Dynamical Systems in Neuroscience:

308 Simple Modelschattering neuron (in vivo)simple modelI=600 pAI=400 pAI=300 pA+25 mVI=200 pA50 ms-40 mVFigure 8.23: Comparison of in vivo recordings from cat’s primary visual cortex withsimulations of the simple model 50 ˙v = 1.5(v+60)(v+40)−u+I, ˙u = 0.03{(v+60)−u},if v ≥ +25, then v ← −40, u ← u+150. Data were kindly provided by D. McCormick,and are available on the author’s webpage.neuron by increasing the after-spike reset voltage to c = −40 mV, mimicking decreasedK + and increased Na + currents activated during each spike. The phase portrait inFig. 8.24 explains the mechanism of chattering of the simple model (8.5, 8.6). Astep of depolarizing current shifts the fast quadratic nullcline up and the trajectoryquickly moves rightward to fire a spike. The after-spike reset point (white squaremarked “1” in the figure) is outside the parabola nullcline, so another spike is firedimmediately, etc., until the total amount of outward current is large enough to stopthe burst, that is, until the variable u moves the reset point (white square marked“5”) inside the quadratic parabola. The trajectory makes a brief excursion to theleft knee (afterhyperpolarization) and then moves rightward again, initiating anotherburst. Since the second burst starts with an elevated value of u, it has fewer spikes —a phenomenon exhibited by many CH neurons.8.2.5 Low-threshold spiking (LTS) interneuronsLow-threshold spiking interneurons behave similarly to RS excitatory neurons (b > 0)in the sense that they exhibit regular spiking patterns in response to injected pulses of