Flexible traffic control of the synfire-mode transmission by inhibitory modulation:
Nonlinear noise reduction
Takashi Shinozaki,
1,
*
Masato Okada,
2,1
Alex D. Reyes,
3
and Hideyuki Câteau
1,4
1
RIKEN Brain Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
2
Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan
3
Center for Neural Science, New York University, 4 Washington Place, New York, New York 10003, USA
4
Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, 2-4 Hibikino, Kitakyushu,
Fukuoka 808-0196, Japan
Received 18 May 2009; revised manuscript received 2 December 2009; published 22 January 2010
Intermingled neural connections apparent in the brain make us wonder what controls the traffic of propa-
gating activity in the brain to secure signal transmission without harmful crosstalk. Here, we reveal that
inhibitory input but not excitatory input works as a particularly useful traffic controller because it controls the
degree of synchrony of population firing of neurons as well as controlling the size of the population firing
bidirectionally. Our dynamical system analysis reveals that the synchrony enhancement depends crucially on
the nonlinear membrane potential dynamics and a hidden slow dynamical variable. Our electrophysiological
study with rodent slice preparations show that the phenomenon happens in real neurons. Furthermore, our
analysis with the Fokker-Planck equations demonstrates the phenomenon in a semianalytical manner.
DOI: 10.1103/PhysRevE.81.011913 PACS numbers: 87.19.lm, 05.10.Gg, 87.18.Sn, 87.80.Jg
I. INTRODUCTION
Inhibitory input to network of neurons or more generally
excitable media can modulate their activity in a way more
complex than the simple activity suppression. For instance,
inhibitory input delivered to a physiologically modeled neu-
ron but not the leaky integrate-and-fire LIF neuron, can
paradoxically increase the firing probability if it is delivered
at a right timing 1–3. For a population of neurons, this
increase in firing probability of a single neuron is interpreted
as an increase in the number of firing neurons in a population
due to inhibitory input 4. Here, we demonstrate a mecha-
nism by which inhibitory input also enhance the synchrony
of population firing. We carefully study this synchrony en-
hancement, that was actually visible in our previous study
4 but out of focus there. We indicate that a nonlinear
mechanism is responsible for this synchrony enhancement.
The synchrony enhancement by inhibitory input shows a
clear contrast to the previously studied synchronization of
neurons in mutually connected neural networks 5, which
was observed even for a linear neuron model.
For the best illustration of the synchrony enhancement in
the feedforward setting, we take the so-called the synfire
chain as an example 4,6–24 which is stable propagation of
population firing of neurons. Let us consider the population
firing that is described with a bell-shaped pulse packet Fig.
1a which indicates the number of firing neurons versus
time 9. The pulse packet is specified with the number of
total firing, a, the degree of synchrony measured with the
width, , and the peak time of the population firing, t. The
present study shows that properly timed inhibitory input can
enhance synchrony of a pulse packet ↓. This generalizes
the previous observations 1–4 that are interpreted as an
increase in the number of firing neurons a ↑ in the present
context.
Our numerical simulations coupled with a dynamical sys-
tem analysis reveal a mechanism through which the mem-
brane potential histogram in a neural population gets sharp-
ened by inhibitory input via a nonlinear effect. We refer to
this effect as nonlinear noise reduction. Importantly, this
nonlinear noise reduction occurs with a population of physi-
ologically plausible neuron models but not the LIF model.
Furthermore, our electrophysiological experiments with
rodent brain slice preparations demonstrate that this mecha-
nism works also in real neurons. Finally, we demonstrate
semianalytically with Fokker-Planck FP equations how the
mechanism works. Thus, the present study points out the
*
Present address: Center for Neural Science, New York Univer-
sity, 4 Washington Place, New York, New York 10003, USA.
inhibitory
neuron
excitatory
neuron
all-to-all
connection
time (ms)
inhibitory
excitatory
0 -20
(a) (c)
(b)
time
FIG. 1. Definition of a pulse packet and simulation setup. a
Firing time histogram is parametrized with its total area, a, width,
and peak time, t a pulse packet9. b Schematic illustration of
the time course of excitatory top and inhibitory bottom synaptic
currents. c Feedforward network of excitatory neurons which are
modeled with Eqs. 1 and 2. Each neuron in a layer sends input to
all the neurons in the following layer as in 9. The excitatory neu-
rons in the layer in the question center receive phasic inhibitory
input with uniform strength at a specified timing. Open and filled
circles, respectively, represent excitatory and inhibitory neurons.
PHYSICAL REVIEW E 81, 011913 2010
1539-3755/2010/811/0119137 ©2010 The American Physical Society 011913-1