Bifurcation analysis in a single-compartment Traub model for hardware based emulation

Event Abstract Back to Event Bifurcation analysis in a single-compartment Traub model for hardware based emulation Juan C. Moctezuma1*, Víctor Breña-Medina2, Jose Nunez-Yanez3 and Joe McGeehan1 1 University of Bristol, CCR Group, Electrical and Electronic Engineering Department, United Kingdom 2 Universidad Nacional Autónoma de México, Departamento de Nanotecnología Centro de Física Aplicada y Tecnología Avanzada, Mexico 3 University of Brisol, Microelectronics Research Group, Electrical and Electronic Engineering Department, United Kingdom In this work we make a bifurcation analysis for a single compartment representation of Traub model, one of the most important conductance-based models. The analysis focuses in two principal parameters: current and leakage conductance. Study of stable and unstable solutions is explored; also Hopf-bifurcation and frequency interpretation when current varies are examined. This is the first analysis done that considers single-compartment version of a Traub model. This study allows having control of neuron dynamics and neuron response when these parameters change. Analyses like these are particularly important for several applications such as: tuning parameters in learning processes, neuron excitability tests, measure bursting properties of the neuron, among others. Finally a hardware implementation tests were developed to corroborate these results. The leakage conductance value was tuned in order the neuron remains at fixed value when it is at resting state. This parameter is the best option to change if does not want to compromise the dynamic of the original model. Through bifurcation analysis, it was detected one stable and one unstable solution (equilibrium points) for this model. A Hopf bifurcation was discovered at the point I = 90 mA, given to the current range [0 90]mA a set of stable periodic orbits with different action potentials amplitudes. The frequencies range for this periodic orbits are from 50 to 341 Hz. Figure 2 Figure 4 References 1. Traub, R.D., et al., A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J Neurophysiol, 1991. 66(2): p. 635-50. 2. Zhang, Y., J. Nunez, and J. McGeehan, Biophysically Accurate Floating Point Neuroprocessors. University of Bristol, 2010. 3. Pinsky, P.F. and J. Rinzel, Intrinsic and network rhythmogenesis in a reduced Traub model for Ca3 neurons. Journal of Computational Neuroscience, 1995. 2(3): p. 275-275. 4. Guckenheimer, J. and I.S. Labouriau, Bifurcation of the Hodgkin and Huxley Equations - a New Twist. Bulletin of Mathematical Biology, 1993. 55(5): p. 937-952. 5. Jiang, W., G. Jianming, and F. Xiangyang, Two-parameter Hopf bifurcation in the Hodgkin-Huxley model. Chaos, Solitons & Fractals, 2005. 23: p. 973-980. 6. Beuter, A., et al., Nonlinear dynamics in Physiology and Medicine. 2003: Springer. 7. Izhikevich, E.M., Neural Excitability, Spiking and Bursting. International Journal of Bifurcation and Chaos, 2000. 10(6): p. 1171-1266. 8. Guevara, M., Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems, in Nonlinear Dynamics in Physiology and Medicine, A. Beuter, et al., Editors. 2003, Springer New York. p. 41-85. 9. Fei, X.Y., Jiangwang, and L.Q. Chen, Bifurcation control of Hodgkin-Huxley model of nerve system. WCICA 2006: Sixth World Congress on Intelligent Control and Automation, Vols 1-12, Conference Proceedings, 2006: p. 9406-9410. 10. Moctezuma, J.C., J.P. McGeehan, and J.L. Nunez-Yanez. Numerically efficient and biophysically accurate neuroprocessing platform. in Reconfigurable Computing and FPGAs (ReConFig), 2013 International Conference on. 2013. 11. Izhikevich, E.M., Dynamical Systems in Neuroscience. 2007, Cambridge, Massachusetts. London, England: The MIT Press. 12. Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 1952. 117(4): p. 500-44. 13. Hassard, B., Bifurcation of periodic solutions of Hodgkin-Huxley model for the squid giant axon. J Theor Biol, 1978. 71(3): p. 401-20. 14. Rinzel, J. and R.N. Miller, Numerical-Calculation of Stable and Unstable Periodic-Solutions to the Hodgkin-Huxley Equations. Mathematical Biosciences, 1980. 49(1-2): p. 27-59. 15. Jiang, W., et al., Multi-parameter Hopf-bifurcation in Hodgkin-Huxley model exposed to ELF external electric field. Chaos Solitons & Fractals, 2005. 26(4): p. 1221-1229. 16. Wang, J., J.M. Geng, and X.Y. Fei, Two-parameters Hopf bifurcation in the Hodgkin-Huxley model. Chaos Solitons & Fractals, 2005. 23(3): p. 973-980. 17. Wang, J., L.Q. Chen, and X.Y. Fei, Analysis and control of the bifurcation of Hodgkin-Huxley model. Chaos Solitons & Fractals, 2007. 31(1): p. 247-256. 18. A.Naghilou and S.H.Sabzpoushan, Evaluation of ELF Electric Fields Effects on Bifurcation Phenomenon of Spaced-Clamped Coductance-Based Minimal Cell Models. Asian Journal of Biomedical & Pharmaceutical sciences, 2013. 3(20): p. 8-16. 19. Wang, J., H. Zhang, and K.M. Tsang, Hopf Bifurcation in the Hodgkin-Huxley model exposed to ELF electrical field. Annual International Conference of the IEEE EMBS, 2003: p. 2323-2326. 20. Coombes, S. and P.C. Bressloff, Bursting The Genesis of Rhythm in the Nervous System. 2005: world Scientific Printers. 21. Yi, G.S., et al., Exploring how extracellular electric field modulates neuron activity through dynamical analysis of a two-compartment neuron model. J Comput Neurosci, 2013. 22. Traub, R.D., Simulation of intrinsic bursting in CA3 hippocampal neurons. Neuroscience, 1982. 7(5): p. 1233-42. 23. Booth, V. and A. Bose, Neural mechanisms for generating rate and temporal codes in model CA3 pyramidal cells. J Neurophysiol, 2001. 85(6): p. 2432-45. 24. Feng, J.F. and G.B. Li, Behaviour of two-compartment models. Neurocomputing, 2001. 38: p. 205-211. 25. Kepecs, A. and X.J. Wang, Analysis of complex bursting in cortical pyramidal neuron models. Neurocomputing, 2000. 32: p. 181-187. 26. Hirsch, M.W., S. Smale, and R.L. Devaney, Differential equations, dynamical systems, and an introduction to chaos. 2004: ElSevier. 27. Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos. 2000: Springer. 28. Ermentrout, A.B. and R.A. Mahajan, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. Applied Mechanics Reviews, 2003. 56(4): p. B53-B53. Keywords: traub model, Pinsky-Rinzel model, Hopf bifurcation, single-compartment models, bifurcation analysis, neuron modeling. Conference: Neuroinformatics 2014, Leiden, Netherlands, 25 Aug - 27 Aug, 2014. Presentation Type: Poster, to be considered for oral presentation Topic: Computational neuroscience Citation: Moctezuma JC, Breña-Medina V, Nunez-Yanez J and McGeehan J (2014). Bifurcation analysis in a single-compartment Traub model for hardware based emulation. Front. Neuroinform. Conference Abstract: Neuroinformatics 2014. doi: 10.3389/conf.fninf.2014.18.00081 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 28 Apr 2014; Published Online: 04 Jun 2014. * Correspondence: Mr. Juan C Moctezuma, University of Bristol, CCR Group, Electrical and Electronic Engineering Department, Bristol, United Kingdom, eejcme@bristol.ac.uk Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. 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