Dynamical Systems in Neuroscience:

Excitability 247AResonant for BResonant for C12 ms 18 msPeriod12 msB2 mVCPeriod18 ms2 mV20 mVFigure 7.23: Selective communication via bursts: Neuron A sends bursts of spikes toneurons B and C that have different natural periods (12 ms and 18 ms, respectively;both are simulations of the Hodgkin-Huxley model). As a result of changing the interspikefrequency, neuron A can selectively affect either B or C without changing theefficacy of synapses. Modified from Izhikevich (2002).case, the most optimal input is a resonant burst with a slowly decreasing (adapting)interspike frequency. We will see many examples of such bursts in Chap. 9.The fact that resonator neurons prefer inputs with “resonant” frequencies is notinteresting by itself. What makes it interesting is the observation that the same inputcan be resonant for one neuron and non-resonant for another, depending on theirnatural periods. For example, in Fig. 7.23 neurons B and C have different periods ofsubthreshold oscillations: 12 and 18 ms, respectively. By sending a burst of spikeswith interspike interval of 12 ms, neuron A can elicit a response in neuron B, butnot in C. Similarly, the burst with interspike interval of 18 ms elicits a response inneuron C, but not in B. Thus, neuron A can selectively affect either neuron B or Cby merely changing the intra-burst frequency without changing the efficacy of synapticconnections. In contrast, integrators do not have this property.7.2.3 Frequency preference in vivoFigure 7.20 and 7.21 demonstrate convincingly the essence of frequency preference andresonance phenomenon in vitro, i.e., when the neuron is quiescent and “waiting” forthe resonant burst to come. What if the neuron is under a constant bombardment ofsynaptic input, as it happens in vivo, firing 10 or so spikes per second; Would it beable to tell the difference between the resonant and non-resonant inputs?To address this question, we performed a frozen-noise experiment pioneered byBryant and Segundo (1976) and depicted in Fig. 7.24. We generated a noisy signal