Bursting Activity in Weakly Electric Fish - Computational Neuroscience: A Comprehensive Approach - page 238

changes in firing properties with increasing input current exhibit an unusual bifurca-
tion structure. As shown in the slice preparation [75] and in both the reduced models
[32, 71], the firing properties pass from quiescence for subthreshold input current
through tonic firing for intermediate current levels to bursting. Other systems, in
contrast, have been shown to pass from quiescence through bursting to tonic firing
(e.g. [27, 36, 43, 100, 104, 112, 116, 129]). Accordingly, for a given input cur-
rent, bursting systems are usually described as switching between quiescence (fixed
point) and spiking (limit cycle) [57]. As shown by the reduced ELL pyramidal cell
models, however, the fast subsystem can always follow a limit cycle [32, 71]. Since
the slow subsystem is itself oscillating, it modulates the period of the fast subsystem
and forces it to pass near the ghost of an infinite-period bifurcation, which yields the
long interburst intervals, as opposed to bifurcating to a fixed point solution.

8.6.3 Intra-burst ISI sequences

Within a burst fired by an ELL pyramidal cell, instantaneous firing rate increases un-
til a spike doublet eventually terminates the burst. Due to its long refractory period,
the dendrite fails to actively backpropagate the action potential allowing the AHP
to set in and repolarize the soma ( Figure 8.9b ). From a dynamical systems point
of view, the burst termination can be understood as a bifurcation from a period-one
to a period-two limit cycle of the fast, spike-generating, system ( Figure 8.11b) . In
all other models of bursting neurons, bursts end with a transition form a period-one
limit cycle to a fixed point (quiescence; [57]). This corresponds to the observation
that, in most systems, bursts begin with a very high instantaneous firing rate and
then slow down. One reason for the slow-down can be the gradual activation of
a dendritic K + channel which reduces current flow to the soma and increases the
time to reach threshold for action potential firing [92, 100, 129]. Alternatively, spike
backpropagation, and with it the somatic DAP, can fail when dendritic Na + chan-
nels cumulatively inactivate [25, 61, 114] or when synaptic inhibition sufficiently
hyperpolarizes the dendritic membrane [20, 77, 122].

8.7 Conclusions

Two main lines of evidence indicate that bursts can play an important role in neuronal
information transmission. First, bursts have been shown to surpass single spikes
in their information carrying performance [35, 40, 46, 86, 99]. Besides acting as
unitary events, burst duration, that is the number of spikes, may also be a mode of
information transmission [28, 65]. Second, high-frequency burst firing increases the
reliability of synaptic transmission at unreliable synapses [76, 113, 120, 128, 129,
132]. The development of the technique of feature extraction analysis has given us
a powerful tool to quantify how reliably neurons indicate the occurrence of certain