Dynamical Systems in Neuroscience:

300 Simple Models(a)simple modellayer 5 neuron (in vitro)20 mV20 ms(b)32 nS8 nSg GABAg AMPAresponseinput(c)1 seclayer 5 neuron(in vitro)simple modelFigure 8.17: (a) Comparison of responses of a rat motor cortex layer 5 pyramidal neuronof RS type and the simple model (8.5, 8.6) to in vivo-like stochastic input (8.7) withthe random conductances in (b). Part (a) is a magnification of a small region in (c).Shown are simulations of 30 ˙v = 3(v+55)(v+42)−u+I(t), ˙u = 0.01{−0.25(v+55)−u},if v ≥ +10, then v ← −40, u ← u + 90. Data was kindly provided by Niraj S. Desaiand Betsy C. Walcott.In vivo-like conditionsIn Fig. 8.17a (dashed curve) we show the response of in vitro recorded layer 5 pyramidalneuron of rat motor cortex to fluctuating in vivo-like input. First, random excitatoryand inhibitory conductances, g AMPA (t) and g GABA (t) (Fig. 8.17b), were generated usingthe Ornstein-Uhlenbeck stochastic process (Uhlenbeck and Ornstein 1930), which wasoriginally developed to describe Brownian motion, but can equally well describe invivo-like fluctuating synaptic conductances produced by random firings (Destexhe etal. 2001). Let E AMPA = 0 mV and E GABA = −65 mV denote the reverse potentials ofexcitatory and inhibitory synapses, respectively. The corresponding currentI(t) =excitatory input{ }} {g AMPA (t)(E AMPA − V (t)) +inhibitory input{ }} {g GABA (t)(E GABA − V (t)) , (8.7)was injected into the neuron using the dynamic clamp protocol (Sharp et al. 1993),where V (t) denotes the instantaneous membrane potential of the neuron. The sameconductances were injected into the simple model (8.5, 8.6), whose parameters wereadjusted to fit this particular neuron. The superimposed voltage traces, depicted in