Abstract
Many mathematical models of different neurons have been proposed so far, however, the way of modeling Ca2 + regulation mechanisms has not been established yet. Therefore, we try to construct a physiologically plausible model which contains many regulating systems of the intracellular Ca2 + , such as Ca2 + buffering, Na + /Ca2 + exchanger and Ca2 + pump current. In this paper, we seek the plausible values of parameters by analyzing the global bifurcation structure of our temporary model.
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Osanai, M., Takeno, Y., Hasui, R., Yagi, T.: Electrophysiological and optical studies on the signal propagation in visual cortex slices. In: Proc. of 2005 Annu. Conf. of Jpn. Neural Network Soc., pp. 89–90 (2005)
Herz, A.V.M., Gollisch, T., Machens, C.K., Jaeger, D.: Modeling single-neuron dynamics and computations: a balance of detail and abstraction. Science 314, 80–85 (2006)
Hodgkin, A.L., CHuxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol(Lond) 177, 500–544 (1952)
Brown, A.M., Schwindt, P.C., Crill, W.E.: Voltage dependence and activation kinetics of pharmacologically defend components of the high-threshold calcium current in rat neocortical neurons. J. Neurophysiol. 70, 1516–1529 (1993)
Peterson, B.Z., Demaria, C.D., Yue, D.T.: Calmodulin is the Ca 2 + sensor for Ca 2 + dependent inactivation of L-type calcium channels. Neuron. 22, 549–558 (1999)
Cummins, T.R., Xia, Y., Haddad, G.G.: Functional properties of rat and human neocortical voltage-sensitive sodium currents. J. Neurophysiol. 71, 1052–1064 (1994)
Korngreen, A., Sakmann, B.: Voltage-gated K + channels in layer 5 neocortical pyramidal neurons from young rats: subtypes and gradients. J. Neurophy. 525, 621–639 (2000)
Kang, J., Huguenard, J.R., Prince, D.A.: Development of BK channels in neocortical pyramidal neurons. J. Neurophy. 76, 188–198 (1996)
Hayashida, Y., Yagi, T.: On the interaction between voltage-gated conductances and Ca + regulation mechanisms in retinal horizontal cells. J. Neurophysiol. 87, 172–182 (2002)
Naraghi, M., Neher, E.: Linearized buffered Ca + diffusion in microdomains and its implications for calculation of [Ca + ] at the mouth of a calcium channel. J. Neurosci. 17, 6961–6973 (1997)
Noble, D.: Influence of Na/Ca exchanger stoichiometry on model cardiac action potentials. Ann. N.Y, Acad. Sci. 976, 133–136 (2002)
Yuan, W., Burkhalter, A., Nerbonne, J.M.: Functional role of the fast transient outward K + current I A in pyramidal neurons in (rat) primary visual cortex. J. Neurosci. 25, 9185–9194 (2005)
Doedel, E.J., Champeny, A.R., Fairgrieve, T.F., Kunznetsov, Y.A., Sandstede, B., Xang, X.: Continuation and bifurcation software for ordinary differential equations (with HomCont). Technical Report, Concordia University (1997)
Doi, S., Kumagai, S.: Generation of very slow neuronal rhythms and chaos near the Hopf bifurcation in single neuron models. J. Comp. Neurosci. 19, 325–356 (2005)
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Ishiki, T., Tanaka, S., Osanai, M., Doi, S., Kumagai, S., Yagi, T. (2008). Global Bifurcation Analysis of a Pyramidal Cell Model of the Primary Visual Cortex: Towards a Construction of Physiologically Plausible Model. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds) Neural Information Processing. ICONIP 2007. Lecture Notes in Computer Science, vol 4984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69158-7_2
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DOI: https://doi.org/10.1007/978-3-540-69158-7_2
Publisher Name: Springer, Berlin, Heidelberg
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