Possible roles of electrical synapse in temporal
information processing: a computational study
Possible roles of electrical synapse in temporal
information processing: a computational study
Xu-Long Wang, Xiao-Dong Jiang & Pei-Ji Liang
Department of Biomedical Engineering, Shanghai Jiao Tong University. * Correspondence should be addressed to Pei-Ji Liang (pjliang@sjtu.edu.cn).
and motor tasks. Neuroscientists roughly categorize
ABSTRACT temporal information processing in the neural system
into four different time scales: microseconds, millisec-
Temporal information processing in the onds, seconds and circadian rhythm, which serve for
range of tens to hundreds of milliseconds is different physiological functions and rely on differ-
critical in many forms of sensory and motor ent neural mechanisms. The process within the scale
tasks. However, little has been known about of millisecond is perhaps the most sophisticated and
the neural mechanisms of temporal informa-the least well understood one among these categories.
tion processing. Experimental observations Behavioral tasks with temporal information process-
indicate that sensory neurons of the nervous ing falling within this scale include speech discrimi-
system do not show selective response to nation in the auditory system, motion information
temporal properties of external stimuli. On processing in the visual systems, and movement
the other hand, temporal selective neurons in coordination in the motor system [1-3].
the cortex have been reported in many Information processing in neural systems normally
species. Thus, processes which realize the consists of a number of successive stages. Neural
temporal-to-spatial transformation of activities in a certain stage are mostly determined by
neuronal activities might be required for neural activities of the preceding stages and our
temporal information processing. In the perception of the world in the brain is based on the
present study, we propose a computational spatio-temporal patterns of neuronal activities
model to explore possible roles of electrical produced at sensory stages [4-5]. Physiological
synapses in processing the duration of observations indicate that neurons in the sensory
external stimuli. Firstly, we construct a levels do not respond selectively to the temporal
small-scale network with neurons intercon-properties of external stimuli. Temporal information
nected by electrical synapses in addition to is thus suggested to be contained in the temporal
chemical synapses. Basic properties of this patterns of neuronal activities in the sensory layer.
small-scale neural network in processing On the other hand, neurons which show selective
duration information are analyzed. Secondly, response to specific temporal properties, especially
a large-scale neural network which is more the duration content, have been reported in the cortex
biologically realistic is further explored. Our of many species [6-10]. Temporal information is
results suggest that neural networks with therefore suggested to be transformed into the
electrical synapses functioning together spatially distributed neuronal activities in the cortex
with chemical synapses can effectively work and neural mechanisms which contribute to the
for the temporal-to-spatial transformation of temporalto-spatial transformation of neuronal
neuronal activities, and the spatially distrib-activities are required.
uted sequential neural activities can poten-Electrical synapse is another type of widely
tially represent temporal information.distributed neuronal connection in the neural systems
in addition to chemical synapse [11-12]. Functional
role of electrical synapse has been identified in fine
motor coordination which requires temporal infor-
mation processing in milliseconds scale [13]. In the
1. INTRODUCTIONpresent work, we try to explore possible neural
Biological neural systems are endowed with the mechanisms of electrical synapse in processing the
ability to process temporal information given the duration content of external stimuli via computa-
inherent temporal nature of sensory environments tional approach. Briefly, we construct neural net-
Keywords: Model; Neural network; Electrical
synapse; Temporal information processing
J. Biomedical Science and Engineering, 2008, 1, 27-36Scientific
Published Online May 2008 in SciRes. http://www.srpublishing.org/journal/jbise
SciRes Copyright © 2008
works containing both electrical and chemical scale model are listed as follows:
synapses, which are activated by stimuli with various IS : Intensity of the input current;
durations. Computational results show that electrical CS : Strength of chemical synapse from input
synapse can substantially contribute to the temporal-neuron to excitatory neurons;
to-spatial transformation of neuronal activities, and CS : Strength of chemical synapse between
the neuronal activities in such networks can poten-excitatory neurons;
tially represent information about stimulus durations.ES: Strength of electrical synapse between
excitatory neurons;
2. MODELS AND METHODSCS : Strength of chemical synapse from excitatory
2.1. Model structureneurons to inhibitory neurons;
Two types of computational models are constructed. CS : Strength of chemical synapse from inhibitory
One is a small-scale neural network which contains ie
only several tens of neurons. Another is a large-scale neurons to excitatory neurons.
one which is more biologically realistic. We use the The large-scale neural network model contains
simple model to clarify the basic properties of neural 400 excitatory neurons and 100 inhibitory neurons.
networks with electrical synapses functioning The ratio between the excitatory and inhibitory
together with chemical synapse in temporal informa-neurons follows the experimental observations from
tion processing. The overall behavior is further tested neocortical area [14]. The neural network is further
in the large-scale model which is more biologically divided into 100 subgroups with each subgroup
realistic. consisting of 4 excitatory neurons and 1 inhibitory
The schematic structures of the small- and large-neuron. Excitatory and inhibitory neurons in each
scale neural networks are illustrated in , A individual subgroup are connected recurrently. Input
and B respectively. Stimuli with various durations neuron is connected to excitatory and inhibitory
are applied, as represented by various durations of neurons on a random basis. All excitatory neurons are
the input currents. The input current is injected to an further connected with each other probabilistically in
input neuron (S) and then transformed into spike a recurrent way, and the synaptic strengths are
trains of this neuron.variables which follow normal distributions.
The input neuron is connected to some of the ten Parameters used for synaptic connections in the
excitatory neurons (E) in the small-scale model. extended model are listed as follows:
Electrical synapses are presented among assigned CP: Probability of chemical synapse from input
neurons, as indicated in the figure. Excitatory to excitatory neurons;
neurons are connected to each other recurrently by CM and CD: Mean and standard deviation of
se se
chemical synapses and each excitatory neuron is strength of chemical synapse from input to excitatory
further coupled with an inhibitory neuron (I) to neurons;
ensure its stability. Parameters used in the small-CP : Probability of chemical synapse from input
Figure 1
Figure 1. A. Schematic structure of the small-scale neural network model. The input neuron (S) is connected to 4 of the 10
the excitatory neurons (E). All excitatory neurons are connected to each other in a recurrent way and each excitatory neuron
is coupled with an inhibitory neuron (I). Excitatory and inhibitory synapses are represented by open and solid circles,
respectively. Neurons in grey shadow are electrically coupled together recurrently.B. Schematic structure of the large-scale
neural network model. Input neuron is connected to excitatory (E) and inhibitory (I) neurons in the network on a random basis.
All excitatory neurons are further connected with each other probabilistically in a recurrent way. Electrical synapses are
formed between some of the excitatory neurons randomly.
SciRes JBiSE Copyright © 2008
X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
to inhibitory neurons;potentials of excitatory and inhibitory synapses,
CM and CD : Mean and standard deviation of respectively;
si si I represents the current passing through
strength of chemical synapse from input to inhibitory esyn
neurons;electrical synapses.
CP : Probability of chemical synapse between In addition, when the membrane potential reaches
ee a threshold (V), the neuron fires an action potential,
excitatory neurons;th
CM and CD: Mean and standard deviation of and the membrane potential is immediately reset to
ee eethe equilibrium potential (V) after a firing lasting
strength of chemical synapse between excitatory eq
neurons;time (T).
CM and CD : Mean and standard deviation of Parameter values chosen for the I-F neuron model
ei ei
strength of chemical synapse from excitatory to are listed in . These values are mostly adopted
inhibitory neurons;from Troyer and Miller (1997) [15], except that the
CM and CD : Mean and standard deviation of firing lasting time of inhibitory neurons is chosen as
ie ie4 to ensure the neurons' inhibitory effect on the
strength of chemical synapse from inhibitory to activities of excitatory neurons.
excitatory neurons;
EP : Probability of electrical connection
ee12.2.2 Description of synaptic current
between excitatory neurons within one subgroup;The chemical synapses are modeled as follows [16-
EP : Probability of electrical connection
between excitatory neurons in different subgroups;
EM and ED: Mean and standard deviation of
ee ee
strength of electrical synapse between excitatory
neurons. where g(t) and g(t) in eqns (2) and (3) are
ex in
presented by g(t)g(t) here, with g representing
2.2. Mathematical description of neurons and csyn csyn
synaptic strength which is modified by a factor of g(t):
2.2.1 Description of integrate-and-fire neuron
Neurons are described in an integrate-and-fire
manner (I-F neuron) [5]. Membrane potential of the
input neuron (V), excitatory neuron (V), and where
inhibitory neuron (V) can be determined as follows:
in which =15 ms , E= - 40 mV, and(u)
syn thr
follows a step function:
The electrical synapses are described as follows:
Where g represents the synaptic strength. We
whereadopt this abstract function which simply depicts that
C represents the membrane capacitance; the current passing through the electrical synapses is
V denotes the equilibrium membrane potential;
eq generally dependent on the membrane potential
g is the leak conductance;
leak difference between the pre-synaptic and post-
g and g represent the conductance of excitatory synaptic neurons [18].
ex in
and inhibitory synapses, respectively;
E and E represent the reversal membrane 3. RESULTS
ex in
Table 1
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X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
Table 1. Parameter values for the I-F neuron model. The firing lasting time (T) for sensory and excitatory neurons is set as
1.75 ms whereas that for inhibitory neuron is set as 4 ms.
neuronal groups are electrically coupled together
3.1 Stimulus duration is represented by spike
which contain 2, 3 and 4 neurons, respectively.
trains of input neuronRaster plots of the firing performances of the model
The injected current is first transformed into a spike neurons in absence and presence of electrical
train of the input neuron. Spiking properties of the synapses are compared with stimulus duration being
input neuron (S) are shown in . Injected 50 ms () and 100 ms (),
currents with different magnitudes and durations are respectively.
applied to the input neuron to test its performance. A Results given in suggest that
sustained current elicits periodic spikes from the electrical synapses in a neural network can effec-
input neuron and the duration of the spike train is tively transform the temporal domain spike train of
determined by the stimulus duration. Input neuron the input neuron into the spatial-temporal firing
can therefore mimic the function of sensory neuron in pattern of a group of neurons. Each activated neuron
neural system.in the group fires within a specific time window,
which is determined by the configuration of the
3.2 Performance of the small-scale neural synaptic connection of the neural network. Furthermore,
network modelstimulus with longer duration can evoke spikes from
3.2.1 Temporal information can be represented by more neurons and therefore the stimulus durations
the spatially distributed activities of a group of can be represented by the spatial and temporal
neurons structure of the sequential neuronal activities.
Representative firing patterns of the simple model
are given in . Parameters used for 3.2.2 The output pattern is closely related to the
are listed in and the synaptic connection electrical coupling configuration
follows that illustrated in . Input neuron is Electrical synapses between excitatory neurons and
connected to four of the ten excitatory neurons. Three
Figure 2Figure 3A&BFigure 3C&D
Figure 3B&D
Figure 3Figure 3
Table 2
Figure 1A
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30 X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
Figure 2. Spike activities of the input neuron (S) in response to constant injected currents with various intensities and
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X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
Figure 3. Raster plots for neuronal activities of the small-scale model elicited by 50 and 100 ms stimulus durations. Stimuli
are indicated by grey shadows. A, 50 ms duration, without electrical synapses; B, 50 ms duration, with electrical synapses; C,
100 ms duration, without electrical synapses; D, 100 ms, with electrical synapses.
Table 2. Parameter values used in the small-scale neural network model.
CS (S)
CS (S)
ES (S)
CS (S)
CS (S)
synaptic connections from input neuron to the neural network kept unaltered. The spiking activities
network are important factors that influence the of these three neurons under the test conditions are
model's performance. There are three groups of plotted in . The firing activities are quite
neurons electrically coupled together in the small-different with different synaptic configurations.
scale model presented in . Neurons within Generally, spikes can be elicited from the neurons
each group are all electrically coupled in a recurrent that are chemically connected to the input neuron,
manner. Furthermore, only one neuron in each group and longer delay is produced when the chemically
is connected to the input neuron. The model outputs activated neuron is electrically coupled with more
in response to stimuli with different durations are neurons that do not receive chemical input from the
presented in . However, any change in the input neuron (e.g. vs ).
configurations of the electrical coupling and input
neuron connection may also cause relevant changes 3.3 Performance of the large-scale neural
in the results. Take the 3-neuron group in network model
(E4, E5 and E6) for an example, relevant possibilities Performance of the small-scale model suggests a
of the electrical coupling within this group as well as mechanism for temporal information processing in a
the chemical synapses between these neurons and the neural network containing electrical synapses. In real
input neuron are tested, with the rest structure of the neural network, the synaptic strengths as well as the
Figure 4
Figure 1A
Figure 3A&FB&D
Figure 1A
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32 X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
Figure 4. Raster plots for spike activities of threeneuron group with different synaptic configurations. Neurons receive
synaptic input from input neuron are represented by solid circle. Electrical synapses are represented by solid lines. The
stimulus duration is 100 ms with the current intensity to input neuron being 2.0 pA.
electrical coupling configuration are not fixed but The inset graphs represent the recruitment process of
variable. A large-scale model which is more biologi-the neuronal spiking activities. The temporal distribu-
cally realistic is constructed with parameter varia-tion of the neuronal activities under these two condi-
tions, and its performance is tested.tions is compared by analyzing the recruitment
Representative firing patterns of the large-scale process in ten independent trials. The results are
model in absence and presence of electrical synapses shown in and . It is clear that the
are shown in and , respectively. The presence of electrical synapses results in a broader
stimulus duration time is 100 ms. Neural network temporal distribution of the sequential spike activi-
parameters used for are listed in . ties of the neurons (), while the neuronal firing
Figure 5CD
Figure 5AB
Figure 5Table 3B & D
Figure 5. A and B are representative raster plots of the neuronal activities of the large-scale model in absence and presence
of electrical synapses, respectively. The stimulus duration is 100 ms. Inset graphs represent the processes of spike activity
recruitment. C and D show the recruitment processes in absence and presence of electrical synapses, respectively. Data are
averaged based on 10 independent trails (MeanS.D.).
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X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
Table 3. Parameter values used in the large-scale neural network model.
CM /CD (S)
se se
CM /CD (S)
si si
CM /CD (S)
ee ee
CM /CD (S)
ei ei
CM /CD (S)
ie ie
EM /ED (S)
ee ee
EM /ED (S)
ee ee
0.03/ 0.01
Figure 6. Raster plots of the large-scale neural network in response to stimuli with different durations. The configuration of
the model is identical for Figure A to F.
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34 X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
activities are limited within a narrow temporal temporal firing pattern of neuronal ensembles while
window in absence of electrical coupling ().each neuron within the ensemble fires within
The firing patterns of the large-scale model in different time windows, and the spatio-temporal
response to stimuli with various durations are further pattern of the neuronal activities is capable of
tested. Stimuli with durations varying from 50 ms to representing stimulus duration in the form of
100 ms are applied to the network, with steps being 10 sequential firing activities of the spatially distributed
ms. Raster plots of typical spike activities of the neurons.
network are given in , to . It is revealed The contribution of electrical synapses in the
that the model neurons fire in a sequential pattern, formation of spatio-temporal firing pattern is
with more neurons being sequentially recruited in particularly examined in the present study. However,
response to longer duration. Such recruitment it is necessary to mention that other factors can also
process in response to durations ranging from 50 ms contribute to this process. For example, membrane
to 100 ms is averaged based on ten independent trials capacitance of specific neurons can be variable
and the result is shown in.because of variation in surface area as well as the
Stimuli with durations varying from 50 ms to 100 membrane capacitance value per unit area [25-28].
ms are applied and relevant results are given in These changes can function in parallel to electrical
and . However, models with this synapses in influencing the sequential firing patterns
structure can effectively represent durations in other of neuronal ensembles.
ranges while relevant parameters are changed. These Special role of electrical synapse is proposed in
parameters include the capacitance value of the I-F our models and there are also experimental clues
neuronal model, the time constant for chemical which indicated possible roles of electrical synapse
synaptic strength, the synaptic strengths from input in temporal information processing. Data demon-
neuron to the network et al. Stimuli with durations strated that gap junction coupling within inferior
ranging from 100 ms to 200 ms are applied to the olive mediated by connexin 36 could add 10-20 of
network, in which the mean value of synaptic precision to the fine temporal coordination of muscle
strength from input neuron to the neural network firing during movement [13].
(Cm) are changed (from 0.055 S to 0.038 S ). Neurons in the present work are modeled follow-
se ing the classic I-F neuron fashion without any
The performance of the model (averaged across ten specific properties for temporal information process-
independent trials) is plotted in .ing. These neurons can be tuned to response to any
non-temporal properties of natural stimulus and
4. DISCUSSIONthereby function for the corresponding behavioral
Temporal information processing in neural system is tasks. For example, these neurons could be tone
critical for animal behavior. Neuroscientists have selective neuron which function for auditory behav-
tried a lot in understanding the neural basis of ior, or mechanosensory neurons which function for
relevant processes via both experimental [6-10] and mechanosensation. While both electrical and
computational approaches [19-24].chemical synapses are universal in the central
In the present study, the computational results nervous system, the model results suggest that both
demonstrate that electrical synapses could effec-the spatial and temporal neuronal activities produced
tively contribute to the formation of a spatio-
A & C
Figure 6AF
Figure 7A
Figure 6Figure 7A
Figure 7B
Figure 7. Recruitment of neuronal activities (activated numbers) for the large-scale model in response to stimuli with
durations ranging from 50 to 100 ms (A, step 10 ms) and 100 to 200 ms (B, step 20 ms). The mean values of synaptic strength
from input to excitatory neurons are 0.055 and 0.038 for results in Figure A and B, respectively. Data are analyzed from 10
independent trials in the form of (MeanS.D.).
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X.L. Wang et al./J. Biomedical Science and Engineering 1 (2008) 27-36
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