Dynamical Systems in Neuroscience:

302 Simple Models(a)burstingspiking20 mVADP100 ms(b)increasing ISIs(c)decreasing ISIs20 mV 20 mV100 ms 100 ms500 pA 600 pAFigure 8.18: (a) bursting and spiking in an IB neuron (layer 5 of somatosensory cortexof a 4 week old rat at 35C; data was kindly provided by Greg Stuart and MaartenKole). Notice the afterdepolarization (ADP). (b) IB neuron of a cat (modified fromFig. 2 of Timofeev et al. (2000)). (c) pyramidal neuron of rat’s visual cortex. Noticethat IB neurons may exhibit bursts with increasing or decreasing inter-spike intervals(ISIs).the intersection of the v-nullcline (dashed parabola) and the u-nullcline (straight line).Injection of a depolarizing current moves the v-nullcline up. The pulse of current ofmagnitude I = 300 pA is below the neuron’s rheobase, so the trajectory moves fromthe old resting state (black square) to the new one (black circle). Since b > 0, thetrajectory overshoots the new equilibrium. The pulse of magnitude I = 370 pA isbarely above the rheobase, so that the model exhibits low-frequency tonic firing withsome spike frequency adaptation. Elevating the fast nullcline by injecting I = 500pA transforms the first spike into a doublet. Indeed, the after-the-first-spike resettingpoint (white square marked “1”) is below the parabola, so the second spike is firedimmediately. Similarly, injection of an even stronger current of magnitude I = 550 pAtransforms the doublet into a burst of three spikes, each raising the after-spike resettingpoint. Once the resetting point is inside the parabola, the neuron is in tonic spikingmode.Figure 8.20a shows simultaneous recording of somatic and dendritic membrane potentialsof a layer 5 pyramidal neuron. Somatic spike backpropagates into the dendrite,activates voltage-gated dendritic Na + and Ca 2+ currents (Stuart et al. 1999, Hausseret al. 2000), and results in a slower dendritic spike clearly seen in the figure. The slowdendritic spike depolarizes the soma resulting in an ADP, which is typical in many