Journal of Computational Neuroscience

, Volume 31, Issue 2, pp 419–440

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

DOI: 10.1007/s10827-011-0319-y

Cite this article as:
Maran, S.K., Sieling, F.H., Demla, K. et al. J Comput Neurosci (2011) 31: 419. doi:10.1007/s10827-011-0319-y


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.


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

Supplementary material

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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)

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High resolution image (EPS 2261 kb)
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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)

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High resolution image (EPS 2388 kb)
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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)

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High resolution image (EPS 8867 kb)
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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)

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High resolution image (EPS 18349 kb)

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