Mathematical modeling of the biphasic dopaminergic response to glucose


In this work, we specify potential elements of the brain to sense and regulate the energy metabolism of the organism. Our numerical investigations base on neurochemical experiments demonstrating a biphasic association between brain glucose level and neuronal activity. The dynamics of high and low affine KATP channels are most likely to play a decisive role in neuronal activity. We develop a coupled Hodgkin-Huxley model describing the interactive behavior of inhibitory GABAergic and excitatory dopaminergic neurons projecting into the caudate nucleus. The novelty in our approach is that we include the synaptic coupling of GABAergic and dopaminergic neurons as well as the interaction of high and low affine KATP channels. Both are crucial mechanisms described by kinetic models. Simulations demonstrate that our new model is coherent with neurochemical in vitro experiments. Even experimental interventions with glibenclamide and glucosamine are reproduced by our new model. Our results show that the considered dynamics of high and low affine KATP channels may be a driving force in energy sensing and global regulation of the energy metabolism, which supports central aspects of the new Selfish Brain Theory. Moreover, our simulations suggest that firing frequencies and patterns of GABAergic and dopaminergic neurons are correlated to their neurochemical outflow.

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Chung, M. , Göbel, B. , Peters, A. , Oltmanns, K. and Moser, A. (2011) Mathematical modeling of the biphasic dopaminergic response to glucose. Journal of Biomedical Science and Engineering, 4, 136-145. doi: 10.4236/jbise.2011.42020.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Steinkamp, M., Li, T., Fuellgraf, H. and Moser, A. (2007) K(ATP)-dependent neurotransmitter release in the neuronal network of the rat caudate nucleus. Neurochemistry international, 50, 159-163. doi:10.1016/j.neuint.2006.07.011
[2] Baldwin, S.A. (1993) Mammalian passive glucose transporters: members of an ubiquitous family of active and passive transport proteins. Biochimica et Biophysica Acta, 1154, 17-49.
[3] Karschin, C., Ecke, C., Ashcroft, F.M. and Karschin, A. (1997) Overlapping distribution of K(ATP) channel- forming Kir6.2 subunit and the sulfonylurea receptor SUR1 in rodent brain. FEBS Letters, 401, 59-64. doi:10.1016/S0014-5793(96)01438-X
[4] During, M.J., Leone, P., Davis, K.E., Kerr, D. and Sherwin, R.S. (1995) Glucose modulates rat substantia nigra GABA release in vivo via ATP-sensitive potassium channels. Journal of Clinical Investigation, 95, 2403-2408. doi:10.1172/JCI117935
[5] Ramrath, L., Levering, J., Conrad, M., Thuemen, A., Fuellgraf, H. and Moser, A. (2009) Mathematical identification of a neuronal network consisting of GABA and DA in striatal slices of the rat brain. Computational and Mathematical Methods in Medicine, 10, 273-285. doi:10.1080/17486700802616526
[6] Conti, L.R., Radeke, C.M., Shyng, S.-L. and Vandenberg, C.A. (2001) Transmembrane topology of the sulfonylurea receptor SUR1. Journal of Biology and Chemistry, 276, 41270-41278. doi:10.1074/jbc.M106555200
[7] Ashcroft, F.M. and Gribble, F.M. (200) New windows on the mechanism of action of K(ATP) channel openers. Trends in Pharmacological Sciences, 21, 439-445. doi:10.1016/S0165-6147(00)01563-7
[8] Levin, B.E., Routh, V.H., Kang, L., Sanders, N.M. and Dunn-Meynell, A.A. (2004) Neuronal glucosensing: what do we know after 50 years? Diabetes, 53, 2521-2528. doi:10.2337/diabetes.53.10.2521
[9] Destexhe, A., Mainen, Z. and Sejnowski, T.J. (1998) Methods in Neuronal Modeling, Chapter Kinetic models of synaptic transmission. 2nd Edition, MIT Press, Cambridge. doi:10.1152/jn.00422.2007
[10] Canavier, C., Oprisan, S., Callaway, J.C., Ji, H. and Shepard, P. (2007) Computational model predicts a role for ERG current in repolarizing plateau potentials in dopamine neurons: implications for modulation of neuronal activity. Journal of Neurophysiology, 98, 3006-3022.
[11] Amini, B., Clark, J.W. and Canavier, C.C. (1999) Calcium dynamics underlying pacemaker- like and burst firing in midbrain dopaminergic neurons: a computational study. Journal of Neurophysiology, 82, 2249-2261.
[12] Komendantov, A. and Canavier, C. (2002) Electrical coupling between model midbrain dopamine neurons: effects on firing pattern and synchrony. Journal of Neurophysiology, 87, 1526-1541.
[13] Kuznetsov, A.S. (2010) Models of midbrain dopaminergic neurons. Scholarpedia., doi:10.4249/scholarpedia.1812, 2(10), 1812.
[14] Hodgkin, A.L. and Huxley, A.F. (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117, 500-544.
[15] Nomura, M., Fukai, T. and Aoyagi, T. (2003) Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses. Neural Computation, 15, 2179-2198. doi:10.1162/089976603322297340
[16] Ainscow, E.K., Mirshamsi, S., Tang, T., Ashford, M.L.J. and Rutter, G.A. (2002) Dynamic imaging of free cytosolic ATP concentration during fuel sensing by rat hypothalamic neurones: evidence for ATP-independent control of ATP-sensitive K(+) channels. The Journal of Physiology, 544, 429-445. doi:10.1113/jphysiol.2002.022434
[17] Nichols, C.G., Lederer, W.J. and Cannell, M.B. (1991) ATP dependence of K(ATP) channel kinetics in isolated membrane patches from rat ventricle. Biophysical Journal, 60, 1164-1177. doi:10.1016/S0006-3495(91)82152-X
[18] Rall, W. (1967) Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input. Journal of Neurophysiology, 30, 1138-1168.
[19] Destexhe, A., Mainen, Z. and Sejnowski, T.J. (1994) An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Computation, 6, 14-18. doi:10.1016/S0006-3495(91)82152-X
[20] Lundstrom, B.N. and Fairhall, A.L. (2006) Decoding stimulus variance from a distributional neural code of inter-spike intervals. The Journal of Neuroscience Online, 26, 9030-9037.
[21] Wang, M., Hou, Z. and Xin, H. (2004) Double-system- size resonance for spiking activity of coupled Hodgkin- Huxley neurons. ChemPhysChem, 5, 1602-1605. doi:10.1002/cphc.200400255
[22] Clements, J.D. (1996) Transmitter timecourse in the synaptic cleft: its role in central synaptic function. Trends in Neurosciences, 19, 163-171. doi:10.1016/S0166-2236(96)10024-2
[23] Calabrese, E.J. (2004) Hormesis: a revolution in toxicology, risk assessment and medicine. EMBO Reports, 5, S37-S40. doi:10.1038/sj.embor.7400222
[24] Peters, A., Conrad, M., Hubold, C., Schweiger, U., Fischer, B. and Fehm, H.L. (2007) The principle of homeostasis in the hypothalamus-pituitary-adrenal system: new insight from positive feedback. American Journal of Physiology: Regulatory, Integrative and Comparative Physiology, 293, R83-98. doi:10.1152/ajpregu.00907.2006
[25] Conrad M., Hubold, C., Fischer, B. and Peters A. (2009) Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback. Journal of Biological Physics, 35, 149-162. doi:10.1007/s10867-009-9134-3
[26] Peters, A., Schweiger, U., Pellerin, L., Hubold, C., Oltmanns, K.M., Conrad, M., Schultes, B., Born, J. and Fehm, H.L. (2004) The selfish brain: competition for energy resources. Neuroscience and Biobehavioral Reviews, 28, 143-180. doi:10.1016/j.neubiorev.2004.03.002
[27] Graybiel, A.M. (2005) The basal ganglia: learning new tricks and loving it. Current Opinion in Neurobiology, 15, 638-644. doi:10.1016/j.conb.2005.10.006
[28] Packard, M.G. and Knowlton, B.J. (2002) Learning and memory functions of the basal ganglia. Annual Review of Neuroscience, 25, 563-593. doi:10.1146/annurev.neuro.25.112701.142937

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