- Email: [email protected]
Postsynaptic current analysis of a model prefrontal cortical circuit for multi-target spatial working memory
Neurocomputing 44–46 (2002) 855 – 861
www.elsevier.com/locate/neucom
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
856
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
858
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
859
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
860
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. References [1] D. Durstewitz, J.K. Seamans, T.J. Sejnowski, Neurocomputational models of working memory, Nat. Neurosci. 3 (2000) 1184–1191. [2] S. Funahashi, C.J. Bruce, P.S. Goldman-Rakic, Mnemonic coding of visual space in the monkey’s dorsolateral prefrontal cortex, J. Neurophysiol. 61 (1989) 331–349. [3] P.S. Goldman-Rakic, Cellular basis of working memory, Neuron 14 (1995) 477–485.
M. Iida, S. Tanaka / Neurocomputing 44–46 (2002) 855 – 861
861
[4] K. Morooka, S. Tanaka, Correlation analysis of signal Kow in a model prefrontal cortical circuit, Neurocomputing 44–46 (2002) 541–548, this issue. [5] S.G. Rao, G.V. Williams, P.S. Goldman-Rakic, Isodirectional tuning of adjacent interneurons and pyramidal cells during working memory: evidence for microcolumnar organization in PFC, J. Neurophysiol. 81 (1999) 1903–1916. [6] S.G. Rao, G.V. Williams, P.S. Goldman-Rakic, Destruction and creation of spatial tuning by disinhibition: GABAA blockade of prefrontal cortical neurons engaged by working memory, J. Neurosci. 20 (2000) 485–494. [7] S. Tanaka, Architecture and dynamics of the primate prefrontal cortical circuit for spatial working memory, Neural Networks 12 (1999) 1007–1020. [8] S. Tanaka, Roles of intracortical inhibition in the formation of spatially tuned delay-period activity of prefrontal neurons: computational study, Prog. Neuro-Psychopharm. Biol. Psychiat. 24 (2000) 483–504. [9] S. Tanaka, Post-cue activity of prefrontal cortical neurons controlled by local inhibition, Neurocomputing 32=33 (2000) 563–572. [10] S. Tanaka, Computational approaches to the architecture and operations of the prefrontal cortical circuit for working memory, (Review) Prog. Neuro-Psychopharm. Biol. Psychiat. 25 (2001) 259–281. [11] S. Tanaka, Multi-directional representation of spatial working memory in a model prefrontal cortical circuit, Neurocomputing 44–46 (2002) 1001–1008, this issue. [12] S. Tanaka, A. Yoshida, Signal Kow in a prefrontal cortical circuit model for working memory loading, Neurocomputing 38– 40 (2001) 957–964. [13] K. Yamashita, S. Tanaka, Circuit simulation of memory 3eld modulation by dopamine D1 receptor activation, Neurocomputing 44–46 (2002) 1035–1042, this issue. 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.
www.elsevier.com/locate/neucom
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
856
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
858
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
859
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
860
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. References [1] D. Durstewitz, J.K. Seamans, T.J. Sejnowski, Neurocomputational models of working memory, Nat. Neurosci. 3 (2000) 1184–1191. [2] S. Funahashi, C.J. Bruce, P.S. Goldman-Rakic, Mnemonic coding of visual space in the monkey’s dorsolateral prefrontal cortex, J. Neurophysiol. 61 (1989) 331–349. [3] P.S. Goldman-Rakic, Cellular basis of working memory, Neuron 14 (1995) 477–485.
M. Iida, S. Tanaka / Neurocomputing 44–46 (2002) 855 – 861
861
[4] K. Morooka, S. Tanaka, Correlation analysis of signal Kow in a model prefrontal cortical circuit, Neurocomputing 44–46 (2002) 541–548, this issue. [5] S.G. Rao, G.V. Williams, P.S. Goldman-Rakic, Isodirectional tuning of adjacent interneurons and pyramidal cells during working memory: evidence for microcolumnar organization in PFC, J. Neurophysiol. 81 (1999) 1903–1916. [6] S.G. Rao, G.V. Williams, P.S. Goldman-Rakic, Destruction and creation of spatial tuning by disinhibition: GABAA blockade of prefrontal cortical neurons engaged by working memory, J. Neurosci. 20 (2000) 485–494. [7] S. Tanaka, Architecture and dynamics of the primate prefrontal cortical circuit for spatial working memory, Neural Networks 12 (1999) 1007–1020. [8] S. Tanaka, Roles of intracortical inhibition in the formation of spatially tuned delay-period activity of prefrontal neurons: computational study, Prog. Neuro-Psychopharm. Biol. Psychiat. 24 (2000) 483–504. [9] S. Tanaka, Post-cue activity of prefrontal cortical neurons controlled by local inhibition, Neurocomputing 32=33 (2000) 563–572. [10] S. Tanaka, Computational approaches to the architecture and operations of the prefrontal cortical circuit for working memory, (Review) Prog. Neuro-Psychopharm. Biol. Psychiat. 25 (2001) 259–281. [11] S. Tanaka, Multi-directional representation of spatial working memory in a model prefrontal cortical circuit, Neurocomputing 44–46 (2002) 1001–1008, this issue. [12] S. Tanaka, A. Yoshida, Signal Kow in a prefrontal cortical circuit model for working memory loading, Neurocomputing 38– 40 (2001) 957–964. [13] K. Yamashita, S. Tanaka, Circuit simulation of memory 3eld modulation by dopamine D1 receptor activation, Neurocomputing 44–46 (2002) 1035–1042, this issue. 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.