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The Metabolism of Neurons and Astrocytes Through Mathematical Models

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Abstract

Mathematical modeling of the energy metabolism of brain cells plays a central role in understanding data collected with different imaging modalities, and in making predictions based on them. During the last decade, several sophisticated brain metabolism models have appeared. Unfortunately, the picture of the metabolic details that emerges from them is far from coherent: while each model has its justification and is in agreement with some experimental data, some of the predictions of different models can diverge from each other significantly. In this article, we review some of the recent published models, emphasizing similarities and differences between them to understand where the differences in predictions stem from. In that context we present a probabilistic approach, which rather than assigning fixed values to the model parameters, regard them as random variables whose distributions are inferred on in the light of stoichiometric information and different observations. The probabilistic approach reveals how much intrinsic variability a metabolic system may contain, which in turn may be a valid explanation of the different findings.

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References

  1. Attwell, D., and S. B. Laughlin. An energy budget for signaling in the grey matter of the brain. J. Cereb. Blood Flow Metab. 21:1133–1145, 2001.

    Article  PubMed  CAS  Google Scholar 

  2. Aubert, A., and R. Costalat. A model of the coupling between brain electrical activity, metabolism, and hemodynamics: application to the interpretation of functional neuroimaging. NeuroImage 17:1162–1181, 2002.

    Article  PubMed  Google Scholar 

  3. Aubert, A., and R. Costalat. Interaction between astrocytes and neurons studied using a mathematical model of compartmentalized energy metabolism. J. Cereb. Blood Flow Metab. 25:1476–1490, 2005.

    Article  PubMed  CAS  Google Scholar 

  4. Aubert, A., R. Costalat, P. J. Magistretti, and L. Pellerin. Brain lactate kinetics: modeling evidence for neuronal lactate uptake upon activation. Proc. Natl Acad. Sci. U.S.A. 102:16448–16453, 2005.

    Article  PubMed  CAS  Google Scholar 

  5. Aubert, A., R. Costalat, and R. Valabrègue. Modelling of the coupling between brain electrical activity and metabolism. Acta. Biotheor. 49:301–326, 2001.

    Article  PubMed  CAS  Google Scholar 

  6. Bergersen, L. H., and A. Gjedde. Is lactate a volume transmitter of metabolic states of the brain? Front. Neuroenergetics 4:5, 2012.

    PubMed  CAS  Google Scholar 

  7. Calvetti, D., R. Occhipinti, and E. Somersalo. The inverse problem of brain energetics: ketone bodies as alternative substrates. Proceedings of the applied inverse problems 2007: theoretical and computational aspects. J. Phys. Conf. Ser. 124:012013, 2008.

    Article  Google Scholar 

  8. Calvetti, D., and E. Somersalo. Large scale statistical parameter estimation in complex systems with an application to metabolic models. Multiscale Model. Simul. 5:1333–1366, 2006.

    Article  Google Scholar 

  9. Calvetti, D., and E. Somersalo. Introduction to Bayesian Scientific Computing—Ten Lectures on Subjective Computing. New York: Springer, 2007.

    Google Scholar 

  10. Calvetti, D., and E. Somersalo. Dynamic activation model for a glutamatergic neurovascular unit. J. Theor. Biol. 274:12–29, 2010.

    Article  PubMed  Google Scholar 

  11. Calvetti, D., and E. Somersalo. Ménage à trois: the role of neurotransmitters in the energy metabolism of astrocytes, glutamatergic and GABAergic neurons. J. Cereb. Blood Flow Metab. 32:1472–1483, 2012.

    Article  PubMed  CAS  Google Scholar 

  12. Chih, C. P., and E. L. Roberts, Jr. Energy substrates for neurons during neural activity: a critical review of the astrocyte–neuron lactate shuttle hypothesis. J. Cereb. Blood Flow Metab. 23:1263–1281, 2003.

    Article  PubMed  CAS  Google Scholar 

  13. Cloutier, M., F. B. Bolger, and J. P. Lowry. An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurement. J. Comput. Neurosci. 27:391–414, 2009.

    Article  PubMed  Google Scholar 

  14. Dash, R. K., Y. Li, J. Kim, G. M. Saidel, and M. E. Cabrera. Modeling cellular metabolism and energetics in skeletal muscle: large-scale parameter estimation and sensitivity analysis. IEEE Trans. Biomed. Eng. 55:1298–1318, 2008.

    Article  PubMed  Google Scholar 

  15. Dienel, G. Brain lactate metabolism: the discoveries and controversies. J. Cereb. Blood Flow Metab. 32:1107–1138, 2011.

    Article  PubMed  Google Scholar 

  16. DiNuzzo, M., S. Mangia, B. Maraviglia, and F. Giove. Changes in glucose uptake rather than lactate shuttle take center stage in subserving neuroenergetics: evidence from mathematical modeling. J. Cereb. Blood Flow Metab. 30:586–602, 2010.

    Article  PubMed  CAS  Google Scholar 

  17. Fillenz, M. The role of lactate in brain metabolism. Neurochem. Int. 47:413–417, 2005.

    Article  PubMed  CAS  Google Scholar 

  18. Fox, P. T., and M. E. Raichle. Focal physiological uncoupling of cerebral blood flow and oxidative metabolism during somatosensory stimulation in human subjects. Proc. Natl Acad. Sci. U.S.A. 83:1140–1144, 1986.

    Article  PubMed  CAS  Google Scholar 

  19. Fox, P. T., M. E. Raichle, M. A. Mintun, and C. Dence. Nonoxidative glucose consumption during focal physiologic neural activity. Science 241:462–464, 1988.

    Article  PubMed  CAS  Google Scholar 

  20. Gjedde, A. Rapid steady-state analysis of blood–brain glucose transfer in the rat. Acta Physiol. Scand. 108:331–339, 1980.

    Article  PubMed  CAS  Google Scholar 

  21. Gjedde, A. The relation between brain function and cerebral blood flow and metabolism. In: Cerebrovascular Disease, edited by H. H. Batjer. Philadelphia: Lippincott-Raven, 1997, pp. 23–40.

    Google Scholar 

  22. Gjedde, A. Coupling of brain function to metabolism: evaluation of energy requirements. In: Handbook of Neurochemistry and Molecular Neurobiology3rd, edited by A. Lajtha. Berlin: Springer, 2007.

    Google Scholar 

  23. Gjedde, A., and S. Marrett. Glycolysis in neurons, not astrocytes, delays oxidative metabolism of human visual cortex during sustained checkerboard stimulation in vivo. J. Cereb. Blood Flow Metab. 21:1384–1392, 2001.

    Article  PubMed  CAS  Google Scholar 

  24. Gjedde, A., S. Marrett, and M. Vafaee. Oxidative and nonoxidative metabolism of excited neurons and astrocytes. J. Cereb. Blood Flow Metab. 22:1–14, 2002.

    Article  PubMed  CAS  Google Scholar 

  25. Gruetter, R., E. R. Seaquist, and K. Ugurbil. A mathematical model of compartmentalized neurotransmitter metabolism in the human brain. Am. J. Physiol. Endocrinol. Metab. 281:E100–E112, 2001.

    PubMed  CAS  Google Scholar 

  26. Heino, J., D. Calvetti, and E. Somersalo. Metabolica: a statistical research tool for analyzing metabolic networks. Comput. Methods Programs Biomed. 97:151–167, 2010.

    Article  PubMed  Google Scholar 

  27. Heinrich, R., and S. Schuster. The Regulation of Cellular Systems. New York: ITP Chapman & Hall, 1996.

    Book  Google Scholar 

  28. Hertz, L. The astrocyte–neuron lactate shuttle: a challenge of a challenge. J. Cereb. Blood Flow Metab. 24:1241–1248, 2004.

    Article  PubMed  Google Scholar 

  29. Hertz, L. Brain glutamine synthesis requires neuronal aspartate: a commentary. J. Cereb. Blood Flow Metab. 31:384–387, 2011.

    Article  PubMed  CAS  Google Scholar 

  30. Hertz, L., L. Peng, and G. A. Dienel. Energy metabolism in astrocytes: high rate of oxidative metabolism and spatiotemporal dependence on glycolysis/glycogenolysis. J. Cereb. Blood Flow Metab. 27:219–249, 2007.

    Article  PubMed  CAS  Google Scholar 

  31. Hyder, F., A. B. Patel, A. Gjedde, D. L. Rothman, K. L. Behar, and R. G. Shulman. Neuronal-glial glucose oxidation and glutamatergic-GABAergic function. J. Cereb. Blood Flow Metab. 26:865–877, 2006.

    Article  PubMed  CAS  Google Scholar 

  32. Ivanov, K. P., Yu. Ya. Kislayokov, and M. O. Samoilov. Microcirculation and transport of oxygen to neurons of the brain. Microvasc. Res. 18:434–441, 1979.

    Article  PubMed  CAS  Google Scholar 

  33. Jolivet, R., I. Allaman, L. Pellerin, P. J. Magistretti, and B. Weber. Comment on recent modeling studies of astrocyte–neuron metabolic interactions. J. Cereb. Blood Flow Metab. 30:1982–1986, 2010.

    Article  PubMed  CAS  Google Scholar 

  34. Kasischke, K. A., H. D. Vishwasrao, P. J. Fisher, W. R. Zipfel, and W. W. Webb. Neural activity triggers neuronal oxidative metabolism followed by astrocytic glycolysis. Science 305:99–103, 2004.

    Article  PubMed  CAS  Google Scholar 

  35. Kauffman, K. J., P. Prakesh, and J. S. Edwards. Advance in flux balance analysis. Curr. Opin. Biotechnol. 14:491–496, 2003.

    Article  PubMed  CAS  Google Scholar 

  36. Kemp, G. J. Non-invasive methods for studying brain energy metabolism: what they show and what it means. Dev. Neurosci. 22:418–428, 2000.

    Article  PubMed  CAS  Google Scholar 

  37. Krogh, A. The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J. Physiol. 52:409–415, 1919.

    PubMed  CAS  Google Scholar 

  38. LaNoue, K. F., V. Carson, D. A. Berkich, and S. M. Hutson. Mitochondrial/cytosolic interactions via metabolite shuttles and transporters. In: Handbook of Neurochemistry and Molecular Neurobiology. Brain Energetics. Integration of Molecular and Cellular Processes. Part VI, Chapter 1. Berlin: Springer, pp. 589–616, 2007.

  39. Lovatt, D., U. Sonnewald, H. S. Waagepetersen, A. Schousboe, W. He, J. H. Lin, X. Han, T. Takano, S. Wang, F. J. Sim, S. A. Goldman, and M. Nedergaard. The transcriptome and metabolic gene signature of protoplasmic astrocytes in the adult murine cortex. J. Neurosci. 27:12255–12266, 2007.

    Article  PubMed  CAS  Google Scholar 

  40. Mangia, S., M. DiNuzzo, F. Giove, A. Carruthers, I. A. Simpson, and S. J. Vannucci. Response to ‘comment on recent modeling studies of astrocyte–neuron metabolic interactions’: much ado about nothing. J. Cereb. Blood Flow Metab. 31:1346–1353, 2011.

    Article  PubMed  CAS  Google Scholar 

  41. Mangia, S., I. A. Simpson, S. J. Vannucci, and A. Carruthers. The in vivo neuron-to-astrocyte lactate shuttle in human brain: evidence from modeling of measured lactate levels during visual stimulation. J. Neurochem. 109(Suppl 1):55–62, 2009.

    Article  PubMed  CAS  Google Scholar 

  42. Marangoni, A. G. Enzyme Kinetics, a Modern Approach. Hoboken: Wiley, 2003.

    Google Scholar 

  43. Mintun, M. A., A. G. Vlassenko, M. M. Rundle, and M. E. Raichle. Increased lactate/pyruvate ratio augments blood flow in physiologically activated human brain. Proc. Nat. Acad. Sci. U.S.A. 101:659–664, 2003.

    Article  Google Scholar 

  44. Morris, A. A. M. Cerebral ketone body metabolism. J. Inherit. Metab. Dis. 28:109–121, 2005.

    Article  PubMed  CAS  Google Scholar 

  45. Occhipinti, R., M. A. Puchowicz, J. C. LaManna, E. Somersalo, and D. Calvetti. Statistical analysis of metabolic pathways of brain metabolism at steady state. Ann. Biomed. Eng. 6:886–902, 2007.

    Article  Google Scholar 

  46. Occhipinti, R., E. Somersalo, and D. Calvetti. Interpretation of NMR spectroscopy human brain data with multi-compartment computational model of cerebral metabolism. In: Oxygen Transport to Tissue XXXII, edited by J. C. LaManna, M. A. Puchowicz, K. Xu, D. K. Harrison, and D. F. Bruley, 2009, pp. 249–254.

  47. Occhipinti, R., E. Somersalo, and D. Calvetti. Astrocytes as the glucose shunt for glutamatergic neurons at high activity: an in silico study. J. Neurophysiol. 101:2528–2538, 2009.

    Article  PubMed  CAS  Google Scholar 

  48. Occhipinti, R., E. Somersalo, and D. Calvetti. Energetics of inhibition: insights with a computational model of the human GABAergic neuron–astrocyte cellular complex. J. Cereb. Blood Flow Metab. 30:1834–1846, 2010.

    Article  PubMed  CAS  Google Scholar 

  49. Papin, J. A., J. Stelling, N. D. Price, S. Klamt, S. Shuster, and B. O. Palsson. Comparison of network-based pathway analysis methods. Trends Biotechnol. 22:400–405, 2004.

    Article  PubMed  CAS  Google Scholar 

  50. Pardo, B., T. B. Rodrigues, L. Contreras, M. Garzón, I. Llorente-Folch, K. Kobayashi, T. Saheki, S. Cerdan, and J. Satrústegui. Brain glutamine synthesis requires neuronal-born aspartate as amino donor for glial glutamate formation. J. Cereb. Blood Flow Metab. 31:90–101, 2011.

    Article  PubMed  CAS  Google Scholar 

  51. Pellerin, L., and P. J. Magistretti. Glutamate uptake into astrocytes stimulates aerobic glycolysis: a mechanism coupling neuronal activity to glucose utilization. Proc. Natl Acad. Sci. U.S.A. 91:10625–10629, 1994.

    Article  PubMed  CAS  Google Scholar 

  52. Pellerin, L., and P. J. Magistretti. Food for thought: challenging the dogmas. J. Cereb. Blood Flow Metab. 23:1282–1286, 2003.

    Article  PubMed  Google Scholar 

  53. Schulman, R. G., F. Hyder, and D. L. Rothman. Lactate efflux and the neuroenergetic basis of brain function. NMR Biomed. 14:389–396, 2001.

    Article  Google Scholar 

  54. Siesjö, B. K. Brain Energy Metabolism. New York: Wiley, 1978.

    Google Scholar 

  55. Simpson, I. A., A. Carruthers, and S. J. Vannucci. Supply and demand in cerebral energy metabolism: the role of nutrient transporters. J. Cereb. Blood Flow Metab. 27:1766–1791, 2007.

    Article  PubMed  CAS  Google Scholar 

  56. Vannucci, S. J., F. Maher, and I. A. Simpson. Glucose transporter proteins in brain: delivery of glucose to neurons and glia. Glia 21:2–21, 1997.

    Article  PubMed  CAS  Google Scholar 

  57. Zhou, L., J. E. Salem, G. E. Saidel, W. C. Stanley, and M. E. Cabrera. Mechanistic model of cardiac energy metabolism predicts localization of glycolysis to cytosolic subdomain during ischemia. Am. J. Physiol. Heart Circ. Physiol. 288:H2400–H2411, 2005.

    Article  PubMed  CAS  Google Scholar 

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Correspondence to D. Calvetti.

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Associate Editor Michael R. King oversaw the review of this article.

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Somersalo, E., Cheng, Y. & Calvetti, D. The Metabolism of Neurons and Astrocytes Through Mathematical Models. Ann Biomed Eng 40, 2328–2344 (2012). https://doi.org/10.1007/s10439-012-0643-z

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  • DOI: https://doi.org/10.1007/s10439-012-0643-z

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