Spike propagation in driven chain networks with dominant global inhibition
Wonil Chang
1,2
and Dezhe Z. Jin
1,
*
1
Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
2
Department of Bio and Brain Engineering, KAIST, Daejeon 305–701, Korea
Received 13 August 2008; published 20 May 2009
Spike propagation in chain networks is usually studied in the synfire regime, in which successive groups of
neurons are synaptically activated sequentially through the unidirectional excitatory connections. Here we
study the dynamics of chain networks with dominant global feedback inhibition that prevents the synfire
activity. Neural activity is driven by suprathreshold external inputs. We analytically and numerically demon-
strate that spike propagation along the chain is a unique dynamical attractor in a wide parameter regime. The
strong inhibition permits a robust winner-take-all propagation in the case of multiple chains competing via the
inhibition.
DOI: 10.1103/PhysRevE.79.051917 PACS numbers: 87.18.Sn, 05.45.Xt, 84.35.+i
Synfire chain activity, in which synchronous spikes propa-
gate along a chain of successive groups of neurons connected
unidirectionally via excitatory synaptic connections 1, has
been extensively studied 2 and suggested as the underlying
mechanism for precisely timed sequential firings of neurons
observed in a number of neural systems, including songbirds
3–5, cortical activity 6, and primate motor cortex 7.
Synfire activity requires the excitation be in a restricted re-
gime: the excitation must be strong enough for the synaptic
activity to evoke spikes in subsequent groups of neurons, but
weak enough to avoid runaway instability 4,8.
In this paper, we demonstrate that precisely timed spike
propagation in chain networks can be robustly established
beyond the synfire regime. Instead of the synaptic activation,
neural activity is sustained by suprathreshold external inputs.
The activity is controlled by a strong global feedback inhi-
bition and shaped by the unidirectional excitatory connec-
tions between the groups. The inhibition dominates the exci-
tation and the synfire activity is suppressed. We show that
spike propagation is a unique attractor to which the dynamics
flows from all initial conditions when the external inputs are
on. This mechanism is robust, with a large working param-
eter regime for the excitation and inhibition strengths. The
strong inhibition also permits a robust winner-take-all selec-
tion of a single chain for spikes to propagate when there are
multiple chains competing for the activity, which could be a
mechanism for action selection if each chain encodes an ac-
tion element such as a song syllable in songbirds 4,5.
Our results in the “driven-chain” regime are obtained
through analytical analysis and numerical simulations of
chain networks of leaky integrate-and-fire neurons. The ana-
lytical analysis is aided with three simplifications: the groups
of neurons are replaced by single neurons, the global inhibi-
tion is modeled with all-to-all inhibitory connections be-
tween the neurons, and the synaptic interactions are approxi-
mated as pulse coupling. We prove that sequential spiking
along the chain with precise timings is the unique global
attractor in a wide parameter regime of the excitation and
inhibition; furthermore, in the same parameter regime, the
spike propagation selects a single chain if multiple chains
compete. The analytical results are confirmed numerically
with the simplifications removed and noise added.
Many models of biological and physical systems includ-
ing heart cells, fireflies, earthquakes, and neural networks
belong to a broad class of models consisting of systems of
pulse-coupled oscillators 9–11; our simplified neural net-
work model fits into this class as well. Our analytical analy-
sis should add insights into the relationship between the
structure of coupling and the dynamics, a key for under-
standing these diverse systems. Sequential spiking in chains
of pulse-coupled oscillating single neurons has been investi-
gated before 12–14 and it has been shown that spike se-
quences are stable in generic inhibition-dominant networks
15. However, these works do not show that the dynamics of
a given network is attracted to a unique spike sequence at-
tractor regardless of the initial conditions. A unique attractor
is robust against perturbations and noise since the basin of
attraction is large. This is an important characteristic if the
pattern drives a single motor action such as a song syllable
3,4. Our analysis establishes that the spike propagation in
chain networks in the driven-chain regime is a unique stable
attractor to which the dynamics converges from all initial
conditions.
The dynamics of the neurons in the simplified model is as
follows:
dV
j
t
dt
= E
R
+ I - V
j
t + I
s
, 1
where I
s
is the synaptic current and is given by
I
s
=
n=1
- G
E
j,s
n
V
j
t + G
I
E
I
- V
j
tt - t
n
. 2
Here is the membrane time constant; V
j
t is the membrane
potential of neuron j ; E
R
and E
I
are the resting membrane
potential and the reversal potential of the inhibitory synapse,
respectively the reversal potential of the excitatory synapse
is 0; I is the constant external input; G
E
j,i
is the excitatory
conductance from neuron i to neuron j , which is G
E
0 if
j = i +1 is the neuron next to neuron i down the chain and 0
otherwise; G
I
0 is the global inhibitory conductance be-
*
djin@phys.psu.edu
PHYSICAL REVIEW E 79, 051917 2009
1539-3755/2009/795/0519175 ©2009 The American Physical Society 051917-1