Effects of The Peak to Baseline Ratio on Phase Difference of The Coupled Hodgkin Huxley Neurons

Abstract

Phase response curve (PRC) examines how weak perturbation effects spike time of neurons. Peak-to-baseline ratio is one of the most important specification of type II PRC neurons and it gives a brief explanation of PRC in terms of numerical sense. In this study, Hodgkin Huxley (HH) model neurons coupled via gap junction under three different applied currents were investigated in terms of PRCs, peak-to-baseline ratio and required time interval of minimum phase difference. Although the used three HH model neurons had same type of excitability and PRCs, the shapes and maximum and minimum peaks were varied. The close relationship between peak-to-baseline ratio and the required time interval of minimum phase difference of coupled neurons were found. To sum up, the results of our simulations indicated that the required time of minimum phase differences of two coupled HH neurons via gap junction were related to calculated peak-to-baseline ratios.

Keywords

• Peak-to-baseline ratio,PRC,HH Model,phase difference

References

1. Abouzeid, A., Ermentrout, B., Type-II phase resetting curve is optimal for stochastic synchrony, Physical Review E, 80(1)(2009), 011911.
2. Brown, E., Moehlis, J., Holmes, P., On the phase reduction and response dynamics of neural oscillator populations, Neural Computation, 16(4)(2004), 673–715.
3. Canavier, C. C, Phase response curve, Scholarpedia, 1(12)(2006), 1332.
4. Canavier, C. C., Phase-resetting as a tool of information transmission, Current Opinion in Neurobiology, 31(2015), 206–213.
5. Couto, J., Linaro, D., De Schutter, E., Giugliano, M., On the firing rate dependency of the phase response curve of rat purkinje neurons in vitro, PLoS Comput Biol, 11(3)(2015), e1004112.
6. Ermentrout, B., Type I membranes, phase resetting curves, and synchrony, Neural Computation, 8(5)(1996), 979–1001.
7. Ermentrout, G. B., Galan, R. F., Urban, N. N., Reliability, synchrony and noise, Trends in Neurosciences, 31(8)(2008), 428–434.
8. Fitzhugh, R., Thresholds and plateaus in the Hodgkin-Huxley nerve equations, The Journal of General Physiology, 43(5)(1960), 867–896.

9. Hansel, D., Mato, G., Meunier, C., Synchrony in excitatory neural networks, Neural Computation, 7(2)(1995), 307–337.
10. 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)(1952), 500–544.
11. Hoppensteadt, F. C., Izhikevich, E. M., Weakly Connected Neural Networks, Springer Science & Business Media, Vol. 126, 2012.
12. Izhikevich, E. M., Which model to use for cortical spiking neurons?, IEEE Transactions on Neural Networks, 15(5) (2004), 1063–1070.
13. Izhikevich, E. M., Dynamical Systems in Neuroscience, MIT Press, 2007.
14. Jiao, X., Zhu, D. Phase-response synchronization in neuronal population, Sci China Tech Sci, 57(2014), 923–928.
15. Kurths, J., Pikovsky, A., Rosenblum, M., Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, New York, 2001.
16. Lengyel, M., Kwag, J., Paulsen, O., Dayan, P., Matching storage and recall: hippocampal spike timing dependent plasticity and phase response curves, Nature Neuroscience, 8(12)(2005), 1677–1683.
17. Lu, M., Che, Y., Li, H.,Wei, X.,Wang, J., Effects of synaptic coupling on phase response curve of neurons, In 2014 7th International Conference on Biomedical Engineering and Informatics (pp. 745–749). IEEE.
18. Lu, M., Liu, B., Che, Y., Han, C., Eect of coupling types on synchronization of weakly coupled Bursting Neurons, International Symposium on Computers & Informatics, Beijing (2015), 1930–1937.
19. Morris, C., Lecar, H., Voltage oscillations in the barnacle giant muscle fiber, Biophysical Journal 35(1)(1981), 193–213.
20. Nagumo, J., Arimoto, S., Yoshizawa, S., An active pulse transmission line simulating nerve axon, Proceedings of the IRE,50(10) (1962), 2061–2070.
21. Nakao, H., Phase reduction approach to synchronisation of nonlinear oscillators, Contemporary Physics, 57(2)(2016), 188–214.
22. Novicenko, V., Pyragas, K., Computation of phase response curves via a direct method adapted to infinitesimal perturbations, Nonlinear Dynamics, 67(1)(2012), 517–526.
23. Phoka, E., Cuntz, H., Roth, A., Hausser, M., A new approach for determining phase response curves reveals that Purkinje cells can act as perfect integrators, PLoS Comput Biol, 6(4)(2010), e1000768.
24. Schultheiss, N. W., Prinz, A. A., Butera, R. J., Phase Response Curves in Neuroscience: Theory, Experiment, and Analysis, Springer Science Business Media, 2011.
25. Siegelbaum, S. A., Hudspeth, A. J., Kandel, E. R., Schwartz, J. H., Jessell, T. M., Principles of Neural Science, McGraw-Hill, New York, Vol. 4, pp. 1227–1246, 2000.
26. Smeal, R. M., Ermentrout, G. B. White, J. A., Phase-response curves and synchronized neural networks, Philosophical Transactions of The Royal Society of London B: Biological Sciences, 365(1551)(2010), 2407–2422.
27. Şengül, S., Clewley, R., Bertram, R., Tabak, J., Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model, Journal of Computational Neuroscience 37(3) (2014), 403–415.
28. Tateno, T., Robinson, H. P. C., Phase resetting curves and oscillatory stability in interneurons of rat somatosensory cortex, Biophysical Journal, 92(2)(2007), 683–695.