described in this paper, total somatic reset was applied on the somatic potential of the TNLI.
Therefore, the main differences of the TNLI from other models are: i the separation of den-
dritic and somatic integration similar to the mod- els of Kohn, 1989 and Rospars and La´nsky´, 1993;
ii the modelling of the temporal summation of the PSPs in the dendrites; and iii the use of
stochastic synapses represented by the pRAMs.
3. Simulation data and results
The parameter values used for the postsynaptic current responses Fig. 1 are: t
d
= 5 ms, d
r
= d
f
= 5 ms, t
p
= 10 ms, h = 5 pA. For simplicity, the
inhibitory currents have an equal but opposite magnitude to the excitatory ones − 5 pA. The
other TNLI parameters are: t
R
= 2 ms, V
th
= 15
mV, R = 166 MV, C=60 pF giving a realistic membrane time constant t = RC 10 ms. The
simulation time step used was Dt=1 ms and the system was left to operate for T = 10 000 ms. At
the TNLI inputs, random spike trains of con- trolled mean frequency f
j
were utilised with f
j
= p
Dt, where p is the 0-pRAM probability value. These random spike trains were unaffected
by the 1-pRAM action in the current simulations. f
j
was the same for both excitatory and inhibitory inputs.
Results were taken with 100 excitatory PSR generators and 0, 40, 80 and 95 inhibitory ones
denoting the number of excitatory and inhibitory synaptic inputs. Fig. 2 shows the C
V
as a function of Dt
M
mean interspike interval of firing while the number of inhibitory inputs was increased.
Full dendritic reset has been applied for these results. The full line shows the theoretical curve
for a random spike train with discrete time steps given by:
C
V
= Dt
M
− t
R
Dt
M
see Bugmann, 1995; Bugmann et al., 1997. If the simulated firing ISIs are poissonian, then their C
V
versus Dt
M
curve should follow this theoretical curve. The C
V
values obtained with 100 excitatory inputs and 80 inhibitory inputs 100 ex80 inh, Fig.
Fig. 2. Coefficient of variation C
V
versus mean interpike interval Dt
M
showing the firing variability obtained with the TNLI neuron at different levels of inhibition. These results are
taken with full dendritic reset. For the rest of the details and parameter values, see text.
2 are very similar to those observed in cortical neurons see Fig. 9 in Softky and Koch, 1993. By
looking also at the ISI histogram distributions for mean ISI Dt
M
of 15 ms Fig. 3 for the different inhibition levels, we can see that with 80 inhibi-
tion when C
V
= 0.870, the distribution follows a
Poisson tail exponential decay. The small initial hump at the beginning of the distribution is due to
the presence of clusters of spikes at short intervals. Moreover it can also be observed from Fig. 2 that
high variability and near Poisson distributions with 80 inhibitions are obtained at the cost of
C
V
’s slightly larger than one at long intervals around Dt
M
of 30 ms. By near Poisson firing we mean that the C
V
versus Dt
M
curve is very close to
Fig. 3. Interspike Interval histogram distributions for Dt
M
= 15 ms with dendritic reset for different inhibition levels. T
indicates the total time the system was left to operate.
Fig. 4. ISI histogram distributions for different mean ISI lengths for the case of 80 inhibition with dendritic reset. The
system is left to operate for T = 50 000 ms.
4. Discussion and conclusions
