Dynamical Systems in Neuroscience:

244 Excitability1coincidencedetectionintegratorresonatorcombined PSP amplitude(normalized)resonantfrequency0.30 3 6 9 12 15 18interpulse period, msFigure 7.19: Dependence of combined PSP amplitude on the inter-pulse period; seeFig. 7.18.of current simulating synaptic bombardment. The response of any neuron to inputpulses depends on the frequency content of these pulses. In Fig. 7.18 we use tripletswith various inter-pulse periods to illustrate the issue. The pulses may arrive fromthree different presynaptic neurons or from a single presynaptic neuron firing shortbursts.In Fig. 7.18, top, we show that integrators prefer high-frequency inputs. The firstpulse in each triplet evokes a post-synaptic potential (PSP) that decays exponentially.The PSP evoked by the second pulse adds to the first one, and so on. The dependenceof the combined PSP amplitude on the inter-pulse period is shown in Fig. 7.19. Apparently,the integrator acts as a coincidence detector because it is most sensitive tothe pulses arriving simultaneously.Resonators can also detect coincidences, as one can see in Fig. 7.19. In addition,they can detect resonant inputs. Indeed, the first pulse in each triplet in Fig. 7.18,bottom, evokes a damped oscillation of the membrane potential, which results in anoscillation of the firing probability. The natural period of such an oscillation is around9 ms for the mesencephalic V neuron used in the figure. The effect of the second pulsedepends on its timing relative to the first pulse: If the interval between the pulses isnear the natural period, e.g., 10 ms in Fig. 7.18 and Fig. 7.20, the second pulse arrivesduring the rising phase of oscillation, and it increases the amplitude of oscillation evenfurther. In this case the effects of the pulses add up. The third pulse increases theamplitude of oscillation even further thereby increasing the probability of an actionpotential, as in Fig. 7.20.If the interval between pulses is near half the natural period, e.g., 5 ms in Fig. 7.18and Fig. 7.20, the second pulse arrives during the falling phase of oscillation, and itleads to a decrease in oscillation amplitude. The spikes effectively cancel each other