Neural Networks PERGAMON

Neural Networks 12 (1999) 1007–1020 www.elsevier.com/locate/neunet

Architecture and dynamics of the primate prefrontal cortical circuit for spatial working memory Shoji Tanaka* Department of Electrical and Electronics Engineering, Sophia University, 7-1 Kioicho, Tokyo 102, Japan Received 24 November 1998; accepted 6 April 1999

Abstract In the experimental protocol of working memory tasks using a monkey as a subject, tuned activity of the prefrontal cortical neurons that is sustained during the delay period is a neuronal substrate of the working memory. This study addresses the question as to how this tuned activity is formed and maintained in the prefrontal cortex by means of computer simulations of the dynamics of a model prefrontal cortical circuit. The model assumes that pyramidal cells receive two types of intracortical inhibition, “parallel” and “anti-parallel”, in accordance with recent experimental findings. The parallel and anti-parallel refer to the relationship between the preferred directions of presynaptic interneurons and postsynaptic pyramidal cells. The following three factors are suggested to be crucial for the formation and maintenance of spatial working memory: cortical amplification of the activity due to excitatory closed-loop circuitry, suppression of excessive excitation by the parallel inhibition, and sharpening of the activity profile by the anti-parallel inhibition. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: Working memory; Delay-period activity; Short-term memory; Spatial; Cerebral cortex; Cortical circuit; Excitatory connections; Local inhibition

1. Introduction In the research of higher brain functions such as thought processes, working memory has been attracting much attention (Baddeley, 1986; Goldman-Rakic, 1991; GoldmanRakic, 1995a). Working memory is active for a short period of time, usually for seconds, and is distinguished from passive short-term memory as well as other memories which are considered to be associative (Baddeley, 1986; Goldman-Rakic, 1991). Many researchers are using various kinds of working memory tasks, such as visual, visuospatial, auditory and verbal working memory tasks in behavioral, neurophysiological and functional mapping studies. These mapping experiments demonstrate, for most of the tested tasks, that the prefrontal cortex (PFC) in primates, including human, are commonly activated while performing those tasks, though further task-dependent dissociation could be possible (Braver, Cohen, Nystrom, Jonides, Smith & Noll, 1997; Cohen et al., 1997; Courtney, Ungerleider, Keil & Haxby, 1997; D’Esposito, Detre, Alsop, Shin, Atlas & Grossman, 1995; Haxby, Ungerleider, Horwitz, Rapport & Grady, 1995; Owen, Ewans & Petrides, 1996; Petrides, Alivisatos, Evans & Meyer, 1993a,b; Sweeney et al., 1996). It is now considered that working memory processes are * Tel.: 1 81-3-3238-3331; fax: 1 81-3-3238-3321. E-mail address: [email protected] (S. Tanaka)

centrally executed by the PFC (Goldman-Rakic, 1991; Goldman-Rakic, 1995a,b). In the early 1970s, single-unit recordings from the monkey PFC during delayed-response performance showed sustained activity during the delay period for the first time (Fuster & Alexander, 1971; Kubota & Niki, 1971). Since then, the relevance of the delay-period activity of PFC neurons to working memory has been argued (Fuster, 1990, 1994; Goldman-Rakic, 1990a,b,c, 1991). Later, deeper insights into the delay-period activity were gained by behavioral and electrophysiological studies employing an oculomotor paradigm. Goldman-Rakic and coworkers (Funahashi, Bruce & Goldman-Rakic, 1989, 1990) observed from the monkey PFC that, for oculomotor delayedresponse tasks, the delay-period activity had directional characteristics. That is, the firing frequency of the delayperiod activity of a neuron reached the maximum when the direction at which the subject was to saccade coincided with the preferred (or best) direction of the neuron, and decreased in other directions. Their results strengthened the evidence that the PFC (especially the area within and surrounding the principal sulcus) is the principal area to form and maintain a visuospatial working memory. However, how the PFC performs such mnemonic processes is not clear. The processes would be synergistic phenomena; i.e. they would emerge from the interaction between neurons rather than the dynamics of individual

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Fig. 1. Columnar organization of the model. The triangles symbolize the pyramidal cells and the circles symbolize the interneurons. Ps: pyramidal cell in the superficial layer, Pd: pyramidal cell in the deep layer, Na: interneuron in group A, Nb: interneuron in group B. There are 40 columns in this model, each of which contains three Ps cells, three Pd cells, one Na cell, and one Nb cell.

neurons. As the interaction would be specified by the circuitry of the neurons, the mechanism would be attributable to the dynamical aspects of the circuit (Tanaka, 1997a,b). This paper will analyze the circuit dynamics by means of computer simulations of a model PFC circuit. In the circuit, balance between excitation and inhibition would be important to attain appropriately controlled activity. Then the simulations will address the roles of pyramidal-to-pyramidal connections and intracortical inhibition in the formation and maintenance of spatial working memory. 2. Model 2.1. Architecture of the model While performing an oculomotor delayed-response task, many neurons in the PFC of monkeys (especially within and

Fig. 2. Directional columns (circles) and the strength of the excitatory intercolumnar connections. The arrows in the circles denote the characteristic directions of the columns. The size of the squares denote the relative strengths of the excitatory intercolumnar connections.

surrounding the principal sulcus) exhibit directionally selective activity. Experiments by Goldman-Rakic and coworkers showed that the preferred directions of PFC cells during both the cue and the delay period were widely distributed (Funahashi et al., 1989, 1990; Funahashi, Bruce & Goldman-Rakic, 1991). They also showed that the distribution of the preferred direction of cortical cells in one hemisphere tended to be weighted such that more neurons preferred directions toward the contralateral visual field, and fewer neurons preferred directions toward the ipsilateral visual field or along the vertical meridian (Funahashi et al., 1989, 1990; Funahashi, Bruce & GoldmanRakic, 1991). The distribution of the preferred directions of neurons in the other hemisphere is weighted in the opposite direction. This model, therefore, postulates that neurons in both the hemispheres constitute a whole population that represents the directional information of the cue and the preferred directions of the neurons in the population are distributed almost uniformly in the whole directional space. This model consists of 240 pyramidal cells and 80 inhibitory interneurons, all of which are assumed to have directional selectivity. The pyramidal cells are divided into two groups; i.e. Ps and Pd cells. The Ps cells are the pyramidal cells in the superficial layers and the Pd cells are the pyramidal cells in the deep layers. The inhibitory interneurons are also divided into two groups, i.e. Na and Nb cells. The Na cells are defined to mediate “parallel inhibition” and the Nb cells to mediate “anti-parallel inhibition” (see below). Goldman-Rakic (1995a) proposed a hypothetical model of working memory modules or columns. Recently, GoldmanRakic and coworkers reported that the interneurons they examined had the preferred directions close to those of immediately adjacent pyramidal cells (Williams, Rao & Goldman-Rakic, 1998). In accordance with these studies, this model assumes that the cortical neurons with close preferred directions constitute columns. There are 40 columns in this model, each of which contains six pyramidal cells (three Ps and three Pd cells) and two interneurons (a pair of Na and Nb cells), as shown in Fig. 1. Every column has its own characteristic direction, which is defined by the average of the preferred directions of the Ps and Pd cells in the column. This model assumes that the preferred

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Fig. 3. Circuit components from which the model is composed. PP: pyramidal-to-pyramidal, PN: pyramidal-to-interneuron, NP: interneuron-topyramidal, NN: interneuron-to-interneuron.

directions of the pyramidal cells and the interneurons are distributed uniformly in the whole directional space. Then the characteristic directions are also distributed uniformly, and the difference in the characteristic directions between neighboring columns is 98. These directional columns and the strength of the intercolumnar excitatory connections are illustrated in Fig. 2. Neuroanatomical tracing studies revealed that pyramidal cells in the PFC have (i) extensive horizontal connections in the superficial layers and less extensive intercolumnar connections in the deep layers, (ii) downward or forward interlaminar connections from the superficial to the deep layers, and (iii) intracolumnar and intercolumnar projections from the deep to the superficial layers (Kritzer and Goldman-Rakic, 1995; Levitt, Lewis, Yoshioka & Lund, 1993; Melchitzky, Sesack, Pucak & Lewis, 1998; Pucak, Levitt, Lund & Lewis, 1996). The model PFC circuit contains direct pyramidal-to-pyramidal connections, termed

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here as the PP-type connections, and indirect connections between pyramidal cells via interneurons. The PP-type connections consist of three subtypes: the forward connection (from a Ps cell to a Pd cell), the backward connection (from a Pd cell to a Pd cell), and the lateral connection (from a Ps cell to a Ps cell or from a Pd cell to a Pd cell). They are depicted in Fig. 3. Besides direct pyramidal-to-pyramidal connections, anatomical studies from the PFC observed pyramidal-to-interneuron connections and interneuron-topyramidal connections (Melchitzky et al., 1998; Williams, Goldman-Rakic & Leiranth, 1992). As for the circuits involving interneurons, this model assumes the following types of connections—the PN-type connection (from a Ps cell or Pd cell to an N cell), the NP-type connection (from an N cell to a Ps cell or a Pd cell), the NN-type connection (from an Na cell or an Nb cell to an Na cell or an Nb cell), and the self-feedback connection of N cells. According to the experimental observation that the self-feedback connection of the interneurons are common but those of the pyramidal cells are unlikely to be common (Tamas, Buhl & Somoyogi, 1997), only the interneurons have such connections in this model. Note that, in Fig. 3, exact locations of the synapses on the dendrites are not specified because we employ a point neuron model (i.e. a model with no spatial extension of dendrites and somas). Recent behavioral and electrophysiological findings by Goldman-Rakic and coworkers (Wilson, O’Scalaidhe & Goldman-Rakic, 1994; Williams et al., 1998) suggest that pyramidal cells in the PFC area related to spatial working memory receive two types of intracortical inhibition. One is the inhibition by the interneurons with the preferred directions almost parallel to that of the postsynaptic cell, and the other is the inhibition by the interneurons with the preferred directions almost anti-parallel to that of the postsynaptic cell. We term them “parallel inhibition” and “anti-parallel inhibition” (Fig. 4), and assume that, via the NP-type connections, the Na (Nb) cells mediate the parallel (anti-parallel) inhibition. The above experimental results show that the pyramidal cells receive inputs from interneurons with different directional preferences that are opposite with each other. We model different connectivity of the Na and Nb cells with the postsynaptic pyramidal cells (see Appendix A). All the pyramidal cells contained in this model circuit are assumed to receive these two types of inhibitory inputs. 2.2. Dynamic equations We employ a firing rate model to describe the dynamics of the PFC neurons, which is governed by the following set of differential equations:

Fig. 4. Definitions of the parallel and anti-parallel components of the local inhibition. The gray circles denote the interneurons and the open triangles denote the pyramidal cells. This illustration shows that the Na cells with the preferred direction of 908 and the Nb cells with the preferred direction of 2708 have the strongest inhibition on the pyramidal cell with the preferred direction of 908.

X dux …t† ux …t† ˆ sy wyx f y ‰uy …t 2 Dt†Š 2 x t dt y

…1†

…x; y ˆ Ps; Pd; Na; Nb† where u x(t) is the internal state variable of neuron i of type x,

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Fig. 5. Temporal evolution of the activity profiles of the Pd cells. Among the 120 Pd cells, the time courses of the 40 sample Pd cells are depicted. They are aligned along the axis that labels column# according to the characteristic directions of the columns they reside in. The characteristic directions of the columns are 21808 (#0), 2908 (#10), 08 (#20), 908 (#30), and 1808 (#40). The cue direction was 08 and the cue-related input was onset at 0 ms (indicated by the horizontal line) and its duration was 100 ms (indicated by the second horizontal line). In this case, therefore, column #20 received the strongest cue-related input. The inset shows the spatial profile of the cue-related input, which is described by the Gaussian distribution function with the standard deviation of 458 (Eq. (3)).

w is the synaptic coefficient matrix (which is ny × nx ; nx and ny are the numbers of the neurons of types x and y), f y(·) is the activation function, t x is the time constant of the change in the internal state variable, and sy ˆ 11 for y ˆ Ps or Pd and sy ˆ 21 for y ˆ Na or Nb. The activation function describes the nonlinearity of the neuronal activity (i.e. the thresholding and the saturation) as ( fmax tanh‰…u 2 uth †=h; for u . uth ; …2† f …u† ˆ 0; for u # uth

1995); (ii) the firing rates of the interneurons are often higher than those of the pyramidal cells in the delay period (Wilson et al., 1994). At the beginning of an oculomotor delayed-response task, the subject is required to fixate on the central spot on a screen. Then a visual cue is displayed in oculomotor delayed-response task, indicating the target position to which the eyes move after the delay period. The cue is turned off immediately (usually several hundred milliseconds after the onset), beginning the delay period. Disappearance of the fixation spot at the end of the delay period instructs the subject to saccade to the target position displayed before the delay period. The cue signal would be processed first in the visual system of the brain, then the cue-related signal generated is ultimately input to a population of neurons in the PFC via specific afferent fibers. According to the electrophysiological recordings from the PFC, the responses of the neurons to the cue-related signal were transient (the firing rate increases rapidly and then decreases rapidly) and their duration short (usually around 100 ms) (Funahashi et al., 1990). We approximately describe this temporal profile then to be triangular-shaped; the input is onset at 0 ms, reaches its maximum strength at 50 ms, and is turned off at 100 ms. Goldman-Rakic and coworkers observed that the directional selectivity of these responses were broad and had a Gaussian profile (Funahashi et al., 1990). Therefore, we describe the spatiotemporal profile of the cue-related input signal as Iicue …u; t† ; I0 exp‰2…u 2 ui †2 =2s2c Šc…t†; where

yx

where uth is the threshold for activation. All the model neurons of each type have the same value for t x, uth, fmax and h. In our simulations, the synaptic delays are all taken to be Dt ˆ 2 ms and the values of the other parameters are: tx ˆ 20 ms for P cells and 10 ms for N cells, uth ˆ 15 for all cells, f max ˆ 100 sp/s for P cells and 200 sp/s for N cells, h ˆ 100 for P cells and 50 for N cells. These values were chosen so that this model could include the following features—(i) the membrane time constant, which is of the order of 10 ms, would be larger for the pyramidal cells than for the interneurons because of the larger membrane capacitance of the pyramidal cells (Somers, Nelson & Sur,

…3†

c…t† ;

8 > > < > > :

0; 2t=T; 22…t 2 T†=T;

t , 0 or t . T 0 # t , T=2 :

…4†

…T=2† # t # T

In the above equations, u is the cue direction, T, the duration of the input to the PFC (T ˆ 100 ms), I0 ˆ 3:0, and sc ˆ 458. In this model, the cue-related input is assumed to be given only to the Ps cells directly; then u i is the preferred direction of Ps cell i. The Ps cell whose preferred direction is closest to the cue direction thus receives the maximum cue-related input. As our model circuit contains only a small number of neurons, we assume that all the model neurons are involved in the signal processing. In the actual cortex, however, there would exist a number of neurons that contribute only indirectly to the signal processing. Inputs from these neurons constitute a nonsignal component, which may cause only subthreshold events. We model this kind of input by adding a nonspecific constant current input to all neurons. The strength of the nonspecific current input is 0.66 for all the neurons. This input is weak enough to cause only subthreshold events unless it is given with the signal component simultaneously.

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Fig. 6. Time courses of the firing rates of the Pd cells in columns #5 (thin solid line), #10 (dashed line), #15 (dot-dashed line), and #20 (thick solid line). The time course for #5 is not labelled. The preferred directions of the Pd cells are 2 1358 (#5), 2 908 (#10), 2 458 (#15), and 08 (#20), and the cue direction was 08. The horizontal bar indicates the period in which the cue-related input was given to the circuit.

3. Results 3.1. Spatiotemporal dynamics A cue-related input triggered the dynamics of the model PFC circuit. The dynamics consisted of the increase in the activity in the early phase, the gradual transition to an equilibrium state, and the activity in the equilibrium-state. Fig. 5 shows the spatiotemporal profile of the activity of the Pd cells. The columns are aligned one-dimensionally according to the characteristic directions, which span the whole directional space. Column #20 has the characteristic direction of 08 and column #40 has the direction of 1808. In the figure, the data for column #40 are depicted as those for column #0, which has the equivalent characteristic direction of 2 1808 as column #40. Fig. 5 shows the activity of the Pd cells that have the same preferred directions with the characteristic direction of the columns (every column has one Pd cell having the same preferred direction as the characteristic direction of the column; see Model). In this case, the cue direction was 08, so that the Pd cell in column #20 was activated more strongly than the Pd cells in the other columns. The firing rate in the equilibrium-state decreased monotonically in moving away from column #20. The Pd cells in the columns of #0–10 and #30–40 were not activated at all or activated only weakly and transiently. This shows that the cue-related input selects the columns to activate. Another cue-related input with a different cue direction activated another set of columns; the column whose characteristic direction was closest to the cue direction was always activated the most. Fig. 6 shows the time course of the firing rates of the Pd cells in several columns more clearly. The horizontal bar shows the period in which the cue-related input was applied to the circuit. The figure shows that the selection of the columns to activate was almost completed in the early stage of the response (0– 100 ms). After this (. 100 ms), the firing rates of the Pd cells in the selected columns increased gradually and the Pd cells in the non-selected columns were kept inactivated. It took about 400 ms for the circuit to reach the equilibrium-

state. The dynamics is slow compared to the time constants of the dynamics of the individual neurons, which are 20 ms for the P cells and 10 ms for the N cells. To determine what happened inside the circuit during this course, the sum of the excitatory and inhibitory synaptic current inputs (i.e. the first term on the right hand side of Eq. (1)) to the Pd cells in columns #0 and #20 are depicted in Fig. 7. The synaptic inputs to both the Pd cells increased in the very first stage. The input to the Pd cell in column #20 increased rapidly to reach a high positive value, indicating a net excitatory input, whereas the input to the Pd cell in column #0 decreased to become a negative value, indicating a net inhibitory input. The change slowed down at about 100 ms, and the inputs gradually reached steady-state levels. In the equilibrium-state, the Pd cells in some columns received continuous net excitatory inputs, and the Pd cells in other columns received continuous net inhibitory inputs. The profile of the input across the columns at 500 ms is shown in Fig. 7(C). The figure shows that the Pd cells in columns of #11–29 received continuous net excitatory inputs. This input in the equilibrium-state was well-tuned, which is necessary for the maintenance of the tuned activity. This mechanism did not work in the early stage of the dynamics (between 0 and 100 ms) as no such input was formed in this stage. Then the activity in this period of time spread widely, though it was still tuned (see Fig. 5). The profile of the cue-related input was Gaussian with the standard deviation of 458, so that this was not due to the spatial distribution of the cue-related input. Changing the profile of the cue-related input changed neither the profile of the early response nor the profile of the activity in the equilibrium-state (Okada and Tanaka, 1998). The peak position of the activity, however, shifted according to the cue direction. These results suggest that the tuned activity was formed and maintained by the intrinsic dynamics of the circuit rather than respond passively to the external input, and that this tuned activity represents the spatial information of the cue. The tuned activity maintained after the termination of the cue-related input was robust against distractor stimuli. Fig. 8

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Fig. 8. Temporal evolution of the activity of the Pd cells when a transient distractor input was applied at 500 ms (the duration was 100 ms). The peak of the distractor input was located at 908, while the cue direction was 08. The characteristic directions of the columns are 21808 (#0), 2908 (#10), 08 (#20), 908 (#30), and 1808 (#40). Both the cue-related input, applied at 0 ms, and the distractor input had the same spatiotemporal profile and the same magnitude. The thick straight bars indicate the durations in which the cuerelated and the distractor inputs were given. Cue: the cue-related input, Distract: the distractor input.

shows the activity of the Pd cells that received a cue-related input at 0 ms and a second transient input at 500 ms. The magnitude and the spatiotemporal profile of the second input were found to be the same as those of the first input except that the peak of the second input was located at 908. The activity shifted slightly towards the second peak direction but the amount was very small. The effect was even weaker for the second input with the peak at 308, 608, and 1208, and the second input with the peak at 1808 resulted in no effect. In the case of 1808, the activation of the columns were completely symmetric and there was no overlapping between the columns activated by the first input and those to be activated when the second input alone would be applied. 3.2. Pyramidal-to-pyramidal connections

Fig. 7. Sum of the excitatory and inhibitory current inputs to the Pd cells, which is given by the first term on the right hand side of Eq. (1) and denoted by I_syn in the figure. The cue direction was 08 and the cue-related input was onset at 0 ms and its duration was 100 ms. (A) Three-dimensional view of the inputs; (B) time courses of the inputs to the Pd cells in the columns of #20 (solid line) and of #0 (dashed line); and (C) the profile of the sum of the excitatory and inhibitory current inputs to the Pd cells in the equilibriumstate.

The last section showed that the optimum columns (#11– 29) received sustained excitatory inputs and the non-optimum columns (#0–10 and #30–40) received continuous inhibitory inputs to maintain the tuned activity. As no external sources existed after the termination of the cue-related input, there should be a certain mechanism that accounts for the generation of the sustained inputs. This section analyzes the excitatory signal transmission through the pyramidal-topyramidal connection. The model PFC circuit contains a number of lateral, forward and backward pyramidal-topyramidal connections, which form multiple closed-loop circuits. Then the signal circulating through these closedloop circuits would be amplified, and the amplified signal

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would be balanced with the local inhibition mediated by the local inhibitory connections. It would, therefore, be interesting to see how the circuit dynamics change if we change the strength of the pyramidal-to-pyramidal connections.

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When the overall strength of the pyramidal-to-pyramidal connection was reduced, the firing rates of the cortical neurons decreased. Here, the overall strength of the connections is specified by the maximum value of the Gaussian connectivity profile, which is given in the Appendix. One interesting thing is that the activity was no longer sustained when the maximum strength of the pyramidal-to-pyramidal connections was below a certain value (0.70 relative to the normal value in this model given in Appendix A). Fig. 9(A) shows the transient response of the Pd cells. The amplitude of this transient response was very low, and no response was seen after the termination of the cue-related input. When the overall strength of the pyramidal-to-pyramidal connections was increased, the firing rates of the cortical neurons increased. Fig. 9(B) shows the response of the Pd cells when the strength of the pyramidal-to-pyramidal connections was 1.25 relative to the normal value. In this case, the tuning of the activity was rather weak. Further increasing the strength of the connections lost the tuning. In this model, the critical value for the relative strength of the connections at which the tuning was lost was 1.4. The activity of the Pd cells with the relative strength of the connections of 1.50 is shown in Fig. 9(C). Although the Pd cells in the optimum columns tended to increase the firing rates more rapidly, all the Pd cells exhibited high frequency firing within tens of milliseconds after the termination of the cuerelated input. In this case, the other cortical cell (Ps, Na and Nb cells) exhibited high frequency firing as well. Fig. 10(A) shows the synaptic input to the Pd cell in column #20 (i.e. the very optimum column) for various strengths of the pyramidal-to-pyramidal connections. When the relative strength of the connections were as low as 0.70 relative to the normal value, the cue-related input caused only a transient synaptic input. The time course of the input shows damping oscillation with a small amplitude. When the relative strength of the connections was 0.75 or higher, however, the synaptic input did not decay to zero after the termination of the cue-related input but exhibited a persistent component. Note that a positive value of the synaptic input means a net excitatory input, and, therefore, the persistent component is net excitatory. The magnitude of the persistent component of the synaptic input increased as the strength of the pyramidal-to-pyramidal connections was increased. However, as shown in Fig. 9, the activity lost the selectivity when the strength exceeded 1.4. Fig. 10(B), on the contrary, shows the synaptic input to the Pd cell in column #0 (i.e. the very non-optimum column). In this case, the synaptic input driven by the cue-related input also decayed to zero when the relative strength of the

Fig. 9. Temporal evolution of the activity profiles of the Pd cells for different strengths of the pyramidal-to-pyramidal connections, which were (A) 0.70, (B) 1.25, and (C) 1.50 relative to the normal value (see text). The cue direction was 08 and the cue-related input was onset at 0 ms (indicated by the horizontal line) and its duration was 100 ms (indicated by the second horizontal line).

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connections was 0.70 relative to the normal value. However, the behavior of the synaptic input for connections stronger than 0.70 was rather peculiar. The persistent component, which appeared for connections stronger than 0.70, was negative and decreased (increased in the absolute value) when the strength was increased. The negative value of the synaptic input means a net inhibitory input. In contrast to the input to column #20 (Fig. 10(A)), the persistent component did not decrease very much, so that the components for the strengths of the connections of 1.0, 1.1 and 1.3 were not significantly different. Moreover, the persistent component did not decrease monotonically; the component for the relative strengths of the connections of 1.3 was slightly higher (smaller in magnitude) than that for 1.1 and the component for 1.5 suddenly became a large positive value. Fig. 10(A) and (B) show that the persistent components of the inputs to columns #0 and #20 were the same when the activity lost the selectivity.

Fig. 11. Temporal evolution of the activity profiles of the Pd cells for different strengths of the two types of the local inhibition. The strengths of the (parallel, anti-parallel) inhibition were (A) (2.0, 1.0) and (B) (1.0, 6.0) relative to the normal value (see text). The cue direction was 08 and the cue-related input was onset at 0 ms (indicated by the horizontal line) and its duration was 100 ms (indicated by the second horizontal line).

3.3. Local inhibition Fig. 10. Time courses of the synaptic inputs to the Pd cell of column #20 (A) and #0 (B) for different strengths of the pyramidal-to-pyramidal connections. The numbers in the figure denote the relative strengths of the pyramidal-to-pyramidal connections. The horizontal bar indicates the duration of the cue-related input.

As the local inhibition affects the excitatory signal transmission through the circuit, it would contribute to the formation and maintenance of the tuned activity. To see this, the overall strength of the local inhibition (both for the NP and NN connections) was changed. As this model circuit has

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Fig. 12. Activity profiles of the Pd cells in the equilibrium-state for various strengths of the parallel and anti-parallel inhibition.

two types of local inhibition, the strengths of the parallel and the anti-parallel inhibition were changed independently. When the overall strength of the parallel inhibition was increased, the firing rates of both the pyramidal cells and the interneurons decreased. Fig. 11(A) shows the activity of the Pd cells for the relative strength of the parallel inhibition of 2.0 with unchanged strength of the anti-parallel inhibition. As the activity was strongly inhibited by parallel inhibition in this case, the cortical cells exhibited only a transient response. Decreasing the overall strength of the parallel inhibition, on the contrary, increased the firing rates of the cortical cells. A further decrease (below 0.28) yielded non-selective firing with a high frequency. These changes are similar to those obtained in the last section, in which the strength of the pyramidal-to-pyramidal connections was changed. This means that the parallel inhibition can effectively control the excitatory signal transmission through the circuit. In the reversed situation, when the anti-parallel inhibition was changed and the parallel inhibition was unchanged, the activity was rather insensitive to the change in the strength of the anti-parallel inhibition. When the overall strength of the anti-parallel inhibition was increased, the firing rates of the cortical neurons decreased slowly. Fig. 11(B) shows the activity of the Pd cells for the relative strength of the anti-parallel inhibition of 6.0 with unchanged strength of the parallel inhibition. Note that the effect of the strength of the antiparallel inhibition is significantly weaker than that of parallel inhibition. A further increase in the strength did not eliminate the sustained activity. Instead, the tuning width became narrower and narrower as the strength of the antiparallel inhibition increased. This tendency is entirely different from that for the parallel inhibition, suggesting different roles of these two types of local inhibition. These differences were marked when the inhibition was strong. For weaker inhibition, on the contrary, the activity showed

similar changes. Decreasing the overall strength of the anti-parallel inhibition increased the firing rates of the cortical cells. A further decrease (below 0.42) yielded non-selective firing with a high frequency, which was similar to the parallel inhibition case. Fig. 12 shows how the changing in the overall strengths of the parallel and the anti-parallel inhibition affects the tuning profile of the Pd cells. The results show that the directional selectivity or the sharpness of the tuning depends almost exclusively on the strength of the anti-parallel inhibition. The firing rate or the height of the tuning curve, on the contrary, depends mainly on the strength of the parallel inhibition and weakly on the strength of the anti-parallel inhibition. In the case in which both the relative strengths of the parallel and the anti-parallel inhibition were 0.5, the activity lost the selectivity completely.

4. Discussion 4.1. Sustainment of tuned activity This study investigated the architecture and dynamics of the PFC circuit for the formation and maintenance of spatial working memory. The cue-related input caused a brief transient response followed by gradually formed, tuned tonic activity. The activity profile was robust against a distractor stimulus. However, the peak shifted according to the cue direction, suggesting that the activity stably represents the spatial information of the cue. The tuned activity, therefore, accounts for the delay-period activity for the spatial working memory observed in experiments (Funahashi et al., 1989). The transition to an equilibrium state took about 400 ms in this simulation. As the cue-related input terminated at 100 ms after the onset, the transition to the equilibriumstate occurred without an external input. This was due to

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the intrinsic dynamics of the circuit triggered by the cuerelated input, rather than the dynamics of each neuron. The simulations suggest that the maintenance of the tuned activity requires sustained excitatory inputs to the pyramidal cells in the optimum columns, and sustained inhibitory inputs to the pyramidal cells in the non-optimum columns. The model circuit equips the forward and backward connections between the pyramidal cells in the superficial and deep layers. The pyramidal cells in both layers have extensive lateral connections. These connections form multiple closed-loop circuitry, and, via these connections, all the pyramidal cells receive converging excitatory inputs from the other pyramidal cells. Therefore, once the optimum columns are excited by the cue-related inputs, the excitatory signal circulates through the close-loop circuits. The signal circulating through these closed-loop circuits would be amplified, and the amplified signal would be balanced with the local inhibition mediated by the local inhibitory connections. Changing the strength of the pyramidal-topyramidal connections hence changed the activity of the cortical neurons. When the strength was decreased, a change occurred suddenly at a critical strength, below which the cortical neurons exhibited only transient responses. This was due to the termination of the excitatory and inhibitory current inputs after the early response. On the contrary, when the strength was increased, the firing rates of the active neurons increased and, above a critical strength, all the neurons began to fire at a high frequency. In this case, all the total current inputs to the cortical neurons suddenly turned out to be positive or excitatory. Well-formed sustained activity was obtained in an intermediate level of the strength of the pyramidal-to-pyramidal connections. The dependence of the activity of the cortical neurons on the strength of the pyramidal-to-pyramidal connections was non-linear, suggesting that the formation and maintenance of the tuned activity is a kind of synergistic phenomenon. The importance of excitatory circuits in the sustainment of the activity during the delay period has been suggested repeatedly (Fuster, 1994, 1997; Goldman-Rakic, 1991). However, there is no experimental study that demonstrates how the excitatory circuits contribute to the sustainment of the activity. This study suggests the importance of excitatory circuits by showing how the change in the strength of the overall excitatory connections changed the spatiotemporal activity of the cortical neurons. 4.2. Local inhibitory circuits This model assumed the two types of intracortical inhibition, the parallel and the anti-parallel inhibition in accordance with recent experimental findings (Wilson et al., 1994; Williams et al., 1998). The simulations showed that both types of inhibition contribute to the formation and maintenance of the tuned activity; without either of them, all the neurons fire at a high frequency. The roles of these types of inhibition in the formation and maintenance of the

tuned activity were investigated by changing the strengths of the action of these two types of inhibition. The positive feedback via the pyramidal-to-pyramidal connections tends to make the system unstable. Without the inhibiton, the cortical neurons receive excessive excitation due to this positive feedback. Then the activity goes to its maximum level and spreads all over the network (epileptiform activity). The parallel inhibition prevents this unstable epileptiform activity by suppressing the excessive cortical excitation. The balance between the excitation and the suppression is so delicate that the activity is sensitive to the change of the strength of the parallel inhibition as shown in the simulations. Appropriate parallel inhibition regulates the magnitude of the persistent excitatory synaptic input, by which the activity of the optimum columns is maintained. In contrast to the parallel inhibition, the activity is less sensitive to the change in the strength of the antiparallel inhibition. However, this does not necessarily mean that this type of inhibition is less important for the maintenance of the tuned activity. The extensive horizontal connections in the model allow the activity to spread all over the circuit if there is no such mechanism that prevents it. As the working memory has to be maintained in the whole delay period, which is usually several seconds, the prevention of the spread of the activity is critically important. That the sharpness of the tuning is controlled almost exclusively by the anti-parallel inhibition indicates the importance of this type of inhibition. The anti-parallel inhibition maintains the persistent inhibitory synaptic input into the non-optimum columns, which plays an important role in keeping the shape of the activity profile during the delay period. The model also assumed that the distinct subtypes of interneurons mediate distinct types of intracortical inhibition. However, this has no experimental evidence. The same interneurons could mediate both types of inhibition if they have two groups of axons. One of the axon groups would convey the parallel inhibitory signal to the postsynaptic cells, with the preferred directions similar to that of the presynaptic cell, while the other axon group would convey the anti-parallel inhibitory signal to the postsynaptic cells, with the preferred directions almost parallel to that of the presynaptic cell. Interneurons in the real brain may have more than two groups of axons. Actually, anatomical studies showed that the axonal arborizations of cortical interneurons are distributed in a patchy fashion (Martin, Somoyogi & Whitteridge, 1983; Somogyi, Kisvarday, Martin & Whitteridge, 1983). This suggests that the axons select columns or populations of neurons to project, and that there are more than one targeted columns or populations of neurons. The above idea may not be incompatible with this. At the same time, however, it is also the fact that there exist many subtypes of interneurons in the cortex including the PFC (Conde, Lund, Jacobowitz, Baibridge & Lewis, 1994; Lund & Lewis, 1993). Therefore, the assumption that the different types of inhibition are mediated by distinct

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Fig. 13. Schematic illustration for the circuit mechanism of the formation and maintenance of the tuned activity. In this case, the column whose characteristic direction is 908 received the strongest cue-related input. The profile of the activity in the equilibrium-state in this figure is only for illustration; the exact profile is shown in Fig. 5.

subtypes of interneurons would not be unnatural as well. Both cases bring the same results at least in the framework of this model. Then this model could assume either of them without loosing generality. However, these two cases would have distinct anatomical and physiological meaning when analyzing the roles of intracortical inhibition in more detail. This issue is to be studied. Goldman-Rakic (1995a) suggested the importance of intracortical inhibition circuit for working memory processing in the PFC. She proposed a hypothetical model in which pyramidal cells with opposite preferred directions communicate via interneurons (GoldmanRakic, 1995a), and argued that this scheme might contribute to the formation of spatial working memory. Her model is based on the finding that the interneurons observed in her laboratory had the preferred directions opposite to that of the nearby pyramidal cells (Wilson et al., 1994). The anti-parallel inhibition in the model proposed in this paper mediates this type of interaction, and the simulation here also suggested the importance. This study further suggests the importance of the parallel inhibition as well because it can control the firing rates of the activated neurons very effectively. The fact would be that well-regulated actions of both the parallel and the antiparallel inhibition form and maintain the appropriate tuned activity.

4.3. Circuit mechanism of the sustainment of tuned activity Fig. 13 summarizes the results discussed above. This figure illustrates the proposed circuit mechanism of the formation and maintenance of the tuned activity. The Ps cells in the optimum columns receive stronger cue-related inputs than those in the non-optimum columns. This difference makes the succeeding activity of the optimum and nonoptimum columns entirely different from each other. The cortical neurons receive a well-tuned persistent synaptic input in the equilibrium-state when the circuit maintains tuned dynamics. In the optimum columns, the excitatory synaptic input is greater than the inhibitory synaptic input, yielding net cortical amplification. In the non-optimum columns, on the contrary, the inhibitory synaptic input is greater than the excitatory synaptic input, yielding net cortical attenuation. The circuit thus maintains a well-tuned activity. It is important to recognize that no single neuron property can account for this type of dynamics. Rather, this study suggests that the circuit properties enable the PFC to form and maintain the tuned activity or spatial working memory. Among them the following three factors were found to be crucial: the cortical amplification of the activity due to the excitatory circuitry, the suppression of excessive excitation by the parallel inhibition, and the sharpening of the activity profile by the anti-parallel inhibition.

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This model contains many horizontal pyramidal-to-pyramidal connections, thereby the excitatory effects spread rapidly throughout the circuit. This model also contains another type of excitatory connections; i.e. the connections between the Ps and the Pd cells. This type of connections is almost intracolumnar or vertical because of the small standard deviation of this connectivity profile (4.58) compared with the difference of the characteristic directions between adjacent columns of 98. Although the roles of this type of connections have not been discussed in this article, the simulations confirmed that this type of connections contributes to the amplification of the activity of the pyramidal cells and then the sustainment of the activity in the delay period. In addition to these excitatory actions, the activity of the pyramidal cells has indirect inhibitory effects on the other pyramidal cells via the local interneurons. The two types of interneurons contribute very differently to the formation and maintenance of the tuned activity. Through the different actions of the parallel and the anti-parallel inhibition, as well as the mutual excitation, the columns interact cooperatively to generate and maintain the spatially tuned activity. This model does not suggest that the PFC contains only four types of cortical neurons (Ps, Pd, Na, and Nb). This paper studied the rather simplified architecture and dynamics of the model PFC circuit to account for the mechanism of the formation of spatial working memory from a computational point of view. Neuroanatomical and neurophysiological studies from the PFC reported many subtypes of the cortical neurons (Conde et al., 1994; Kawaguchi, 1993; Kawaguchi & Kubota, 1997). How these neurons contribute differentially to the formation of spatial working memory is to be studied. Acknowledgements The author acknowledges valuable discussions with Prof. P.S. Goldman-Rakic and Dr. G.V. Williams at Yale University School of Medicine. The author would also like to appreciate the helpful suggestions offered by the reviewers. A part of this work was done during the author’s sabbatical at the Goldman-Rakic Lab, Yale University School of Medicine.

responses were evoked in single neurons when stimulation and recording electrode were located in orientation columns sharing the same angle preference, and (ii) both the excitatory and inhibitory responses gradually decreased in amplitude when the difference between the preferred orientations of the stimulation and the recording columns gradually increased until they were orthogonal (Weliky & Katz, 1994; Weliky et al., 1995). In the motor cortex, the strongest excitatory connections were between the neurons with similar directional preferences. The negatively strongest connections were between those whose preferred directions were anti-parallel with each other, and the weakest or no connections were between those with the preferred directions perpendicular to each other (Georgopoulos, Taira & Lukashin, 1993). Both findings indicate essentially the same feature of the connectivity profile, i.e. the neurons with similar preferences (either direction or orientation) connect strongly with each other. No such data has been obtained from the PFC as far as the author knows. However, it has been suggested that neurons with similar response preferences in the PFC are interconnected (Goldman-Rakic, 1995a; Levitt et al., 1993; Pucak et al., 1996). This model, therefore, postulates that the PFC obeys the same rule of connectivity. The profile of connectivity, which is not yet known, is approximated by the Gaussian distribution function in this model. The neurons with the same preferred direction are connected most strongly and the strength of the connection decreases as the difference in the preferred directions of the pre- and postsynaptic neurons increases. The connectivity profile for the lateral and forward PP-type connections is thus given by 2 2 ˆ wPsPd ; wPP wPsPs ij ij S exp‰2…ui 2 uj † =2s1 Š;

…A:1†

wPP S

is the maximum strength of the connection where (0.0033 as the normal value in this model), ui and uj , the preferred directions of the presynaptic neuron and the postsynaptic neuron, respectively, and s1 ˆ 608. Projections from the Pd to Pd cells are less extensive (Kritzer & Goldman-Rakic, 1995; Levitt et al., 1993). The profile of the connection between the Pd cells is described by a Gaussian distribution function with a narrower width as 2 2 ; wPP wPdPd ij D exp‰2…ui 2 uj † =2s2 Š;

…A:2†

Appendix A. Connectivity profiles

where wPP D ˆ 0:0033 and s2 ˆ 278.

A.1. Lateral and forward PP-type connections

A.2. Backward PP-type connections

Many experiments confirmed that the connections between neurons with similar preferred orientations are stronger than the others in the visual cortex (Gilbert & Wiesel, 1989; Hata, Tsumoto, Sato, Hagihara & Tamura, 1993; Schwarz & Bolz, 1991; Ts’o, Gilbert & Wiesel, 1986; Weliky & Katz, 1994; Weliky, Kandler, Fitzpatrick & Katz, 1995). Moreover, Weliky and coworkers observed that—(i) the largest-amplitude excitatory and inhibitory

Assuming the same connectivity profile, the backward projections from Pd cell i to Ps cell j is given by 2 2 ; wPP wPdPs ij B exp‰2…ui 2 uj † =2s3 Š:

…A:3†

As the projections do not seem to extend beyond many columns (Kritzer & Goldman-Rakic, 1995; Levitt et al., 1993), the connectivity strength is assumed to be stronger than that for the forward and lateral connections …wPP B ˆ

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0:032† and the standard deviation is assumed to be smaller (s3 ˆ 4:58). A.3. PN-type connections The forward PN-type connections are assumed to have the same connectivity profile with the forward PP-type connections. Then, the connectivity is given by 2 2 ˆ wPsNb ; wPN wPsNa ik ik S exp‰2…ui 2 uj † =2s4 Š;

…A:4†

where wPN S ˆ 0:0042 and s4 ˆ 608. Similarly, Pd cells would have connections with the interneurons. As the lateral spread of the Pd axons are less extensive as suggested experimentally, this model assumes rather restricted connections with N cells. Then the profile of the connection from Pd cell i to N cell j is given by 2 2 ˆ wPdNb ; wPN wPdNa ij ij D exp‰2…ui 2 uj † =2s5 Š;

…A:5†

where wPN D ˆ 0:000627 and s5 ˆ 278. A.4. NP-type connections Inhibitory interneurons in the cortex make local connections with pyramidal cells and other non-pyramidal cells. This model assumes all types of connections from Na or Nb cell to Ps or Pd cells. As defined in the Model, the Na cells mediate the parallel inhibition and Nb cells mediate the anti-parallel inhibition. As these two subtypes of the interneurons have preferred directions that are opposite to each other, the synaptic strength of the local inhibitory projections from N cell i to P cells j is given by ˆ wNaPd ; wNP exp‰2…ui 2 uj †2 =2s26 Š wNaPs ij ij

…A:6†

and ˆ wNaPd ; wNP exp‰2…ui 2 uj 2 1808†2 =2s26 Š; wNaPs ij ij

…A:7†

where wNP ˆ 0:03 and s6 ˆ 4:58. A.5. NN-type connections The interneurons make local connections with other interneurons. The NN-type connections in this model include Na-to-Na, Na-to-Nb, Nb-to-Na, and Nb-to-Nb connections. Recent study from the visual cortex shows that the autapses are abundant on GABAergic basket and dendrite-targeting cells (Tamas et al., 1997). The autofeedback connections of the interneurons are included into the Na-to-Na and Nb-toNb connections. The connectivity profiles are then given by 2 2 ˆ wNbNb ; wNN wNaNa ij ij a exp‰2…ui 2 uj † =2s7 Š

…A:8†

and 2 2 ˆ wNbNa ; wNN wNaNb ij ij c exp‰2…ui 2 uj 2 1808† =2s7 Š …A:9† NN where wNN a ˆ 0:012; wc ˆ 0:0036; and s7 ˆ 4:58.

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References Baddeley, A. (1986). Working memory, New York: Oxford University Press. Braver, T. S., Cohen, J. D., Nystrom, L. E., Jonides, J., Smith, E., & Noll, D. C. (1997). A parametric study of prefrontal cortex involvement in human working memory. Neuroimage, 5, 49–62. Cohen, J. D., Perlstein, W. M., Braver, T. S., Nystrom, L. E., Noll, D. C., Jonides, J., & Smith, E. E. (1997). Temporal dynamics of brain activation during a working memory task. Nature, 386, 604–608. Conde, F., Lund, J. S., Jacobowitz, D. M., Baibridge, K. G., & Lewis, D. A. (1994). Local circuit neurons immunoreactive for calretinin, calbindin D-28k or parvalbumin in monkey prefrontal cortex: distribution and morphology. Journal of Comparative Neurology, 341, 95–116. Courtney, S. M., Ungerleider, L. G., Keil, K., & Haxby, J. V. (1997). Transient and sustained activity in a distributed neural system for human working memory. Nature, 386, 608–611. D’Esposito, M., Detre, J. A., Alsop, D. C., Shin, R. K., Atlas, S., & Grossman, M. (1995). The neural basis of the central executive system of working memory. Nature, 378, 279–281. Funahashi, S., Bruce, C. J., & Goldman-Rakic, P. S. (1989). Mnemonic coding of visual space in the monkey’s dorsolateral prefrontal cortex. Journal of Neurophysiology, 61, 331–349. Funahashi, S., Bruce, C. J., & Goldman-Rakic, P. S. (1990). Visuospatial coding in primate prefrontal neurons revealed by oculomotor paradigms. Journal of Neurophysiology, 63, 814–831. Funahashi, S., Bruce, C. J., & Goldman-Rakic, P. S. (1991). Neuronal activity related to saccadic eye movements in the monkey’s dorsolateral prefrontal cortex. Journal of Neurophysiology, 65, 1464–1483. Fuster, J. M. (1990). Behavioral electrophysiology of the prefrontal cortex of the primate. Progress in Brain Research, 85, 313–324. Fuster, J. M. (1994). Memory in the cerebral cortex, Cambridge, MA: MIT Press. Fuster, J. M. (1997). The prefrontal cortex, 3/e, Philadelphia: Lippincott– Raven Press. Fuster, J. M., & Alexander, G. E. (1971). Neuron activity related to shortterm memory. Science, 173, 652–654. Georgopoulos, A. P., Taira, M., & Lukashin, A. (1993). Cognitive neurophysiology of the motor cortex. Science, 260, 47–52. Gilbert, C. D., & Wiesel, T. N. (1989). Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex. Journal of Neuroscience, 9, 2432–2442. Goldman-Rakic, P. S. (1990). Cellular and circuit basis of working memory in prefrontal cortex of nonhuman primates. Progress in Brain Research, 85, 325–336. Goldman-Rakic, P. S. (1990). Cortical localization of working memory. In J. L. McGaugh & N. M. Weinberger & G. Lynch, Brain organization and memory: cells, systems, and circuits, (pp. 285–298). New York, Oxford: Oxford University Press. Goldman-Rakic, P. S. (1990). The prefrontal contribution to working memory and conscious experience. In J. C. Eccles & O. Creutzfeldt, The principles of desing and operation of the brain, Experiments in Brain Research, 21, (pp. 389–410). New York: Springer. Goldman-Rakic, P. S. (1991). Prefrontal cortical dysfunction in schizophrenia: the relevance of working memory. In B. J. Carroll & J. E. Barrett, Psychopathology and the brain, (pp. 1–23). New York: Raven Press. Goldman-Rakic, P. S. (1995). Cellular basis of working memory. Neuron, 14, 477–485. Goldman-Rakic, P. S. (1995). Architecture of the prefrontal cortex and the central executive. In Structure and functions of the human prefrontal cortex. In J. Graftman & K. J. Holyoak & F. Boller, (pp. 71–83). Annals of New York Academy of Science, 769. New York: New York Acad Sci. Hata, Y., Tsumoto, T., Sato, H., Hagihara, K., & Tamura, H. (1993). Development of local horizontal interactions in cat visual cortex

1020

Shoji Tanaka / Neural Networks 12 (1999) 1007–1020

studied by cross-correlation analysis. Journal of Neurophysiology, 69, 40–56. Haxby, J. V., Ungerleider, L. G., Horwitz, B., Rapport, S. I., & Grady, C. L. (1995). Hemispheric differences in neural systems for face working memory: a PET-rCBF study. Human Brain Mapping, 3, 68–82. Kawaguchi, Y. (1993). Groupings of nonpyramidal and pyramidal cells with specific physiological and morphological characteristics in rat frontal cortex. Journal of Neurophysiology, 69, 416–431. Kawaguchi, Y., & Kubota, Y. (1997). GABAergic cell subtypes and their synaptic connections in rat frontal cortex. Cerebral Cortex, 7, 476–486. Kritzer, M. F., & Goldman-Rakic, P. S. (1995). Intrinsic circuit organization of the major layers and sublayers of the dorsolateral prefrontal cortex in the rhesus monkey. Journal of Comparative Neurology, 359, 131–143. Kubota, K., & Niki, H. (1971). Prefrontal cortical unit activity and delayed alternation performance in monkeys. Journal of Neurophysiology, 34, 337–347. Levitt, J. B., Lewis, D. A., Yoshioka, T., & Lund, J. S. (1993). Topography of pyramidal neurons intrinsic connections in macaque monkey prefrontal cortex (areas 9 and 46). Journal of Comparative Neurology, 338, 360–376. Lund, J. S., & Lewis, D. A. (1993). Local circuit neurons of developing and mature macaque prefrontal cortex: Golgi and immunocytochemical characteristics. Journal of Comparative Neurology, 328, 282–312. Martin, K. A. C., Somogyi, P., & Whitteridge, D. (1983). Physiological and morphological properties of identified basket cells in the cat’s visual cortex. Experiments in Brain Research, 50, 193–200. Melchitzky, D. S., Sesack, S. R., Pucak, M. L., & Lewis, S. A. (1998). Syaptic targets of pyramidal neurons providing intrinsic horizontal connections in monkey prefrontal cortex. Journal of Comparative Neurology, 390, 211–224. Okada, S., & Tanaka, S. (1998). Roles of horizontal connectivity and local inhibition in memory field dynamics in a model prefrontal cortical circuit. Supplement Journal of Cognit Neuroscience (Cognit Neurosci Abstr 1998), 115. Owen, A. M., Evans, A. C., & Petrides, M. (1996). Evidence for a two-stage model of spatial working memory processing within the lateral frontal cortex: a positron emission tomography study. Cerebral Cortex, 6, 18–31. Petrides, M., Alivisatos, B., Evans, A. C., & Meyer, E. (1993). Dissociation of human mid-dorsolateral from posterior dorsolateral frontal cortex in memory processing. Proceedings of the National Academy of Sciences, USA, 90, 873–877. Petrides, M., Alivisatos, B., Meyer, E., & Evans, A. C. (1993). Functional activation of the human frontal cortex during the performance of verbal working memory tasks. Proceedings of the National Academy of Science, USA, 90, 878–882. Pucak, M. L., Levitt, J. B., Lund, J. S., & Lewis, D. A. (1996). Patterns of

intrinsic and associational circuitry in monkey prefrontal cortex. Journal of Comparative Neurology, 376, 614–630. Schwarz, C., & Bolz, J. (1991). Functional specificity of a long-range horizontal connections in cat visual cortex: a cross-correlation study. Journal of Neuroscience, 11, 2995–3007. Somers, D. C., Nelson, S. B., & Sur, M. (1995). An emergent model of orientation selectivity in cat visual cortical simple cells. Journal of Neuroscience, 15, 5448–5465. Somogyi, P., Kisvarday, Z. F., Martin, K. A. C., & Whitteridge, D. (1983). Synaptic connections of morphologically identified and physiologically characterized large basket cells in the striate cortex of cat. Neuroscience, 10, 261–294. Sweeney, J. A., Mintun, M. A., Kwee, S., Wiseman, M. B., Brown, D. L., Rosenberg, D. R., & Carl, J. R. (1996). Positron emission tomography study of voluntary saccadic eye movements and spatial working memory. Journal of Neurophysiology, 75, 454–468. Tamas, G., Buhl, E. H., & Somogyi, P. (1997). Fast IPSPs elicited via multiple synaptic release sites by different types of GABAergic neurone in the cat visual cortex. Journal of Physiology, 500, 715–738. Tanaka, S. (1997). A model of the prefrontal cortical circuit for memory field formation during oculomotor delayed-response performance. Neuroscience Research Supplement, 21, S251. Tanaka, S. (1997). Formation of memory fields for oculomotor delayedresponse performance: a model of the prefrontal cortical circuit. Society for Neuroscience Abstracts, 23, 1602. Ts’o, D. Y., Gilbert, C. D., & Wiesel, T. N. (1986). Relationships between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis. Journal of Neuroscience, 6, 1160–1170. Weliky, M., & Katz, L. C. (1994). Functional mapping of horizontal connections in developing ferret visual cortex: experiments and modeling. Journal of Neuroscience, 14, 7291–7305. Weliky, M., Kandler, K., Fitzpatrick, D., & Katz, L. C. (1995). Patterns of excitation and inhibition evoked by horizontal connections in visual cortex share a common relationship to orientation columns. Neuron, 15, 541–552. Williams, S. M., Goldman-Rakic, P. S., & Leiranth, C. (1992). The synaptology of parvalbumin-immunoreactive neurons in the primate prefrontal cortex. Journal of Comparative Neurology, 320, 353–369. Williams, G. V., Rao, S. G., & Goldman-Rakic, P. S. (1998). Iso- and crossdirectional inhibition in the spatial tuning of regular- and fast-spiking neurons in primate prefrontal cortex. Society for Neuroscience Abstracts, 24, 1523. Wilson, F. A., O’Scalaidhe, S. P., & Goldman-Rakic, P. S. (1994). Functional synergism between putative gamma-aminobutyrate-containing neurons and pyramidal neurons. Proceedings of the National Academy of Sciences, USA, 91, 4009–4013.