.1016/j.jtbi.2019.07.008 31302207

123. Quistorff B, Secher NH, Van Lieshout JJ. Lactate fuels the human brain during exercise. The FASEB Journal. 2008;22(10):3443–3449. doi: 10.1096/fj.08-106104 18653766

124. Rasmussen P, Wyss MT, Lundby C. Cerebral glucose and lactate consumption during cerebral activation by physical activity in humans. The FASEB Journal. 2011;25(9):2865–2873. doi: 10.1096/fj.11-183822 21602451

125. Lam S, Goussis D. Conventional asymptotics and computational singular perturbation for simplified kinetics modelling. In: Reduced kinetic mechanisms and asymptotic approximations for methane-air flames; 1991. p. 227–242.

126. Tingas EA, Kyritsis DC, Goussis DA. Ignition delay control of DME/air and EtOH/air homogeneous autoignition with the use of various additives. Fuel. 2016;169:15–24. doi: 10.1016/j.fuel.2015.11.081

127. Goussis DA, Najm HN. Model reduction and physical understanding of slowly oscillating processes: the circadian cycle. Multiscale Modeling & Simulation. 2006;5(4):1297–1332. doi: 10.1137/060649768

128. Valorani M, Najm HN, Goussis DA. CSP analysis of a transient flame-vortex interaction: time scales and manifolds. Combustion and Flame. 2003;134(1):35–53. doi: 10.1016/S0010-2180(03)00067-1

129. Goussis DA, Skevis G. Nitrogen chemistry controlling steps in methane-air premixed flames. In: Bathe KJ, editor. Computational Fluid and Solid Mechanics. Elsevier, Amsterdam; 2005. p. 650–653.

130. Diamantis DJ, Mastorakos E, Goussis DA. H2/air autoignition: The nature and interaction of the developing explosive modes. Combustion Theory and Modelling. 2015;19(3):382–433. doi: 10.1080/13647830.2015.1027273

131. Goussis D, Lam S. A study of homogeneous methanol oxidation kinetics using CSP. In: Symposium (International) on Combustion. vol. 24. Elsevier; 1992. p. 113–120.

132. Goussis DA. Quasi steady state and partial equilibrium approximations: their relation and their validity. Combustion Theory and Modelling. 2012;16(5):869–926. doi: 10.1080/13647830.2012.680502

133. Kourdis PD, Palasantza AG, Goussis DA. Algorithmic asymptotic analysis of the NF-κB signaling system. Computers & Mathematics with Applications. 2013;65(10):1516–1534. doi: 10.1016/j.camwa.2012.11.004

134. Valorani M, Creta F, Donato F, Najm H, Goussis D. A CSP-based skeletal mechanism generation procedure: auto-ignition and premixed laminar flames in n-heptane/air mixtures. In: ECCOMAS CFD 2006: Proceedings of the European Conference on Computational Fluid Dynamics, Egmond aan Zee, The Netherlands, September 5-8, 2006. Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS); 2006.

135. Bouzier-Sore AK, Voisin P, Bouchaud V, Bezancon E, Franconi JM, Pellerin L. Competition between glucose and lactate as oxidative energy substrates in both neurons and astrocytes: a comparative NMR study. European Journal of Neuroscience. 2006;24(6):1687–1694. doi: 10.1111/j.1460-9568.2006.05056.x 17004932

136. Lovatt D, Sonnewald U, Waagepetersen HS, Schousboe A, He W, Lin JHC, et al. The transcriptome and metabolic gene signature of protoplasmic astrocytes in the adult murine cortex. Journal of Neuroscience. 2007;27(45):12255–12266. doi: 10.1523/JNEUROSCI.3404-07.2007 17989291

137. Ueki M, Linn F, Hossmann K-A. Functional activation of cerebral blood flow and metabolism before and after global ischemia of rat brain. Journal of Cerebral Blood Flow & Metabolism. 1988;8(4):486–494. doi: 10.1038/jcbfm.1988.89

138. Bohnen NI, Koeppe RA, Minoshima S, Giordani B, Albin RL, Frey KA, Kuhl DE. Cerebral glucose metabolic features of Parkinson disease and incident dementia: longitudinal study. Journal of Nuclear Medicine. 2011;52(6):848–855. doi: 10.2967/jnumed.111.089946 21571793

139. Action to Control Cardiovascular Risk in Diabetes Study Group. Effects of intensive glucose lowering in type 2 diabetes. New England journal of medicine. 2008;358(24):2545–2559. doi: 10.1056/NEJMoa0802743 18539917

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