Model-Compte-spatial wm.-CCortex2000 April18 2013

Model-Compte-spatial wm.-CCortex2000 April18 2013
Synaptic Mechanisms and Network
Dynamics Underlying Spatial Working
Memory in a Cortical Network Model
Albert Compte, Nicolas Brunel1, Patricia S. Goldman-Rakic2
and Xiao-Jing Wang
Single-neuron recordings from behaving primates have established a
link between working memory processes and information-specific
neuronal persistent activity in the prefrontal cortex. Using a network
model endowed with a columnar architecture and based on the
physiological properties of cortical neurons and synapses, we have
examined the synaptic mechanisms of selective persistent activity
underlying spatial working memory in the prefrontal cortex. Our
model reproduces the phenomenology of the oculomotor delayedresponse experiment of Funahashi et al. (S. Funahashi, C.J. Bruce
and P.S. Goldman-Rakic, Mnemonic coding of visual space in
the monkey's dorsolateral prefrontal cortex. J Neurophysiol
61:331–349, 1989). To observe stable spontaneous and persistent
activity, we find that recurrent synaptic excitation should be
primarily mediated by NMDA receptors, and that overall recurrent
synaptic interactions should be dominated by inhibition. Isodirectional tuning of adjacent pyramidal cells and interneurons can
be accounted for by a structured pyramid-to-interneuron connectivity. Robust memory storage against random drift of the tuned
persistent activity and against distractors (intervening stimuli during
the delay period) may be enhanced by neuromodulation of recurrent
synapses. Experimentally testable predictions concerning the neural
basis of working memory are discussed.
Dorsolateral prefrontal cortex (PFC) plays a pre-eminent role in
visuospatial working memory, as demonstrated by convergent evidence from ablation and reversible lesion studies
(Goldman-Rakic, 1987; Fuster, 1988), brain imaging (McCarthy
et al., 1994; Courtney et al., 1998; Zarahn et al., 1999) and
primate physiological studies (Fuster, 1973; Niki and Watanabe,
1976; Funahashi et al., 1989; Chafee and Goldman-Rakic, 1998;
Rainer et al., 1998; Sawaguchi and Yamane, 1999). In an
oculomotor delayed-response task (Funahashi et al., 1989), when
a monkey is required to retain information of a visual cue
location through a delay period (a few seconds) between the
stimulus and memory-guided behavioral response, PFC neurons
show location-tuned elevated activity through the entire delay
period. Presumably, information about the cue location is
encoded by a selective neural assembly that subserves active
memor y storage by virtue of its sustained firing activity.
Persistent activity has also been reported for neurons in posterior parietal cortex (PPC) during delayed oculomotor response
experiments (Gnadt and Andersen, 1988; Colby et al., 1996;
Constantinidis and Steinmetz, 1996; Chafee and Goldman-Rakic,
1998). It is thus conceivable that mnemonic activity is
maintained by reverberatory loops between the PFC and PPC
(Fuster, 1988; Goldman-Rakic, 1987; Chafee and Goldman-Rakic,
1998; Sarnthein et al., 1998). However, location-specific persistent activity in PPC was found to be easily disrupted by
intervening stimuli during the delay period, while the monkey's
working memory performance was not impaired (Constantinidis
and Steinmetz, 1996). An alternative mechanism is that a neural
circuit within the PFC may be by itself capable of sustaining
selective persistent activity. In support of that idea, recent
studies have demonstrated local recurrent excitatory connections both anatomically (Levitt et al., 1993; Kritzer and
Goldman-Rakic, 1995) and physiologically (González-Burgos et
al., 2000), as well as interactions between pyramidal and nonpyramidal neurons at microcolumnar and macrocolumnar ranges
(Rao et al., 1999) in the PFC.
A number of theoretical models have attempted to account for
selective persistent activity, based on the assumption that
persistent activity is sustained by reverberatory excitation
within a local recurrent neural network (Hebb, 1949; Amit,
1995). Most previous computational analyses have used firing
rate models (Wilson and Cowan, 1973; Amari, 1977; Zipser et
al., 1993; Amit et al., 1994; Seung, 1996; Camperi and Wang,
1998; Moody et al., 1998; Durstewitz et al., 1999). Firing rate
models, however, are difficult to relate directly with the
physiological data. In particular, the issue of spontaneous versus
persistent activity cannot be properly analyzed. Moreover,
realistic time courses of synaptic interactions between neurons
are typically ignored. For these reasons, a direct dialog between
models and cortical synaptic physiology has been lacking.
Recently, several studies have brought models closer to experimental data. Amit and Brunel used a spiking neuron model,
instead of a rate model, for object working memory (Amit and
Brunel, 1997). This approach allowed them to explicitly address
the question of spontaneous activity and the generation of
persistent activity by a specific structured connectivity.
Lisman and co-workers proposed that the voltage sensitivity of
NMDA receptors (NMDARs) at recurrent synapses could underlie the stimulus-selectivity of neuronal persistent activity (Lisman
et al., 1998). On the other hand, Wang found that, in order to
realize a stable, low-rate, persistent activity coexisting with a
stable resting state, recurrent excitation should be primarily
mediated by kinetically slow synapses of the NMDA type (Wang,
1999).
In this paper, we present a PFC network model for spatial
working memory that combines insights from previous
modeling studies on persistent activity in recurrent circuits
(Amit and Brunel, 1997; Camperi and Wang, 1998; Wang, 1999).
The structure of recurrent connnectivity is consistent with a
columnar organization of cortical circuitry (Levitt et al., 1993;
Goldman-Rakic, 1995; Kritzer and Goldman-Rakic, 1995;
Mountcastle, 1997), similar to network architectures that have
been proposed in other cortical network models (Ben-Yishai et
al., 1995; Douglas et al., 1995; Somers et al., 1995). The model
incorporates physiological data from slice preparations on the
membrane parameters and input-output transductions of pyramidal and nonpyramidal neurons (McCormick et al., 1985), and on
the postsynaptic current gating kinetics of A MPA receptor
(AMPAR), NMDAR (Hestrin et al., 1990; Jahr and Stevens, 1990;
© Oxford University Press 2000
Cerebral Cortex Sep 2000;10:910–923; 1047–3211/00/$4.00
Introduction
Volen Center for Complex Systems, Brandeis University,
Waltham, MA 02254 and 2Section of Neurobiology, Yale
University School of Medicine, 333 Cedar Street, New Haven,
CT 06510, USA
1
Permanent address: LPS (Laboratory associated with CNRS,
Paris 6 and Paris 7 Universities), Ecole Normale Supérieure, 24
rue Lhomond, 75231 Paris Cedex 05, France
Spruston et al., 1995) and GABAA receptor (GABAAR) (Salin and
Prince, 1996; Xiang et al., 1998) mediated synaptic transmission.
By using our model to reproduce the Funahashi experiment, we
investigated synaptic mechanisms and network dynamics that
may account for the salient observations on neuronal correlates
of working memor y. We also investigated the robustness of
working memory storage against distraction stimuli and noise.
Predictions from our theoretical results that are testable by in
vitro physiological studies and single-neuron recording from
behaving monkeys will be discussed.
Materials and Methods
The network model represents a local circuit of the monkey dorsolateral
prefrontal cortex. It includes NE pyramidal cells, and NI interneurons.
Pyramidal cells are four times more numerous than interneurons (NE/NI =
4). We assume a network architecture that is consistent with a columnar
organization of the monkey PFC (Goldman-Rakic, 1995; Rao et al., 1999;
Constantinidis et al., 1999; Ó Scalaidhe and Goldman-Rakic, 1999), and
similar to models of the primary visual cortex (Ben-Yishai et al., 1995;
Somers et al., 1995; Tsodyks and Sejnowski, 1995). Neurons are spatially
distributed according to the stimulus to which they are most sensitive
(preferred cue in an oculomotor delayed response task) and their
collaterals may differentially target neighboring (isodirectional) and
distant (crossdirectional) neurons. Cells receive external synaptic inputs
which are indicative of the angle of the peripheral cue during its
presentation. Each model neuron is labeled by its preferred cue position
(an angle), and neurons of the network cover uniformly all the angles
along a circle. Therefore, the cells are spatially distributed on a ring and
their position in the ring has a linear relationship with their preferred cue
angle.
Both pyramidal cells and interneurons are modeled as leaky integrate
and fire units (Tuckwell, 1988). Each type of cell is characterized by six
intrinsic parameters: the total capacitance Cm, the total leak conductance
gL, the leak reversal potential EL, the threshold potential Vth, the reset
potential Vres, and the refractory time τref. The values that we use in
the simulations are Cm = 0.5 nF, gL = 25 nS, EL = –70 mV, Vth = –50 mV,
Vres = –60 mV, and τref = 2 ms for pyramidal cells; and Cm = 0.2 nF, gL =
20 nS, EL = –70 mV, Vth = –50 mV, Vres = –60 mV, and τref = 1 ms for
interneurons (Troyer and Miller, 1997; Wang, 1999). All cells receive
external excitatory inputs from other cortical areas. This overall external
input is modeled as uncorrelated Poisson spike trains to each neuron at a
rate of νext = 1800 Hz per cell (or equivalently, 1000 presynaptic Poisson
spike trains at 1.8 Hz). The external input is exclusively mediated by
AMPARs, with the maximum conductance gext,E = 3.1 nS on pyramidal
cells, and gext,I = 2.38 nS on interneurons.
Neurons receive their recurrent excitatory inputs through AMPARand NMDAR-mediated transmission and their inhibitory inputs through
GABAARs. Synaptic responses are modeled as by Wang (Wang, 1999):
postsynaptic currents are modeled according to Isyn = gsyns(V – Vsyn),
where gsyn is a synaptic conductance, s a synaptic gating variable, and Vsyn
the synaptic reversal potential (Vsyn = 0 for excitatory synapses, Vsyn =
–70 mV for inhibitory synapses). AMPAR and GABAAR synaptic gating
variables are modeled as an instantaneous jump of magnitude 1 when a
spike occurs in the presynaptic neuron followed by an exponential decay
with time constant 2 ms for AMPA (Hestrin et al., 1990; Spruston et al.,
1995) and 10 ms for GABAA (Salin and Prince, 1996; Xiang et al., 1998).
The NMDA conductance is voltage dependent, with gsyn multiplied by
1/(1 + [Mg2+]exp(–0.062Vm)/3.57) (Jahr and Stevens, 1990), [Mg2+] = 1.0
mM. The channel kinetics is modeled by the following equations:
b g
ds
1
= − s + αsx 1 − s
dt
τs
c
dx
1
x + ∑ δ t − ti
=−
dt
τx
i
taking the conductance between neuron i and neuron j to be gsyn,ij = W(θi
– θj)Gsyn, where W(θi – θj) is the ‘connectivity footprint’ normalized as
z
e
j
1 360
W θi − θ j dθ j = 1
360 0
The functional form of W is chosen to be either a constant for
unstructured connections or the sum of a constant term plus a Gaussian
centered at θi – θj = 0: W(θi – θj) = J– + (J+ – J–)exp[–(θi – θj)2/2σ2]. In this
equation, the dimensionless parameter J– represents the strength of the
weak crossdirectional connections, J+ the strength of the stronger
isodirectional connections, and σ is the width of the connectivity
footprint (see Fig. 1). Note that the normalization condition of W imposes
a functional relationship between the three parameters defining
the connectivity. Therefore, we only mention in the following two
parameters, J+ and σ. J– is then determined using the normalization
condition. In most simulations, only the excitatory-to-excitatory
connectivity is structured. Parameters of the corresponding footprint are
J+EE, σEE. In a few simulations (Fig. 7), the excitatory-to-inhibitory
connectivity is also structured. The parameters of the corresponding
footprint are J+EI, σEI. In all simulations, the inhibitory connections are
unstructured, i.e. the cross- and isodirectional components of inhibitory
connections are equally strong.
In order to produce a desired level of spontaneous activity, we set the
values of the conductances of external synapses gext,E, gext,I, and the
frequency of external inputs νext so that each neuron receives strong
suprathreshold input from external sources. We then impose that
inhibition be stronger than recurrent excitation, by choosing a high
enough ratio of inhibitory to excitatory conductances on each cell type,
i.e. a high enough value of GIE/GEE = GII/GEI. Adjusting these parameters
allows control of the level of spontaneous activity of both excitatory and
inhibitory populations (Amit and Brunel, 1997). A structured pyramidto-pyramid connectivity gives rise to tuned network persistent activity
states. This is accomplished by a gradual increase of J+, until the network
shows a bistability between homogeneous spontaneous activity and
tuned persistent activity (Amit and Brunel, 1997). An important point to
make here is that the pyramid-to-pyramid footprint WEE is always
normalized to 1, so that an increase in the synaptic strength between
neurons with similar preferred cues implies a decrease in the strength of
connection between neurons with dissimilar preferred cues. This allows
the preservation of the level of spontaneous activity as the connectivity
footprint is varied.
In most of the simulations shown in this paper, only NMDAR channels
were included at the recurrent excitatory synapses (for simplicity), since
previous work suggested that dominance of the recurrent excitation by
NMDARs favors network stability (Wang, 1999). In some simulations we
assessed the network stability when the A MPAR contribution to the
recurrent connections was included (see below). Typically (for the
‘control parameter set’), NE = 2048, NI = 512. The recurrent excitatory
synapses mediated by NMDAR channels have conductances GEE =
h
where s is the fraction of open channels, x is an intermediate gating
variable, ti are the presynaptic spike times, τs = 100 ms is the decay time
of NMDA currents, τx = 2 ms controls the rise time of NMDAR channels,
and αs = 0.5 kHz controls the saturation properties of NMDAR channels at
high presynaptic firing frequencies.
The recurrent connections between neurons in the network depend
on the difference between their preferred cues. This is implemented by
Figure 1. Structured connectivity of the model. The synaptic connection strength
decreases with the difference in the preferred cues of two neurons, with strong
interactions between neighboring neurons and weak interactions between more distant
neurons.
Cerebral Cortex Sep 2000, V 10 N 9 911
Figure 2. Working memory maintained by a tuned network activity state (a ‘bump state’). C, cue period (250 ms, peak stimulus 200pA); D, delay period (8.75 s); R, response period
(250 ms, external current increase 500 pA). (A) Pyramidal neurons rastergram. The x axis represents time, while the y axis represents neuron label according to its preferred cue. A
dot in the rastergram indicates a spike of a neuron whose preferred location is at y, at time x. Note the enhanced and localized neural activity that is triggered by the cue stimulus and
persists during the delay period. The population firing profile, averaged over the delay period, is shown on the right. (B) Color-coded spatiotemporal activity pattern (see Materials and
Methods). (C) Same as (B), with less specific cue stimulation (5-fold increase in cue width). The network reaches a bump state with the same width as in (B) during the delay. In
these simulations, inhibitory interneurons (not shown) display a spontaneous activity rate of 9 Hz and an increased delay activity rate of 13 Hz.
0.381 nS (pyramid-to-pyramid), GEI = 0.292 nS (pyramid-to-interneuron);
inhibitory synaptic conductances are GIE = 1.336 nS (interneuronto-pyramid), GII = 1.024 nS (interneuron-to-interneuron); the connectivity
footprint has characteristics σEE = 18° and J+EE = 1.62. Recurrent
conductances are scaled inversely proportionally to N when network size
is varied, to keep the total synaptic conductances unchanged. We also
performed simulations with a different parameter set (Figs 4, 8), referred
to as a ‘modulated’ parameter set. It has the same parameters as the
control, except for an enhancement in the recurrent conductances: 20%
increase for NMDAR-mediated synaptic transmission (GEE and GEI) and
40% increase for GA BA synapses (GIE and GII). In other simulations,
AMPAR-mediated synaptic transmission was introduced in the recurrent
connectivity (Fig. 6). For a 67% NMDA contribution to recurrent
excitatory charge entry at a holding potential of –65 mV (Fig. 6A) the
parameters are GEE,AMPA = 0.251 nS, GEE,NMDA = 0.274 nS, GEI,AMPA = 0.192
nS, and GEI,NMDA = 0.212 nS. For a 50% NMDA contribution to recurrent
912 A Cortical Model of Spatial Working Memory • Compte et al.
connections at a holding potential of –65 mV (Fig. 6C), the parameters are
GEE,AMPA = 0.393 nS, GEE,NMDA = 0.214 nS, GEI,AMPA = 0.304 nS, and GEI,NMDA
= 0.164 nS.
The simulation protocol was chosen to mimic the protocol used in
the experiment of Funahashi et al. (Funahashi et al., 1989). In that
experiment, monkeys were trained to fixate a central spot during a brief
presentation (0.5 s) of a peripheral cue and throughout a subsequent
delay period (1–6 s), and then to make a saccadic eye movement to where
the cue had been presented in order to obtain a reward. In our
simulations, cue presentation to the network is modeled through
selective transient current injection to pyramidal cells whose preferred
cues are close to the stimulus. During the delay period, all selective
external currents are absent. After the end of the delay period, we model
the effect of the motor response and reward on the network by a transient
nonspecific current injection to all neurons. In several simulations, we
tested the inf luence of distractors on the network dynamics. Distractors
are modeled as a cue stimulus (same strength, same duration) but at a
different location relative to the cue stimulus.
To visualize network activity, pseudo-color spatiotemporal firing
patterns were calculated. A spike time rastergram for all pyramidal
neurons (or interneurons) is smoothed with a sliding window both in
time (500 ms in Figs 2 and 7, 10 ms in Fig. 6A,C, 5 ms in Fig. 6B, and 250
ms in Fig. 8) and along the neuron population (15 neurons in all figures
except Fig. 6, where it is 125 neurons). The resulting firing rate is color
encoded using the Matlab package. The population vector (Georgopoulos
et al., 1986) was used to estimate the evolution of the peak location of the
bump state (see Fig. 5). To compute the population vector during a given
time interval, we first compute a vector for each pyramidal cell, with
direction given by the preferred direction of that cell and the amplitude
proportional to the firing rate of the cell during the corresponding time
interval. The population vector is then given by the sum of all individual
vectors. Its angle with respect to a reference frame is a measure of the
stored positional cue in the corresponding time interval. It is a simple and
convenient method to estimate the peak of the activity profile at a given
time. In Figure 8 a maximum likelihood estimator was used to assess the
memorized angle at a given time (angles θ1 and θ2 in Fig. 8). The population activity profile before the distractor was fitted to the population
profile after the distractor. This method picks the position of the most
salient bump present in the profile in contrast to the population vector,
which computes the mean position of all bumps in the profile. ‘Local field
potentials’ (see Fig. 6) were computed by averaging the synaptic variable
sAMPA across all the pyramidal neurons at each time step.
The integration method used is a second-order Runge–Kutta algorithm
with the firing time interpolation scheme (Hansel et al., 1998b) and a
time step of ∆t = 0.02 ms. The code for the simulations has been written
in C++. When run on a Linux 550 MHz Pentium III PC, a 6 s trial with 2048
pyramidal neurons and 512 interneurons typically takes 2 h to complete.
Results
Persistent Activity and Memory Fields
Our network model simulation used the protocol of the
experiment of Funahashi et al. (Funahashi et al., 1989),
consisting of a cue presentation (C) followed by a delay period
(D) then a response period (R) (see Materials and Methods
for details). The network activity during any given trial was
monitored by plotting its spatiotemporal firing pattern. Figure
2A,B shows two different ways of showing the temporal
evolution of network activity. In both plots, the abscissa
represents time, while the ordinate represents pyramidal
neurons arranged according to their preferred cue directions. In
Figure 2A, spikes of all pyramidal neurons are shown in a
rastergram. In Figure 2B, spatiotemporal activity is smoothed
(see Materials and Methods) and shown in a continuous and
color-coded map. The main features of network activity can be
read out from these graphs from left to right. First, before cue
presentation, neurons show spontaneous activity at a few spikes
per second. This activity is uniform in space: the network
is untuned. Such a low spontaneous activity is an emergent
property of the network. It is achieved through a combination of
suprathreshold external inputs representing background activity
in other brain areas, and of a strong feedback inhibition in the
network.
Second, during the cue period (C), a pattern of increased
activity develops around the location of the cue (180°). This
increased activity is due to the external input to the
subpopulation of neurons with preferred cues closest to the cue
stimulus (approximately those with preferred cues between
162° and 198°, see Materials and Methods).
Third, in the delay period (D), the network initially localized
response widens and stabilizes. The elevated persistent activity
remains restricted to a selective neural subpopulation throughout the delay period. This is quantified by the peaked network
profile of the averaged delay-period activity (right panel in
Fig. 2A). The enhanced persistent rates (∼20 Hz) are achieved
through the strong excitatory feedback between cells sharing
similar tuning properties. In Figure 2C, the same simulation is
repeated, but with a more broadly tuned cue stimulus (cells
between 90° and 270° are activated by the stimulus). Thus, the
network response during the cue period is more widespread.
However, the network persistent activity eventually evolves to
the same profile during the delay period as with a more specific
cue stimulation (Fig. 2B). Therefore, the tuned persistent activity
profile is independent of the precise shape (or intensity) of the
cue stimulus. Such a ‘bump state’ is an attractor of the network
dynamics.
Finally, during the response period (R), a transient and overall
increase of external inputs to the whole network leads to a
transient increase of neuronal firing, which turns off the
persistent activity (Funahashi et al., 1991; Goldman-Rakic et al.,
1990). This ‘switching off’ of persistent activity by excitation is
due to the strong inhibitory feedback. A global excitatory drive
to the network increases the firing rate of inhibitory cells in a
way that is strong enough to effectively wipe out persistent
activity and refresh the short-term memory.
An example of a single neuron's selective persistent activity is
shown in Figure 3 for a pyramidal cell with preferred cue at
260°. During a delayed-response simulation in which the cue
location was 270°, the spike trains were recorded for several
trials (Fig. 3A). The cell shows a low rate (3.5 Hz) of spontaneous
activity. In response to a transient cue at 270° (250 ms), the cell
displays an enhanced persistent activity during the delay period
(8.75 s). Both spontaneous and delay-period firing activities are
quite irregular in time (Fig. 3A). The cell is switched back to the
spontaneous state during the response period (250 ms). With
eight cue presentations, the average firing rate of the neuron’s
persistent activity for each cue is computed and the resulting
tuning curve is shown in Fig. 3B. The persistent activity is tuned
to a memor y field around 270°. Note that the maximum
persistent activity rate is ∼20 Hz, within the physiological range
of PFC neurons. Moreover, the firing rate of delay period activity
for a non preferred cue is lower than the spontaneous rate, as is
often obser ved experimentally (Funahashi et al., 1989). The
tuning curve can be fitted by a Gaussian function. It is
significantly broader (with a width of ∼40°) than the width of the
recurrent excitator y connectivity (18°, see Materials and
Methods). The width of the tuning curve (or the size of the
neuron’s memory field) depends also on a variety of network
parameters, such as the relative strengths of recurrent synaptic
excitation and inhibition, as we shall see below.
The persistent activity of a single neuron is sustained by
synaptic excitation from the rest of the network. To dissect various contributions to the synaptic drive to a cell, we calculated
separately the components of the synaptic inputs to the cell
during both spontaneous state and delay period (Fig. 3C). The
time-average over the delay period of the different types of
synaptic inputs to the cell (external excitatory, recurrent
excitatory and recurrent inhibitory inputs) are plotted as a
function of the cue stimulus. Several important features of the
network activity can be seen from the graph. It shows that the
overall recurrent (excitatory plus inhibitory) input from the
other cells in the network is negative, so that the net effect is
hyperpolarizing, and the neuron is restrained from firing at the
high rates that would otherwise be imposed by external inputs
alone. This is a consequence of the inhibition dominance of the
recurrent interactions, which is crucial to the network function.
Cerebral Cortex Sep 2000, V 10 N 9 913
Another important point can be made from Figure 3C by
comparing the persistent activity state with the spontaneous
state. Even though there is a significant increase in both
excitatory and inhibitory recurrent currents in the persistent
activity state, the summated total recurrent input remains
approximately unchanged with respect to the spontaneous state.
Thus, in the present network, excitation and inhibition balance
each other dynamically. A balance between excitation and
inhibition has also been suggested to account for the irregularity
of interspike intervals of cortical cells in vivo (Shadlen and
Newsome, 1994; Tsodyks and Sejnowski, 1995; Amit and
Brunel, 1997; van Vreeswijk and Sompolinsky, 1998). For cues
within the neuron’s memory field, neighboring cells with similar
preferred cues show enhanced firing and send increased lateral
excitation to each other, so that the total recurrent input to the
cell is higher than during spontaneous activity, leading to an
enhanced persistent activity. On the other hand, when the cue
location is very different from the preferred cue, cells with
enhanced persistent activity are far away from (and thus send
little excitation to) the recorded cell, and the total recurrent
input shows actually a slight decrease during the delay period,
which explains why the firing rate is lower than spontaneous
activity in that situation (Fig. 3B).
As mentioned above, the size of the memory field depends on
the interplay between recurrent excitation and inhibition.
Memory fields are thus under modulatory control of various
neurotransmitters via their action on synaptic transmissions. In
particular, a concomitant enhancement of recurrent synaptic
excitation (20%) and inhibition (40%) (modulated parameter set,
see Materials and Methods) leads to a sharper tuning of persistent
activity (in Fig. 4A, the width of the tuning curve is 30°.
Compare with 40° in Fig. 3). Stronger inhibition reduces the
spontaneous activity, whereas stronger excitation leads to a
higher mnemonic activity for the preferred cue, thereby
increasing the separation between the firing rates of the two
states (the signal-to-noise ratio). We show in Figure 4A the rastergrams of a pyramidal neuron with a preferred cue at 270° for
eight cue stimuli. For comparison, the data from a neuron in the
principal sulcus recorded by Funahashi et al. (Funahashi et al.,
1989, Figs 3 and 9) is plotted in Figure 4C. Note the similarities
between the simulated cell and the real cell. Indeed, both cells
show a low spontaneous activity, a cue-selective delay activity
after stimulus presentation, a high degree of variability of spike
trains during both spontaneous and persistent states, and a
transient increase in the firing rate during the response period
before the cell returns to its spontaneous state. Activity during
the cue period is controlled by the intensity of the external
stimulation during that period and it is not directly related to the
delay activity, which is intrinsically set by the network synaptic
conductances. Finally, the tuning curves of both simulated and
real cells during the delay period show comparable shape and
rates (Fig. 4B,D respectively).
Random Drift of Memory
In the model, a network persistent activity can be peaked at an
angle any where between 0° and 360°, which encodes the
memory of a cue stimulus in a graded fashion. Thus, there is a
continuum of such structured activity profiles (‘bump states’),
which is realized by the circular symmetry of the network. A
particular bump state is selected by the cue during the stimulus
presentation. However, after the cue is withdrawn, no external
input is present to constrain the peak's location of the network
activity profile during the delay period. This raises the question
914 A Cortical Model of Spatial Working Memory • Compte et al.
Figure 3. Synaptic mechanisms underlying spontaneous and persistent activity
(‘control’ parameter set, see Materials and Methods). (A) Rastergram and average
discharge rate vs time of a cell in trials in which a cue is shown close to the preferred
angle of the cell. (B) Tuning curve of the cell in the delay period. The standard deviation
of the Gaussian fit is 40°. (C) Components of the synaptic inputs of the cell. The shaded
area shows the average inputs during spontaneous activity. To the right, we show the
average synaptic components of the cell as a function of cue position: recurrent
excitatory, recurrent inhibitory and external excitatory (labelled ‘external’). The sum of
both recurrent inputs is labelled ‘total recurrent’ and the sum of all independent inputs
is labelled ‘total’. Depolarizing inputs are positive and hyperpolarizing inputs negative.
Note the increase in both recurrent excitatory and inhibitory inputs during the delay.
Because of the balance between excitation and inhibition, the sum of the two (total
recurrent) remains close to the level of the spontaneous state.
of the stability of one particular bump against random
f luctuations that can move it to another adjacent bump, in which
case the memory of the cue location would be lost.
The simulation of Figure 5 shows clearly that the bump, once
elicited by a cue, is not completely stationary. Rather, it slowly
Figure 4. Single cell recording in experiment (Funahashi et al., 1989) and in the simulation reveals directional delay period activity. (A,B) Network simulation with the modulated
parameter set (see Materials and Methods); (C,D) Experiment of Funahashi et al. [(Funahashi et al., 1989), see their Figs 3 and 9]. Each rastergram represents the response of the cell
when the cue was shown in one of the eight locations indicated in the center diagram. Both cells respond vigorously in the delay only for one direction (270°), and are suppressed
relative to inter-trial spontaneous activity in the upper visual field. The delay period tuning curves (B,D) show the average discharge rate during the delay period (circles), together with
a Gaussian fit of the data. The horizontal line indicates average inter-trial spontaneous activity. Note the similarity between experiment and simulation.
drifts in a seemingly random fashion. Such a drift is due to the
random inputs that the network continuously receives from
outside. This random bombardment has a small effect on the
bump location, so that even though the shape of the bump is
stable, its location is only marginally stable as a result of the
translational invariance along the circle. To quantify this drift
behavior, we have estimated the instantaneous location of the
bump (the peak of the network activity profile) using the
population vector (see Materials and Methods). The time evolution of the population vector is shown for different trials and
network sizes in Figure 5. For a given network size, the
population vector drifts away in any single trial from the cue
location during the delay period, indicating a slow deterioration
of memory for the cue location. Note that the network has equal
probabilities of drifting up and down, due to the circular
symmetry (Fig. 5A). The three panels in Figure 5A clearly show
Cerebral Cortex Sep 2000, V 10 N 9 915
Figure 5. The network pattern of persistent activity drifts randomly in time due to noise, but memory storage is robust in large networks and weaker recurrent synaptic connections.
(A) Population vector position versus time for different runs and different network sizes. (B) Variance of the population vector position around the initial stimulation point averaged
across trials and plotted versus time for each of the three network sizes studied. Note the linear trend, similar to a diffusion process.
that the drift effect is smaller for larger network sizes, indicating
that the memory of the cue location is more robust with a larger
neural population in the network. The variance of the population vector as a function of time is plotted for different network
sizes in Figure 5B, showing an approximate linear trend. This
linear trend is consistent with a diffusion process (Berg, 1983).
The figure shows also that the slope of the variance dramatically
decreases with network size. Indeed, after a 4 s delay, the
location has drifted on average by 20° in a network of 1024
neurons; by ∼15° in a network of 2048 neurons; and by <10° in
a network of 4096 neurons. Further simulations with the
modulated parameter set of Figure 4A showed a remarkably
smaller degree of drift at each network size compared to Figure
5 (data not shown), indicating that the memory drift can be
controlled by neuromodulation of recurrent synapses.
Stability, Synchrony and the NMDA to AMPA Ratio
As can be seen in Figure 2A, neural discharges appear quite
asynchronous both during the spontaneous state and the delay
period. The lack of synchronicity is due to the predominance of
NMDA R-mediated transmission at the recurrent excitatory
synapses. To show this, we performed simulations with different
relative contributions of the A MPA R and NMDAR to the
recurrent synaptic excitation. This was done by var ying the
contribution of the NMDAR to the total charge entry into a cell
by a unitary EPSC at recurrent connections. The neuronal
916 A Cortical Model of Spatial Working Memory • Compte et al.
firings are essentially asynchronous, as long as NMDAR currents
contribute at least 75% to the total charge entry mediated by
excitatory recurrent inputs (at a holding potential of –65 mV).
With less NMDA contribution, neurons become partially
synchronized, as shown in Figure 6A. On a large scale (Fig. 6A),
the structure of the network persistent activity profile remains
similar to that in Figure 2A. On a fine temporal scale, however
(Fig. 6B), the temporal structure of the network activity has
dramatically changed from asynchronous behavior to pronounced synchronized oscillations at ∼40 Hz (see power
spectrum in the right panel). These oscillations are due to the
fact that when the contribution of AMPAR channels to recurrent
connections becomes large, these synaptic inputs with a fast
time constant tend to produce surges of activity, that are later
dampened by the slower synaptic inhibition. Thus, an oscillatory
behavior emerges. The network behavior remains irregular due
to external noise. Another important characteristic of the network is that firing rates of persistent activity tend to be higher as
the NMDA contribution decreases. This can be explained by the
lack of saturation of the steady-state, AMPAR-mediated synaptic
response at physiological firing rates, while NMDARs saturate at
rather low presynaptic frequencies. For still smaller NMDA
contribution to total charge entry, oscillations become more
pronounced. Fluctuations in the network dynamics eventually
destroy persistent activity (Fig. 6C).
Therefore, our simulations show that (i) NMDA Rs are
Figure 6. A decrease of the NMDAR channel contribution to recurrent synapses gives rise to oscillations in the delay period. (A) Network spatiotemporal firing pattern with moderate
AMPA component in recurrent interactions. Here the NMDAR channels contribute 67% to the total recurrent excitatory charge entry at a holding potential of –65 mV (NMDA:AMPA
ratio 0.038 in terms of the peak elicited EPSC). (B) 500 ms blowup of the upper panel to show the AMPA-induced oscillations, the local field potential and the membrane potential of
a single neuron. On the right is shown the power spectrum of the local field, demonstrating a large peak at ∼40 Hz. (C) Example of the disruptive effect of weak NMDA component in
the delay period activity of the network. The NMDA contribution to the recurrent excitatory charge entry is here 50% at a holding potential of –65 mV (NMDA:AMPA ratio 0.019 in
terms of peak EPSC). Note the eventual recruitment of the whole network that abolishes persistent activity. The network then goes back to the asynchronous spontaneous activity.
The local field shows a very strong oscillation before disruption of persistent activity.
necessary for sustaining a dynamically stable persistent activity;
and (ii) rhythmic oscillations in the gamma frequency range
(20–80 Hz) readily occur in such a strongly recurrent network, if
a substantial component of recurrent excitation is mediated by
A MPA receptors. This is a phenomenon produced by the
interplay between a fast positive feedback followed by a slower
negative feedback (Wang, 1999).
Tuning in Inhibitory Cells
Recently, recordings from putative inhibitory neurons in the PFC
have been reported in monkey experiments using the same
oculomotor delayed-response paradigm (Rao et al., 1999). It was
found that some PFC fast-spiking interneurons display tuned
persistent activity, similar to pyramidal cells. In our network
simulation of Figure 2, only excitatory cells show tuning to the
Cerebral Cortex Sep 2000, V 10 N 9 917
Figure 7. Memory fields of interneurons with structured pyramid-to-interneuron connections. Left panels show pyramidal neurons, and right panels show inhibitory neurons.
(A) Spatiotemporal firing patterns showing a ‘bump state’ during the delay period both in the pyramidal neurons and in the interneurons. (B) Tuning curves for a single pyramidal neuron
and a single neighboring interneuron (preferred cue 260°), tested with eight cues.
cue. This is due to the fact that in that simulation, only connections between excitatory cells were structured. Tuning in
inhibitory cells can be realized by introducing a structured
pyramid-to-interneuron connections. Network simulations were
performed with the parameter set of Figure 2, except for σEI =
18° and J+EI = 1.25. Results are shown in Figure 7. In that figure,
the population of inhibitory cells shows a peaked activity profile
(‘bump state’) during the delay period, similar to excitatory cells
(Fig. 7A). The tuning of inhibitory cells is less pronounced (Fig.
7B) because the pyramid-to-interneuron connectivity was
chosen to be more weak ly modulated than the pyramid-topyramid connectivity. Sharpening further the pyramid-to-interneuron connectivity results in higher inhibitory rates that
eventually destabilize persistent activity. Similar to the experimental data (Rao et al., 1999), in our model a pair of pyramidal
cell and interneuron show similar tuning if they are close to each
other; and orthogonal tuning if they are far apart.
Distractors
If information about a cue stimulus is required for a delayed
behavioral response, it is important that the memory of the cue
is maintained in spite of possible distraction inputs from outside
of the memory network. We tested the resistance of the network
memory storage to distractors presented as intervening stimuli
during the delay period. The simulation protocol in the presence
of distractors is shown in Figure 8. First, a cue stimulus is shown
at angle θS. It elicits a bump state that stores the memory of that
stimulus, up to a small drift. The bump state peaks at an angle θ1
918 A Cortical Model of Spatial Working Memory • Compte et al.
(close to θS) just prior to the presentation of a distractor at angle
θD. A distractor has identical characteristics as a cue stimulus (in
particular, it has the same intensity and duration), except that
it is presented at a different location and during the delay period.
We then measure the effect of the distractor by measuring the
peak location of the bump state after distraction (angle θ2). The
effect of distraction is quantified by the difference in the peak
location of the bump state before and after the distractor, θ2 – θ1.
Distraction stimuli are presented at various cue positions, close
to or far away from the original cue, in separate trials.
We studied how the behavior of the network is affected by
distractors in the ‘control’ case (network parameters of Fig. 2),
and with a modulatory enhancement of both NMDA (by 20%)
and GABA (by 40%) recurrent synapses, resulting in an enhanced
‘signal-to-noise’ ratio (modulated parameter set as in Fig. 4A). We
stress that in all cases, cue and distractor stimulation amplitudes
were identical. If the stimulation amplitude is sufficiently large,
the distractor is powerful enough to overcome the intrinsic
dynamics of the recurrent circuit, and the network is always
perturbed to a location close to the intervening stimulus (see
sample trial in Fig. 8A, and red points in Fig. 8C). However, with
a lower stimulus intensity (blue points in Fig. 8C), or with an
enhanced signal-to-noise ratio (sample trial in Fig. 8B or orange
trace in Fig. 8D), the network was found to be much more
resistant to an intervening stimulus. If the distractor is close to
the initial cue, the amount of distraction increases approximately
linearly with the distance, reaching a maximum around θD – θS =
90°. At larger distances (if the distractor and the initial cue are
separated by >90°), the distraction becomes very small (<10°),
Figure 8. The network resists to distractors when the stimulus intensity is low. (A,B) Network spatiotemporal firing pattern The cue is presented initially for 250 ms at θS, triggering
a tuned persistent activity. After a 2.5 s delay, a distractor stimulus is presented at θD, with the same intensity and duration as the cue stimulus. The population vector is computed
in a window of 500 ms just before the distractor (θ1) and 500 ms after the distractor (θ2). (A) A case of complete distraction for the control network parameter set (see Materials and
Methods) and strong stimulation (200 pA). (B) A case of perfect robustness to distraction for the modulated parameter set (see Materials and Methods) and moderate stimulation
(100 pA). (C) Dependence of network distraction on the distance between the cue and distractor and on the stimulation intensity. The ‘distracted’ angle θ2 – θ1 is plotted versus
distraction angle θD – θS for several distractor cues. The dashed line indicates perfect distraction (as in A) while points on the x-axis show absence of distraction (as in B). Stimulation
intensity is 50 pA (red) and 200 pA (blue) (control parameter set). (D) Comparison between control and modulated cases for a given stimulation paradigm (250 ms duration, 120 pA
intensity). Modulation of both NMDAR- and GABAAR-mediated synaptic transmission enhances dramatically the network’s resistance to distractors, particularly at high distraction
angles. NE = 4096, NI = 1024.
which shows that the network is essentially unaffected by
distractors far from the cue location. The resistance to distractors
can be understood by the fact that inhibition is much stronger in
the persistent activity state. Thus, it is harder to elicit a new
bump during the delay period than from the spontaneous
activity state. This explains why in Figure 8B the distractor just
elicits a transient increase in cells that receive direct inputs from
the intervening stimulus. Inhibition dominance of the synaptic
circuitry underlies the network's ability to ignore distractors, as
long as the external inputs are not too strong to overrule the
recurrent network dynamics. This resistance can be facilitated
by an increased signal-to-noise ratio, which in our network can
be brought about by concomitant modulation of recurrent
conductances. On the other hand, if the inputs are very strong,
the network is no longer resistant to intervening stimuli. In this
case, the network can be reset by every new transient stimulus,
and retains a memor y of the last stimulus in the form of a
refreshed selective persistent activity state.
Cerebral Cortex Sep 2000, V 10 N 9 919
Discussion
We have used a recurrent cortical network model that incorporates physiological properties of cortical neurons and
synapses, to decipher the neuronal mechanisms underlying
persistent activity in a spatial working memory circuit. In the
paper we have focused on spatial working memory in PFC, in
order to compare the model with physiological data from behaving monkeys, and thus be able to draw specific experimental
predictions. However, we believe that the synaptic mechanisms
identified in this study could be applicable to other types of
mnemonic persistent activity observed in PFC as well as in other
cortical areas.
Neuronal Mechanisms of Spatial Working Memory
Since the emergence of persistent activity requires sufficiently
strong recurrent synaptic excitation, one may ask how a spontaneous activity state with low firing rates can be realized, and
how the firing rates of persistent activity can be controlled
within a physiological range (20–40 Hz), in spite of such an
explosive positive feedback. We found that the dynamic stability
of both states depends critically on the predominant contribution of NMDARs to the recurrent synaptic excitation, and
on a strong inhibition that overall dominates the recurrent
synaptic circuit. Strong recurrent excitation between nearby
cells (with similar preferred cues), in interplay with recurrent
inhibition, produces a structured network activity profile of
persistent activity, which gives rise to ‘memory fields’ in individual neurons. Neuronal firing properties in both spontaneous
and selective persistent states are found to be in agreement with
single-neuron recording data from the PFC of the behaving
monkey (Funahashi et al., 1989; Chafee and Goldman-Rakic,
1998; Rao et al., 1999).
The study of pattern formation in neural models has a
long histor y (Wilson and Cowan, 1972, 1973; A mari, 1977;
Ben-Yishai et al., 1995; Skaggs et al., 1995; Somers et al., 1995;
Tsodyks and Sejnowski, 1995; Redish et al., 1996; Seung, 1996;
Zhang, 1996; Bressloff and Coombes, 1998; Camperi and Wang,
1998; Hansel and Sompolinsky, 1998) [reviewed recently by
Ermentrout (Ermentrout, 1998)]. In most of these studies,
spatially tuned activity patterns (‘bump states’) appear through a
continuous (‘Turing’) bifurcation; therefore they do not coexist
with the resting state. On the other hand, to fulfil a working
memory function, a PFC network should display bistability (or
multistability) between the resting state and structured activity
states, so that the network can be switched on and off between
the two by transient inputs (Amit and Brunel, 1997; Camperi
and Wang, 1998). The main conceptual novelty of the present
work is to build a network of spiking neurons that shows
bistability between two different types of active states: a resting
state with spontaneous firing rates of a few Hertz, and a spatially
structured state with firing rates of ∼20–30 Hz (comparable to
the physiological data). This property is mainly brought about by
the dominance of recurrent synaptic inputs by the GABAergic
contribution; and the network is stabilized by NMDARs at the
recurrent synapses. Both features were not present in previous
pattern formation studies.
A Mechanism for Switching Off Working Memory
Persistent activity is usually turned off following a transient
increase of neuronal firing during the response period [see e.g.
Fig. 3 of (Funahashi et al., 1989), and Fig. 16 of (Goldman-Rakic
et al., 1990)]. Our simulations show that a simple way to turn
off persistent activity is to increase transiently the external
920 A Cortical Model of Spatial Working Memory • Compte et al.
excitatory inputs to a large neural population of the network.
These transient inputs increase the firing rates of pyramidal cells
as well as interneurons. The increase in recurrent inhibitory
inputs switches off the bump state. Such a mechanism is
plausible given the available data. However, our model does not
address the specific neuronal source of the input signal for
memory erasure.
In a model of one-population spiking neurons without noise,
Laing et al. also use an excitatory pulse to switch off a bump to a
silent state (Laing et al., 2000). However, this is achieved in
their network through a quite different mechanism, i.e. by
synchronizing all cells so that the persistent activity destabilizes.
Physiological data show that activity during the response
period in PFC has two distinct phases (Funahashi et al., 1991;
Rao et al., 1999). Earlier activity (in the ‘pre-saccadic’ period) is
primarily tuned to the direction of the cue, while later activity
(in the ‘post-saccadic’ period) is in many cases tuned to
the opposite direction (especially for interneurons). Our model
accounts for the tuning properties obser ved during the
pre-saccadic period, since the tuned network activity takes some
time, of the order a few hundred of milliseconds, to vanish. On
the other hand, it does not account for the inversion of tuning
reported in experiments during the post-saccadic period. A
detailed modeling of the PFC activity during the saccade is
outside the scope of the present paper.
Random Drift of Memory
Persistent network activity that encodes an analog quantity
typically displays random drifts in time, because the activity
pattern is marginally stable (Ben-Yishai et al., 1995; Seung, 1996;
Zhang, 1996; Lee et al., 1997; Camperi and Wang, 1998). This
has the consequence that the memory of the cue will become
less and less precise as time goes by. Our simulations show that
though this effect can be important in small networks, it
becomes less pronounced in large networks. However, these
simulations were performed under two assumptions. First, with
an increased network size the recurrent coupling is normalized
by the number of cells, so as to maintain a fixed average
recurrent drive to the cells. As a result, the signal-to-noise ratio of
the input to a cell decreases with the network size. This would
not be the case for a sparsely connected network where, when
network size is varied, both the number of synapses per cell and
the strength of each individual synapse could remain constant.
Second, we assumed that noise in the input is uncorrelated from
cell to cell. If significant correlations are present between noise
signals in different cells, drifts are likely to occur even in a very
large network.
The magnitude of random drifts in a realistic working
memory circuit storing an analog variable is therefore still an
open question. Our study predicts that, independently of the
amplitude of the random drift, the variance of the distance
between the bump location and the stimulus location increases
linearly with time, as for a diffusion process. This implies that, in
a visuospatial delayed-response task, the variance of the distance
between the cue and the eye position following the saccade to
the memorized cue position should increase linearly with the
delay time interval. In a psychophysical study using a visuospatial
delayed-response task, White et al. plotted the scatters of eye
positions following the saccade versus delay time in monkeys
[(White et al., 1994), see their Fig. 5B]. The data in this figure
(squared in order to get the saccade error variance) can be fitted
by a straight line, similarly to the drifting mechanism that occurs
in our model, for delay times up to 4 s. Similar data are also
available for humans (Ploner et al., 1998), showing also a linearly
increasing saccade error variance up to 20 s delay times. It is thus
possible that such a gradual loss of accuracy in memory-guided
saccade is a manifestation of slow random drifts of the persistent
activity in PFC during the delay period.
NMDA Contribution to Recurrent Synapses: Implications
for Synchronous Network Behavior and Stability of
Working Memory
Our simulations show that the network dynamics are critically
dependent on the ratio of NMDA R and A MPA R channels at
recurrent synapses. When NMDA R channels dominate, persistent activity is stable at physiological rates (20–40Hz), and
the network dynamics are essentially asynchronous. With a
substantial AMPA component of the recurrent excitation, the
network displays coherent oscillations; if the AMPAR-mediated
recurrent excitation is too large, persistent activity is abolished.
This result was initially obtained with a spatially unstructured
network model (Wang, 1999). Here, we found that the same
conclusion holds for a spatially structured network as well. Our
working memory model requires that at recurrent synapes the
NMDA receptors should contribute >65% of the charge entry
by a unitar y EPSC at –65 mV. However, the precise value of
the required NMDA:AMPA ratio is likely to depend on the details
of the model, as well as the type of neuron models (e.g.
integrate-and-fire model versus compartmental conductancebased model).
The relative contributions by NMDARs and AMPARs to charge
entry of a unitary EPSC remain unknown for intrinsic synapses
of the PFC. Estimates from other cortical areas vary considerably.
For example, the NMDA component contributes 17% to the EPSP
integral (at –60 mV) for pyramidal cells in layer 5 somatosensory
cortex (Markram et al., 1997), and 65% of EPSC’s charge entry
(at –65 mV) for hippocampal pyramidal cells of the young rat
(Spruston et al., 1995). At intrinsic synapses of the layer 4
somatosensory cortex, NMDA receptors contribute 39% to the
EPSP integral (at –60 mV) in the young rat (Feldmeyer et al.,
1999), and >90% of EPSC’s charge entry (at –70 mV) in the
mouse (Fleidervish et al., 1998). Further studies of this issue
would be worthwhile.
The crucial features of NMDA R-mediated transmission for
stable persistent activity in our model are its slow synaptic
kinetics [for stability with respect to synchronized oscillations
(Wang, 1999; Laing et al., 2000)] and its saturation properties
[for robust low persistent rates, see also (Wang, 1999)]. On the
other hand, the voltage-dependence of the NMDA conductance
due to magnesium block is not crucial here. However, the
voltage-gating of the NMDA current could conceivably contribute to selectivity of persistent activity in a neural assembly.
This is because during a cue presentation the cells that are tuned
to the cue stimulus are more active, and their membrane potential is more depolarized, than those that are not tuned to the cue.
Therefore, the NMDA conductance should be differentially
unblocked in those cells that are excited by the cue stimulus
(Lisman et al., 1998).
Thus, the model predicts that the long decay time constant of
NMDAR-mediated synaptic transmission is critically important to
the persistent activity underlying working memory function of
PFC. This conclusion is supported by behavioral experiments
with rats performing a spatial delayed alternation task, where it
was found that systemic administration (Verma and Moghaddam,
1996) or microinjection into the PFC (Romanides et al., 1999)
of NMDA R antagonists in PFC impaired working memory.
However, in these studies, pharmacological manipulation has not
been combined with physiological recordings from PFC
neurons. Thus, changes in the mnemonic neuronal dynamics
caused by the NMDA R blockade are presently unknown.
Furthermore, evidence suggests that dysfunction of NMDA Rmediated synaptic transmission may lead to working memory
deficits similar to those observed in schizophrenia (Javitt and
Zukin, 1991; Krystal et al., 1994; Akbarian et al., 1996). Our
model study identified a candidate mechanism through which
working memory relies on NMDARs at recurrent synapses of
PFC, namely asynchronous firing resulting in persistent activity
stability. Moreover, according to the hypothesis that dopamine
differentially modulates NMDAR-mediated synaptic transmission
(Cepeda et al., 1992), a malfunction of the dopaminergic inner vation of PFC would also give rise to working memory
deficits, as has been shown by many studies in humans and
animals (Sawaguchi et al., 1990; Sawaguchi and Goldman-Rakic,
1991; Goldman-Rakic, 1994; Okubo et al., 1997; Arnsten, 1998).
Tuning in Inhibitory Cells
Recently, Rao and co-workers reported memory fields in
interneurons as well as in pyramidal cells (Rao et al., 1999). In
our model, a structured connectivity from pyramidal cells to
interneurons leads to a persistent state with tuned interneurons
as well as pyramidal cells. This result suggests that the selectivity
of persistent activity in putative inhibitory neurons observed
experimentally (Rao et al., 1999) may be explained by a structured pyramid-to-interneuron connectivity that is similar to the
pyramid-to-pyramid connectivity. However, we have been
unable to stabilize a network state in which the tuning is
identical between interneurons and pyramidal cells. Thus, we
would predict that pyramidal cells are more sharply tuned than
interneurons in the delay period.
Maintaining Working Memory in the Face of Distractors
An important property of working memory is its ability to resist
distractions. Neurophysiological studies of working memory in
the associative cortex of monkeys have shown that delay activity
is typically resistant to distractors in the PFC (Miller et al., 1996),
though it is not in areas which are closer to primary sensory
areas such as PPC (Constantinidis and Steinmetz, 1996) or inferotemporal cortex (Miller et al., 1996). A main result of the present
study is that a network model of spatial working memory with
strong recurrent inhibition is intrinsically resistant to distractors,
provided stimulus intensities are low. On the other hand,
persistent activity is disrupted by distractors when stimuli are
strong. Moreover, the network is less distractable with enhanced
NMDAR-mediated recurrent excitation and feedback inhibition.
Thus, we propose two candidate factors that may explain
the areal differences observed with respect to response to
distractors. In areas close to primary sensory areas, stimulus
intensities are probably stronger, as indicated by the magnitude
of visual responses during cue presentation, and delay activity
would be easily disrupted by distractors. In the PFC, which is
further away from sensory areas, direct afferent inputs are likely
to be weaker, hence persistent activity of PFC neurons is more
resistant to distractors. Alternatively, the PFC circuit may be
uniquely equipped with an optimal balance between NMDARmediated excitation and recurrent inhibition, while other
cortical areas are not optimal in that respect. This would endow
the PFC with an exceptional ability to hold behaviorally relevant
information on-line, in spite of external distractions.
Cerebral Cortex Sep 2000, V 10 N 9 921
Experimentally Testable Predictions
The present work raises a number of mechanistic issues about
working memor y processes that could be addressed experimentally.
(i) In vitro slice experiments can be carried out to investigate
whether NMDARs indeed dominate recurrent synaptic excitation in PFC, as suggested by the model.
(ii) In experiments with behaving animals, a combination of
pharmacology with single-neuron recordings, similar to the
iontophoresis experiments of other workers (Williams and
Goldman-Rakic, 1995; Rao et al., 2000), would elucidate how
working memor y performance is affected by modulation or
blockade of NMDARs in PFC; and what are the concomitant
changes in the neuronal persistent activity.
(iii) A n open question is whether neuronal firings in a
persistent activity state during the delay period are asynchronous. A lternatively, neurons may be partially synchronized
and/or display coherent oscillations. This question can be
addressed with simultaneous recordings from multiple neurons,
and using local field recordings from the monkey PFC to probe
population activity in a delayed-response task. Moreover, we
predict that the propensity of a network to display coherent
oscillations is higher if the relative contribution of NMDA R
channels to recurrent excitation is smaller.
(iv) As mentioned above, memory-guided saccadic response
has been found to be less accurate with longer delay periods
(White et al., 1994; Ploner et al., 1998). It would be interesting
to study more systematically whether the loss of accuracy in the
saccade is correlated with slow random drifts of persistent
neuronal activity in the PFC during the delay period.
(v) Distractor experiments similar to those of Miller (Miller et
al., 1996) could be performed in combination with pharmacological manipulation of synaptic transmission. We predict that
a cooperative facilitation of recurrent inhibition and NMDARmediated recurrent excitation would enhance the network’s
ability to resist distractors and preserve the memory of behaviorally relevant information in spite of intervening stimuli.
Notes
This work was supported by NSF (IBN-9733006), the A.P. Sloan
Foundation, the W.M. Keck Foundation and CNRS. We thank J. Tegnér for
useful discussions.
Address correspondence to Xiao-Jing Wang, Volen Center for Complex Systems, MS 013, Brandeis University, 415 South Street, Waltham,
MA 02254–9110, USA. Email: [email protected]
References
Akbarian S, Sucher NJ, Bradley D, Tazzofoli A, Trinh D, Hetrick WP,
Potkin SG, Sandman C,A Bunney W E, Jones EG (1996) Selective
alterations in gene expression for NMDA receptor subunits in
prefrontal cortex of schizophrenics. J Neurosci 16:19–30.
Amari, S (1977) Dynamics of pattern formation in lateral-inhibition type
neural fields. Biol Cybernet 27:77–87.
Amit DJ (1995) The Hebbian paradigm reintegrated: local reverberations
as internal representations. Behav Brain Sci 18:617.
Amit DJ, Brunel N (1997) Model of global spontaneous activity and local
structured activity during delay periods in the cerebral cortex. Cereb
Cortex 7:237–252.
Amit D, Brunel N, Tsodyks MV (1994) Correlations of cortical Hebbian
reverberations: experiment vs theory. J Neurosci 14:6435–6445.
Arnsten AFT (1998) Catecholamine modulation of prefrontal cortical
cognitive function. Trends Cogn Sci 2:436–447.
Ben-Yishai R, Lev Bar-Or R, Sompolinsky H (1995) Theory of orientation
tuning in visual cortex. Proc Natl Acad Sci USA 92:3844–3848.
Berg HC (1983) Random walks in biology. Princeton, NJ: Princeton
University Press.
Bressloff PC, Coombes S (1998) Spike train dynamics underlying pattern
922 A Cortical Model of Spatial Working Memory • Compte et al.
formation in integrate-and-fire oscillator networks. Phys Rev Lett
81:2384–2387.
Camperi M, Wang X-J (1998) A model of visuospatial short-term memory
in prefrontal cortex: recurrent network and cellular bistability. J
Comput Neurosci 5:383–405.
Cepeda C, Radisavljevic Z, Peacock W, Levine MS, NA Buchwald (1992)
Differential modulation by dopamine of responses evoked by
excitatory amino acids in human cortex. Synapse 11:330–341.
Chafee MV, Goldman-Rakic PS (1998) Neuronal activity in macaque
prefrontal area 8a and posterior parietal area 7ip related to memory
guided saccades. J Neurophysiol 79:2919–2940.
Colby CL, Duhamel JR, Goldberg ME (1996) Visual, presaccadic, and
cognitive activation of single neurons in monkey lateral intraparietal
area. J Neurophysiol 76:2841–2852.
Constantinidis C, Steinmetz MA (1996) Neuronal activity in posterior
parietal area 7a during the delay periods of a spatial memory task. J
Neurophysiol 76:1352–1355.
Constantinidis C, Franowicz MN, Goldman-Rakic PS (1999) Multiple
electrode analysis of local circuitry in the primate prefrontal cortex
during spatial working memory. Soc Neurosci Abstr 25:44.1.
Courtney SM, Petit L, Maisog JM, Ungerleider LG, Haxby JV (1998) An
area specialized for spatial working memory in human frontal cortex.
Science 279:1347–1351.
Douglas RJ, Koch C, Mahowald M, Martin KM, Suarez HH (1995)
Recurrent excitation in neocortical circuits. Science 269:981–985.
Durstewitz D, Kelc M, Güntürkun O (1999) A neurocomputational theory
of the dopaminergic modulation of working memory functions. J
Neurosci 19:2807–2822.
Ermentrout GB (1998) Neural networks as spatio-temporal patternforming systems. Rep Progr Phys 61:353–430.
Feldmeyer D, Egger V, Lubke J, Sakmann B (1999) Reliable synaptic
connections between pairs of excitatory layer 4 neurones within a
single ‘barrel’ of developing rat somatosensory corte. J Physiol
521:169–190.
Fleidervish IA, Binshtok AM, Gutnick MJ (1998) Functionally distinct
NMDA receptors mediate horizontal connectivity within layer 4 of
mouse barrel cortex. Neuron 21:1055–1065.
Funahashi S, Bruce CJ, Goldman-Rakic PS (1989) Mnemonic coding of
visual space in the monkey’s dorsolateral prefrontal cortex. J
Neurophysiol 61:331–349.
Funahashi S, Bruce CJ, Goldman-Rakic PS (1991) Neuronal activity
related to saccadic eye movements in the monkey’s dorsolateral
prefrontal cortex. J Neurophysiol 65:1464–1483.
Fuster JM (1973) Unit activity in prefrontal cortex during delayedresponse performance: neuronal correlates of transient memory. J
Neurophysiol 36:61–78.
Fuster JM (1988) The prefrontal cortex. New York: Raven Press.
Georgopoulos AP, Schwartz AB, Kettner RE (1986) Neuronal population
coding of movement direction. Science 233:1416–1419.
Gnadt JW, Andersen R A (1988) Memory related motor planning activity
in posterior parietal cortex of macaque. Exp Brain Res 70:216–220.
Goldman-Rakic PS (1987) Circuitry of primate prefrontal cortex and
regulation of behavior by representational memory. In: Handbook of
physiology, vol. V: The nervous system (Plum F, Mountcastle V, eds),
chap. 9, pp. 373–417. Bethesda, MD: American Physiological Society.
Goldman-Rakic PS (1994) Working memory dysfunction in schizophrenia. J Neuropsychol Clin Neurosci 6:348–357.
Goldman-Rakic PS (1995) Cellular basis of working memory. Neuron
14:477–485.
Goldman-Rakic PS, Funahashi S, Bruce CJ (1990) Neocortical memory
circuits. In: Cold Spring Harbor Symposia on Quantitative Biology, vol.
LV, pp. 1025–1038.
González-Burgos G, Barrionuevo G, Lewis DA (2000) Horizontal synaptic
connections in monkey prefrontal cortex: an in vitro electrophysiological study. Cereb Cortex 10:82–92.
Hansel D, Sompolinsky H (1998) Modeling feature selectivity in local
cortical circuits. In: Methods in neuronal modeling, 2nd edn (Koch C,
Segev I, eds). Cambridge, MA: MIT Press.
Hansel D, Mato G, Meunier C, Neltner (1998) On numerical simulations of
integrate-and-fire neural networks. Neural Comput 10:467–483.
Hebb DO (1949) Organization of behavior. New York: Wiley.
Hestrin S, Sah P, Nicoll R (1990) Mechanisms generating the time course
of dual component excitator y synaptic currents recorded in
hippocampal slices. Neuron 5:247–253.
Jahr CE, Stevens CF (1990) Voltage dependence of NMDA-activated
macroscopic conductances predicted by single-channel kinetics. J
Neurosci 10:3178–3182.
Javitt DC, Zukin SR (1991) Recent advances in the phencyclidine model
of schizophrenia. Am J Psychiat 148:1301–1308.
Kritzer MF, Goldman-Rakic PS (1995) Intrinsic circuit organization of the
major layers and sublayers of the dorsolateral prefrontal cortex in the
rhesus monkey. J Comp Neurol 359:131–143.
Krystal JH, Karper LP, Seibyl JP, Freeman GK, Delaney R, Bremner JD,
Heninger GR, Bowers MB, Charney DS (1994) Subanesthetic effects of
the noncompetitive NMDA antagonist, ketamine, in humans. Psychotomimetic, perceptual, cognitive, and neuroendocrine responses.
Arch Gen Psychiat 51:199–214.
Laing CR, Chow CC, Ermentrout GB (2000) Stationary bumps in
networks of spiking neurons. Preprint, University of Pittsburgh.
Lee DD, Reis BY, Seung HS, Tank DW (1997) Nonlinear network models
of the oculomotor integrator. In: Computational neuroscience (Bower
J, ed.). New York: Plenum Press.
Levitt B, Lewis DA, Yoshioka T, Lund J (1993) Topography of pyramidal
neuron intrinsic connections in macaque monkey prefrontal cortex
(areas 9 and 46). J Comp Neurol 338:360–376.
Lisman JE, Fellous J-M, Wang X-J (1998) A role for NMDA-receptor
channels in working memory. Nature Neurosci 1:273–275.
Markram H, Lubke J, Frotscher M, Roth A, Sakmann B (1997) Physiology
and anatomy of synaptic connections between thick tufted pyramidal
neurones in the developing rat neocortex. J Physiol 500:409–440.
McCarthy G, Blamire A M, Puce A, Nobre AC, Bloch G, Hyder F,
Goldman-Rakic PS, Shulman RG (1994) Functional magnetic resonance imaging of human prefrontal cortex activation during a spatial
working memory task. Proc Natl Acad Sci USA 91:8690–8694.
McCormick D, Connors B, Lighthall J, Prince D (1985) Comparative
electrophysiology of pyramidal and sparsely spiny stellate neurons in
the neocortex. J Neurophysiol 54:782–806.
Miller EK, Erickson CA, Desimone R (1996) Neural mechanisms of visual
working memory in prefrontal cortex of the macaque. J Neurosci
16:5154–5167.
Moody SL, Wise SP, di Pellegrino G, Zipser D (1998) A model that
accounts for activity in primate frontal cortex during a delayed
matching-to-sample task. J Neurosci 18:399–410.
Mountcastle VB (1997) The cortical organization of the neocortex. Brain
120:701–722.
Niki H, Watanabe M (1976) Prefrontal unit activity and delayed response:
relation to cue location versus direction of response. Brain Res
105:79–88.
Okubo Y, Suhara T, Suzuki K, Kobayashi K, Inoue O, Terasaki O, Someya
Y, Sassa T, Sudo Y, Matsushima E, Iyo M, Tateno Y, Toru M (1997)
Decreased prefrontal dopamine D1 receptors in schizophrenia
revealed by PET. Nature 385:634–636.
Ó Scalaidhe SP, Goldman-Rakic PS (1999) Functional organization of
prefrontal cortical columns in the macaque. Soc Neurosci Abstr
25:620.2.
Ploner CJ, Gaymard B, Rivaud S, Agid Y, Pierrot-Deseilligny C (1998)
Temporal limits of spatial working memory in humans. Eur J Neurosci
10:794–797.
Rainer G, Assad WF, Miller EK (1998) Memory fields of neurons in the
primate prefrontal cortex. Proc Natl Acad Sci USA 95:15008–15013.
Rao SG, Williams GV, Goldman-Rakic PS (1999) Isodirectional tuning of
adjacent interneurons and pyramidal cells during working memory:
evidence for microcolumnar organization in PFC. J Neurophysiol
81:1903–1916.
Rao SG, Williams GV, Goldman-Rakic PS 2000 Destruction and creation of
spatial tuning by disinhibition: GABAA blockade of prefrontal cortical
neurons engaged by working memory. J Neurosci 20:485–494.
Redish AD, Elga AN, Touretzky DS (1996) A coupled attractor model of
the rodent head direction system. Network 7:671–685.
Romanides AJ, Duff y P, Kalivas PW (1999) Glutamatergic and dopaminergic afferents to the prefrontal cortex regulate spatial working
memory in rats. Neuroscience 92:97–106.
Salin PA, Prince DA (1996) Spontaneous GA BAA receptor mediated
inhibitory currents in adult rat somatosensory cortex. J Neurophysiol
75:1573–1588.
Sarnthein J, Petsche H, Rappelsberger P, Shaw GL, von Stein A (1998)
Synchronization between prefrontal and posterior association cortex
during human working memor y. Proc Natl Acad Sci USA 95:
7092–7096.
Sawaguchi T, Goldman-Rakic PS (1991) D1 dopamine receptors in
prefrontal cortex: involvement in working memory. Science 251:
947–950.
Sawaguchi T, Yamane I (1999) Properties of delay-period neuronal
activity in the monkey dorsolateral prefrontal cortex during a spatial
delayed matching-to-sample task. J Neurophysiol 82:2070–2080.
Sawaguchi T, Matsumara M, Kubota K (1990) Catecholaminergic effects
on neuronal activity related to a delayed response task in monkey
prefrontal cortex. J Neurophysiol 63:1385–1400.
Seung HS (1996) How the brain keeps the eyes still. Proc Natl Acad Sci
USA 93:13339–13344.
Shadlen MN, Newsome WT (1994) Noise, neural codes and cortical
organization. Curr Opin Neurobiol 4:569.
Skaggs WE, Knierim JJ, Kudrimoti HS, McNaughton BL (1997) A model of
the neural basis of the rat’s sense of direction. In: Advances in neural
information processing systems 7 (Tesauro G, Touretzky DS, Leen TK,
eds). Cambridge, MA: MIT Press.
Somers DC, Nelson SB, Sur M (1995) An emergent model of orientation
selectivity in cat visual cortical simple cells. J Neurosci 15:5448–5465.
Spruston N, Jonas P, Sakmann B (1995) Dendritic glutamate receptor
channel in rat hippocampal CA3 and CA1 pyramidal neurons. J
Physiol 482:325–352.
Troyer TW, Miller KD (1997) Physiological gain leads to high ISI
variability in a simple model of a cortical regular spiking cell. Neural
Comput 9:971–983.
Tsodyks MV, Sejnowski T (1995) Rapid state switching in balanced
cortical network models. Network 6:111–124.
Tuckwell HC (1988) Introduction to theoretical neurobiology. Cambridge: Cambridge University Press.
van Vreeswijk C, H Sompolinsky (1998) Chaotic balanced state in a model
of cortical circuits. Neural Comput 10:1321–1371.
Verma A, Moghaddam B (1996) NMDA receptor antagonists impair
prefrontal cortex function as assessed via spatial delayed alternation performance in rats: modulation by dopamine. J Neurosci
16:373–379.
Wang X-J (1999) Synaptic basis of cortical persistent activity: the
importance of NMDA receptors to working memory. J Neurosci
19:9587–9603.
White JM, Sparks DL, Stanford TR (1994) Saccades to remembered target
locations: and analysis of systematic and variable errors. Vis Res
34:79–92.
Williams GV and Goldman-Rakic PS (1995) Modulation of memory fields
by dopamine D1 receptors in prefrontal cortex. Nature 376: 572–575.
Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in
localized populations of model neurons. Biophys J 12:1–24.
Wilson HR, Cowan JD (1973) A mathematical theory of the functional
dynamics of cortical and thalamic nervous tissue. Kybernetik
13:55–80.
Xiang Z, Huguenard JR, Prince DA (1998) GABAA receptor mediated
currents in interneurons and pyramidal cells of rat visual cortex. J
Physiol 506:715–730.
Zarahn E, Aguirre GK, D’Esposito M (1999) Temporal isolation of the
neural correlates of spatial mnemonic processing with fMRI. Brain Res
Cogn Brain Res 7:255–268.
Zhang K (1996) Representation of spatial orientation by the intrinsic
dynamics of the head-direction cell ensembles: a theory. J Neurosci
16:2112–2126.
Zipser D, Kehoe B, Littlewort G, Fuster J (1993) A spiking network model
of short-term active memory. J Neurosci 13:3406–3420.
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