Animation of Single Cell Bursting in a Model of pre-Botzinger Complex Respiratory Neurons
This page is intended to accompany the discussion of Figure 8 in the following paper:
RJ Butera, J Rinzel, and JC Smith. Models of respiratory rhythm generation in the pre-Botzinger complex: I. Bursting pacemaker neurons. Journal of Neurophysiology (1999) 82:382-397.
The model discussed here is a single bursting neuron with intrinsic bursting properties. The model is relatively simple, consisting of spike generating currents (INa and IK) as well as subthreshold currents (INaP and IL, collectively referred to as Isub). INap is a persistent Na+current with slow voltage-dependent inactivation and fast voltage-dependent activation, and ILis a leakage current.
In the generation of cyclical bursting, the cycle proceeds as follows. When gNaP, the conductance of INaP, exceeds a critical value, sufficient subthresehold current (Isub) exists to initiate a burst. Action potentials start to fire. The firing of action potentials progressively inactivates h, the slow inactivation component of INaP. The burst terminates when INaP is sufficiently inactivated such that Isub is net outward at the minimum voltage encountered during the firing of action potentials, and at this point the burst ceases and the cell hyperpolarizes. Once hyperpolarized, h gradually deinactivates, gNaP gradually increases, and eventually a new burst is triggered. A single panel from the animation of this process is shown below:
The top left panel illustrates V (voltage) and h (inactivation of gNaP) as they vary in time. The bottom left panel illustrates Isub as it varies in time. The top right panel illustrates an instantaneous I-V plot of the model. The bottom right panel plots Isub(V) as a function of h. Observe three things about the interaction of the instantaneous and QSS I-V curves in this panel:
- As h decreases (during bursting), Isub shifts upward in this panel, reflecting an outward shift in the quasi-steady-state (QSS) I-V relationship of the subthreshold currents.
- The instataneous I-V plot is also plotted on this panel -- you can see the I-V trajectory circling through this panel with the firing of each action potential. Notice that the burst ends when the instantaneous I-V trajectory hits the QSS I-V curve, and the DAP (depolarizing after potential) occurs as the I-V trajectory follows this curve in the hyperpolarizing direction.
- During the interburst interval, the I-V trajectory effectively sits at a fixed point (positive 0 axis crossing) of the QSS I-V plot. The next burst begins at a bifurcation of this fixed point: the QSS I-V curve shifts inward far enough such that this fixed point no longer exits, and the trajectory must depolarize. Dynamically, this looks like the trajectory "falling off" the QSS I-V curve.
OK, by now, you are wondering "what is he talking about." So here is the movie! The QuickTime version is viewable on any platform equipped with a QuickTime player (use /usr/bin/X11/xanim on Linux machines).
QuickTime Movie (warning - 14 Mb!)
QuickTime Movie (gzipped version - 1.2 Mb)
Questions? Email me at robert.butera@ece.gatech.edu