Skip to main content
NCBI home page
Biophysical Journal logoLink to Biophysical Journal
. 1997 Feb;72(2 Pt 1):579–594. doi: 10.1016/s0006-3495(97)78697-1

Phase Sensitivity and Entrainment in a Modeled Bursting Neuron

S S Demir *, R J Butera Jr *, A A DeFranceschi *, J W Clark Jr *, J H Byrne †
PMCID: PMC1185586  PMID: 9017188

Abstract

A model of neuron R15 in Aplysia was used to study the mechanisms determining the phase-response curve (PRC) of the cell in response to both extrinsic current pulses and modeled synaptic input and to compare entrainment predictions from PRCs with those from actual simulations. Over the range of stimulus parameters studied, the PRCs of the model exhibited minimal dependence upon stimulus amplitude, and a strong dependence upon stimulus duration. State-space analysis of the effect of transient current pulses provided several important insights into the relationship between the PRC and the underlying dynamics of the model, such as a correlation between the prestimulus concentration of Ca2+ and the poststimulus phase of the oscillation. The system nullclines were also found to provide well-defined limits upon the perturbatory extent of a hyperpolarizing input. These results demonstrated that experimentally applied current pulses are sufficient to determine the shape of the PRC in response to a synaptic input, provided that the duration of the current pulse is of a duration similar to that of the evoked synaptic current. Furthermore, we found that predictions of phase-locked 1:m entrainment from PRCs were valid, even when the duration of the periodically applied pulses were a significant portion of the control limit cycle.

Full text

PDF
579

Images in this article

586FIGURE 5
on p.586
588FIGURE 7
on p.588
589FIGURE 8
on p.589

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Adams W. B., Benson J. A. The generation and modulation of endogenous rhythmicity in the Aplysia bursting pacemaker neurone R15. Prog Biophys Mol Biol. 1985;46(1):1–49. doi: 10.1016/0079-6107(85)90011-2. [DOI] [PubMed] [Google Scholar]
  2. Best E. N. Null space in the Hodgkin-Huxley Equations. A critical test. Biophys J. 1979 Jul;27(1):87–104. doi: 10.1016/S0006-3495(79)85204-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Brown G. L., Eccles J. C. The action of a single vagal volley on the rhythm of the heart beat. J Physiol. 1934 Sep 19;82(2):211–241. doi: 10.1113/jphysiol.1934.sp003176. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Butera R. J., Jr, Clark J. W., Jr, Byrne J. H. Dissection and reduction of a modeled bursting neuron. J Comput Neurosci. 1996 Sep;3(3):199–223. doi: 10.1007/BF00161132. [DOI] [PubMed] [Google Scholar]
  5. Butera R. J., Jr, Clark J. W., Jr, Canavier C. C., Baxter D. A., Byrne J. H. Analysis of the effects of modulatory agents on a modeled bursting neuron: dynamic interactions between voltage and calcium dependent systems. J Comput Neurosci. 1995 Mar;2(1):19–44. doi: 10.1007/BF00962706. [DOI] [PubMed] [Google Scholar]
  6. Clay J. R., Brochu R. M., Shrier A. Phase resetting of embryonic chick atrial heart cell aggregates. Experiment and theory. Biophys J. 1990 Sep;58(3):609–621. doi: 10.1016/S0006-3495(90)82404-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Dong E., Jr, Reitz B. A. Effect of timing of vagal stimulation on heart rate in the dog. Circ Res. 1970 Nov;27(5):635–646. doi: 10.1161/01.res.27.5.635. [DOI] [PubMed] [Google Scholar]
  8. Gardner D., Stevens C. F. Rate-limiting step of inhibitory post-synaptic current decay in Aplysia buccal ganglia. J Physiol. 1980 Jul;304:145–164. doi: 10.1113/jphysiol.1980.sp013316. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Guevara M. R., Shrier A., Glass L. Phase-locked rhythms in periodically stimulated heart cell aggregates. Am J Physiol. 1988 Jan;254(1 Pt 2):H1–10. doi: 10.1152/ajpheart.1988.254.1.H1. [DOI] [PubMed] [Google Scholar]
  10. Guttman R., Feldman L., Jakobsson E. Frequency entrainment of squid axon membrane. J Membr Biol. 1980 Aug 21;56(1):9–18. doi: 10.1007/BF01869347. [DOI] [PubMed] [Google Scholar]
  11. Jalife J., Moe G. K. Effect of electrotonic potentials on pacemaker activity of canine Purkinje fibers in relation to parasystole. Circ Res. 1976 Dec;39(6):801–808. doi: 10.1161/01.res.39.6.801. [DOI] [PubMed] [Google Scholar]
  12. Kowtha V. C., Kunysz A., Clay J. R., Glass L., Shrier A. Ionic mechanisms and nonlinear dynamics of embryonic chick heart cell aggregates. Prog Biophys Mol Biol. 1994;61(3):255–281. doi: 10.1016/0079-6107(94)90002-7. [DOI] [PubMed] [Google Scholar]
  13. Levy M. N., Martin P. J., Lano T., Zieske H. Paradoxical effect of vagus nerve stimulation on heart rate in dogs. Circ Res. 1969 Sep;25(3):303–314. doi: 10.1161/01.res.25.3.303. [DOI] [PubMed] [Google Scholar]
  14. Magleby K. L., Stevens C. F. A quantitative description of end-plate currents. J Physiol. 1972 May;223(1):173–197. doi: 10.1113/jphysiol.1972.sp009840. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Nemoto I., Miyazaki S., Saito M., Utsunomiya T. Behavior of solutions of the Hodgkin-Huxley equations and its relation to properties of mechanoreceptors. Biophys J. 2009 Jan 1;15(5):469–479. doi: 10.1016/S0006-3495(75)85831-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. PERKEL D. H., SCHULMAN J. H., BULLOCK T. H., MOORE G. P., SEGUNDO J. P. PACEMAKER NEURONS: EFFECTS OF REGULARLY SPACED SYNAPTIC INPUT. Science. 1964 Jul 3;145(3627):61–63. doi: 10.1126/science.145.3627.61. [DOI] [PubMed] [Google Scholar]
  17. Pinsker H. M. Aplysia bursting neurons as endogenous oscillators. I. Phase-response curves for pulsed inhibitory synaptic input. J Neurophysiol. 1977 May;40(3):527–543. doi: 10.1152/jn.1977.40.3.527. [DOI] [PubMed] [Google Scholar]
  18. Pinsker H. M. Aplysia bursting neurons as endogenous oscillators. II. Synchronization and entrainment by pulsed inhibitory synaptic input. J Neurophysiol. 1977 May;40(3):544–556. doi: 10.1152/jn.1977.40.3.544. [DOI] [PubMed] [Google Scholar]
  19. Reid J. V. The cardiac pacemaker: effects of regularly spaced nervous input. Am Heart J. 1969 Jul;78(1):58–64. doi: 10.1016/0002-8703(69)90259-2. [DOI] [PubMed] [Google Scholar]
  20. WEIDMANN S. Effect of current flow on the membrane potential of cardiac muscle. J Physiol. 1951 Oct 29;115(2):227–236. doi: 10.1113/jphysiol.1951.sp004667. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Wessel R. In vitro study of phase resetting and phase locking in a time-comparison circuit in the electric fish, Eigenmannia. Biophys J. 1995 Nov;69(5):1880–1890. doi: 10.1016/S0006-3495(95)80058-5. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES