Abstract
We present a minimal neuron model that captures the essence of the persistent firing behavior of interneurons as discovered recently in the field of Neuroscience. The mathematical model reproduces the phenomenon that slow integration in distal axon of interneurons on a timescale of tens of seconds to minutes, leads to persistent firing of axonal action potentials lasted for similar duration. In this model, we consider the axon as a slow leaky integrator, which is capable of dynamically switching the neuronal firing states between normal firing and persistent firing, through axonal computation. This model is based on the Izhikevich neuron model and includes additional equations and parameters to represent the persistent firing dynamics, making it computationally efficient yet bio-plausible, and thus well suitable for large scale spiking network simulations.
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References
Baddeley, A.: Working memory. Science 255(5044), 556 (1992)
Boahen, K.: Neuromorphic microchips. Scientific American 292(5), 56–63 (2005)
Brette, R., Rudolph, M., Carnevale, T., Hines, M., Beeman, D., Bower, J.M., Diesmann, M., Morrison, A., Goodman, P.H., Harris, F.C., et al.: Simulation of networks of spiking neurons: A review of tools and strategies. Journal of Computational Neuroscience 23(3), 349–398 (2007)
D’Esposito, M., Detre, J.A., Alsop, D.C., Shin, R.K., Atlas, S., Grossman, M.: The neural basis of the central executive system of working memory. Nature 378(6554), 279–281 (1995)
Durstewitz, D., Seamans, J.K., Sejnowski, T.J.: Neurocomputational models of working memory. Nature Neuroscience 3, 1184–1191 (2000)
Egorov, A.V., Hamam, B.N., Fransén, E., Hasselmo, M.E., Alonso, A.A.: Graded persistent activity in entorhinal cortex neurons. Nature 420(6912), 173–178 (2002)
Fitzhugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal 1(6), 445–466 (1961)
de Garis, H., Shuo, C., Goertzel, B., Ruiting, L.: A world survey of artificial brain projects part I: Large-scale brain simulations. Neurocomputing 74(1-3), 3–29 (2010)
Goldman-Rakic, P.S.: Cellular basis of working memory. Neuron 14(3), 477 (1995)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117(4), 500 (1952)
Izhikevich, E.M.: Resonate-and-fire neurons. Neural Networks 14(6-7), 883–894 (2001)
Izhikevich, E.M.: Simple model of spiking neurons. IEEE Transactions on Neural Networks 14(6), 1569–1572 (2003)
Izhikevich, E.M., Edelman, G.M.: Large-scale model of mammalian thalamocortical systems. Proceedings of the National Academy of Sciences 105(9), 3593 (2008)
Markram, H.: The blue brain project. Nature Reviews Neuroscience 7(2), 153–160 (2006)
Miller, E.K., Erickson, C.A., Desimone, R.: Neural mechanisms of visual working memory in prefrontal cortex of the macaque. The Journal of Neuroscience 16(16), 5154 (1996)
Miller, G.A.: The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review 63(2), 81 (1956)
Morris, C., Lecar, H.: Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal 35(1), 193–213 (1981)
Peterson, L., Peterson, M.J.: Short-term retention of individual verbal items. Journal of Experimental Psychology 58(3), 193 (1959)
Rose, R.M., Hindmarsh, J.L.: The assembly of ionic currents in a thalamic neuron i. the three-dimensional model. Proceedings of the Royal Society of London B Biological Sciences 237(1288), 267 (1989)
van Schaik, A., Jin, C., McEwan, A., Hamilton, T.J.: A log-domain implementation of the izhikevich neuron model. In: IEEE International Symposium on Circuits and Systems (ISCAS), pp. 4253–4256 (2010)
Sheffield, M.E., Best, T.K., Mensh, B.D., Kath, W.L., Spruston, N.: Slow integration leads to persistent action potential firing in distal axons of coupled interneurons. Nature Neuroscience 14(2), 200–207 (2010)
Shi, L.P., Yi, K.J., Ramanathan, K., Zhao, R., Ning, N., Ding, D., Chong, T.C.: Artificial cognitive memory—changing from density driven to functionality driven. Applied Physics A: Materials Science & Processing 102(4), 865–875 (2011)
Szatmáry, B., Izhikevich, E.M.: Spike-timing theory of working memory. PLoS Computational Biology 6(8) (2010)
Wijekoon, J.H., Dudek, P.: Compact silicon neuron circuit with spiking and bursting behaviour. Neural Networks 21(2-3), 524–534 (2008)
Wilson, H.R.: Simplified dynamics of human and mammalian neocortical neurons. Journal of Theoretical Biology 200(4), 375–388 (1999)
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Ning, N., Yi, K., Huang, K., Shi, L. (2011). Axonal Slow Integration Induced Persistent Firing Neuron Model. In: Lu, BL., Zhang, L., Kwok, J. (eds) Neural Information Processing. ICONIP 2011. Lecture Notes in Computer Science, vol 7062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24955-6_56
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DOI: https://doi.org/10.1007/978-3-642-24955-6_56
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