Appendix 4. Modelneuron

The model neuron involves three state variables that include transmembrane potential (U), a potassium current () and the neuronal output (S). The evolution of a neuron's state is described by the following coupled differential equations

(1)

(2)

(3)

in which and (5 ms) are the transmembrane resting potential and time constant respectively. Excitatory () or inhibitory () input drives the potential towards the respective ionic equilibrium values and . is the equilibrium potential of the potassium conductance , the evolution of which is governed by Equation (2). When an output event S occurs, the potassium conductance rises abruptly by a given amount b for excitatory and inhibitory cells respectively), and then decays exponentially with time constant . The potassium conductance parameters are chosen such that the firing rate of inhibitory cells is higher than that of the excitatory ones. Equation (3) is a conventional threshold rule. Unlike in the MacGregor model neuron [ref. MacGregor], we used a fixed threshold value . The values of the equilibrium potentials, the resting potential and the threshold, may be linearly transformed to physiological values (= 0 º -75 mV; =1 º -60 mV; = 7 º 30 mV; = -1 º -90 mV ; =-1 º -90 mV; b = 12 and = 15 ms for pyramidal cells; b = 5 and = 7.5 ms for stellate cells). The conductances of pyramidal cells are

(4)

(5)

in which the excitatory conductance is the sum of synaptic inputs from connected pyramidal cell and an external input conductance , given by a stochastic spike train with probability of spike event (0.075, with one time of 1 ms) and a strength (0.4). The inhibitory conductance is the weighted sum of synaptic inputs from connected stellate cells.