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Neurocomputing 44–46 (2002) 855 – 861
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Postsynaptic current analysis of a model
prefrontal cortical circuit for multi-target
spatial working memory
Masafumi Iida, Shoji Tanaka ∗
Department of Electrical and Electronics Engineering, Laboratory of Cortical Circuits and Computation,
High-Tech Research Center, Sophia University, 7-1 Kioicho Chiyoda-ku, 102-8554 Tokyo, Japan
Abstract
The two-layer prefrontal cortical circuit model proposed by Tanaka and Yoshida (Neurocomputing 38– 40 (2001) 957) produces cue-period activity in one layer and delay-period activity in the other layer. We have extended this model to have three layers and analyzed the
spatio-temporal structures of the postsynaptic currents of neurons representing multiple target locations as well as single target locations. The computer simulation shows the three-dimensional
spatio-temporal pro3les of the excitatory and inhibitory postsynaptic currents of the pyramidal
c 2002 Elsevier Science B.V.
cells representing multiple target locations in the delay period. All rights reserved.
Keywords: Inhibition; NMDA; Postsynaptic current; Prefrontal; Working memory
1. Introduction
One of the essential functions of working memory is to store temporally the information for forthcoming cognitive actions. From monkey prefrontal cortex (PFC)
during performing an oculomotor delayed-response task, Funahashi et al. [2] recorded
selective delay-period activity that represented the working memory for the upcoming
correct response (i.e., the saccade to the memorized target). If this activity is an emergent property of the PFC circuit, the circuit mechanisms for the formation of such
delay-period activity would be central to our understanding to the basic mechanisms of
working memory formation. So far, several researchers have devoted to computational
∗
Corresponding author. Tel.: +81-3-3238-3331; fax: +81-3-3238-3321.
E-mail addresses: [email protected] (M. Iida), [email protected] (S. Tanaka).
c 2002 Elsevier Science B.V. All rights reserved.
0925-2312/02/$ - see front matter PII: S 0 9 2 5 - 2 3 1 2 ( 0 2 ) 0 0 4 8 3 - 6
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M. Iida, S. Tanaka / Neurocomputing 44–46 (2002) 855 – 861
studies of the PFC circuit for working memory formation [1,10]. These studies elucidated the roles of recurrent excitatory connections and local inhibitory connections in
the formation of memory 3elds. However, the network architectures of their models
were too simple to investigate the complexity of the actual neuronal activities, such as
the coexistence of various types of activities related to working memory processing.
Tanaka and Yoshida [12] recently proposed a two-layer PFC circuit model. This network with asymmetric interlaminar connections produces cue-period transient activity
in one layer and delay-period sustained activity in the other layer. In this article, we
extend this model to have three layers and elaborate the neuron model by adding several ion channels. With this new model, we analyze the spatio-temporal structures of
the postsynaptic currents (PSCs) of the neurons representing multiple target locations
as well as single target locations.
2. Model
2.1. Circuit architecture
The network contains 1320 neurons, of which 1080 (81.8%) are pyramidal cells and
240 (18.2%) are inhibitory interneurons. The network have three layers, which are the
super3cial, the intermediate, and the deep layers. The pyramidal cells in the intermediate
layer receive external inputs cueing target locations. The activity is then transmitted to
the neurons in the other layers. The connectivity between neurons are described by the
◦
Gaussian functions with the standard deviations of 10 for the pyramidal-to-pyramidal
◦
and pyramidal-to-interneuron connections and 52 for the interneuron-to-pyramidal and
interneuron-to-interneuron connections. The interneuron-to-pyramidal connections in this
model have two types: one is for the isodirectional inhibition and the other is for the
cross-directional inhibition [5–13]. A half of the interneurons has one type of the connections and the remaining half has the other.
2.2. Neuron model
The neurons (pyramidal cells and interneurons) are described here with a single
compartment, leaky integrate-and-3re neuron model:
C
dVi
+ IAMPA + INMDA + IGABAA + INaP + IK(Ca) + Ileak = 0;
dt
where
IAMPA =
(1)
gAMPA; ji (t − tji )(Vi − EAMPA );
(2)
gNMDA; ji (t − tji )fMg (Vi )(Vi − ENMDA );
(3)
j
INMDA =
j
M. Iida, S. Tanaka / Neurocomputing 44–46 (2002) 855 – 861
IGABAA =
gGABA; ji (t − tji )(Vi − EGABAA );
857
(4)
j
INaP = gNaP (Vi )(Vi − ENa );
(5)
IK(Ca) = gK(Ca) ([Ca2+ ]i )(Vi − EK );
(6)
Ileak = gleak (Vi − Eleak );
(7)
1
;
1 + 0:5 exp(−0:062Vi )
Vi + 56
gNaP (Vi ) = gNaP; max
1 + exp −
7
fMg (Vi ) =
gK(Ca) ([Ca2+ ]i ) = K [Ca2+ ]i ;
(8)
(9)
(10)
where tji = tspike; j + Htji (tspike; j being the time at which the presynaptic neuron j spikes
and Htji being the transmission and synaptic delay). The conductances, gAMPA; ji (t);
gNMDA; ji (t); and gGABAA , are described by second-order systems. The ratios of the
excitatory and the inhibitory conductances are: gNMDA; max =gAMPA; max = 0:0847 and
The
equilibrium
potentials
are:
gGABAA ;max(cross) =gGABAA ;max(iso) = 0:177.
EAMPA = 0 mV; ENMDA = 0 mV; EGABAA = −90 mV; ENa = 50 mV; EK = −80 mV; Eleak =
−70 mV. The conductances for the AMPA, NMDA, and GABAA channels and the
dynamics of the internal Ca2+ concentration, [Ca2+ ]i , are described by the linear
second-order and 3rst-order systems, respectively:
d 2 gs (t)
1
1 dgs (t)
1
1
1
J (t)
+
+
gs (t) =
+
+
dt 2
1
2
dt
1 2
1
2
(s = AMPA; NMDA; GABAA );
[Ca2+ ]i
d[Ca2+ ]i
= Ca
(t − tspike; i ) −
:
dt
Ca
(11)
(12)
spike
3. Results
3.1. Time courses
The time courses of the PSCs of the pyramidal cells in the three layers are shown
in Fig. 1. The model circuit has the strong connections from the pyramidal cells in
the intermediate layer to the pyramidal cells in the super3cial layer and the strong
horizontal connections in the super3cial layer. ReKecting these connectivity, the PSC
of the pyramidal cell in the super3cial layer increases very sharply to a high level
in the cue period (200 –400 ms). The sustainment of the PSC, then the 3ring, of the
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M. Iida, S. Tanaka / Neurocomputing 44–46 (2002) 855 – 861
Fig. 1. Time histograms of the EPSCs (¿ 0) and IPSCs (¡ 0) of the pyramidal cell (in the super3cial,
◦
intermediate, and deep layers) whose preferred direction is 0 . The horizontal bar indicates the duration in
which the cue-related input was given.
Fig. 2. Two-target task. The network loads two target locations sequentially.
pyramidal cell in the super3cial layer is due to the horizontal connections. The vertical
connections from the super3cial layer to the deep layer and the horizontal connections
in the deep layer (which is weaker than those in the super3cial layer) makes the
increase and sustainment of the PSC of the pyramidal cell in the deep layer.
3.2. Spatio-temporal pro6les
Fig. 2 shows the task employed in our simulation. In this task, two target locations are given sequentially. The network shows several diLerent patterns of response
depending on the parameter values [11]. Fig. 3 shows the spike raster plots of the pyramidal cells. The pyramidal cells in the intermediate layer exhibit transient responses
to both the 3rst and the second cue inputs. The activities of the pyramidal cells in
the other layers persist during the delay periods. The activity shifts from the neurons
representing the 3rst target to the neurons representing the second target after the input
of the second cue.
Fig. 4 shows the spatio-temporal pro3les of the PSCs of the pyramidal cells in the
deep layer. The EPSCs have sharp peaks at the target locations (Fig. 4A). The IPSCs,
on the contrary, have wider pro3les (Fig. 4B). The IPSCs mediating the isodirectional
M. Iida, S. Tanaka / Neurocomputing 44–46 (2002) 855 – 861
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Fig. 3. Spike raster plots of the pyramidal cells in the super3cial (A), the intermediate (B), and the deep
layer (C). The cue inputs were given during 200 – 400 and 2000 –2200 ms (indicated by the horizontal bars).
inhibition is much larger than the cross-directional inhibition (Figs. 4C and D). The
isodirectional inhibition contributes to the stable representation of the target locations
[7–10]. The cross-directional inhibition, on the other hand, suppresses the background
activity of the pyramidal cells (Fig. 4D).
4. Discussion
We have analyzed the spatio-temporal structures of the postsynaptic currents of the
neurons representing multiple-target locations as well as single-target locations. The
computer simulation shows the spatio-temporal pro3les of the postsynaptic currents
including the inhibitory postsynaptic currents mediating the iso- and cross-directional
inhibition. The cross-directional inhibition plays an important role in the representation and operation of multiple-target spatial working memory [11]. This type of inhibition was originally proposed by Goldman-Rakic [3] for single-target representation.
Later, it was studied experimentally [5,6] and computationally [4,7–12]. Our simulation
shows a spatio-temporal pro3le of the cross-directional inhibition. The model assumed
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M. Iida, S. Tanaka / Neurocomputing 44–46 (2002) 855 – 861
Fig. 4. Spatio-temporal structures of the PSCs of the pyramidal cells in the deep layer. (A) EPSCs. (B)
IPSCs. (C) IPSCs mediating isodirectional inhibition. (D) IPSCs mediating cross-directional inhibition. The
cue inputs were given during 200 – 400 and 2000 –2200 ms.
that the ratio of the cross-directional inhibition to the isodirectional inhibition for the
interneuron-to-pyramidal synaptic strength is 0.177. Then the cross-directional inhibition
is much weaker than the isodirectional inhibition. Nevertheless, the cross-directional
inhibition has a strong inKuence in the representation of multiple-target locations.
When it is stronger or weaker than this level, the switching in the representation
from the 3rst target location to the second does not occur. When switching occurs,
the cross-directional inhibition suppresses background activity of the pyramidal cells.
In another case, in which more than one target location is simultaneously represented,
this inhibition regulates the competition between targets [11].
Acknowledgements
This work was supported by Grants-in-Aid for Scienti3c Research on Priority Areas
to S.T. (#13210123) from the Ministry of Education, Science, and Technology, Japan.
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Masafumi Iida received BE from Sophia University, Tokyo, in 2001. He is a graduate student at the Program of Electrical and Electronics Engineering, Sophia University. He is currently studying computational
neuroscience and computer science.
Shoji Tanaka received BE, ME, and Ph.D. degrees from Nagoya University, Japan, in 1980, 1982, and 1985,
respectively. In 1985, he was a postdoctoral fellow at Japan Atomic Energy Research Institute, Tokai-mura,
Japan. He joined the Department of Electrical and Electronics Engineering, Sophia University, Tokyo, in
1986. He is Professor of Electrical and Electronics Engineering at Sophia University. During 1998–1999, he
was a Visiting Scientist at the Section of Neurobiology, Yale University School of Medicine, USA.