Dynamical Systems in Neuroscience:

Excitability 273(a)(b)(c)spikes cut at 0 mVdendriticspikeADP20 mV25 ms-40 mV0 pAADP10 mV10 msADP120 pA60 pA10 mV10 ms-40 mVADPsFigure 7.52: (a) Somatic spike evokes dendritic spike, which in turn produces afterdepolarization(ADP) in the soma of the pyramidal neuron of rat somatosensory cortex(in vitro recording was provided Greg Stuart and Maarten Kole). (b) and (c) Increasedlevel of depolarization in another neuron (the same as in Fig. 7.49) converts ADP to asecond spike.activates a slow voltage- or Ca 2+ -dependent outward K + current, which eventuallystops the burst and hyperpolarizes the membrane potential. During the AHP period,the slow outward current deactivates and the neuron can fire again. The neuron canswitch from bursting to tonic spiking mode due to the incomplete deactivation of theslow current. The same explanation holds if we substitute “activation of outward” by“inactivation of inward” current.Similarly, slow inactivation of the transient Ca 2+ T-current explains the reboundresponse and the long afterdepolarization (marked ADP) in Fig. 7.51: The currentwas deinactivated by the preceding hyperpolarization, so upon release from the hyperpolarization,it quickly activates and slowly inactivates, thereby producing a slowdepolarizing wave on which fast spikes can ride. The ADP seen in the figure is the tailof the wave.Probably the most common mechanism of ADPs is due to the dendritic spikes,at least in pyramidal neurons of neocortex and hippocampus considered in the nextchapter. In Fig. 7.52a we depict dual somatic/dendritic recording of membrane potentialof a pyramidal neuron. The somatic spike backpropagates into the dendritictree, activates voltage-gates conductances there, and results in a slower dendritic spike.The latter depolarizes the soma and produces a noticeable ADP. Recordings of anotherneuron in Fig. 7.52b and c show that if there is an additional source of depolarization,such as the injected dc-current, the ADPs can grow and result in a second spike. Thismay evoke another dendritic spike, another ADP or spike, etc., resulting in a burstingactivity discussed in Sect. 8.2.2.Slow ADPs can also be generated due to a nonlinear interplay of fast currentsresponsible for spiking, rather than due to slow currents or dendritic spikes. Oneobvious example is the damped oscillation of membrane potential of the I Na,p +I K -model in Fig. 7.53 right after the spike, with the trough and the peak corresponding toan AHP and an ADP, respectively. Notice that the duration of the ADP is ten timesthe duration of the spike even though the model does not have any slow currents. Such