INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The prefrontal cortex (PFC) and its dense dopaminergic input are critically involved in working-memory functions (Brozoski et al. 1979; Fuster 1989; Goldman-Rakic 1995; Müller et al. 1998; Petrides 1995; Sawaguchi and Goldman-Rakic 1994; Seamans et al. 1998). Working memory refers to the ability to hold temporally active goal-related information and to use it in preparing actions and guiding behavior. During working-memory tasks, which involve a delay component, many PFC neurons show stimulus- and/or goal-specific, sustained activity during the delay. This activity is presumed to reflect the active holding of task-related information or motor preparation while external cues are absent (Funahashi and Kubota 1994; Fuster 1989; Goldman-Rakic 1990; Quintana and Fuster 1999), and it can be maintained even in the presence of interfering stimuli (Miller et al. 1996).

Task-related electrical activity in the PFC is modulated by dopamine (DA), mainly via the D1 receptor (Sawaguchi et al. 1988, 1990a,b; Williams and Goldman-Rakic 1995). Dopaminergic midbrain neurons are activated at the onset of working-memory tasks (Schultz et al. 1993), and DA levels in the PFC increase during delay-task performance (Watanabe et al. 1997). Blockade of the dopaminergic input to the PFC or of dopaminergic D1 receptors in the PFC disrupt delay-task performance (Brozoski et al. 1979; Sawaguchi and Goldman-Rakic 1994; Seamans et al. 1998; Simon et al. 1980). DA has been shown in vitro to influence the biophysical properties of multiple intrinsic ionic and synaptic currents of PFC neurons (Gulledge and Jaffe 1998; Kita et al. 1999; Law-Tho et al. 1994; Seamans et al. 1999; Shi et al. 1997; Yang and Seamans 1996; Zheng et al. 1999; Zhou and Hablitz 1999). However, it is unclear how these relate to DA's role in working memory. Thus although it is clear that DA plays an important role in working memory and alters the properties of PFC single neurons and synapses, its specific functions and the underlying biophysical mechanisms remain elusive.

One function of DA may be to stabilize neural representations in the PFC and thus enable PFC networks to sustain task-related activity even in the presence of interfering input (Durstewitz et al. 1999a), which could be a unique feature of prefrontal networks (Miller et al. 1996). In other words, DA might increase the robustness of (sustained) delay activity with respect to distracting input and noise. In a previous study, the general concept of DA-induced stability was explored in a simple model with leaky-integrator units that lacked detailed channel kinetics and spiking behavior (Durstewitz et al. 1999a). Here we confirm and extend the general results of this study under more realistic conditions in a network of compartmental model neurons with Hodgkin-Huxley-like channel kinetics devised to reproduce in vitro and in vivo results from deep layer PFC neurons. Greater physiological detail allowed dopaminergic effects on network activity to be explored in ways that were beyond the scope of the former model. In addition, we investigate the possible functional implications of the differential dopaminergic modulation of N-methyl-D-aspartate (NMDA) and AMPA synaptic conductances (Cepeda et al. 1992; Kita et al. 1999; Law-Tho et al. 1994; Seamans et al. 1999) and provide a functional interpretation of the DA-induced increase in GABA_A currents for working-memory processes (Rétaux et al. 1991; Seamans et al. 1999; Yang et al. 1997; Zhou and Hablitz 1999).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

In vitro recordings

To obtain voltage traces for adjustment of the model neurons, in vitro recordings from PFC layer V intrinsically bursting (IB) pyramidal cells were made. Details for recording methods can be found in Seamans et al. (1997). Briefly, the brains of male Sprague-Dawley rats (14-28 days) were rapidly dissected and immersed for 1 min in cold (4°C) oxygenated artificial cerebrospinal fluid (ACSF). After cutting, 300-µm slices containing the prelimbic/infralimbic region of the PFC were transferred to ACSF containing (in mM) 126 NaCl, 3 KCl, 26 NaHCO₃, 1.3 MgCl₂, 2.3 CaCl₂, and 10 glucose at 30°C. Thick-walled borosilicate pipettes (serial resistance = 4-25 M for somatic recordings was 80% compensated) were filled with (in mM) 130 K-gluconate, 10 KCl, 1 ethylene glycol-bis(-aminoethyl ether)-N, N,N',N'-tetraacetic acid (EGTA), 2 MgCl₂, 2 NaATP, and 10 N-2-hydroxyethylpiperazine-N'2-ethanesulfonic acid (HEPES). Pipettes were connected to the headstage of an Axoclamp-2B or Axopatch-200B amplifier (Axon Instruments) with Ag/AgCl wire.

Pyramidal cell model

A compartmental model was developed that reproduced somatic voltage recordings from a layer V IB pyramidal cell in rat PFC (Fig. 1A). Deep layer pyramidal cells are the ones most strongly innervated by dopaminergic fibers in the rat and primate PFC and express the highest levels of mRNA for all DA receptor subtypes (Berger et al. 1988, 1991; Goldman-Rakic et al. 1992; Joyce et al. 1993; Lewis et al. 1992; Lidow et al. 1998). Furthermore they constitute the major portion of neurons exhibiting sustained delay activity (Fuster 1973). Intrinsically bursting pyramidal cells were chosen because they are the most common pyramidal cell type in the deep layers of the rat PFC as assessed by intracellular in vitro recordings (>60%) (Yang et al. 1996). The model layer V neurons consisted of a soma, a basal dendritic, a proximal and a distal apical dendritic compartment, as depicted in Fig. 1A. The cellular dimensions of the model were in agreement with a morphological reconstruction of a PFC layer V pyramidal cell obtained in our laboratory. (Test simulations performed with a more detailed 20-compartment model yielded the same basic results, not shown here.)

View larger version (20K): [in this window] [in a new window]   Fig. 1. Schematic of the prefrontal cortex (PFC) network model. A: compartmental representations of the pyramidal cells (PC) and the GABAergic interneurons (IN), and their synaptic interconnections in the model network. B: 2 partly overlapping patterns were stored in the pyramidal cell network by connecting pyramidal cells within these patterns by high synaptic weights while connecting them to pyramidal neurons outside the pattern by low synaptic weights. One of these patterns was used as the target pattern, whereas the other was used as a distractor.

The passive properties of the model were adjusted to approximately reproduce the input resistance (R_IN), membrane time constant (_m), and resting potential (V_rest) of prefrontal IB cells recorded in vitro. The resulting values for the specific membrane resistance, membrane capacity, and cytoplasmatic (axial) resistivity were, respectively, R_m = 30 k-cm², C_m = 1.2 µF/cm², and R_i = 150 -cm, which are well in the range of empirically derived estimations for pyramidal cells from other studies (Destexhe and Paré 1999; Spruston et al. 1994; Stuart and Spruston 1998). The leakage reversal potential (E_leak) was 70 mV. These values (together with the active processes) gave rise to a V_rest ~ 66 mV (matching the empirically measured mean, about 66 mV), R_IN ~ 164 M (empirically measured mean, ~163 M), _m= R_mC_m= 36 ms (empirically, ~33 ms), which conjointly with the active processes resulted in an effective time constant at the soma of ~44 ms, which is well within the range of recordings from IB cells in vitro (range ~16-55 ms). Dendritic spines were implemented by increasing the effective dendritic C_m and dividing the effective dendritic R_m by a factor of 1.92, accounting for a 92% increase in dendritic membrane area due to spines as estimated from data of Larkman (1991; see also Rhodes and Gray 1994).

DA controls various active ionic processes in the soma and dendrites of deep layer prefrontal pyramidal cells, and as we were interested specifically in the effects of DA on network behavior, the selection of active conductances included in our model was motivated primarily by this aim. Six different ionic conductances were distributed over the soma and the dendritic compartments with densities estimated from empirical data. All conductance kinetics were modeled by Hodgkin-Huxley-like equations, where ionic conductance per unit area is given by a product of powers of one or two voltage-, time-, and, sometimes, [Ca²⁺]_i-dependent, dimensionless gating variables and a maximum conductance density (Tables 1 and 2).

Gating variables develop in time according to the first-order differential equation dx/dt = [x(V)  x(V, t)]/_x(V), where x is the voltage-dependent steady state and _x a voltage-dependent time constant. Table 2 provides an overview over the gating variables and their respective powers for all ionic conductances used in the present study. Voltage gradients were computed according to the spatially discrete form of the cable equation (e.g., Rall 1989).

SODIUM CURRENTS. A fast, spike-generating Na⁺ current (I_Na) was distributed uniformly across all three dendritic compartments (Huguenard et al. 1989; Magee and Johnston 1995; Stuart and Sakmann 1994) but was given a higher density at the soma. This was done to transfer the lower threshold spike-generating mechanism of the axon (Colbert and Johnston 1996), which was not explicitly modeled and is probably partly due to much higher nodal Na⁺ channel densities (Black et al. 1990; Westenbroek et al. 1989), to the soma. Conductance densities in the dendrites were adjusted to ensure spike back-propagation (Spruston et al. 1995b; Stuart and Sakmann 1994) with spike amplitudes and widths as recorded in vitro (Seamans et al. 1997). The biophysical description of I_Na was taken from a computational study by Warman et al. (1994) and adapted to fit kinetics determined by Cummins et al. (1994), who analyzed Na⁺ currents in rat and human neocortical pyramidal cells.

CALCIUM CURRENTS AND CALCIUM ACCUMULATION. The biophysical description of a high-voltage-activated (HVA) Ca²⁺ current was taken from Brown et al. (1993), who studied these currents in dissociated rat sensorimotor cortex pyramidal cells. For simplicity we did not distinguish between L- and N-type Ca²⁺ currents, which according to Brown et al. (1993) have the same activation kinetics, but assumed that the HVA Ca²⁺ current implemented in the model represents a mixture of the two. Immunocytochemical, Ca²⁺ influx, and electrophysiological data suggest that HVA Ca²⁺ channels are highly clustered in the proximal dendrites around the soma, are present with significant densities along the apical stem, but are quite low in density in the distal apical tuft, in neocortical including prefrontal pyramidal cells (Hell et al. 1993; Schiller et al. 1995; Seamans et al. 1997; Westenbroek et al. 1990, 1992). Densities of the HVA channel in the present study were adjusted accordingly (Table 1).

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POTASSIUM CURRENTS AND POTASSIUM ACCUMULATION. The Hodgkin-Huxley-like formulas for the delayed rectifier (DR) channel were taken from a computational study by Warman et al. (1994) on hippocampal neurons. Following Rhodes and Gray (1994), the deactivation of the DR was sped up by 1.5 to better reproduce spike repolarization observed in PFC IB neurons in vitro. The distribution of DR conductance densities matched that of the fast Na²⁺ current (Table 1).

Model of fast-spiking GABAergic interneurons

A basket-type fast spiking (FS) neocortical aspiny interneuron was implemented by a two-compartment model as depicted in Fig. 1A (Kawaguchi 1993, 1995; Kawaguchi and Kubota 1997) [the morphological dimensions of this cell were estimated roughly from data on FS cells in frontal cortex given in Kawaguchi (1995)]. FS interneurons provide most of the inhibition in the neocortex including the PFC (Gabbott et al. 1997; Kawaguchi and Kubota 1997), are involved in working memory (Rao et al. 1999; Wilson et al. 1994), and are the major type of interneuron modulated by DA (Gorelova and Yang 1998; Muly et al. 1998; Sesack et al. 1998; Zhou and Hablitz 1999). Passive membrane properties were as follows: R_m = 100 k-cm², C_m = 1.0 µF/cm², R_i = 150 -cm, and E_leak = 68 mV (the behavior of the interneurons in the network was largely insensitive to the exact values of these parameters). K⁺ accumulation dynamics were the same as for the pyramidal cells. The fast Na⁺ and K⁺ DR channels included in the somatic and dendritic compartment (Table 1) were sufficient to reproduce the fast-spiking, nonadapting behavior and the strong, brief afterhyperpolarizations after each spike exhibited by FS basket-type cells (Kawaguchi 1993, 1995; Kawaguchi and Kubota 1997). The kinetics of these channels (taken from Lytton and Sejnowski 1991) differed from those of the pyramidal neuron to reproduce the much shorter spike duration in interneurons compared with pyramidal cells (Kawaguchi 1993, 1995; Rao et al. 1999; Wilson et al. 1994) and the faster recovery from Na⁺ channel inactivation (Martina and Jonas 1997a), allowing higher spike firing rates (Table 2).

Network architecture and synaptic currents

Because little is known about the detailed connectivity of neurons within the PFC and the associated synaptic strengths, we intentionally kept the network model as general and as simple as possible (Fig. 1). A total of 20 deep layer pyramidal cells and 10 GABAergic interneurons were simulated. (Test simulations with larger networks suggested that network size is not a crucial factor for the questions addressed in the present paper.) All pyramidal cells and GABAergic interneurons were fully connected (but see following text). Extensive lateral connections between layer V pyramidal cells (ranging up to millimeters) in the PFC have been demonstrated by Levitt et al. (1993) and Kritzer and Goldman-Rakic (1995). According to Lübke et al. (1996) and Markram et al. (1997a), these connections between deep layer pyramidal cells involve about four to eight synaptic contacts distributed mainly on the proximal dendritic tree. Thus pyramidal cells in the present model were connected reciprocally within the proximal dendritic region; that is, synapses were placed both on the basal and proximal apical dendritic compartment (Fig. 1A). Pyramidal-to-GABAergic cell synapses were placed on the dendritic compartments of the interneurons. Inhibitory feedback connections from interneurons to pyramidal cells consisted of GABA_A-like synapses on the somata of pyramidal cells where most inhibitory synapses converge (Douglas and Martin 1990; Thomson and Deuchars 1997). Direct reciprocal interactions between pyramidal cells and FS interneurons are suggested both by in vitro data (Tarczy-Hornoch et al. 1998; Thomson and Deuchars 1997) and by the observation of correlated firing of pyramidal cells and interneurons in the PFC in vivo during working-memory tasks (Constantinidis et al. 1999; Rao et al. 1999). GABAergic interneurons also were interconnected reciprocally by GABA_A-like conductances on their somata. All axonal transmission delays varied in the range of 2-4 ms.

Both pyramidal-to-pyramidal and pyramidal-to-GABAergic cell connections involved both AMPA- and NMDA-like synaptic conductances [for evidence on NMDA-like synaptic conductances on FS interneurons in frontal cortex, see Kawaguchi (1993)]. AMPA-like synaptic currents were modeled by a double exponential function of the form g_AMPA,max × [₁₂/(_2  1)] × [exp(t/₂)  exp(t/₁)] with time constants ₁= 0.55 ms and ₂ = 2.2 ms. NMDA-like synaptic currents were modeled as in Mel (1993) by the product of a voltage-dependent gate s = 1.50265 × [1 + 0.33 exp(0.06 V_m)]¹ with _s = 0.1 ms (implementing the voltage-dependent Mg²⁺ block) and a double exponential with time constants ₁ = 10.6 ms and ₂ = 285.0 ms. Time constants for the AMPA and NMDA currents were taken directly from a study of glutamate receptor channels by Spruston et al. (1995a). The voltage dependency of the NMDA current as given by the s-gate in the preceding text also matched the one measured by Spruston et al. (1995a; see their Fig. 4F). Furthermore the relative contributions of AMPA- and NMDA-like currents to excitatory postsynaptic currents (EPSCs; i.e., the ratio g_AMPA,max:g_NMDA,max) were matched to data from Spruston et al. (1995a). In the absence of more specific knowledge, g_AMPA,max and g_NMDA,max for pyramidal cells and interneurons were assumed to be of equal strength (g_AMPA,max = 15.1392 nS, g_NMDA,max = 0.0912 nS, for the baseline configuration, see following text). These conductances were set high enough to allow in concert with spontaneous synaptic inputs (see following text) the maintenance of recurrent activity in the small network for some time similar to that observed in PFC neurons during delayed reaction-type tasks (Funahashi and Kubota 1994; Fuster 1989; Goldman-Rakic 1995). Synaptic reversal potentials were set to E_AMPA = E_NMDA = 0 mV (Angulo et al. 1997; Seamans et al. 1997; Spruston et al. 1995a). GABA_A-like currents were modeled by alpha-functions of the form g_GABAA,max × t/_GABAA × exp(t/_GABAA + 1) with _GABAA = 1.5 ms and g_GABAA,max = 8.4 nS, yielding fast inhibitory postsynaptic potentials as found in neocortical pyramidal cells (Thomson and Deuchars 1997). The reversal potential was E_GABAA = 75 mV (Ling and Benardo 1998; Thomson et al. 1996).

Stimulus- and/or response-specific delay activity and "opponent memory fields" have been observed in the PFC during working-memory tasks (Funahashi et al. 1989; Goldman-Rakic 1995, 1996; Quintana et al. 1988; Rainer et al. 1998a; Rao et al. 1997). Thus for example, in the oculomotor delayed response task (Funahashi et al. 1989; Goldman-Rakic 1995, 1996), neurons in the PFC show enhanced firing for a preferred target direction but suppressed firing for targets opposite to the preferred direction. To produce stimulus/response-specific activity patterns in the small model network used here, two partly overlapping subsets of 10 neurons each (Fig. 1B) were connected by high synaptic weights (g_max values as given in the preceding text) within each group and by low synaptic weights (10% of the g_max values given in the preceding text) between neurons not belonging to the same cell assembly. These two subsets were meant to represent two different stimuli or motor plans encoded by the synaptic connections of the network (for the present purposes the precise nature of the information encoded in the delay activity is not relevant). Formation of such cell assemblies as originally proposed by Hebb (1949) is suggested by Hebb-like long-term synaptic plasticity mechanisms in the cortex (Levy and Steward 1983; Markram et al. 1997) and is supported by recent multiple-electrode recordings from the PFC (Brody et al. 1999; Constantinidis et al. 1999). Specific activity patterns were evoked by stimulating one of the stored cell assemblies via afferent synapses (see following text) or current injections.

To achieve low spontaneous firing rates in the network as observed in vivo in the PFC (Fuster 1989; Fuster et al. 1985; Rosenkilde et al. 1981), random background synaptic activity was delivered to all pyramidal and GABAergic cells, generated according to Poisson processes convolved with the excitatory (AMPA and NMDA) or inhibitory (GABA_A) synaptic conductance changes defined in the preceding text. Background excitatory synaptic inputs were placed on all dendritic compartments of pyramidal cells and interneurons, whereas inhibitory inputs were limited to the proximal stems and somata where pyramidal cells receive most of their inhibitory input (Douglas and Martin 1990; Thomson and Deuchars 1997; Thomson et al. 1996). These inputs mimicked synaptic connections from other neurons within the PFC as well as afferent connections from other cortical or subcortical areas. In low-activity states, the network was driven mainly by this random background activity, which accounted for >90% of the total synaptic current in pyramidal cells. In contrast, in high-activity states, the network was dominated by recurrent synaptic activity and the relative contribution of background synaptic inputs was ~50%. The strength and number of background synaptic inputs furthermore were adjusted to approximately produce membrane voltage fluctuations as observed in vivo (Destexhe and Paré 1999; Paré et al. 1998).

Specific afferent network inputs

The main question of the present study was how DA might affect the robustness of delay (sustained) activity in PFC circuits with respect to distracting input. A distracting input could be any environmental or internally generated stimulus that is incompatible with (or irrelevant to) the current behavioral goal and that tends to evoke a specific representation (activity pattern) in the PFC networks. It thereby interferes (or competes) with the current prefrontal delay activity pattern that encodes information related to the present behavioral goal (Miller et al. 1996; Quintana et al. 1988; Rainer at al. 1999). In delayed-reaction tasks, interfering stimuli have been introduced as part of the experimental design (Fuster 1973; Miller et al. 1996).

Distracting input might arise from many different anatomic sources, involving inputs to the PFC from subcortical (e.g., thalamic), sensory neocortical, or even other prefrontal areas (Fuster 1989; Fuster et al. 1985; Goldman-Rakic 1988; Pandya and Yeterian 1990). Depending on the site of origin, association and transcallosal fiber connections target mainly layers I, III, and V, layers I, IV, and VI, or all layers in the prefrontal cortices (Goldman-Rakic 1988; Isseroff et al. 1984; Melchitzky et al. 1998; Pucak et al. 1996). Hippocampal inputs predominantly contact layers I and V (Swanson 1981). Thalamic inputs distribute mainly throughout layers I, III, and V-VI (Berendse and Groenewegen 1991; Kuroda et al. 1993, 1996) where they contact the dendrites of layer V-VI pyramidal cells (Kuroda et al. 1993). Thus distracting inputs might basically affect all dendritic compartments of deep layer pyramidal cells in the PFC, probably exerting their strongest impact in the proximal basal and apical dendrite region. Hence, in addition to nonspecific background inputs (see preceding text) to all compartments, afferent excitatory (NMDA and AMPA) synapses that specifically target one of the stored cell assemblies were placed on the proximal basal and apical dendrite compartments of the model cells (placing them in addition on the distal model dendrites did not change the results).

To probe stability of PFC representations and to vary the strength of an afferent stimulus, the afferent stimulation frequency rather than the synaptic conductance strength was varied because the subjective importance and behavioral relevance of stimuli in prefrontal areas is correlated with firing frequency (Tremblay and Schultz 1999; Watanabe 1996). The synaptic (AMPA- and NMDA-like) conductances of the afferent connections were arbitrarily set five times higher than those of the recurrent synapses. This choice yielded a physiologically reasonable range of afferent stimulation frequencies (i.e., F_crit values, see RESULTS) and allowed sufficient discrimination between conditions.

Dopaminergic modulation

DA has physiological effects that might vary between different brain regions [for example, DA has effects on NMDA currents in the hippocampal CA1 region (Hsu 1996; Otmakhova and Lisman 1999) opposite from those observed in the PFC and striatum (see following text)]. Hence only effects of DA reported for PFC neurons were used in the present study. We also focused on D1-mediated effects because D1 receptors are much more abundant in the PFC than D2 receptors (Joyce et al. 1993; Lidow et al. 1991) and, more importantly, both working-memory performance as well as delay-activity recorded in vivo in behaving animals is susceptible mainly or exclusively to D1 but not D2 receptor agonists and antagonists (Arnsten et al. 1994; Müller et al. 1998; Sawaguchi and Goldman-Rakic 1994; Sawaguchi et al. 1988, 1990b; Seamans et al. 1998; Williams and Goldman-Rakic 1995; Zahrt et al. 1997). Hence, the short-lasting D2 effects (Godbout et al. 1991; Gulledge and Jaffe 1998; Pirot et al. 1992) may subserve other functions not directly related to holding representations in working memory (see also Durstewitz et al. 1999a). Both deep layer pyramidal cells (Berger et al. 1990; Bergson et al. 1995; Smiley et al. 1994; Yang and Seamans 1996) and FS interneurons (Gorelova and Yang 1998; Muly et al. 1998) in the PFC are equipped with D1 receptors.

DA-induced parameter shifts in the model were varied systematically over some range (see RESULTS) but for some simulations, "baseline" (0% DA shift) and "high DA" (100% DA shift) standard configurations were defined as in Tables 1 and 2 and as described below. The high-DA configuration is based on the average shifts in DA-dependent parameters observed in vitro (Gorelova and Yang 1997; Seamans et al. 1999; Yang and Seamans 1996; Yang et al. 1997). The following effects of DA on intrinsic ionic and synaptic currents were implemented (see Tables 1 and 2):

1) DA shifts the activation threshold of the persistent Na⁺ current toward more hyperpolarized potentials and slows the inactivation process of this current (Gorelova and Yang 1997; Seamans et al. 1999; Yang and Seamans 1996) (Table 2). This likely contributes to the DA-induced increase in firing rate and reduced adaptation as observed in vitro (Cepeda et al. 1992; Seamans et al. 1999; Shi et al. 1997; Yang and Seamans 1996) and in vivo (Sawaguchi et al. 1988, 1990a,b) in prefrontal pyramidal cells.

2) DA reduces a slowly inactivating K⁺ current in PFC pyramidal cells (Yang and Seamans 1996), as is the case in striatal neurons (Nisenbaum et al. 1998). This was modeled as a reduction in g_KS,max (Table 1).

3) DA reduces the half-width and amplitude of isolated dendritic Ca²⁺ spikes (Yang and Seamans 1996). The data of Yang and Seamans (1996) made it likely that this reduction is due to a diminishing effect of DA on a HVA Ca²⁺ current located more in the distal dendrites and thus probably of the N type, which reaches a local maximum in the distal dendrites of pyramidal cells (Westenbroek et al. 1992; Yuste et al. 1994). A reduction of N-type HVA Ca²⁺ currents by DA has been shown more directly in striatal neurons (Surmeier et al. 1995), in isolated dorsal root ganglia sensory neurons (Formenti et al. 1998), and recently in PFC neurons by Yang et al. (1998). As L- and N-type HVA Ca²⁺ channels for simplicity were collapsed into a single description in the present model, HVA Ca²⁺ conductances in the proximal and distal dendrites were affected differentially by DA, based on the assumption that DA diminishes the N-type current only. L-type channels are highly clustered within the proximal region and strongly decline toward the distal dendrites (Hell et al. 1993; Westenbroek et al. 1990). In contrast, immunolabeling for N-type channels falls off in the middle of the apical stem of deep layer neurons but rises again within layers II-III (Westenbroek et al. 1992). Thus we assumed that the total HVA Ca²⁺ current in the distal dendritic compartment was of the N-type, whereas in the proximal region it contributed only 40% to the total HVA Ca²⁺ current as shown in vitro by Brown et al. (1993). DA-induced reductions in the maximum HVA Ca²⁺ conductance (g_HVA,max) were implemented accordingly (Table 1).

4) Recent evidence shows that DA via the D1 receptor enhances NMDA-like synaptic currents in the PFC (Kita et al. 1999; Moore et al. 1998; Seamans et al. 1999; Zheng et al. 1999), as in striatal neurons (reviewed in Cepeda and Levine 1998; Cepeda et al. 1993; Levine et al. 1996) and as shown earlier in slices from human frontal neocortex (Cepeda et al. 1992). In the high DA configuration, this was modeled by an increase of 40% in g_NMDA,max (Seamans et al. 1999).

5) In contrast to NMDA-like synaptic currents, non-NMDA or AMPA-like currents seem to be reduced in the frontal neocortex including the PFC (Cepeda et al. 1992; Kita et al. 1999; Law-Tho et al. 1994), as in the striatum (Cepeda et al. 1993). However, this reduction may only be slight in the PFC (Seamans et al. 1999). Nevertheless we investigated the effect of a reduction in AMPA currents as possibly induced by DA by decreasing g_AMPA,max by 20% in the high DA configuration.

The overall effect of the combined DA-induced changes in AMPA and NMDA currents was to reduce the excitatory postsynaptic potential (EPSP) amplitude but prolong the duration as suggested by in vitro experiments (Cepeda et al. 1992; Kita et al. 1999; Law-Tho et al. 1994; Seamans, unpublished observations).

6) The DA-induced enhancement of GABA_A-like synaptic currents in the PFC (Penit-Soria et al. 1987; Pirot et al. 1992; Rétaux et al. 1991; Seamans et al. 1999; Yang et al. 1997; Zhou and Hablitz 1999) was modeled by an increase in g_GABAA,max of 30% in the high-DA configuration (Seamans et al. 1999). In addition, DA might enhance spontaneous activity of GABAergic neurons or GABAergic transmitter release in the PFC (Rétaux et al. 1991; Yang et al. 1997; Zhou and Hablitz 1999). This effect was accounted for by increasing the spontaneous background firing rate of GABAergic inputs by 10% in the high DA condition.

Computational techniques

The simulation software was written in C++ and run on Pentium PCs using the LINUX operating system. The system of differential equations was integrated numerically using a semi-implicit extrapolation method as described in Press et al. (1992, Ch. 16.6) with an adaptive time step procedure. The (local truncation) error criterion was set to 10⁴, and the minimum time step was limited to 0.1 µs. To produce random background activity, a (uniform) random-number generator based on data encryption methods as described in Press et al. (1992, Ch. 7.5) was used because it has much better statistical properties than the C++ standard library "rand" function (see Press et al. 1992). A NEURON implementation of the pyramidal cell model is available under ftp://ftp.cnl.salk.edu/pub/dd/pcell.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The first two sections serve to illustrate that the model as devised in the METHODS can reproduce basic electrophysiological features of PFC neurons recorded in vitro and in vivo. The main part of the RESULTS then will examine how DA-induced parameter variations affect network states indicated by these electrophysiological features and which functional implications for working memory this might have.

Reproduction of the firing pattern of PFC IB pyramidal cells

The passive properties of the model neuron matched the average V_rest, R_IN, and _m of prefrontal IB cells recorded in vitro (see METHODS). In addition, the single pyramidal cell model reproduced the basic properties of spiking behavior of these neurons (Fig. 2A). Current injections into the model cell soma elicited a spike doublet followed by a train of action potentials with adaptation properties similar to those of IB neurons recorded in vitro. With the dopaminergic modulation of intrinsic ion channels in place (high-DA condition; see Tables 1 and 2), the spike frequency of the cell increased almost threefold to the same somatic current step (compare Fig. 2, B with 3rd row in A), as reported for PFC pyramidal cells recorded in vitro after bath application of DA (Yang and Seamans 1996).

View larger version (25K): [in this window] [in a new window]   Fig. 2. Comparison of in vitro whole cell recordings and model responses. A, left: somatic patch-clamp recordings from an intrinsically bursting (IB) layer V PFC neuron (2nd trace is from a different neuron than the other 3) while different somatic current steps were applied. Right: responses of the model pyramidal cell to similar current steps. B: implementing the dopaminergic modulation of intrinsic currents yields an about threefold increase in the spike frequency of the model neuron in response to the same current step as used in the 3rd row of A.

Basic network properties

Figures 3 and 4 illustrate that neurons in the fully connected network model with all internal and external synaptic inputs in place (see METHODS) could reproduce the most salient electrophysiological features of PFC neurons recorded in vivo. Without any additional input or stimulation, neurons in the model network driven by the spontaneous background activity fired at low rates (mean 1.4 Hz), comparable with the low spontaneous firing rates of 1-3 Hz observed for the majority of pyramidal neurons in the primate and rat PFC [Fuster 1973; Fuster et al. 1985; Jung et al. 1998; Rosenkilde et al. (1981) provide a distribution of spontaneous rates; Sawaguchi et al. 1990a]. The spontaneous activity alone, however, was not sufficient to drive the network spontaneously into a state of high, sustained activity, although transient episodes of burst-like activity occasionally appeared in the baseline condition (see Fig. 3A, left). When a high-activity state was evoked by a short-lasting stimulation of one of the stored cell assemblies (either by a current injection or by stimulation of afferent synapses), this activity was sustained at ~17.3 Hz for prolonged periods of time if the background noise was not too high (Fig. 3A). Thus in a manner similar to delay-active neurons in a working-memory task that hold active a representation of the stimulus or the forthcoming action, high activity was maintained in the network for many seconds after removal of the eliciting stimulus. The rasterplot in Fig. 3A confirms in addition that this activity was stimulus specific, i.e., it was only present in a subset of encoding neurons. GABAergic feedback inhibition ensures that the spread of activity in the network is limited; competing attractors are suppressed and only one pattern can become active at a time.

View larger version (41K): [in this window] [in a new window]   Fig. 3. Dopaminergic modulation of low- and high-activity states in the model network. A: somatic voltage traces (top) of 2 neurons under the baseline condition, 1 of which participates in the target pattern representation (red traces), whereas the other does not (blue traces). A low-activity state of the network driven mainly by the random background activity (left) and a state of high, sustained activity driven mainly by recurrent excitation in one group of neurons (right) are shown. The high-activity state was induced by a short current pulse (red bar) into the target pattern neurons. Bottom: activity of all 20 pyramidal neurons and 2 representative GABAergic interneurons (neurons 21 and 22) as raster-plots (where each point represents a spike in the respective neuron). The raster-plot (right) shows that sustained high activity is specific for target pattern neurons. B: same as in A for the high-dopamine (DA) condition. Note that spontaneous (low) activity was reduced (left), whereas high recurrent activity was enhanced (right) compared with the baseline condition shown in A. Differences in the activity states are mirrored by the firing rates of the GABAergic neurons, which are driven by the pyramidal cells. C: if background noise is increased, a high-activity state in the baseline condition (left) decays much earlier than in the high-DA condition (right).

View larger version (61K): [in this window] [in a new window]   Fig. 4. Simulated DA modulation increases stability of target pattern representations. A: example membrane potential traces from a neuron participating only in the target pattern (red traces) and 1 participating only in the distractor pattern (blue traces) under the baseline condition. Target pattern activity was evoked by a 250-ms current injection (red bar). A second later, distractor pattern neurons were synaptically stimulated for 100 ms (blue bar). At low afferent stimulation frequencies (Fstim), the target pattern stays stable and is maintained for at least another second after offset of distractor pattern stimulation (left). With Fstim increased to 20 Hz, the target pattern collapses and is replaced by the distractor pattern (right). B: same as under A for the high-DA condition. Note that much higher stimulation frequencies were required to disrupt target pattern activity than under the baseline condition shown in A. C: stability of the target pattern, as measured by the minimal afferent stimulation frequency (Fcrit) required to disrupt the target pattern, as a function of the percentage of the shift in DA-modulated parameters relative to the differences between the baseline and the high DA configuration (see text). Error bars indicate SE.

In general, delay frequencies in the present model network ranged from ~12 to 36 Hz (depending on condition, see following text) and were thus well within the range of what has been observed during the delay periods of working-memory tasks (e.g., Di Pellegrino and Wise 1993; Funahashi et al. 1989; Fuster 1973; Miller et al. 1996; Rainer et al. 1998b). Firing frequencies, however, could climb transiently to much higher values, especially during the presentation of a stimulus. The frequency of the interneurons during delay activity ranged from ~45 to 100 Hz, in agreement with available in vivo data (Wilson et al. 1994). The fact that stimulus-specific, recurrent activity could be maintained in the network at quite low rates (<20 Hz) is in itself not trivial because of the short axonal propagation and transmission delays (2-4 ms in the present model) and the fast AMPA-kinetics. In addition, selective high activity could be maintained in the presence of considerable noise (see METHODS). These characteristics depended critically on the slow time course and voltage-dependence of NMDA conductances. Finally, in high-activity states, spike trains were highly irregular (Figs. 3, A and B, and 4, A and B) with coefficients of variation (C_v) ranging from 0.5 to 0.8, as observed in in vivo recordings from neocortical neurons (Bodner et al. 1997; Shadlen and Newsome 1994; Softky and Koch 1993).

In summary, these simulations demonstrate that the network model established here exhibits network states and behavior as observed in the PFC in vivo, thus providing a physiologically plausible starting point to explore the effects of DA-induced parameter variations on these network states and their functional implications.

Differential dopaminergic modulation of activity states

In the present network, a simulated rise in DA level by shifting intrinsic and synaptic ion channel parameters into the high-DA configuration led to suppression of the low firing state (mean 0.3 Hz; Fig. 3B). This suppression was caused by the relative dominance of the inhibitory over the excitatory actions of DA in the low-activity state (i.e., by the increased GABAergic inhibition and the reduced N-type Ca²⁺ and AMPA currents). In contrast, when a high-activity state was elicited by a transient stimulus, DA enhanced this sustained activity, and the average firing frequency rose from ~17.3 Hz in the baseline condition to ~25.8 Hz in the high-DA condition. Conversely the activity of neurons not participating in the representation of the evoked pattern (the "background neurons") was more strongly suppressed in the high-activity state in the high-DA condition compared with the baseline condition (compare raster plots in Fig. 3, A and B). In the high-activity state, the excitatory actions of DA dominated its inhibitory actions. Thus the net effects of DA on neural firing depended on the initial activity state of the network. In the high-DA condition, sustained "delay activity" was also more robust with respect to the random fluctuations in background activity: If the impact of noise on network activity was increased, sustained activity in the baseline condition had the tendency to break down much earlier than in the high-DA condition (Fig. 3C).

The switch from a predominantly "inhibitory" to a predominantly "excitatory" action of DA from low to high levels of activity stems mainly from the highly increased contribution of the slow NMDA currents in the high-activity state: During high activity, DA causes a large boost in long-lasting recurrent excitation, further amplified by the increase in firing frequency by the enhancement of I_NaP. In addition, the fact that the persistent Na⁺ and the NMDA but not the GABA_A and AMPA conductances are voltage-dependent means that the former two but not the latter increase at higher levels of activity. Thus the relative impact of the I_NaP and NMDA conductances grows with network activity.

The simulations reported above highlight a functionally important principle, namely that DA's effects depend on the activity state of a cell assembly such that foreground in relation to background activity is enhanced. It is important to note that the differential modulation of low- and high-activity states by DA is an intrinsic property of the activity/voltage and time dependencies of the particular conductances affected by DA and as such does not depend on the particular parameter configuration. Thus even for parameters for which the low-activity state also was amplified by DA, there was always a much larger enhancement of the high-activity state, which in turn led to increased GABAergic feedback suppressing the background neurons. The differential DA-induced enhancement of sustained activity in the network is also consistent with the enhancements of task-related activity demonstrated in vivo during working-memory tasks (Sawaguchi et al. 1988, 1990a,b).

Effects of DA on the stability of active patterns

In the following sections, the possible functional implications of the differential modulation and the DA-induced parameter changes will be examined. Sustained (delay) activity of neurons in the PFC selectively encodes stimulus or motor information relevant to the current behavioral goal (Asaad et al. 1998; Di Pellegrino and Wise 1993; Funahashi et al. 1989; Fuster 1989; Quintana and Fuster 1999; Rainer et al. 1998a,b, 1999; Rao et al. 1997; Rosenkilde et al. 1981). Both disrupted delay activity as well as delay activity coding for the wrong stimulus or response are correlated with subsequent behavioral errors (Funahashi et al. 1989; Fuster 1973; Quintana et al. 1988). In the following, the activity pattern that has to be maintained during the delay for successful goal achievement or behavioral performance will be referred to as the "target pattern." A stimulus that is not relevant to the present task or behavioral goal and hence interferes with the target pattern will be referred to in the following as the "distractor pattern." Durstewitz et al. (1999a) showed how the PFC might detect patterns that are important to the present goal (and thus differentiate them from distractor patterns) via "match enhancement neurons" (e.g., Miller et al. 1996), and how these neurons could generate a signal that via a cortico-striatonigral feedback loop finally terminates target pattern activity again on achieving the goal.

To explore the idea that DA increases the robustness of target pattern representations (encoded by delay-active neurons) with respect to distracting patterns, parameters modulated by DA were linearly varied, either in combination or independently, within a physiologically reasonable range, using the difference between the baseline and the high-DA configuration as a standard. Thus the differences between the baseline and the high-DA configuration as given in METHODS and in Tables 1 and 2 were defined arbitrarily as a 100% shift in DA-dependent parameters, and other conditions were expressed relative to these standard difference values (i.e., normalized to them). For each of these different "DA levels" (parameter shifts), the minimal frequency of an afferent synaptic stimulation of the distractor pattern neurons that was sufficient to disrupt the target pattern and evoke a transition to the distractor pattern was determined. This is illustrated in Fig. 4, A and B, for the baseline and the high-DA situation, respectively: First a target pattern was evoked by a 250-ms current injection (0.45 nA) into the somata of the neurons coding for that pattern. (Synaptic stimulation yielded the same results, but current injection was used instead to ensure that at the time when the interfering pattern arrived, target pattern activity was driven only by recurrent network inputs and was no longer aided by afferent inputs.) Next, 1 s after the target pattern stimulation was shut off, afferent synapses to the distractor pattern were stimulated for 100 ms. For low-frequency stimulation of the distractor pattern, the target pattern remained stable, but at a certain stimulation frequency (F_crit), it broke down (due to the increased GABAergic feedback induced by the distractor pattern stimulation), and a transition to a new activity state occurred. At this critical frequency, the current contents of working memory are lost.

As a criterion for stability, target pattern activity had to be maintained at frequencies >10 Hz for 1 s after offset of the distractor pattern stimulation. F_crit values were determined in steps of 10 Hz such that each step meant one additional afferent spike within the 100-ms stimulation period. Hence F_crit also can be read as the number of equally spaced afferent spikes within the stimulation period. In a few cases (<6%), stability was not a monotone function of stimulation frequency but could exhibit "jumps" within a narrow critical range. In these cases, F_crit was defined as the first stimulation frequency where disruption of the target pattern occurred. Note from Fig. 4, A and B, that even suprathreshold activity in the distractor pattern neurons may not be sufficient to shut down the target pattern and enforce a transition to the distractor pattern unless the distractor pattern neurons gain sufficiently high firing rates.

Highly irregular firing patterns and strong membrane voltage fluctuations are characteristic features of neocortical neurons recorded in vivo (Destexhe and Paré 1999; Paré et al. 1998; Shadlen and Newsome 1994; Softky and Koch 1993) and are prominent in PFC neurons during the delay periods of working-memory tasks (Bodner et al. 1997). Hence we especially were interested in how DA might affect the robustness of active representations in the presence of high noise and high variance of the membrane potentials and interspike intervals. Because the random synaptic background activity made a major contribution to the total synaptic current (see METHODS), eight sets of simulations with different synaptic background patterns were run, and F_crit values were averaged across these conditions. This procedure also provided a robustness check because different background patterns produced quite different spiking patterns in the recurrent network, thus demonstrating that our results hold despite high levels of noise and with different firing patterns. The F_crit values reported in the following should be interpreted in relative rather than absolute terms because the absolute values depend on other parameters such as the synaptic strength of the afferent inputs (see METHODS) and the delay times, which were kept fixed for these simulations.

Figure 4C shows that the critical afferent frequency (F_crit) increased more than threefold across the range of simulated DA levels, i.e., with the magnitude of the changes in the DA-modulated parameters. Hence over a range of physiologically plausible parameters, the dopaminergic modulation leads to an increase in stability of the currently active representation with respect to interfering stimuli.

Additional simulations confirmed that an increase in stability with increasing DA-induced parameter shifts holds under the following conditions: for longer or shorter time intervals (delays) after target pattern onset; with background activity shut off completely (i.e., no noise); stimulation of the distractor pattern by DC injections into the dendrites of the distractor pattern cells; additional stimulation of GABAergic interneurons conjointly with the distractor pattern pyramidal cells (i.e., including a strong feedforward inhibitory component); and no overlap between the target pattern and the distractor pattern (i.e., no shared neurons). In the latter case, an increase in overall stability occurred while the ordinal relationships between different DA levels were preserved, consistent with previous findings (Durstewitz et al. 1999a).

Ionic currents contributing to the DA-induced stabilization

To assess which of the DA-modulated conductances could contribute to an enhancement of stability, each was varied independently while the other parameters affected by DA were set to the high-DA values given in METHODS. As shown in Fig. 5, A and B, the DA-induced alterations in the persistent Na⁺ conductance, and, somewhat counterintuitively, both, the increase in the NMDA conductance as well as the decrease in the AMPA conductance increased stability of the target pattern over the range of parameters tested. The stability-increasing effects of the DA-induced alterations in these conductances were present in each of the eight different sets of simulations as well as in the control simulations listed above. The enhancement of I_NaP and NMDA conductances might increase stability through several mechanisms. Most importantly, the spike rate of the pyramidal cells increased due to enhanced recurrent excitation and I_NaP-mediated amplification of EPSPs (Schwindt and Crill 1995, 1996; Stuart and Sakmann 1995). This in turn elevated the firing rate of the GABAergic interneurons, which receive inputs from the pyramidal cells, resulting in an enhanced GABAergic feedback to the pyramidal cells that is more difficult for any interfering input to overcome. The increased firing of the target pattern neurons also implies that a higher firing rate has to be obtained in the distractor pattern neurons to achieve the same level of NMDA conductance activation as in the target pattern neurons. The slow kinetics and voltage dependence of the NMDA conductance are critical for this effect as evidenced by the fact that a decrease in g_AMPA, which is voltage-independent and has a short time course, also enhances stability.

View larger version (15K): [in this window] [in a new window]   Fig. 5. Stability of target pattern representations as a function of shifts in each of the DA-modulated channel parameters. A: stability as a function of isolated DA-induced changes in N-methyl-D-aspartate (NMDA), AMPA, and GABAA synaptic conductances. Percentages refer to the magnitude of change relative to the difference between the high-DA and the baseline values (see METHODS). Note that higher percentages mean an enhancement for NMDA and GABAA conductances but a reduction for AMPA currents. For the 0% NMDA condition, no delay activity at all was elicited, i.e., there was an immediate cessation of activity after offset of the stimulation. B: stability as a function of isolated DA-induced changes in the persistent Na+ current (NaP), the slowly inactivating K+ current (KS), and t