Figure 8.6

The Stein model

(a) The Stein (1965) model with balanced excitation and inhibition. The time course of the voltage over 100 ms of an integrate-and-fire neuron that receives inputs from 300 excitatory synapses and 150 inhibitory synapses. Each synapse receives Poisson spike trains at a mean frequency of 100 Hz. The threshold is set arbitrarily to 1 mV, the membrane time constant of the neuron is 10 ms, and there is a refractory period of 2 ms. Each excitatory input has a magnitude of 0.1 of the threshold, and each inhibitory input has double the strength of an excitatory input. Given the numbers of excitatory and inhibitory inputs, the expected levels of excitation and inhibition are therefore balanced. (b) The time course of a neuron receiving 18 excitatory synapses of the same magnitude as in (a). The output firing rate of the neuron is roughly 100 Hz, about the same as the neuron in (a), but the spikes appear to be more regularly spaced. (c) An ISI histogram of the spike times from a sample of 10 s of the firing of the neuron in (a). (d) An ISI histogram for the neuron shown in (b).

Simulation environment:

To reproduce the data behind panel (a) and (c):

  1. In the RunControl window click on Init&Run
  2. A trace of the membrane potential appears in the top window and at the end of the simulation the histogram appears in the lower window.

To reproduce the data behind panel (b) and (d):

  1. In the Parameters window change NE to 18 and change NI to 150.
  2. In the RunControl window click on Init&Run.

You can also explore the effect of changing the strength of the excitatory and inhibitory inputs by changing JE and JI in the Parameters window.