BioSystems 58 2000 41 – 48
Near Poisson-type firing produced by concurrent excitation and inhibition
Chris Christodoulou
a,
, Guido Bugmann
b
a
School of Computer Science Information Systems, Birkbeck College, Uni6ersity of London, Malet Street, London WC
1
E
7
HX, UK
b
School of Computing, Uni6ersity of Plymouth, Drake Circus, Plymouth PL
4 8
AA, UK
Abstract
The effect of inhibition on the firing variability is examined in this paper using the biologically-inspired temporal noisy-leaky integrator TNLI neuron model. The TNLI incorporates hyperpolarising inhibition with negative current
pulses of controlled shapes and it also separates dendritic from somatic integration. The firing variability is observed by looking at the coefficient of variation C
V
standard deviationmean interspike interval as a function of the mean interspike interval of firing Dt
M
and by comparing the results with the theoretical curve for random spike trains, as well as looking at the interspike interval ISI histogram distributions. The results show that with 80 inhibition,
firing at high rates up to 200 Hz is nearly consistent with a Poisson-type variability, which complies with the analysis of cortical neuron firing recordings by Softky and Koch [1993, J. Neurosci. 131 334 – 530]. We also demonstrate that
the mechanism by which inhibition increases the C
V
values is by introducing more short intervals in the firing pattern as indicated by a small initial hump at the beginning of the ISI histogram distribution. The use of stochastic inputs
and the separation of the dendritic and somatic integration which we model in TNLI, also affect the high firing, near Poisson-type explained in the paper variability produced. We have also found that partial dendritic reset increases
slightly the firing variability especially at short ISIs. © 2000 Elsevier Science Ireland Ltd. All rights reserved.
Keywords
:
High firing variability; Inhibition; Coefficient of variation; Temporal noisy-leaky integrator www.elsevier.comlocatebiosystems
1. Review of the problem: determinants of the highly variable neuronal firing and the neural
code
The controversy surrounding the issue of the neural code and of the determinants of the highly
variable neuronal firing has recently been revi- talised by Softky and Koch 1993. These authors
demonstrated that the classical notion of a realis- tic neuron, i.e. being of a leaky-integrator type,
failed in reproducing the high firing variability
Corresponding author. Present address: Department of Electronic Engineering, King’s College, University of London,
Strand, London, WC2R 2LS, UK. Tel.: + 44-20-7631-6718; fax: + 44-20-7631-6727.
E-mail addresses
:
chrisdcs.bbk.ac.uk C. Christodoulou, gbugmannsoc.plym.ac.uk G. Bugmann.
0303-264700 - see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 3 0 3 - 2 6 4 7 0 0 0 0 1 0 5 - 2
they observed in cortical cells at high firing rates. Using a simple leaky integrate-and-fire IF
neuron and
also a
detailed compartmental
model, they could only obtain high variability at low firing rates and concluded that the neural
code is based on temporal precision of input spike trains, i.e. neurons behave as coincidence
detectors rather than leaky integrators. Shadlen and Newsome 1994, used a random walk model
and by appropriate balancing of excitation and inhibition on a single cell, they produced highly
irregular firing. They concluded that the neural code is based on rate encoding rather than pre-
cise processing of coincident presynaptic events. Bell et al. 1995, who supported the coincidence
detection principle, produced high irregular firing using a single compartment Hodgkin and Huxley
1952 model abbreviated HH with balanced excitation and inhibition with the ‘balance
point’ near the threshold in contrast to Shadlen and Newsome, 1994, in addition to weak potas-
sium current repolarisation which corresponds to the degree of somatic reset and fast effective
membrane time constants. Ko¨nig et al. 1996 supported the coincidence detection principle as
a possible mode for neural operation by disput- ing Shadlen and Newsome’s 1994 findings; they
questioned in particular the biological realism of their assumptions, namely that there is an exact
balance between excitatory and inhibitory inputs and the high rate of input signals. The assump-
tion of how balanced excitation and inhibition is brought about naturally in model networks has
also been studied by Van Vreeswijk and Som- polinsky 1996, 1998 and Amit and Brunel
1997. Shadlen and Newsome 1998 reiterate their previous findings by reinforcing both of
their questionable assumptions with experimental evidence.
In an attempt to model high irregularity, we have demonstrated Bugmann et al., 1997, using
a simple leaky integrator model with partial reset on the somatic membrane potential, that irregu-
lar firing can be produced at high firing rates resulting from both temporal integration of ran-
dom excitatory post-synaptic potentials EPSPs and current fluctuation detection partial somatic
reset was also examined previously by La´nsky´ and Smith, 1989; La´nsky´ and Musila, 1991. We
have also showed that the partial reset is a pow- erful parameter to control the gain of the neu-
ron. The results of Softky and Koch 1993 have also been reproduced by Lin et al. 1998, by
using precise stochastic coupling in a network of IF neurons arranged in a one-dimensional ring
topology.
Feng and Brown 1998 used an IF model and showed that the C
V
coefficient of variation — measure of spike train irregularity defined as
the standard deviation divided by the mean ISI of the output firing is an increasing function of
the length of the distribution of the input inter- arrival times and the degree of balance between
excitation and inhibition r. They also showed that there is a range of values of r that C
V
values between 0.5 and 1 can be achieved which is
considered to be the physiological range and this range excludes exact balancing between exci-
tation and inhibition. Moreover these authors demonstrated elsewhere Feng and Brown, 1999
that C
V
values [0.5, 1] can also be obtained using a leaky IF model Stein’s model with
and without reversal potentials when the attrac- tor of the deterministic part of the dynamics is
below the threshold and firing results from ran- dom fluctuations. In another study Brown et al.
1999 examined the variability of the HH and FitzHugh-Nagumo neurons with random synap-
tic input and showed that C
V
[0.5,1] can be ob- tained which are not dependent on the inhibitory
input level.
2. Neuron model used: the temporal noisy-leaky integrator
