Journal of Computational Neuroscience

, Volume 31, Issue 2, pp 419–440 | Cite as

Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms

  • Selva K. Maran
  • Fred H. Sieling
  • Kavita Demla
  • Astrid A. Prinz
  • Carmen C. Canavier
Article

Abstract

Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking in such circuits. PRCs were constructed for a pacemaker bursting complex in the pyloric circuit in the stomatogastric ganglion of the lobster and crab. This complex is comprised of the Anterior Burster (AB) neuron and two Pyloric Dilator (PD) neurons that are all electrically coupled. Artificial excitatory synaptic conductance pulses of different strengths and durations were injected into one of the AB or PD somata using the Dynamic Clamp. Previously, we characterized the inhibitory PRCs by assuming a single slow process that enabled synaptic inputs to trigger switches between an up state in which spiking occurs and a down state in which it does not. Excitation produced five different PRC shapes, which could not be explained with such a simple model. A separate dendritic compartment was required to separate the mechanism that generates the up and down phases of the bursting envelope (1) from synaptic inputs applied at the soma, (2) from axonal spike generation and (3) from a slow process with a slower time scale than burst generation. This study reveals that due to the nonlinear properties and compartmentalization of ionic channels, the response to excitation is more complex than inhibition.

Keywords

Central pattern generator Dynamic clamp Phase response curve Phase locking Stomatogastric ganglion 

Supplementary material

10827_2011_319_Fig11_ESM.gif (22 kb)
Supplemental Figure 1

Coupling current between the dendrites and primary neurite and dendrite is negligible for phase plane analysis. The burst envelope generating currents and the coupling current Ipn,d (red) were plotted for one spontaneous burst cycle. Note there is not much difference in IKCa (blue) and ICa (green) between isolated (A) and coupled (B) cases (GIF 21 kb)

10827_2011_319_MOESM1_ESM.eps (2.2 mb)
High resolution image (EPS 2261 kb)
10827_2011_319_Fig12_ESM.gif (45 kb)
Supplemental Figure 2

Spiking and bursting mechanisms have to be sufficiently separated to prevent immediate branch switching. The axonal and dendritic compartments were coupled strongly with a coupling conductance of 5 μS. A square conductance pulse of 60 nS was applied for 125 ms in the soma at a phase of 0.55. The applied input to the soma (B) causes axonal spikes which always trigger a branch switch in the dendrite (A) as observed in the phase plane projection (C), contrary to the experimental data in which weaker inputs do not always induce a branch switch biological neurons even though they trigger axonal spikes (compare to Fig 3B). The colors and curves in model neuron voltage trace and phase plane analysis correspond to those in Fig. 3 (GIF 45 kb)

10827_2011_319_MOESM2_ESM.eps (2.3 mb)
High resolution image (EPS 2388 kb)
10827_2011_319_Fig13_ESM.gif (73 kb)
Supplemental Figure 3

Slowly activating current can restore bursting for long-lasting somatic, but not dendritic, depolarization. (A) A long, strong (50 nS for 9 seconds) square conductance pulse applied at the soma initially elicits tonic spiking that eventually switches to bursting. Bursting is reestablished for inputs given at soma in both the biological (A1) and model (A2) neuron. The arrow in A2 indicates the approximate point at which the new limit cycle is reached. However, if gKS is set to zero, bursting is not reestablished. In the presence of IKS, several cycles are required to reach the new limit cycle, as shown in the projection onto the plane of dendritic voltage and calcium concentration (A4). The original limit cycle is shown in green, and the new one in solid blue. The transient after pulse onset is shown in dotted blue and the transient after pulse offset is shown in red. In the absence of very slow potassium current (IKs) the model neuron spikes tonically (A3) by staying in the compact phase space indicated by the black circle (A5). The colors and curves in model neuron voltage trace and phase plane analysis correspond to those in Fig. 3 in the main text. (B) The current responsible for restoring bursting in the model cannot be located in the dendrites. A long, strong (20 nS for 9 seconds) pulse applied directly to the dendrite in the model with very slow potassium current causes cessation of spiking. The colors and curves in model neuron voltage trace and phase plane analysis correspond to those in Fig. 3. (GIF 73 kb)

10827_2011_319_MOESM3_ESM.eps (8.7 mb)
High resolution image (EPS 8867 kb)
10827_2011_319_Fig14_ESM.gif (87 kb)
Supplemental Figure 4

Slow potassium current should be separated from burst mechanism but not from spike mechanism. The very slow potassium current was shifted from primary neurite to dendrite. (A) A continuous input of strength 50nS was applied for 8 seconds. (A1)The dendritic voltage trace (A2) Somatic voltage trace (A3) Phase plane diagram. The activation of very slow potassium current in dendrite shifts the neuron to lower branch but did not reestablish bursting. Due to the weak coupling of dendrite to primary neurite, it also did not have much influence on the axon and enabling the input was to evoke continuous spiking. (B) A strong long input of strength 50 ns is applied for a duration of 1,300 milliseconds. Note unlike the original model shifting the location of IKs causes the neuron to spike after the end of input when the neuron in upper branch (compare Fig. 7C). The colors and curves in model neuron voltage trace and phase plane analysis correspond to those in Fig. 3. (GIF 87 kb)

10827_2011_319_MOESM4_ESM.eps (17.9 mb)
High resolution image (EPS 18349 kb)

References

  1. Abbott, L. F., Marder, E., & Hooper, S. L. (1991). Oscillating networks: control of burst duration by electrically coupled neurons. Neural Computation, 3, 487–497.CrossRefGoogle Scholar
  2. Arshavsky, Y. I., Deliagina, T. G., Orlovsky, G. N., & Panchin, Y. V. (1989). Control of feeding movements in the pteropod mollusk, clione-limacina. Experimental Brain Research, 78, 387–397.Google Scholar
  3. Arshavsky, Y. I., Grillner, S., Orlovsky, G. N., & Panchin, Y. V. (1991). Central generators and the spatiotemporal pattern of movements. In J. Fagard & P. H. Wolff (Eds.), The development of timing control and temporal organization in coordinated action: Invariant relative timing, rhythms, and coordination (pp. 93–115). Amsterdam: Elsevier.CrossRefGoogle Scholar
  4. Ayers, J. L., & Selverston, A. I. (1979). Monosynaptic entrainment of an endogenous pacemaker network: a cellular mechanism for von Holst's magnet effect. Journal of Comparative Physiology, 129, 5–17.CrossRefGoogle Scholar
  5. Benson, J. A. (1980). Burst reset and frequency control of the neuronal oscillators in the cardiac ganglion of the crab, Portunus sanguinolentus. The Journal of Experimental Biology, 87, 285–313.PubMedGoogle Scholar
  6. Bucher, D., Johnson, C. D., & Marder, E. (2007). Neuronal morphology and neuropil structure in the stomatogastric ganglion of the lobster, Homarus americanus. The Journal of Comparative Neurology, 501(2), 185–205.PubMedCrossRefGoogle Scholar
  7. Calabrese, R. L., & Peterson, E. L. (1983). Neural control of heartbeat in the leech, hirudo medicinalis. In A. Roberts & B. Roberts (Eds.), Neural origin of rhythmic movements (pp. 195–221). Cambridge: Cambridge Univ. Press.Google Scholar
  8. Canavier, C. C., & Achuthan, S. A. (2010). Pulse coupled oscillators and the phase resetting curve. Mathematical Biosciences, 226, 77–96. [Epub ahead of print] PMID: 20460132.PubMedCrossRefGoogle Scholar
  9. Cangiano, L., & Grillner, S. (2005). Mechanisms of rhythm generation in a spinal locomotor network deprived of crossed connections: the lamprey hemicord. The Journal of Neuroscience, 25, 923–935.PubMedCrossRefGoogle Scholar
  10. Cheng, J., Stein, R. B., Jovanovic, K., Yoshida, K., Bennett, D. J., & Han, Y. (1998). Identification, localization, and modulation of neural networks for walking in the mudpuppy (necturus maculatus) spinal cord. The Journal of Neuroscience, 18, 4295–4304.PubMedGoogle Scholar
  11. Dando, M. R., & Selverston, A. I. (1972). Command fibres from the supra-oesophageal ganglion to the stomatogastric ganglion in Panulirus argus. Journal of Comparative Physiology, 78, 138–175.CrossRefGoogle Scholar
  12. Demir S. S., Butera, R. J. Jr., DeFranceschi A. A., Clark, J. W. Jr., & Byrne J. H. (1997). Phase Sensitivity and Entrainment in a Modeled Bursting Neuron. Biophysical Journal, 72, 579–594.Google Scholar
  13. Dorval, A. D., Christini, D. J., & White, J. A. (2001). Real-time linux dynamic clamp: a fast and flexible way to construct virtual ion channels in living cells. Annals of Biomedical Engineering, 29, 897–907.PubMedCrossRefGoogle Scholar
  14. Ermentrout, G. B., & Kopell, N. (1991). Multiple pulse interactions and averaging in coupled neural oscillators. Journal of Mathematical Biology, 29(3), 195–217.CrossRefGoogle Scholar
  15. Glass, L., & Winfree, A. T. (1984). Discontinuities in phase resetting experiments. The American Journal of Physiology, 246(Regulatory Integrative Comp. Physiol. 15), R251–R258.PubMedGoogle Scholar
  16. Goldberg, J. A., Deister, C. A., & Wilson, C. J. (2007). Response properties and synchronization of rhythmically firing dendritic neurons. Journal of Neurophysiology, 97(1), 208–219. Epub 2006 Sep 6.PubMedCrossRefGoogle Scholar
  17. Guckenheimer, J., Gueron, S., & Harris-Warrick, R. M. (1993). Mapping the dynamics of a bursting neuron. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 341, 345–359.PubMedCrossRefGoogle Scholar
  18. Hammond, C., Bergman, H., & Brown, P. (2007). Pathological synchronization in Parkinson's disease: networks, models and treatments. Trends in Neurosciences, 30, 357–364.PubMedCrossRefGoogle Scholar
  19. Hartline, D. K. (1979). Pattern generation in the lobster (panulirus) stomatogastric ganglion. II. Pyloric network simulation. Biological Cybernetics, 33, 223–236.PubMedCrossRefGoogle Scholar
  20. Hartline, D. K., & Gassie, D. V. (1979). Pattern generation in the lobster (panulirus) stomatogastric ganglion.I. Pyloric neuron kinetics and synaptic interactions. Biological Cybernetics, 33, 209–222.PubMedCrossRefGoogle Scholar
  21. Hooper, S. L., Buchman, E., Weaver, A. L., Thuma, J. B., & Hobbs, K. H. (2009). Slow conductances could underlie intrinsic phase-maintaining properties of isolated lobster (Panulirus interruptus) pyloric neurons. The Journal of Neuroscience, 29, 1834–1845.PubMedCrossRefGoogle Scholar
  22. Huguenard, J. R., & McCormick, D. A. (2007). Thalamic synchrony and dynamic regulation of global forebrain oscillations. Trends in Neurosciences, 30, 350–356.PubMedCrossRefGoogle Scholar
  23. Marder, E., & Calabrese, R. L. (1996). Principles of rhythmic motor pattern generation. Physiological Reviews, 76, 687–717.PubMedGoogle Scholar
  24. McCrea, D. A., & Rybak, I. A. (2008). Organization of mammalian locomotor rhythm and pattern generation. Brain Research Reviews, 57, 134–146.PubMedCrossRefGoogle Scholar
  25. Miller, J. P., & Selverston, A. I. (1982). Mechanisms underlying pattern generation in lobster stomatogastric ganglion as determined by selective inactivation of identified neurons. II. Oscillatory properties of pyloric neurons. Journal of Neurophysiology, 48, 1378–1391.PubMedGoogle Scholar
  26. Nargeot, R., Baxter, D. A., & Byrne, J. H. (1997). Contingent-dependent enhancement of rhythmic motor patterns: an in vitro analog of operant conditioning. The Journal of Neuroscience, 17, 8093–8105.PubMedGoogle Scholar
  27. Nargeot, R., Petrissans, C., & Simmers, J. (2007). Behavioral and in vitro correlates of compulsive-like food seeking induced by operant conditioning in Aplysia. The Journal of Neuroscience, 27, 8059–8070.PubMedCrossRefGoogle Scholar
  28. Netoff, T. I., Acker, C. D., Bettencourt, J. C., & White, J. A. (2005). Beyond two-cell networks: experimental measurement of neuronal responses to multiple synaptic inputs. Journal of Computational Neuroscience, 18(3), 287–295.PubMedCrossRefGoogle Scholar
  29. Oprisan, S. A., Thirumalai, V., & Canavier, C. C. (2003). Dynamics from a time series: can we extract the phase resetting curve from a time series? Biophysical Journal, 84, 2919–2928.PubMedCrossRefGoogle Scholar
  30. Oprisan, S. A., Prinz, A. A., & Canavier, C. C. (2004). Phase resetting and phase locking in hybrid circuits of one model and one biological neuron. Biophysical Journal, 87, 2283–2298.PubMedCrossRefGoogle Scholar
  31. Preyer, A. J., & Butera, R. J. (2005). Neuronal oscillators in aplysia californica that demonstrate weak coupling in vitro. Physical Review Letters, 95(13), 138103.PubMedCrossRefGoogle Scholar
  32. Prinz, A. A., Billimoria, C. P., & Marder, E. (2003a). Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. Journal of Neurophysiology, 90, 3998–4015.CrossRefGoogle Scholar
  33. Prinz, A. A., Thirumalai, V., & Marder, E. (2003b). The functional consequences of changes in the strength and duration of synaptic inputs to oscillatory neurons. The Journal of Neuroscience, 23, 943–954.Google Scholar
  34. Prinz, A. A., Abbott, L. F., & Marder, E. (2004). The dynamic clamp comes of age. Trends in Neurosciences, 27, 218–224.PubMedCrossRefGoogle Scholar
  35. Rinzel, J., & Ermentrout, B. (1989). Analysis of neural excitability and oscillations. In C. Koch & I. Segev (Eds.), Methods in neuronal modelling: From synapses to networks". Cambridge: MIT. revised 1998.Google Scholar
  36. Schultheiss, N. W., Edgerton, J. R., & Jaeger, D. (2010). Phase response curve analysis of a full morphological globus pallidus neuron model reveals distinct perisomatic and dendritic modes of synaptic integration. The Journal of Neuroscience, 30(7), 2767–2782.PubMedCrossRefGoogle Scholar
  37. Sharp, A. A., O'Neil, M. B., Abbott, L. F., & Marder, E. (1993a). Dynamic Clamp: computer-generated conductances in real neurons. Journal of Neurophysiology, 69, 992–995.PubMedGoogle Scholar
  38. Sharp, A. A., O'Neil, M. B., Abbott, L. F., & Marder, E. (1993b). The dynamic clamp—Artificial conductances in biological neurons. Trends in Neurosciences, 16, 389–394.PubMedCrossRefGoogle Scholar
  39. Sieling, F. H., Canavier, C. C., Prinz, A. A. (2009). Predictions of phase-locking in excitatory hybrid networks: excitation does not promote phase-locking in pattern generating networks as reliably as inhibition. J Neurophysiol, 102, 69–84. First published doi:10.1152/jn.00091.2009.Google Scholar
  40. Soto-Treviño, C., Rabbah, P., Marder, E., & Nadim, F. (2005). Computational model of electrically coupled, intrinsically distinct pacemaker neuron. Journal of Neurophysiology, 94, 590–604.PubMedCrossRefGoogle Scholar
  41. Stein, S. G., Grillner, S., Selverston, A. I., & Stuart, D. G., (Eds). (1997). Neurons, networks, and motor behavior. MIT.Google Scholar
  42. Tazaki, K., & Cooke, I. M. (1990). Characterization of Ca current underlying burst formation in lobster cardiac ganglion motorneurons. Journal of Neurophysiology, 63, 370–384.PubMedGoogle Scholar
  43. Tohidi, V., & Nadim, F. (2009). Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency. The Journal of Neuroscience, 29, 6427–6435.PubMedCrossRefGoogle Scholar
  44. Traub, R. D., & Jefferys, J. G. (1994). Are there unifying principles underlying the generation of epileptic afterdischarges in vitro? Progress in Brain Research, 102, 383–394.PubMedCrossRefGoogle Scholar
  45. Turrigiano, G., Abbott, L. F., & Marder, E. (1994). Activity-dependent changes in the intrinsic properties of cultured neurons. Science, 264(5161), 974–977.PubMedCrossRefGoogle Scholar
  46. Turrigiano, G., LeMasson, G., & Marder, E. (1995). Selective regulation of current densities underlies spontaneous changes in the activity of cultured neurons. Journal of Neuroscience, 15(5 Pt 1), 3640–3652.PubMedGoogle Scholar
  47. Winfree, A. T. (1980). The geometry of biological time. New York: Springer.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Selva K. Maran
    • 1
  • Fred H. Sieling
    • 2
  • Kavita Demla
    • 3
  • Astrid A. Prinz
    • 3
  • Carmen C. Canavier
    • 1
    • 4
  1. 1.Neuroscience Center of ExcellenceLSU Health Sciences CenterNew OrleansUSA
  2. 2.Department of Biomedical EngineeringGeorgia Institute of Technology and Emory UniversityAtlantaUSA
  3. 3.Department of BiologyEmory UniversityAtlantaUSA
  4. 4.Department of OphthalmologyLSU Health Sciences CenterNew OrleansUSA

Personalised recommendations