Examining phase response curve of nerve cell by using three different methods

Yıl 2018, Cilt: 2 Sayı: 1, 1 - 9, 28.02.2018

Hasan Eskalen , Şükrü Özğan

https://doi.org/10.32571/ijct.338403

Öz

Rhythmic motion is
observed in a variety of different field including physical, chemical and
biological systems. Neural system, that consists of billions of neurons are
also exhibited periodic motion. Phase Response Curves (PRCs); act like a bridge
between, a single neuron and neural network; briefly measure change in period
of oscillation by giving perturbation at different points of oscillation. PRCs
can determined from measurements of electrical activities of neurons by
experimental methods or theoretically derived from three different methods. As
far as we know from the literature, these three different methods have never
been used at the same time before. The main purpose of this computational study
is to the obtain Phase Response Curve by three different methods and compare them
in terms of simulation times and peak to baseline ratio. First, the kinds of
excitability of neurons, the types of Phase Response Curve and peak to baseline
ratio are mentioned. After then, these three different methods to obtain PRC
are explained deeply. At a final step, Phase Response Curves are obtained from three
theoretical methods and compared regarding to peak to baseline ratio,
simulation time and applicability.

Anahtar Kelimeler

Phase response curve, Direct method, Linear adjoint method, Adapted Direct method

Kaynakça

• 1. Hodgkin, A.L.; Huxley, A. F. J. Physiol. 1952, 117 (4), 500-544.
• 2. Izhikevich, E.M. Dynamical systems in Neuroscience, MIT press: 2007.
• 3. Rich, S.; Booth, V.; Zochowski, M. Front. Neural Circuits 2016, 10, 82.
• 4. Park, Y.; Ermentrout, B. J. Comput. Neurosci. 2016, 40 (3), 269-281.
• 5. Van Der Pol, B.; Van Der Mark, J. The London, Edinburgh, and Dublin Phil. Mag. J. Sci. 1928, 6 (38), 763-775.
• 6. Kralemann, B.; Frühwirth, M.; Pikovsky, A.; Rosenblum, M.; Kenner, T.; Schaefer, J.; Moser, M. Nat. Commun. 2013, 4, 3418.
• 7. Funato, T.; Yamamoto, Y.; Aoi, S.; Imai, T.; Aoyagi, T.; Tomita, N.; Tsuchiya, K. PLoS Comput. Biol. 2016, 12 (5), e1004950.
• 8. Nessler, J.A.; Spargo, T.; Craig-Jones, A.; Milton, J.G. Gait Posture 2016, 43, 187-191.
• 9. Minors, D. S.; Waterhouse, J. M.; Wirz-Justice, A. Neurosci. Lett. 1991, 133 (1), 36-40.
• 10. Eck, S.; Helfrich-Förster, C.; Rieger, D. J. Biol. Rhythm. 2016, 31 (5), 428-442.
• 11. Field, R. J.; Noyes, R. M. J. Chem. Phys. 1974, 60 (5), 1877-1884.
• 12. Proskurkin, I.S.; Vanag, V.K., Phys. Chem. Chem. Phys. 2015, 17 (27), 17906-17913.
• 13. Franović, I.; Kostić, S.; Perc, M.; Klinshov, V.; Nekorkin, V.; Kurths, J. Chaos 2016, 26 (6), 063105.
• 14. Nakao, H. Contemp. Phys. 2016, 57 (2), 188-214.
• 15. Pikovsky, A.; Rosenblum, M.; Kurths, J. Synchronization: a universal concept in nonlinear sciences. Cambridge University Press: 2003; Vol. 12.
• 16. Strogatz, S.H. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Hachette UK: 2014.
• 17. Smeal, R.M.; Ermentrout, G.B.; White, J.A. Philos. Trans. R. Soc. Lond. B: Biol. Sci. 2010, 365 (1551), 2407-2422.
• 18. Stein, R. Proceedings of the Royal Society of London B: Biological Sciences 167 (1006), 64-86, 1967.
• 19. Tateno, T.; Harsch, A.; Robinson, H. J. Neurophysiol. 2004, 92 (4), 2283-2294.
• 20. Uhlhaas, P. J.; Singer, W. Neuron 2006, 52 (1), 155-168.
• 21. Spencer, K.M.; Nestor, P.G.; Perlmutter, R.; Niznikiewicz, M.A.; Klump, M.C.; Frumin, M.; Shenton, M.E.; McCarley, R.W. Proceedings of the National Academy of Sciences of the United States of America 101 (49), 17288-17293, 2004.
• 22. Uhlhaas, P.J.; Linden, D.E.; Singer, W.; Haenschel, C.; Lindner, M.; Maurer, K.; Rodriguez, E. J. Neurosci. 2006, 26 (31), 8168-8175.
• 23. Krishnan, G.P.; Vohs, J.L.; Hetrick, W.P.; Carroll, C. A.; Shekhar, A.; Bockbrader, M. A.; O'Donnell, B.F. Clin. Neurophysiol. 2005, 116 (3), 614-624.
• 24. Stam, C.J.; Jones, B.; Nolte, G.; Breakspear, M.; Scheltens, P. Cereb. Ccortex 2006, 17 (1), 92-99.
• 25. König, T.; Prichep, L.; Dierks, T.; Hubl, D.; Wahlund, L.; John, E.; Jelic, V. Neurobiol. Aging 2005, 26 (2), 165-171.
• 26. Hammond, C.; Bergman, H.; Brown, P. Trends Neurosci. 2007, 30 (7), 357-364.
• 27. Schnitzler, A.; Gross, J., Nat. Rev. Neurosci. 2005, 6 (4), 285-296.
• 28. Holt, A.B.; Wilson, D.; Shinn, M.; Moehlis, J.; Netoff, T.I. PLoS Computat. Biol. 2016, 12 (7), e1005011.
• 29. Milton, J. G. Epilepsy Behav. 2010, 18 (1), 33-44.
• 30. Bressloff, P. C.; Ermentrout, B.; Faugeras, O.; Thomas, P. J. J. Math. Neurosci. 2016, 6 ( 4), 1-9.
• 31. Delaunay, F. B. Cancer 2017, 104 (10), 821-.822.
• 32. Ermentrout, B. Neural Comput. 1996, 8 (5), 979-1001.
• 33. Brown, E.; Moehlis, J.; Holmes, P. Neural Comput. 2004, 16 (4), 673-715.
• 34. Marella, S.; Ermentrout, G.B. Phys. Rev. E, 2008, 77 (4), 041918.
• 35. Ermentrout, G. B.; Galán, R. F.; Urban, N. N. Trends Neurosci. 2008, 31 (8), 428-434.
• 36. Qiao, W.; Wen, J. T.; Julius, A. IEEE T. Automat. Contr. 2017, 62 (1), 445-450.
• 37. Sato, Y. D.; Aihara, K. Neural Comput. 2014, 26 (11), 2395-2418.
• 38. Canavier, C. C. Curr. Opin. Neurobiol. 2015, 31, 206-213.
• 39. Buchin, A.; Rieubland, S.; Häusser, M.; Gutkin, B. S.; Roth, A. PLoS Comput. Biol. 2016, 12(8), e1005000.
• 40. Cui, J.; Canavier, C.C.; Butera, R.J. J. Neurophysiol. 2009, 102 (1), 387-398.
• 41. Tateno, T.; Robinson, H. Biophys. J. 2007, 92 (2), 683-695.
• 42. Galán, R.F.; Ermentrout, G.B.; Urban, N.N. Phys. Rev. Lett. 2005, 94 (15), 158101.
• 43. Saifee, T.A.; Edwards, M.J.; Kassavetis, P.; Gilbertson, T. J. Neurophysiol. 2015, 115 (1), 310-323.
• 44. Jones, J. R.; Tackenberg, M. C.; McMahon, D.G. Nat. Neurosci. 2015, 18 (3), 373-375.
• 45. Ostojic, S.; Szapiro, G.; Schwartz, E.; Barbour, B.; Brunel, N.; Hakim, V. J. Neurosci. 2015, 35 (18), 7056-7068.
• 46. Miranda-Dominguez, O.; Netoff, T.I. J. Neurophysiol. 2013, 109 (9), 2306-2316.
• 47. Kobelevskiy, I. Bifurcation analysis of a system of Morris-Lecar neurons with time delayed gap junctional coupling. Mater Thesis, University of Waterloo, 2008.
• 48. Izhikevich, E.M. IEEE T. Neural Networ. 1999, 10 (3), 499-507.
• 49. Izhikevich, E.M. Int. J. Bifurcat. Chaos 2000, 10 (06), 1171-1266.
• 50. Yu, T.; Sejnowski, T. J.; Cauwenberghs, G. IEEE T. Biomed. Circ. S. 2011, 5 (5), 420-429.
• 51. Phoka, E.; Cuntz, H.; Roth, A.; Häusser, M. PLoS Computat. Biol. 2010, 6 (4), e1000768.
• 52. Couto, J.; Linaro, D.; De Schutter, E.; Giugliano, M. PLoS Comput. Biol. 2015, 11 (3), e1004112.
• 53. Novičenko, V.; Pyragas, K. Nonlinear Dynam. 2012, 67 (1), 517-526.
• 54. Fang, Y.; Yashin, V. V.; Jennings, B. B.; Chiarulli, D. M.; Levitan, S. P. ACM J. Emerg. Tech. Com. 2016, 13 (2), 14.
• 55. Hoppensteadt, F. C.; Izhikevich, E.M. Weakly connected neural networks. Springer Science & Business Media: 2012; Vol. 126.
• 56. Ermentrout, B. Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. Book Code: SE14, SIAM, 2002.
• 57. Nakao, H.; Yanagita, T.; Kawamura, Y. Phys. Rev. X, 2014, 4, 021032 (1-23).
• 58. Novičenko V webpage. http://www.itpa.lt/~novicenko/index.php?page=soft (accessed June 14, 2017).