- Email: [email protected]
Multi-directional representation of spatial working memory in a model prefrontal cortical circuit
Neurocomputing 44–46 (2002) 1001 – 1008
www.elsevier.com/locate/neucom
Multi-directional representation of spatial working memory in a model prefrontal cortical circuit Shoji Tanaka ∗ Laboratory of Cortical Circuits and Computation, High-Tech Research Center, Department of Electrical and Electronics Engineering, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan
Abstract Working memory has a capacity of several items. In a simple experimental paradigm of spatial working memory, such as oculomotor delayed-response tasks, this means that more than one target with di+erent locations can be stored at once. This study explores whether the proposed prefrontal cortical circuit model can have such capability. The simulation shows successful or unsuccessful loading of multiple targets, either simultaneously or sequentially, depending on the values of the circuit parameters. This study suggests that the NMDA receptors and the cross-directional inhibition play critical roles in controlling the multi-target representation of c 2002 Elsevier Science B.V. All rights reserved. spatial working memory. Keywords: Competition; Intracortical inhibition; NMDA; Prefrontal cortex; Working memory
1. Introduction Working memory has a capacity of several items [1]. In a simple experimental paradigm of spatial working memory, such as oculomotor delayed-response tasks, this means that more than one target with di+erent locations can be stored at once. One of the interesting issues regarding this is whether a single network has such capability. If this is the case, it would be interesting to see what network properties contribute to such multiple representation of working memory. This study explores this issue by computer simulation of a proposed prefrontal cortical circuit model. This model circuit has three layers. Layered models can simulate coexisted cue and delay-period activities that were observed in experiments [16]. We will :rst examine whether this model has a capacity of multi-target representation. Then we will investigate as to which ∗
Tel.: +81-3-3238-3331; fax: +81-3-3238-3321. E-mail address: [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 5 0 3 - 9
1002
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
parameters are critical to such multiple representation. Finally, sequential loading of multiple targets will be explored.
2. Model The neurons (pyramidal cells and interneurons) are described with the single compartment, leaky integrate-and-:re 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
IGABAA =
gGABAA ;ji (t − tji )(Vi − EGABAA );
(4)
j
INap = gNap (Vi )(Vi − ENa );
(5)
IK(Ca) = gK(Ca) ([Ca2+ ]i )(Vi − EK );
(6)
Ileak = gleak (Vi − Eleak ):
(7)
Here tji is the time at which an ion conductance of the postsynaptic neuron i starts to open responding to the :ring of the presynaptic neurons j. This time contains the transmission and synaptic delay of the signal transmission (tji = tsp; j + Htji , where tsp; j is the time at which the presynaptic neuron j spikes and Htji is the transmission and synaptic delay: 2.0 –10:0 ms). The gating function of INMDA , fMg (Vi ), represents the dependence of the current on the membrane potential, called the magnesium block. It is approximately given by [7] fMg (Vi ) =
1 ; 1 + 0:5 exp(−0:062Vi )
(8)
where we set the magnesium concentration to be 1:79 mM as a typical value. The persistent sodium current, INap , is described here as non-inactivating, voltage-dependent current [3]: Vi + 56 gNap (Vi ) = gNap; max : (9) 1 + exp − 7
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
1003
The time course of the calcium-dependent potassium conductance, gK(Ca) , is given here by gK(Ca) ([Ca2+ ]i ) = K [Ca2+ ]i :
(10)
The dynamics of the internal calcium concentration, [Ca2+ ]i , is described by the :rstorder response to an impulse (spike) train [17]: d[Ca2+ ]i [Ca2+ ]i (t − tspike; i ) − : (11) = Ca dt Ca spike
The conductances, gAMPA; ji (t), gNMDA; ji (t), and gGABAA , are described by the linear second-order systems: d 2 g(t) 1 1 1 dg(t) 1 1 + J (t): (12) + + g(t) = + dt 2 1 2 dt 1 2 1 2 where J (t)=vji gs; ji; max (t −tji ) (s=AMPA; NMDA; GABAA ) (vji =wji =Ht; Ht being the integration time step). The equilibrium potentials are: EAMPA = 0 mV, ENMDA = 0 mV, EGABAA = −80 mV, ENa = 50 mV, EK = −95 mV, and Eleak = −70 mV. The network consists of 1440 neurons, of which 1080 (75%) are pyramidal cells and 360 (25%) are inhibitory interneurons. The network has three layers, i.e., the “super:cial”, “intermediate”, and “deep” layers. These layers contain 360 pyramidal cells, respectively. The interneurons have two subpopulations; one mediates the isodirectional inhibition and the other mediates the cross-directional inhibition [12–16]. Experimental results support this [5,9,10,18]. The pyramidal cells in the three layers and the interneurons in the two subpopulations have the same values of the neuronal parameters, respectively. But they have di+erent strengths of the connections with each other and with themselves. The connections contain direct pyramidal-to-pyramidal connections and indirect connections between pyramidal cells via interneurons. The connectivity strengths between the layers are asymmetric. In the spatial working memory task used in this simulation, three cue spots are given simultaneously or sequentially on a screen to indicate the target locations to remember. The cue-related signal is modeled here by a transient increase in the frequency of the external Poisson spike-train inputs to the pyramidal cells in the intermediate layer. The pro:le of each input in the directional space is described by the Gaussian distribution ◦ function with a standard deviation of 10 . 3. Results 3.1. Cue- and delay-period activities When a cue signal, conveying a target location, is input to the pyramidal cells in the intermediate layer, the neurons in this layer exhibit transient responses. The signal is transmitted :rst to the super:cial layer, and is ampli:ed by the horizontal connections in the super:cial layer. As a result, the :ring of the pyramidal cells in the super:cial layer sustains even after the termination of the cue signal. The activity is transmitted
1004
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
Fig. 1. Multiple-target spatial working memory tasks used in this simulation. (A) Simultaneous loading. (B) Sequential loading. Each loading session is followed by a delay period during which no external stimulus is given.
to the deep layer by the downward excitatory connections. The pyramidal cells in the deep layer also exhibit sustained activity but the onset of the activity is generally later than the activity of the pyramidal cells in the super:cial layer. The interneurons exhibit sustained activities with higher :ring rates. The activities of both the pyramidal cells and the interneurons have directional selectivity with Gaussian pro:les. 3.2. Multi-directional representation Fig. 1 illustrates the multi-target spatial working memory task used in this simulation. The spatio-temporal pro:les of the activities for the simultaneous loading task (Fig. 1A) are depicted in Fig. 2. The response varies with the ratio of the NMDA conductance to the AMPA conductance (or shortly the NMDA-to-AMPA ratio) and the ratio of the strength of the cross-directional inhibition to the isodirectional inhibition (or in short the cross-to-iso ratio). All the other parameter values are the same. When the NMDA-to-AMPA ratio is low, the neurons exhibit transient responses to all targets in the cue period (Fig. 2A). The background activity is seen in the delay period as well as in the other periods. When the NMDA-to-AMPA ratio is increased from 0.0077 to 0.022, one of the three targets is successfully loaded and is maintained in the delay period (Fig. 2B). The activities representing the other two targets are short lived. In this intermediate regime of the NMDA-to-AMPA ratio, therefore, the network is not ready to load all of the three targets simultaneously. The network successfully loads the three targets simultaneously when this ratio is increased to 0.046 (Fig. 2C). In this case, the background activity is rather high in the pre-cue period, so that there are several bumps in the pre-cue period. Note, however, that the background activity is suppressed in the delay period. This is mainly due to the cross-directional inhibition. There is competition between targets, which is mediated by the cross-directional
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
◦
◦
1005
◦
Fig. 2. Responses to the simultaneous loading of three target locations (−120 ; 0 ; 120 ). This :gure shows three di+erent types of the spatio-temporal activities of the pyramidal neurons in the deep layer. Here (the NMDA-to-AMPA ratio, the cross-to-iso ratio) = A—(0.0077, 0.12), B—(0.022, 0.12), C—(0.046, 0.10). The horizontal bars indicate the durations in which the target-related inputs are given (300 –500 ms). To suppress remarkable Ouctuations in the :ring rates across neurons, every six pyramidal cells are sampled, and the :ring rates are averaged over the seven pyramidal cells (including the sample neurons) whose preferred directions are close to the sample neurons. The time bin is 50 ms.
inhibition. This inhibition works well during the simultaneous multi-target representation. The cross-directional inhibition is set to be weaker in Fig. 2C (the cross-to-iso ratio is decreased from 0.12 to 0.10) in order to obtain stable multi-target representation. 3.3. Sequential loading of multiple targets In the simulation of sequential loading of multiple targets, the network again exhibits various types of responses depending on the NMDA-to-AMPA ratio and the cross-to-iso ratio. Fig. 3A shows the case in which three targets are loaded, but the :rst two are erased when the last target is loaded. An interesting result is that when the NMDA-to-AMPA ratio is increased, the network adds new targets successively (Fig. 3B). This would be due to the increase of the stability of the target representation. Both cases show several bumps even after the loading of the :rst target. This is because the cross-directional inhibition remains rather weak. When the cross-directional inhibition is stronger, the loading of the second and the third targets fails because the sustained activity for the :rst target inhibits the inputs for the successive loading (not
1006
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
◦
◦
◦
Fig. 3. Sequential loading of three target locations (−120 ; 0 ; 120 ). The horizontal bars indicate the durations in which the target-related inputs are given (300 –500, 800 –1000, 1300 –1500 ms). Here (the NMDA-to-AMPA ratio, the cross-to-iso ratio) (0.027, 0.095) in A and (0.042, 0.095) in B. The other parameter values are the same. To suppress the remarkable Ouctuations in the :ring rates across neurons, every six pyramidal cells are sampled, and the :ring rates are averaged over the seven pyramidal cells (including the sample neurons) whose preferred directions are close to the sample neurons. The time bin is 50 ms.
shown here). The background activity is highly suppressed after the loading of the third target (Fig. 3B). 4. Discussion This study has shown that the model PFC circuit can represent multiple targets either simultaneously or sequentially. The simulation suggests that successful loading of multiple target locations critically depends on the NMDA-to-AMPA ratio. So far, NMDA receptors have been suggested to be involved in cortical signal processing [2] and persistent activity [17]. This study suggests that NMDA receptors control the cortical circuit dynamics so that the circuit can load multiple targets di+erently. There is evidence that the NMDA-to-AMPA ratio is a function of D1 receptor activation [4,11,19]. It is, therefore, possible that dopamine contributes to the operations of multi-target spatial working memory. The strength of the cross-directional inhibition is another parameter that regulates the network dynamics. It is important especially for multiple target representation because there is competition between the targets. In Fig. 2C, for example, the spontaneous or background activity is rather high in the pre-cue period. However, the activity is suppressed in the delay period. This suppression is mediated by the inhibitory connections between the pyramidal cells. It is clearly seen in Fig. 2C because the cross-directional inhibition works strongly when the three target locations are represented. Cross-directional inhibition was proposed to play a role in working memory representation [5,18] and further studied experimentally [9,10] and computationally [12–16]. In this model, the cross-directional inhibition regulates the competitive interaction between targets. This has been studied computationally by looking at the spatio-temporal pro:les of the postsynaptic currents [6] and the cross-correlations of the spikes of the model cortical neurons representing multiple targets [8].
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
1007
In summary, this study suggests three important issues: :rst, the cortical circuit can perform operations of multi-target spatial working memory. Second, the circuit can switch the modes of the multi-target operations by changing the ratio of the NMDA-channel conductance to the AMPA-channel conductance. Third, the crossdirectional inhibition contributes to the representation of multi-target spatial working memory by controlling the competition between targets. Acknowledgements This work was supported by Grants-in-Aid for Scienti:c Research on Priority Areas (#13210123) from the Ministry of Education, Science, and Technology, Japan.
References [1] N. Cowan, Visual and auditory working memory capacity, Trends Cogn. Sci. 2 (1998) 77–80. [2] N.W. Daw, P.S.G. Stein, K. Fox, The role of NMDA receptors in information processing, Annu. Rev. Neurosci. 16 (1993) 207–222. [3] P.W. Gage, G.D. Lamb, B.T. Wake:eld, Transient and persistent sodium currents in normal and denervated mammalian skeletal muscle, J. Physiol. 418 (1989) 427–439. [4] W.-J. Gao, L.S. Krimer, P.S. Goldman-Rakic, Presynaptic regulation of recurrent excitation by D1 receptors in prefrontal circuits, Proc. Nat. Acad. Sci. U.S.A. 98 (2001) 295–300. [5] P.S. Goldman-Rakic, Cellular basis of working memory, Neuron 14 (1995) 477–485. [6] M. Iida, S. Tanaka, Postsynaptic current analysis of a model prefrontal cortical circuit for multi-target spatial working memory, Neurocomputing 44–46 (2002) 855–861, this issue. [7] C.E. Jahr, C.F. Stevens, Voltage dependence of NMDA-activated macroscopic conductances predicted by single-channel kinetics, J. Neurosci. 10 (1990) 3178–3182. [8] K. Morooka, S. Tanaka, Correlation analysis of signal Oow in a model prefrontal cortical circuit, Neurocomputing, this issue. [9] 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. [10] 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. [11] J.K. Seamans, D. Durstewitz, B.R. Christie, C.F. Stevens, T.J. Sejnowski, Dopamine D1=D5 receptor modulation of excitatory synaptic inputs to layer V prefrontal cortical neurons, Proc. Nat. Acad. Sci. U.S.A. 98 (2001) 301–306. [12] S. Tanaka, Architecture and dynamics of the primate prefrontal cortical circuit for spatial working memory, Neural Networks 12 (1999) 1007–1020. [13] 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. [14] S. Tanaka, Post-cue activity of prefrontal cortical neurons controlled by local inhibition, Neurocomputing 32=33 (2000) 563–572. [15] 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. [16] S. Tanaka, A. Yoshida, Signal Oow in a prefrontal cortical circuit model for working memory loading, Neurocomputing 38/40 (2001) 957–964.
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[17] X.-J. Wang, Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory, J. Neurosci. 19 (1999) 9587–9603. [18] F.A. Wilson, S.P. O’Scalaidhe, P.S. Goldman-Rakic, Functional synergism between putative gammaaminobutyrate-containing neurons and pyramidal neurons, Proc. Nat. Acad. Sci. U.S.A. 91 (1994) 4009–4013. [19] K. Yamashita, S. Tanaka, Circuit simulation of memory :eld modulation by dopamine D1 receptor activation, Neurocomputing 44–46 (2002) 1035–1042, this issue. Shoji Tanaka received B.E., M.E., 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
Multi-directional representation of spatial working memory in a model prefrontal cortical circuit Shoji Tanaka ∗ Laboratory of Cortical Circuits and Computation, High-Tech Research Center, Department of Electrical and Electronics Engineering, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan
Abstract Working memory has a capacity of several items. In a simple experimental paradigm of spatial working memory, such as oculomotor delayed-response tasks, this means that more than one target with di+erent locations can be stored at once. This study explores whether the proposed prefrontal cortical circuit model can have such capability. The simulation shows successful or unsuccessful loading of multiple targets, either simultaneously or sequentially, depending on the values of the circuit parameters. This study suggests that the NMDA receptors and the cross-directional inhibition play critical roles in controlling the multi-target representation of c 2002 Elsevier Science B.V. All rights reserved. spatial working memory. Keywords: Competition; Intracortical inhibition; NMDA; Prefrontal cortex; Working memory
1. Introduction Working memory has a capacity of several items [1]. In a simple experimental paradigm of spatial working memory, such as oculomotor delayed-response tasks, this means that more than one target with di+erent locations can be stored at once. One of the interesting issues regarding this is whether a single network has such capability. If this is the case, it would be interesting to see what network properties contribute to such multiple representation of working memory. This study explores this issue by computer simulation of a proposed prefrontal cortical circuit model. This model circuit has three layers. Layered models can simulate coexisted cue and delay-period activities that were observed in experiments [16]. We will :rst examine whether this model has a capacity of multi-target representation. Then we will investigate as to which ∗
Tel.: +81-3-3238-3331; fax: +81-3-3238-3321. E-mail address: [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 5 0 3 - 9
1002
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
parameters are critical to such multiple representation. Finally, sequential loading of multiple targets will be explored.
2. Model The neurons (pyramidal cells and interneurons) are described with the single compartment, leaky integrate-and-:re 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
IGABAA =
gGABAA ;ji (t − tji )(Vi − EGABAA );
(4)
j
INap = gNap (Vi )(Vi − ENa );
(5)
IK(Ca) = gK(Ca) ([Ca2+ ]i )(Vi − EK );
(6)
Ileak = gleak (Vi − Eleak ):
(7)
Here tji is the time at which an ion conductance of the postsynaptic neuron i starts to open responding to the :ring of the presynaptic neurons j. This time contains the transmission and synaptic delay of the signal transmission (tji = tsp; j + Htji , where tsp; j is the time at which the presynaptic neuron j spikes and Htji is the transmission and synaptic delay: 2.0 –10:0 ms). The gating function of INMDA , fMg (Vi ), represents the dependence of the current on the membrane potential, called the magnesium block. It is approximately given by [7] fMg (Vi ) =
1 ; 1 + 0:5 exp(−0:062Vi )
(8)
where we set the magnesium concentration to be 1:79 mM as a typical value. The persistent sodium current, INap , is described here as non-inactivating, voltage-dependent current [3]: Vi + 56 gNap (Vi ) = gNap; max : (9) 1 + exp − 7
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
1003
The time course of the calcium-dependent potassium conductance, gK(Ca) , is given here by gK(Ca) ([Ca2+ ]i ) = K [Ca2+ ]i :
(10)
The dynamics of the internal calcium concentration, [Ca2+ ]i , is described by the :rstorder response to an impulse (spike) train [17]: d[Ca2+ ]i [Ca2+ ]i (t − tspike; i ) − : (11) = Ca dt Ca spike
The conductances, gAMPA; ji (t), gNMDA; ji (t), and gGABAA , are described by the linear second-order systems: d 2 g(t) 1 1 1 dg(t) 1 1 + J (t): (12) + + g(t) = + dt 2 1 2 dt 1 2 1 2 where J (t)=vji gs; ji; max (t −tji ) (s=AMPA; NMDA; GABAA ) (vji =wji =Ht; Ht being the integration time step). The equilibrium potentials are: EAMPA = 0 mV, ENMDA = 0 mV, EGABAA = −80 mV, ENa = 50 mV, EK = −95 mV, and Eleak = −70 mV. The network consists of 1440 neurons, of which 1080 (75%) are pyramidal cells and 360 (25%) are inhibitory interneurons. The network has three layers, i.e., the “super:cial”, “intermediate”, and “deep” layers. These layers contain 360 pyramidal cells, respectively. The interneurons have two subpopulations; one mediates the isodirectional inhibition and the other mediates the cross-directional inhibition [12–16]. Experimental results support this [5,9,10,18]. The pyramidal cells in the three layers and the interneurons in the two subpopulations have the same values of the neuronal parameters, respectively. But they have di+erent strengths of the connections with each other and with themselves. The connections contain direct pyramidal-to-pyramidal connections and indirect connections between pyramidal cells via interneurons. The connectivity strengths between the layers are asymmetric. In the spatial working memory task used in this simulation, three cue spots are given simultaneously or sequentially on a screen to indicate the target locations to remember. The cue-related signal is modeled here by a transient increase in the frequency of the external Poisson spike-train inputs to the pyramidal cells in the intermediate layer. The pro:le of each input in the directional space is described by the Gaussian distribution ◦ function with a standard deviation of 10 . 3. Results 3.1. Cue- and delay-period activities When a cue signal, conveying a target location, is input to the pyramidal cells in the intermediate layer, the neurons in this layer exhibit transient responses. The signal is transmitted :rst to the super:cial layer, and is ampli:ed by the horizontal connections in the super:cial layer. As a result, the :ring of the pyramidal cells in the super:cial layer sustains even after the termination of the cue signal. The activity is transmitted
1004
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
Fig. 1. Multiple-target spatial working memory tasks used in this simulation. (A) Simultaneous loading. (B) Sequential loading. Each loading session is followed by a delay period during which no external stimulus is given.
to the deep layer by the downward excitatory connections. The pyramidal cells in the deep layer also exhibit sustained activity but the onset of the activity is generally later than the activity of the pyramidal cells in the super:cial layer. The interneurons exhibit sustained activities with higher :ring rates. The activities of both the pyramidal cells and the interneurons have directional selectivity with Gaussian pro:les. 3.2. Multi-directional representation Fig. 1 illustrates the multi-target spatial working memory task used in this simulation. The spatio-temporal pro:les of the activities for the simultaneous loading task (Fig. 1A) are depicted in Fig. 2. The response varies with the ratio of the NMDA conductance to the AMPA conductance (or shortly the NMDA-to-AMPA ratio) and the ratio of the strength of the cross-directional inhibition to the isodirectional inhibition (or in short the cross-to-iso ratio). All the other parameter values are the same. When the NMDA-to-AMPA ratio is low, the neurons exhibit transient responses to all targets in the cue period (Fig. 2A). The background activity is seen in the delay period as well as in the other periods. When the NMDA-to-AMPA ratio is increased from 0.0077 to 0.022, one of the three targets is successfully loaded and is maintained in the delay period (Fig. 2B). The activities representing the other two targets are short lived. In this intermediate regime of the NMDA-to-AMPA ratio, therefore, the network is not ready to load all of the three targets simultaneously. The network successfully loads the three targets simultaneously when this ratio is increased to 0.046 (Fig. 2C). In this case, the background activity is rather high in the pre-cue period, so that there are several bumps in the pre-cue period. Note, however, that the background activity is suppressed in the delay period. This is mainly due to the cross-directional inhibition. There is competition between targets, which is mediated by the cross-directional
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
◦
◦
1005
◦
Fig. 2. Responses to the simultaneous loading of three target locations (−120 ; 0 ; 120 ). This :gure shows three di+erent types of the spatio-temporal activities of the pyramidal neurons in the deep layer. Here (the NMDA-to-AMPA ratio, the cross-to-iso ratio) = A—(0.0077, 0.12), B—(0.022, 0.12), C—(0.046, 0.10). The horizontal bars indicate the durations in which the target-related inputs are given (300 –500 ms). To suppress remarkable Ouctuations in the :ring rates across neurons, every six pyramidal cells are sampled, and the :ring rates are averaged over the seven pyramidal cells (including the sample neurons) whose preferred directions are close to the sample neurons. The time bin is 50 ms.
inhibition. This inhibition works well during the simultaneous multi-target representation. The cross-directional inhibition is set to be weaker in Fig. 2C (the cross-to-iso ratio is decreased from 0.12 to 0.10) in order to obtain stable multi-target representation. 3.3. Sequential loading of multiple targets In the simulation of sequential loading of multiple targets, the network again exhibits various types of responses depending on the NMDA-to-AMPA ratio and the cross-to-iso ratio. Fig. 3A shows the case in which three targets are loaded, but the :rst two are erased when the last target is loaded. An interesting result is that when the NMDA-to-AMPA ratio is increased, the network adds new targets successively (Fig. 3B). This would be due to the increase of the stability of the target representation. Both cases show several bumps even after the loading of the :rst target. This is because the cross-directional inhibition remains rather weak. When the cross-directional inhibition is stronger, the loading of the second and the third targets fails because the sustained activity for the :rst target inhibits the inputs for the successive loading (not
1006
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
◦
◦
◦
Fig. 3. Sequential loading of three target locations (−120 ; 0 ; 120 ). The horizontal bars indicate the durations in which the target-related inputs are given (300 –500, 800 –1000, 1300 –1500 ms). Here (the NMDA-to-AMPA ratio, the cross-to-iso ratio) (0.027, 0.095) in A and (0.042, 0.095) in B. The other parameter values are the same. To suppress the remarkable Ouctuations in the :ring rates across neurons, every six pyramidal cells are sampled, and the :ring rates are averaged over the seven pyramidal cells (including the sample neurons) whose preferred directions are close to the sample neurons. The time bin is 50 ms.
shown here). The background activity is highly suppressed after the loading of the third target (Fig. 3B). 4. Discussion This study has shown that the model PFC circuit can represent multiple targets either simultaneously or sequentially. The simulation suggests that successful loading of multiple target locations critically depends on the NMDA-to-AMPA ratio. So far, NMDA receptors have been suggested to be involved in cortical signal processing [2] and persistent activity [17]. This study suggests that NMDA receptors control the cortical circuit dynamics so that the circuit can load multiple targets di+erently. There is evidence that the NMDA-to-AMPA ratio is a function of D1 receptor activation [4,11,19]. It is, therefore, possible that dopamine contributes to the operations of multi-target spatial working memory. The strength of the cross-directional inhibition is another parameter that regulates the network dynamics. It is important especially for multiple target representation because there is competition between the targets. In Fig. 2C, for example, the spontaneous or background activity is rather high in the pre-cue period. However, the activity is suppressed in the delay period. This suppression is mediated by the inhibitory connections between the pyramidal cells. It is clearly seen in Fig. 2C because the cross-directional inhibition works strongly when the three target locations are represented. Cross-directional inhibition was proposed to play a role in working memory representation [5,18] and further studied experimentally [9,10] and computationally [12–16]. In this model, the cross-directional inhibition regulates the competitive interaction between targets. This has been studied computationally by looking at the spatio-temporal pro:les of the postsynaptic currents [6] and the cross-correlations of the spikes of the model cortical neurons representing multiple targets [8].
S. Tanaka / Neurocomputing 44–46 (2002) 1001 – 1008
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In summary, this study suggests three important issues: :rst, the cortical circuit can perform operations of multi-target spatial working memory. Second, the circuit can switch the modes of the multi-target operations by changing the ratio of the NMDA-channel conductance to the AMPA-channel conductance. Third, the crossdirectional inhibition contributes to the representation of multi-target spatial working memory by controlling the competition between targets. Acknowledgements This work was supported by Grants-in-Aid for Scienti:c Research on Priority Areas (#13210123) from the Ministry of Education, Science, and Technology, Japan.
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[17] X.-J. Wang, Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory, J. Neurosci. 19 (1999) 9587–9603. [18] F.A. Wilson, S.P. O’Scalaidhe, P.S. Goldman-Rakic, Functional synergism between putative gammaaminobutyrate-containing neurons and pyramidal neurons, Proc. Nat. Acad. Sci. U.S.A. 91 (1994) 4009–4013. [19] K. Yamashita, S. Tanaka, Circuit simulation of memory :eld modulation by dopamine D1 receptor activation, Neurocomputing 44–46 (2002) 1035–1042, this issue. Shoji Tanaka received B.E., M.E., 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.