Dynamical Systems in Neuroscience:

4 Introduction(a)spikes(b)spikes cutthreshold?-40 mVsubthreshold response1 msinjected pulses of current20 mVinjected pulses of current15 msFigure 1.4: Where is the firing threshold? Shown are in vitro recordings of two layer 5pyramidal neurons of rat. Notice the difference of voltage and time scales.(a)(b)20 mV20 mV5 ms100 ms-60 mVFigure 1.5: Where is the rheobase, i.e., the minimal current that fires the cell? (a) invitro recordings of pyramidal neuron of layer 2/3 of rat’s visual cortex show increasinglatencies as the amplitude of the injected current decreases. (b) Simulation of theI Na,p +I K -model shows spikes of graded amplitude.Perhaps, we should measure current thresholds instead of voltage thresholds? Thecurrent threshold, i.e., the minimal amplitude of injected current of infinite durationneeded to fire a neuron, is called rheobase. In Fig. 1.5 we decrease the amplitudesof injected pulses of current to find the minimal one that still elicits a spike or themaximal one that does not. In Fig. 1.5a, progressively weaker pulses result in longerlatencies to the first spike. Eventually the neuron does not fire because the latency islonger than the duration of the pulse, which is 1 second in the figure. Did we reallymeasure the neuronal rheobase? What if we waited a bit longer? How long is longenough? In Fig. 1.5b the latencies do not grow but the spike amplitudes decrease untilthe spikes do not look like spikes at all. To determine the current threshold, we needto draw the line and separate spike responses from “subthreshold” ones. How can wedo that if the spikes are not all-or-none? Is the response denoted by the dashed line aspike?Risking adding more confusion to the notion of a threshold, consider the following:If excitatory inputs depolarize the membrane potential, i.e., bring it closer to the “firingthreshold”, and inhibitory inputs hyperpolarize the potential and move it away from