Dynamical Systems in Neuroscience:

294 Simple Modelscha, cha — real fast”, according to Gray and McCormick (1996). CH neuronswere found in visual cortex of adult cats, and, morphologically, they are spinystellate or pyramidal neurons of layer 2-4, mainly layer 3.• (FS) Fast spiking interneurons fire high-frequency tonic spikes with relatively constantperiod. They exhibit Class 2 excitability (Tateno et al. 2004). When themagnitude of the injected current decreases below a certain critical value, theyfire irregular spikes, switching randomly between resting and spiking states. Morphologically,FS neurons are sparsely spiny or aspiny nonpyramidal cells (basketor chandelier; see Kawaguchi and Kubota 1997) providing local inhibition alongthe horizontal (intra-laminar) direction of the neocortex (Bacci et al. 2003).• (LTS) Low-threshold spiking neurons fire tonic spikes with pronounced spikefrequency adaptation and rebound (post-inhibitory) spikes, often called “lowthresholdspikes” by biologists (hence the name). They seem to be able to firelow-frequency spike trains, though their excitability class has not been determinedyet. Morphologically, LTS neurons are nonpyramidal interneurons providing localinhibition along the vertical (inter-laminar) direction of the neocortex (Bacci etal. 2003).• (LS) Late spiking neurons exhibit voltage ramp in response to injected dc-currentnear the rheobase, resulting in delayed spiking with latencies as long as 1 sec.There is a pronounced sub-threshold oscillation during the ramp, but the dischargefrequency is far less than that of FS neurons. Morphologically, LS neuronsare nonpyramidal interneurons (neurogliaform; see Kawaguchi and Kubota 1997)found in all layers of neocortex (Kawaguchi 1995), especially in layer 1 (Chu etal. 2003).Our goal is to use the simple model (8.5, 8.6) presented in the previous section toreproduce each of the firing types. We want to capture the dynamic mechanism of spikegeneration of each neuron, so that the model reproduces the correct responses to manytypes of the inputs, and not only to the pulses of dc-current. We strive to have notonly qualitative but also quantitative agreement with the published data on neuron’sresting potential, input resistance, rheobase, F-I behavior, the shape of the upstrokeof the action potential, etc., though this is impossible in many cases mostly becausethe data are contradictory. To fine-tune the model, we use recordings of real neurons.We consider the tuning successful when quantitative difference between simulated andrecorded responses is smaller than the difference between responses of two “sister”neurons recorded in the same slice. We do not want to claim that the simple modelexplains the mechanism of generation of any of the firing patterns recorded in realneurons (simply because the mechanism is usually not known). Although in manyinstances we must resist the temptation to use the Wolfram (2002) new-kind-of-sciencecriterion: “if it looks the same — it must be the same”.