Download computational and in vitro studies of persistent activity

Neuroscience 139 (2006) 135–151
COMPUTATIONAL AND IN VITRO STUDIES OF PERSISTENT
ACTIVITY: EDGING TOWARDS CELLULAR AND SYNAPTIC
MECHANISMS OF WORKING MEMORY
ALBERT COMPTE*
ical constraints. Within the attractor framework, a memorycapable system (for instance, a prefrontal neuron, or circuit) is essentially a multistable system: one system that
can remain stably in a collection of possible states (for
instance firing at 5 Hz, or firing at 25 Hz). These stable
states are called fixed-point attractors because small perturbations to the system, while it is in these states, are
followed by restorative forces that bring the system back to
them. Whether the system settles in one or the other
attractor depends uniquely on where external influences
(for instance sensory information) transiently set the system to be, and therefore the readout of this attractor is
indicative of the nature of those extinct external influences:
the system remembers previous external information.
Thus, in a working memory task the brain is conceptually a
multistable system being switched by the sensory cues
across various stable “states,” or attractors, that are univocally associated with the sensory stimulus parameters, or a
categorization thereof. This idea is schematically represented in Fig. 1, where a ball representing the stimulus
falls onto a surface or energy landscape, which represents
the dynamical properties of our system. The ball hits the
surface and then it rolls downhill until it settles in a stable
configuration (attractor). If at that point we were to guess,
just from that final configuration, the original location of the
ball, we would make more or less accurate guesses only if
our surface were of the multistable kind (Fig. 1C–E). A
monostable system as in Fig. 1B cannot serve a mnemonic
purpose.
The conceptualization in terms of attractor dynamics
spurs the distinction between two groups of persistent
activity systems, one where the memories being encoded
are discrete and one where the attractor states form a
continuum, a “line attractor.” In Fig. 1 panels C and D
would correspond to discrete persistent activity systems:
the item encoded comes from a finite family of possible
memories. If a stimulus is presented to the system that
does not correspond to any of the attractors, the system
will enter the attractor that most closely matches the stimulus, thus performing a categorization of the stimuli (panel
C in Fig. 1, for instance, classifies any possible location
along the bar above into three classes: left, middle, right).
In contrast, panel E in Fig. 1 corresponds to a line attractor:
any possible stimulus is faithfully kept in the system’s
attractor memory. As it turns out, discrete and continuous
attractor models of persistent activity share many cellular
and synaptic mechanisms, but continuous models have
some more stringent requirements regarding stability and
robustness (intuitively, panel E in Fig. 1 needs to be per-
Instituto de Neurociencias de Alicante, Universidad Miguel HernándezConsejo Superior de Investigaciones Científicas, 03550 Sant Joan
d’Alacant, Spain
Abstract—Persistent neural activity selective to features of
an extinct stimulus has been identified as the neural correlate
of working memory processes. The precise nature of the
physiological substrate for this self-sustained activity is still
unknown. In the last few years, this problem has gathered
experimental together with computational neuroscientists in
a quest to identify the cellular and network mechanisms
involved. I introduce here the attractor theory framework
within which current persistent activity computational models are built, and I then review the main physiological mechanisms that have been linked thereby to persistent activity
and working memory. Open computational and physiological
issues with these models are discussed, together with their
potential experimental validation in current in vitro models of
persistent activity. © 2005 Published by Elsevier Ltd on behalf of IBRO.
Key words: attractor, reverberation, slice, NMDA, inhibition,
network.
Sustained neuronal firing selective to a stimulus feature no
longer present in the environment is thought to be the
neural correlate of working memory and it is known as
persistent activity. It has been observed in many cortical
areas of awake monkeys performing working memory
tasks (Fuster, 1995; Goldman-Rakic, 1995). Apart from its
implication in working memory, persistent activity has also
been observed in the oculomotor system (for a review, see
Delgado-Garcia, 2000) and in the head-direction system
(for a review, see Taube and Bassett, 2003) in vertebrates.
Thus, persistent activity is probably a general computational strategy developed by the nervous system for all
those situations where information relevant for the organism but no longer available to the senses needs to be kept
over short periods of time for immediate access and evaluation (for a review, see Major and Tank, 2004).
Persistent activity has gathered great interest from the
computational neuroscience community because it lends
itself to a rigorous and rich conceptualization within the
mathematical framework of dynamical systems theory, but
it poses very significant challenges when imposing biolog*Tel: ⫹34 965919210; fax: ⫹34 965919561.
E-mail address: [email protected] (A. Compte).
Abbreviation: AMPAR, AMPA receptor; NMDAR, NMDA receptor;
ACSF, artificial cerebro-spinal fluid; PFC, prefrontal cortex; VTA, ventral tegmental area.
0306-4522/06$30.00⫹0.00 © 2005 Published by Elsevier Ltd on behalf of IBRO.
doi:10.1016/j.neuroscience.2005.06.011
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A. Compte / Neuroscience 139 (2006) 135–151
Fig. 1. A toy, conceptual model is used to illustrate the relation between attractors, multistability and memories. In this model a ball falls
onto a hard surface (one of panels B–E) from a continuum of possible
locations and finds a gravitationally stable configuration on the surface. The surface or energy landscape summarizes all the dynamical
and structural properties of the system. The surface B presents a
monostable configuration, so that the ball always ends up in the same
location irrespective of where it started. This particular case shows that
monostable systems are not useful to encode a memory, because
there is no way that one can make an accurate guess about the
location the ball fell from just by looking at its steady state on the
surface. Contrasting with this situation, panels C–E show multistable
systems with three, nine and a continuum of attractors, respectively.
Any of them allows one to “recall” more or less accurately the original
position of the ball. Discrete attractors (C, D) perform a categorization
of the stimulus, according to each attractor’s basin of attraction (range
of locations that fall onto one same attractor). Panel C, for instance,
categorizes the whole spectrum in A in just three classes: left, middle,
right. Line attractors or continuous attractors (panel E), in contrast,
retain faithfully the properties of the memorandum but have critical
robustness issues (see Sec. 2.2).
fectly flat: any deviation from horizontality, albeit small, will
destroy the line attractor and memories will only be kept
faithfully in time scales of the order of the network dynamics).
Most possibly, this distinction between continuous and
discrete persistent activity models, is also relevant in working memory. There are working memory systems that are
presumably discrete in nature: like working memory for
faces, or objects, or numerical digits and there are other
systems that could possibly have a continuous nature:
working memory for space locations (Constantinidis and
Wang, 2004), or working memory for the frequency of
vibrations (Romo et al., 1999). Note, however, that it might
be very difficult to distinguish experimentally between
closely spaced discrete memories and a true continuum
(see Sec. 2.2). Still, they are distinct theoretical models
and I will refer to object working memory models (see Fig.
2A, discrete attractors are reviewed by Brunel, 2003), to
spatial working memory models line attractors in space or
“bump attractors,” (see Fig. 3A, reviewed by Wang, 2001;
Constantinidis and Wang, 2004) and to parametric working
memory models (line attractors in the rate of firing, see
Seung, 1996; Seung et al., 2000a; Miller et al., 2003).
Now, where does the multistable system actually
reside in the brain? Is it in the synapses? In the neurons? In the local cortical circuit? In highly distributed
brain area networks? These questions are still a matter
of intense research (Wang, 2001; Major and Tank,
2004), and computational models have helped to establish the mechanisms of both intrinsic and circuital mechanisms for persistent activity. Computational models
have thus taken up either the intrinsic or the network
mechanism for persistent activity generation and it is
customary to confront persistent activity models based
on intrinsic cellular mechanisms with persistent activity
models that rely on network recurrent interactions
through reverberation (Durstewitz et al., 2000b; Major
and Tank, 2004). This review concentrates on cellular
and synaptic mechanisms in recurrent network models,
because they have been the subject of most computational research in this field so far. However, models that
invoke intrinsic cellular mechanisms are now catching
renewed attention (see, for instance Camperi and Wang,
1998; Loewenstein and Sompolinsky, 2003), especially
after the experimental observation of intrinsic cellular
multistability in cortical neurons (Egorov et al., 2002).
The question that these biophysical models—whether
discrete or continuous, intrinsic or recurrent—aim to answer is how the multistable property of the model is obtained in a biological situation by means of the known
physiological mechanisms: synaptic receptors, intrinsic
neuronal channels, proportions of excitation and inhibition,
plasticity mechanisms, etc. I review in the following section
some of these mechanisms and the situation in which they
have been implicated by biophysical computational models
of persistent activity in working memory. Recent revision
articles include more specific accounts of some of these
findings: a first general overview of persistent activity models was made by Durstewitz et al. (2000b); the attractor
formalism of object working memory is reviewed by Brunel
(2003); reverberating synaptic mechanisms are reviewed
by Wang (2001); inhibition mechanisms are reviewed by
Amit and Mongillo (2003a); mechanisms for line attractors
by Brody et al. (2003), by Constantinidis and Wang (2004)
and by Major and Tank (2004); mechanisms for dynamical
stability of persistent activity by Tegner et al. (2002). Beyond the scope of this review lie some very active and
related areas of research involving biophysically-based
modeling accounts of working memory, like neuromodulatory effects on persistent activity circuits (see also Tanaka
in this issue; Durstewitz et al., 2000a; Brunel and Wang,
2001; Durstewitz and Seamans, 2002; Navarro-Lopez et
A. Compte / Neuroscience 139 (2006) 135–151
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Fig. 2. Excitatory and inhibitory mechanisms in an attractor network model for object working memory. (A) Example of network performance during
a trial. The network consists of one pool of inhibitory neurons (upper rasters, labeled I) and six pools of excitatory neurons, five of them selective to
different stimuli (rasters labeled 1 through 5) and one of unselective neurons (unlabeled rasters). Within selective populations, neurons are coupled
with potentiated synapses relative to synaptic couplings among cells from different populations. Because of this, when a brief stimulus (labeled
“Sample”) arrives to one of the selective populations, reverberatory activity above baseline firing is maintained in the neurons of this population (thick
black trace) while other populations remain close to their spontaneous firing state (gray traces). Inhibitory neurons also increase their firing slightly,
becoming much more responsive at the time of memory erasure (thin black trace). Reproduced from Fig. 2 in Brunel and Wang (2001) with kind
permission of Springer. (B) Bifurcation diagram for a network as the one in A. The abscissa labels the strength of coupling among neurons of one same
selectivity population, relative to the strength of coupling among neurons belonging to different selectivity groups. In the y axis, the average firing rate
after stimulus presentation (upper branches) or during spontaneous activity (lower branches) is plotted either from a mean-field mathematical
formulation (lines) or from the simulations (symbols). Two cases are represented differing just in a rescaling of all synaptic couplings and external
stimulation rates: connectivity in the rightmost case (thin lines, pluses and diamonds) is approximately 70% of that of the leftmost case (thicker lines,
crosses and squares), and external stimulation is 50% stronger in the rightmost than the leftmost graphs. Notice lower persistent activity rates in the
weaker coupling case. Reproduced from Fig. 6 in Brunel (2000). Copyright Taylor & Francis, Ltd. (C) Feedback inhibition controls the rates of the
persistent activity state weakly, but with the cost of making it less robust and eventually destabilizing it. Bifurcation diagram (see B) as inhibition is
progressively increased in the network. As inhibition increases, persistent rates decrease slightly but soon multistability is abolished. Reproduced from
Fig. 7 in Brunel and Wang (2001) with kind permission of Springer. (D) Illustration of the mechanisms behind the inhibition-dominated regimen of the
network in panel A. Unselective, constant external inputs to the network (labeled AMPA ext) are the primary source of inputs to the neurons of the
network. Recurrent inputs are dominated by inhibition in the spontaneous state (upper panel), so that their sum (Total rec⫽AMPA rec⫹NMDA
rec⫹GABA rec) is negative and suppresses the firing imposed by the external inputs. In the active state (lower panel) both recurrent excitation and
recurrent inhibition increase, but excitation does it to a larger degree so that now recurrent interactions are globally excitatory on average (dashed lines
indicate values in the spontaneous state, i.e. as in the upper panel). Reproduced from Fig. 3 in Brunel and Wang (2001) with kind permission of
Springer.
al., 2004), many-area-interaction in more involved delay
tasks (Renart et al., 2001; Deco and Rolls, 2003, 2005;
Deco et al., 2004), formation of persistent activity attractor
networks through Hebbian learning (Mongillo et al., 2003;
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A. Compte / Neuroscience 139 (2006) 135–151
Fig. 3. NMDA receptors help in stabilizing low-rate persistent activity in an attractor network model of spatial working memory. (A) Example of network
activity during a working memory trial. Neurons are disposed along a ring (y axis, upper and lower limits wrap together to form the ring) and they are
mutually connected with strength modulated according to the distance on that ring, such that excitatory cells are more strongly coupled when they lie
close to each other. As time flows (x axis), neurons fire spontaneously (each dot corresponds to one spike) driven by external Poisson inputs (see
Fig. 2D) until a subpopulation of cells is stimulated externally (between the two first vertical lines, labeled C). After the extinction of this external stimulus
a localized “bump” of activity is actively maintained by local reverberations. This persistent activity state during the delay period (label D) is reset by
means of an unselective stimulation to the whole network (period labeled R). On the right panel, the average firing rate during the delay period between
cue and response is plotted. Borrowed from Fig. 2 in Compte et al. (2000) by permission of Oxford University Press. (B) Rastergrams for the delay
period similar to A but with increasing AMPA participation in excitatory synaptic transmission. As NMDA contribution is diminished, oscillations develop
and eventually persistent activity destabilizes. Borrowed from Fig. 2 in Tegner et al. (2002). Copyright Elsevier Science. (C) The critical aspect for
stability against oscillations is the long time constant of NMDAR-mediated currents as shown here, where only the time constant of excitation is
changed and oscillations appear that eventually disrupt persistent activity. Adapted from Fig. 8 in Wang (1999). Copyright 1999 by the Society for
Neuroscience. (D) NMDA receptors also contribute to rate control in the active state. This is accomplished by means of the saturation properties of
NMDA receptors as illustrated here. Upper panels show the input– output relationships (convex lines) for a neuron with asynchronous synaptic inputs
of varying rate (x axis) through AMPA and NMDA channels, respectively. Notice that the curve in the NMDA case is much more convex than for AMPA,
due to saturation. The straight line is the condition for self-consistency: the rate of the afferent inputs is the same as the output rate if this is just one
of many neurons in a recurrent network in steady-state. The states that do fulfill this self-consistency are indicated by solid dots and can be translated
onto the lower panels as the input– output relationship is changed through the modification of the synaptic efficacy. Notice that, because of NMDA
saturation, increasing synaptic strength augments the range of multistability without increasing the rates significantly (compare with AMPA). Adapted
from Fig. 5 in Wang (1999). Copyright 1999 by the Society for Neuroscience.
Amit and Mongillo, 2003b; Brunel, 2003), and mechanisms
for multi-item working memory (Amit et al., 2003; Amit and
Mongillo, 2003a).
1: Cellular and synaptic mechanisms that have been
associated with persistent activity
1.1: Strong feedback excitation in the local circuit.
This is the longest standing cellular hypothesis for persistent activity. It was formulated as the possible substrate
for memory, based on morphological arguments, even
before persistent activity was first observed experimentally
(Lorente de No, 1933; Hebb, 1949). As it goes, persistent
activity would be the result of mutual excitation between
neurons in a local circuit that would be self-sustained by
virtue of the dense reciprocal synaptic connections existent in most brain areas, notably in the frontal lobes (Goldman-Rakic, 1995). The activity would then be self-maintained for a much longer time than any of the intrinsic or
synaptic time constants. As simple as this idea is, it hides
an important caveat to its actual implementation in a network of physiological neurons: how could such activity be
stable? It just seems that a closed loop of excitatory inter-
A. Compte / Neuroscience 139 (2006) 135–151
actions would lead to runaway excitation up to firing rates
near the neuronal saturation limit (Amit, 1995; Tegner et
al., 2002), which is certainly not the experimental observation. Computational models have substantiated this hypothesis by establishing the conditions for stable reverberation at low rates in neuronal networks (see next two
mechanisms in this section). Early, simple models focused
on laying the theoretical grounds within attractor theory
and, to this end, killed biological detail (Wilson and Cowan,
1973; Amari, 1977; Hopfield, 1982; Zipser et al., 1993).
Later models showed that, for the case of instantaneous
synapses, the stability problem of runaway excitation in the
reverberation hypothesis could be solved by introducing
feedback inhibition into the picture (Amit and Treves, 1989;
Buhmann, 1989; Rubin and Sompolinsky,1989; Amit and
Tsodyks, 1991a,b; Amit, 1995),which also helped in stabilizing a non-silent spontaneous activity state (Amit and
Brunel, 1997; Brunel, 2000). Subsequent network models
have emphasized synaptic dynamics as an important aspect for the stability of reverberatory persistent activity,
both in object working memory (Wang, 1999; Durstewitz et
al., 2000b; Brunel and Wang, 2001; Hansel and Mato,
2001; Koulakov, 2001), in spatial working memory
(Compte et al., 2000; Laing and Chow, 2001; Gutkin et al.,
2001; Tegner et al., 2002) and in parametric persistent
activity models (Seung et al., 2000a; Koulakov et al., 2002;
Miller et al., 2003). What all these models consistently
show is that the maintenance of persistent activity at low
firing rates through reverberation in a local cortical network
is a plausible scenario from the dynamical, computational
standpoint (see examples in Fig. 2A and in Fig. 3A), provided some stabilizing physiological mechanisms are
present in the circuit (see below).
One important issue about the strong reverberation
hypothesis for working memory is to understand how
strong feedback excitation between groups of neurons
selective for the same stimulus might emerge. One possible mechanism is Hebbian learning, as originally assumed
by associative memory models à la Hopfield (Hopfield,
1982) and extensively studied recently in more realistic
models (Mongillo et al., 2003; Amit and Mongillo, 2003b;
Brunel, 2003). Another mechanism is based on the colocalization of same-selectivity neurons in a “micro-column,” which by virtue of the limited extent of axonal and
dendritic arborizations would result in such strong feedback loops among neurons of equal selectivity.
Several predictions, as yet untested, emerge from the
attractor network picture: if it were correct, neuronal hyperpolarization should not interrupt persistent activity in a
hypothetical intracellular recording in an awake behaving
monkey during a working memory task, because this sustained activity is being maintained by synaptic inputs that
persist as opposed to intracellular mechanisms, which
would be switched off by hyperpolarization. Also, a hallmark of the synaptic reverberation hypothesis in an attractor framework is the fact that bistability emerges and disappears abruptly as parameters of the recurrent connectivity are varied (like the strength of excitatory connections,
or the strength of inhibitory connections) in what is known
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mathematically as a “bifurcation” (see diagram in Fig. 2B).
This has been presented as a prediction to be tested
experimentally by using incremental progressive blockade
of excitatory (or inhibitory) synaptic transmission (Durstewitz et al., 2000b).
Dynamically, practically all network models of persistent activity have required a high degree of asynchronous
population firing for proper mnemonic function. In some
models, oscillations can be accommodated during stable
persistent activity, provided they are of sufficiently small
amplitude. Non-synchronous firing is such a critical aspect
in reverberatory persistent activity because the time
course of the bulk of cortical synaptic potentials is typically
much shorter (⬃10 ms) than the average interspike interval in the low-rate persistent activity state of working memory (⬃50 ms at 20 Hz). Therefore, synaptic drive to maintain autonomously a reverberatory firing state in the network cannot rely on inputs coming from neurons that fire in
synchrony. An asynchronous firing state ensures sustained, almost constant, synaptic drive to neurons in the
network, which can underlie their persistent activity. If such
an asynchronous state is stabilized, persistent activity can
be sustained even with very fast synaptic dynamics (Hansel and Mato, 2003) and this necessity for asynchrony is
less stringent, the longer the time course of synaptic interactions is (see Sec. 1.3). Also, for technical reasons, asynchronous population firing is interesting mathematically for
it allows the description of large-scale network simulations
in terms of much simpler, and analytically tractable, meanfield descriptions (Amit and Tsodyks, 1991a; Amit and
Brunel, 1997; Brunel, 2000; Renart et al., 2003a).
Notice that in strongly coupled networks like the ones
considered here, when the asynchronous state destabilizes it usually enters an oscillatory regimen. This underlies
the observation that oscillatory network activity of large
enough amplitude is generally detrimental to persistent
activity stability in recurrent network models. However,
oscillatory activity related to working memory has been
observed experimentally in neurons of the parietal cortex
(Pesaran et al., 2002) and the occipital lobe (Lee et al.,
2005), but not of the prefrontal cortex (Compte et al.,
2003a). One functional role has been proposed for synchronous activation of cells during persistent activity: erasure of the actively held memory (Gutkin et al., 2001).
Because synchrony disrupts persistent activity, if one injects a strong pulse of current to all cells in a recurrent
module that is sustaining asynchronous persistent activity,
many cells will come to fire almost in synchrony and persistent activity will be aborted, resetting the network to the
spontaneous, non-selective state. If this mechanism were
indeed being used for memory erasure in working memory,
the clear prediction to be tested is whether there is an
increase of synchrony to be seen in the local field potential
or in multielectrode recordings around the time when the
monkey responds in a working memory task.
1.2: Strong feedback inhibition in the local circuit. As
mentioned above, strong feedback inhibition was another
mechanism soon brought into the picture for persistent
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A. Compte / Neuroscience 139 (2006) 135–151
activity network models. The very convenient property of
feedback inhibition is the fact that its suppressive effect on
excitatory units of the network is stronger, the higher the
rate of these units is. This looks like an effective rate
control mechanism: the faster the excitatory cells venture
to fire, the deeper their membrane voltage is pushed by
feedback inhibition so they are brought back to sensible
firing rates. This was shown to control the rate of persistent
activity states in early network models with combined recurrent excitation and inhibition (Amit and Treves, 1989;
Rubin and Sompolinsky, 1989; Buhmann, 1989). However,
as a rate control mechanism, inhibition is not totally satisfactory. On the one hand, apart from reducing the rate in
the active state, inhibition to excitatory cells also reduces
dramatically the robustness of multistability in the network
so that realistic firing rates often require very fine-tuned
network connectivity (Wang, 1999). Fig. 2C shows that
increasing feedback inhibition soon renders the network
monostable before affecting too significantly the firing
rates. The fine tuning problem in these network models is
not specifically linked to inhibition. In fact, bringing the
firing rate in the persistent state as close to the spontaneous rates as seen in experiments requires fine tuning
irrespective of what mechanism is being used to control
the rates (Wang, 1999; but see Latham and Nirenberg,
2004). Also, an important family of spiking network models
that incorporate robust spontaneous activity in the network
exclude a role for feedback inhibition in controlling the rate
of persistent activity (Brunel, 2000; Brunel and Wang,
2001). Instead, these models use the saturation of the
input– output neuronal relationship to control the rate of the
persistent activity state (Brunel, 2000). Critically, these
models operate in the sparse coding limit, when neurons
selective for one same stimulus are just a tiny fraction of
the typical size of a synaptically connected population. In
similar network models, Latham and Nirenberg (2004)
have argued that away from the sparse coding limit feedback inhibition keeps playing an important role in controlling the rate of the persistent activity state. Thus, the
sparsity of encoding may be an aspect that determines the
qualitative role of inhibition as a rate control mechanism for
persistent activity.
So, despite the intuitive simplicity of the relationship
between feedback inhibition and neuronal rate control,
inhibition is a mechanism involved in many different ways
in the generation of multistability in these networks (see
below) so that its effects on the network activity are not
always straightforward to understand on the basis of this
intuitive association (in some networks this may even be
the least of the roles played by inhibition, as shown by
Brunel (2000)): see for instance Fig. 2B, where a manipulation that decreases inhibition (and excitation, proportionally) makes persistent activity firing rates much lower.
Apart from its suppressive effects through hyperpolarizing postsynaptic potentials, inhibition has also been implicated differently in the maintenance of highly variable,
low-rate reverberatory activity. In networks where excitation and inhibition are balanced, the average synaptic
current impinging on a neuron keeps it just below firing
threshold on average, and it is the synaptic fluctuations
that make the neuron fire. This leads to very irregular,
low-rate firing patterns (Tsodyks and Sejnowski, 1995; van
Vreeswijk and Sompolinsky, 1996). The addition of recurrent inhibition, therefore, is not just a means to diminish
excitability through hyperpolarization, but in a balanced
state it is also a way to increase current fluctuations
through recurrent interactions, and this results in enhanced, highly irregular firing. It has been proposed that it
is precisely this balanced regime where the low-rate persistent activity dynamics might be realizable at the network
level, taking advantage of the highly fluctuating synaptic
current regime generated by intracortical inhibition (Amit
and Tsodyks, 1991a,b).
A related issue is how to explain unselective, very
low-rate (⬍5 Hz) inter-trial interval firing or “spontaneous
activity” in the context of very strongly reverberatory systems that can sustain a higher rate (⬃20 Hz) persistent
activity state. Especially when the two states do not differ
too much in firing rate, how can spontaneous activity remain stable, not engaging the reverberatory mechanisms
that are recruited by persistent activity? This would not be
a problem if neurons were practically silent in non-mnemonic epochs, but this is not the case experimentally. Amit
and Brunel (1997) set the conditions in which both a lowrate non-selective firing mode and a selective higher-rate
mode could coexist as stable attractors of a spiking-neuron
recurrent network: The net effect of recurrent synaptic
currents, in the spontaneous state, must be inhibitory. The
neurons are driven by external inputs from other parts of
the brain, whence the silent state is not stable, and recurrent connectivity suppresses this firing through an inhibition-dominated circuit that brings it into the balanced regime discussed above (see Fig. 2D). This ensures that a
low-rate, non-silent and non-selective state is stable for
this network. Thus, feedback inhibition should not only be
strong, but also dominant over feedback excitation in baseline conditions (Wang, 2001; Amit and Mongillo, 2003a;
Latham and Nirenberg, 2004). Many network models of
persistent activity have used this inhibition-dominated regime (Amit and Brunel, 1997; Brunel, 2000, 2003; Compte
et al., 2000; Brunel and Wang, 2001; Tegner et al., 2002;
Wang et al., 2004; Latham and Nirenberg, 2004) but other
models have used an excitation-dominated circuit (Durstewitz et al., 2000a; Gutkin et al., 2001; Laing and Chow,
2001) where spontaneous activity, if present, reflects rare
fluctuations in subthreshold inputs that are not sufficiently
amplified by recurrent excitation to generate the activated
mnemonic condition. This might explain discrepancies
among the predictions of the various models. Indeed,
whether the recurrent interactions are primarily excitatory
or inhibitory might have a very profound impact on the
dynamical stability of the attractors (Brunel, 2003).
An additional, and critical, role for feedback inhibition in
many of these models is the maintenance of selectivity: as
persistent activity is maintained for a subset of neurons in
the network, other neurons selective to different stimuli are
being inhibited and prevented from entering the persistent
activity state. Thus, strong cross-inhibition makes possible
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that the original selectivity set by the stimulus is preserved
throughout the mnemonic period. If the cortical ensembles
of distinct selectivity are spatially intermingled in the cortical tissue forming within-column functional networks, this
translates into the need for nonselective inhibitory innervation to these different ensembles from local interneurons, as it has indeed been observed in layer 2/3 of the rat
visual cortex (Yoshimura et al., 2005). On the other hand,
in networks that assume a spatial organization of the selective subpopulations (columnar organization), this translates into the necessity of surround inhibition. This is a
contentious issue for pyramidal cortical neurons are known
to have a rich local axonal arborization which is typically
larger than that of most GABAergic interneurons (Lund and
Wu, 1997; Douglas and Martin, 2004). One possibility, as
yet unproven, is that instead of using far-reaching monosynaptic inhibition these network models could operate
equally well when di-synaptic inhibitory connections reach
farther away than mono-synaptic excitation within the local
circuitry associated to one unitary mnemonic module (as
suggested by Melchitzky et al., 2001; Kang et al., 2003).
Alternatively, possible mediators of this far-reaching inhibition mechanism are large basket cells (Somogyi et al.,
1983; Markram et al., 2004). The existence of significant,
functional surround inhibition remains to be demonstrated
in the nervous tissue that presumably underlies persistent
activity (see, for instance Gonzalez-Burgos et al., 2005).
Intracortical inhibition might also be involved in the
stabilization of non-synchronous firing in the network population. This is a critical stability issue in network models of
persistent activity because when one incorporates the
physiological dynamics of the principal cortical excitatory
(AMPAR-mediated) and inhibitory (GABAA) postsynaptic
currents into recurrent models of working memory, this
induces a dynamical instability that makes persistent activity unstable through the development of synchronized
oscillations (Wang, 1999; Tegner et al., 2002). This is so
because the decay time constant of postsynaptic currents
mediated by GABAA receptors is longer than that of
AMPAR-mediated excitatory postsynaptic currents. A system endowed with fast positive feedback and slower negative feedback is prone to oscillatory behavior, and oscillations are detrimental to the stability of a persistent activity
attractor (Wang, 1999; Compte et al., 2000; Gutkin et al.,
2001). The way in which most models have proposed to
overcome this difficulty is by appealing to the slower form
of ionotropic excitatory transmission in the cortex: NMDA
receptor (NMDAR)-mediated transmission (see Sec. 1.3).
However, (Hansel and Mato, 2001) have proposed that
also inhibition might have a part to play in this respect:
strong inhibitory connections among inhibitory neurons in a
recurrent network can break the synchrony in the population dynamics and thus stabilize persistent activity driven
only by the faster form of excitation; see, however, conflicting results where an increase of inhibition to inhibitory
cells made the network more vulnerable, rather than more
robust, to oscillations (Tegner et al., 2002).
Another use for an inhibition-dominated recurrent circuit
in the context of working memory is the possibility to erase an
141
actively held memory by means of a non-selective excitatory
pulse to the network (Compte et al., 2000; Brunel and Wang,
2001; Brunel, 2003). This is confronted to the more straightforward alternative of resetting the persistent activity state by
means of a hyperpolarizing pulse to all neurons in the network (Wang, 1999). Because this silences the whole network, when the network is released and allowed to evolve
autonomously again, it settles in the spontaneous activity,
non-selective state and the previously active memory is
erased. However, this implies that the resetting operation in
neurons involved in the maintenance of persistent activity
(presumably in the prefrontal cortex) should be characterized
by suppression of firing relative to baseline. Instead, in most
cases one sees strong enhancement of firing during the
animal response and immediate recovery to baseline (Funahashi et al., 1989). Experimental data, therefore, suggest
that the erasure signal is excitatory. An inhibition-dominated
circuit provides a possible network substrate for this excitation-induced suppression of activity: in an inhibition-dominated network, a sufficiently strong pulse of excitation recruits
massive intracortical inhibition that overwhelms intracortical
excitation when the input is withdrawn. This results in the
suppression of firing and eventually the extinction of persistent activity. This can be given a more formal and quantitative
expression within attractor theory (Brunel and Wang, 2001;
Brunel, 2003). As a mechanistically different scenario, an
excitatory pulse can also reset a reverberatory network by
inducing synchronous firing, which destabilizes persistent activity (Gutkin et al., 2001, see a more detailed discussion in
Sec. 1.1).
Wang et al. (2004) identified one final possible functional role for strong inhibition, based on the electrophysiological and morphological diversity of interneurons in the
cortical network. In their network model of spatial working
memory, three classes of interneurons are included with
distinct morphological and electrophysiological properties,
as suggested by experimental data. In a working memory
context, this disposition serves to make mnemonic persistent activity more resistant to intervening distractors. This
is accomplished by means of the disinhibition of active
pyramidal neurons, when dendrite-targeting interneurons
are strongly inhibited by interneuron-targeting interneurons
(Wang et al., 2004).
Feedback inhibition is therefore a fundamental piece in
the stability of the reverberatory hypothesis for persistent
activity in working memory, and it has been associated in
a long list of possible roles (see also Amit and Mongillo,
2003a; Brunel, 2003): rate control for the active mnemonic
firing state maintained by reverberation; generation of a
fluctuating balanced state and stabilization of low-rate reverberatory activity; stabilization of the spontaneous, lowrate state by means of an inhibition-dominated recurrent
connectivity; maintenance of selectivity in the network during
persistent activity; reset of the persistent activity module upon
sudden excitation of the whole network; promotion of asynchronous firing by means of strong inhibitory-to-inhibitory
connections; and increasing the network capability to resist
distractors via pyramidal cell disinhibition.
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1.3: Recurrent excitation primarily mediated by NMDARs.
Several roles have been ascribed to the NMDAR in the
context of recurrent network models of working memory
and persistent activity, in line with the three main features
that differentiate this receptor from the AMPA receptor:
longer decay time constant (approximately 100 ms), much
higher affinity for glutamate (resulting in faster saturation
properties), and voltage dependency of the receptor conductance in the presence of extracellular magnesium (the
channel is virtually closed at hyperpolarized potentials).
As anticipated in the subsection 1.2, NMDARs have
been implicated in the stabilization of persistent activity
against disruption by synchronous population firing (see
Fig. 3). The key aspect of NMDARs here is their long
decay time constant (Fig. 3C), and they can accomplish
this stabilization in two different ways: On the one hand, by
introducing much slower excitatory interactions the binomial fast excitation plus slow inhibition, which is responsible for synchrony generation, is weakened and asynchronous firing is promoted. On the other hand, when some
degree of synchrony is present in the persistent activity
state, the long decay time constant of NMDAR-mediated
postsynaptic currents can bridge the gap in excitatory synaptic drive during synchronized neuronal refractory periods
and maintain stable self-sustained activity (Wang, 1999,
2001; Compte et al., 2000; Tegner et al., 2002; Ermentrout, 2003). Other mechanisms have been proposed that
act along the first of the strategies outlined here (stabilization of the asynchronous firing regime) (Hansel and Mato,
2001; Gutkin et al., 2001), but it seems like stable persistent activity with partially synchronous firing would require
necessarily the action of NMDARs (Tegner et al., 2002;
Ermentrout, 2003).
Also the long decay time constant of NMDAR-mediated postsynaptic currents has been associated by computational models to the robustness problem of line attractor models (see Sec. 2.2). In order to have neurons stably
maintain a continuum of firing rates, depending on what
stimulus is transiently presented (line attractor), reverberatory network models have typically found that the synaptic
weights of the model have to be very carefully tuned to
within 1% accuracy. The accuracy required, however, if
one uses AMPA instead of NMDA in recurrent connections
is orders of magnitude higher (Seung, 1996; Seung et al.,
2000a,b). Both of these accuracy values seem biologically
unrealistic, but NMDARs seem to alleviate the problem.
Note that the key aspect of NMDARs for the stabilization of
persistent activity described so far is its slow dynamics.
Thus, any other form of synaptically induced slow depolarization could also mediate these stabilizing effects. One
candidate is, for instance, the combination of glutamatergic
transmission and cholinergic neuromodulation in the oculomotor system (Navarro-Lopez et al., 2004).
NMDARs can also play a role in the rate control problem (see Sec. 1.1) of stable low-rate reverberatory activity
in a recurrent network. The property of high affinity for
glutamate of NMDARs can be critical in this respect: if
excitatory recurrence in the local network is primarily mediated by NMDARs, then their saturation properties at low
rates help very significantly in avoiding runaway excitation
and near-saturation firing. This is so because NMDARs
would be already completely open by a presynaptic stimulation of around 30 Hz. If a presynaptic neuron ventures
beyond these rates, the postsynaptic neuron will not follow
because the excitatory drive will already be saturated and
the state will be stabilized (Fransén and Lansner, 1995;
Wang, 1999; Fig. 3D).
Finally, NMDARs could also be engaging their voltage
dependency for generating a bistable switch in their synapses (Lisman et al., 1998). This is a mechanism by which
one avoids having to set the selectivity in the model beforehand. It relies also on a recurrent network, where reentrant excitation is able to sustain persistent activity. However,
because of the voltage dependency of NMDARs, only those
synapses that link a presynaptic neuron and a postsynaptic
neuron that are both strongly activated by the external stimulus reach the required synaptic strength to sustain reverberation. Persistent activity remains constrained to the population of neurons that was first recruited by the stimulus, without spreading to nonimplicated neurons. A unique feature
of such a circuit is that it is not preset to store a given set
of memories, but just remembers whatever stimuli one
presents, without requiring learning-induced synaptic modifications (which are considered to be a slow process in the
time scales of this task).
1.4: Intrinsic currents. Even in the framework of recurrent network models, intrinsic membrane properties will
have an effect on the behavior of the system. This has
been explored in recurrent network models that include the
detail of biophysical membrane channels other than synaptic receptors and spike-generating channels (Durstewitz
et al., 2000b; Tegner et al., 2002; Durstewitz and Seamans, 2002; Koulakov et al., 2002; Goldman et al., 2003;
Wang et al., 2004). Specific predictions include: slow calcium-dependent cationic channels (Ican) help in stabilizing
persistent activity against oscillatory activity, much like
NMDARs (see Sec. 1.3) (Tegner et al., 2002), dendritic
channels that induce a bistable switch in the dendrite help
in rendering line attractors more robust (Goldman et al.,
2003), and dopamine neuromodulation of synaptic and
intrinsic channels can make the network more resistant to
distraction (Durstewitz et al, 2000b; Durstewitz and Seamans, 2002). In addition, experiments (see Sec. 3.1) have
also suggested a role for the h-current in controlling the
duration of activity network states maintained by reverberation (Shu et al., 2004). This mechanism remains to be
explored in network models of persistent activity.
2: The computational challenges of recurrent models
of persistent activity
2.1: High variability of firing in delay periods. As I
have outlined in Sec. 1, recurrent models of persistent
activity are plausible biologically and can make use of
well-characterized physiological mechanisms present in
the cortical circuit in order to perform their mnemonic function in a more stable and robust manner, being resistant to
distractors. Recently, however, the statistical characteriza-
A. Compte / Neuroscience 139 (2006) 135–151
tion of firing activity of single neurons in the prefrontal
cortex of monkeys performing a working memory task has
challenged this entire class of models: neurons increase
the variability of their spike trains when they engage in
persistent activity during working memory tasks with respect to their baseline firing (Compte et al., 2003a). This
qualitative feature is very difficult to account for within
current models of persistent activity, that show typically the
opposite trend (Brunel and Wang, 2001; Brunel, 2003).
Qualitatively, these network models produce a highly variable spike output through the balancing of excitatory and
inhibitory synaptic currents in the spontaneous state (van
Vreeswijk and Sompolinsky, 1996). However, the persistent activity state is obtained by sacrificing this balance
locally so that a subpopulation receives more excitation
and fires at relatively higher rates. The cost of this operation is a reduction of the variability of the spike trains in
persistent activity since the neurons depart from the balanced state, where they fire in the fluctuation regime, and
enter the drift regime of firing, much more regular. This
relative reduction in variability is therefore intrinsically associated with these models. Whether matching the experimental observation of high variability during persistence
implies just the necessity of adding on features to existing
recurrent models (bursting properties, additional inhibitory
populations, . . .) or else of developing a new framework to
conceptualize persistent activity, is an open issue. The
only attempt so far to address this issue in a recurrent
network model of working memory proposes a microcolumnar organization for excitation and inhibition (Renart,
2000; Renart et al., 2003a). In their model, increased firing
both in excitatory and inhibitory cells of a subpopulation
during persistent activity occurs through an increase of
current fluctuations with no change in the average current.
As a result, both spontaneous activity and persistent activity would operate in a balanced state and their difference
in firing rate would be due to the increase of fluctuations in
the current. This translates into a persistent activity state
with higher variability than the spontaneous state. However, this network requires a very precise fine tuning of
connectivity parameters to operate in the way described.
Recent findings on the firing properties of neurons with
slow postsynaptic currents, or short membrane time constant, might shed some light onto this challenge for persistent activity network models. It has been shown that,
when the synaptic time constant is much slower than the
effective membrane time constant (one can label this condition “high-conductance state” because a way to achieve
this regime is by intense balanced synaptic bombardment
that reduces dramatically the effective membrane time
constant from its resting value), the neuronal firing threshold can be set in such a way that the neuron responds only
to the largest fluctuations that occur in incoming conductance-based synaptic currents (Moreno-Bote and Parga,
2004). These correspond typically to the synchronous arrival of presynaptic spikes, so that the neuron fires as a
synchrony detector (Bugmann, 1991; Abeles, 1992) and
the output of the neuron is more variable (it is actually
bursty) than that of its inputs (see also Svirskis and Rinzel,
143
2000; Salinas and Sejnowski, 2002). If persistent activity
models could make use of this regime of operation, this
might provide a way in which neurons in the persistent
activity state (presumably a high-conductance state) increase their variability with respect to the spontaneous
state (less of a high-conductance state). A similar idea,
although now relying on the slower intrinsic dynamics of
dendrites, has been experimentally documented by Larkum et al. (2004). In their experiments, they show that
noisy current injection in the soma produces much more
regular firing patterns than the same current injection in the
dendrite. This is accomplished through the involvement of
the slow kinetics of calcium channels in the dendrites,
suggesting a similar operation as the “high conductance”
state described above (Moreno-Bote and Parga, 2004).
2.2: Robustness of line attractors. Computational
models that implement a line attractor for the encoding of
a continuous stimulus, as for spatial working memory or
parametric working memory, suffer from a serious problem
regarding their robustness: their synaptic weights need to
be tuned to an absurdly precise accuracy (Brody et al.,
2003). This is a serious problem in a biological system,
usually characterized by a high level of noise and heterogeneity. Several approaches to this problem have been put
forward.
Firstly, since line attractors can be thought of as the
limit of infinitely many discrete attractors (as in Fig. 1D–E),
one may wonder whether the brain just gets away with a
finite number of discrete attractors, rather than a real continuum (Brunel, 2003; Major and Tank, 2004; Miller et al.,
2002). Discrete attractors do not suffer as severely from
the robustness issue as continuous attractors. Some models have implemented this idea by endowing those discrete
attractors with additional bistability mechanisms, so as to
render the wells in Fig. 1D deeper, more stable (Koulakov
et al., 2002; Goldman et al., 2003). Is there any evidence
that the brain implements an actual line attractor rather
than using closely spaced discrete attractors? There is
only indirect evidence that suggests that, if not strict continuous attractors, spatial working memory uses very
tightly spaced and shallow discrete attractors: subjects in
spatial working memory tasks make on average more
errors, the longer the delay interval is (White et al., 1994;
Ploner et al., 1998), as if mnemonic activity was drifting as
a random walk on a line attractor (Ben-Yishai et al., 1995;
Camperi and Wang, 1998; Seung, 1996; Zhang, 1996;
Compte et al., 2000). The fact that the magnitude of this
average drift depends on the length of the mnemonic
period indicates that it is generated in the memory-maintaining system, rather than the sensory or motor systems.
Similar delay-dependent behavioral errors have been reported also for working memory in other visual experiments and in other sensory modalities (Pasternak and
Greenlee, 2005). This does not invalidate the discrete
attractor approximation to the line attractor (Miller et al.,
2002) and it seems that a statistical analysis of correlations
among the spike trains of neurons in the network during
persistent activity would only help in unambiguously dis-
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entangling this dichotomy by going to fourth order in the
statistics, which is technically not feasible with currently
available data (Miller, unpublished observations).
A second possibility is that indeed, the system is implementing a continuous attractor and that homeostatic
mechanisms in the brain compensate for heterogeneities,
so that the steady state of this homeostatic system is
precisely the fine-tuned condition necessary for line-attractor function. This has been shown to work with a physiologically characterized activity-dependent synaptic scaling
mechanism in a spatial working memory network (Renart
et al., 2003b). There, individual neurons have a target
average firing rate over a long time scale and they scale up
or down their synaptic inputs in order to attain it. This
compensates the heterogeneities in the cellular properties
of the neurons in the network and recovers the continuous
attractor that these heterogeneities destroy.
sive methods on awake behaving animals. This is the
natural test bed for cellular mechanistic hypotheses of
working memory. However, in the last five years a number
of experiments in cortical slices in vitro that attempted to
reproduce dynamics similar to persistent activity have suggested that there might be ways to explore the specific
hypotheses of recurrent working memory models in reduced preparations. Currently, these preparations do not
achieve truly persistent activation, but their activity is of an
intrinsically episodic nature. This indicates that caution
must be exerted when relating findings in these experiments with persistent activity, as discussed below. In this
section I review what we might learn from these systems in
relation to the points discussed in the previous sections,
and I also speculate about where a tight relationship between computational models of persistent activity and in
vitro electrophysiology could take us to in the future.
2.3: Compatibility with cellular physiology. As much
as I have stressed in Sec. 1 all the physiological mechanisms that are beneficial for the purposes of a working
memory module that generates persistent activity through
recurrent connectivity, there are also mechanisms widely
present in cortical neurons that are detrimental and usually
absent (or minimized) in current network models of persistent activity. The most prominent of these mechanisms are
membrane channels responsible for spike-frequency adaptation (calcium-dependent or sodium-dependent potassium channels). Although object working memory models
are robust enough to accommodate a certain degree of
cellular adaptation (Durstewitz et al., 2000a; Durstewitz
and Seamans, 2002), neither spatial working memory
models nor parametric working memory models tolerate
much of it in their constituent neurons (Compte et al., 2000;
Seung et al., 2000a; Tegner et al., 2002; Miller et al., 2003;
Wang et al., 2004). In spatial working memory models, for
instance, spike-frequency adaptation destabilizes localized persistent activity and makes the region of activity
move with constant velocity along the network, as a traveling wave (Hansel and Sompolinsky, 1998; Laing and
Longtin, 2001). This is a very undesirable feature that
cancels all mnemonic function for the network. However,
spike-frequency adaptation is ubiquitous in cortical pyramidal cells. How can one reconcile this? The only proposal
so far, has pointed at the fact that enhanced noisy input
from external sources to the network can stop the continuous drift of the traveling wave (Laing and Longtin, 2001).
However, this is done at the cost of increasing the noisiness of the environment, which in a continuous attractor
results in accentuated random drifting of the bump of activity. Another possibility is that these intrinsic currents are
attenuated by some neuromodulator that is required to
switch on working memory function, like for instance dopamine (Durstewitz et al., 2000a).
3.1: The slowly oscillating slice. An experiment
where cortical slices are maintained in a modified ACSF
(artificial cerebro-spinal fluid) solution that mimics the ionic
concentrations of the cerebrospinal fluid in situ has shown
that cortical slices can maintain sustained activity largely
mediated by synaptic interactions over long periods of time
(Sanchez-Vives and McCormick, 2000). This episodic activity manifests itself in the form of long bouts of activity
(between 300 ms and 4 s) interspersed with longer periods
of silence, in an oscillatory pattern very reminiscent of in
vivo cortical activity during deep anesthesia or natural
slow-wave sleep (see Fig. 4A). In a generalization of the
concept that we have been using here, this episodic phenomenon has been presented as an example of persistent
activity. Although activity is not triggered by a known stimulus, and hence firing is not strictly known to persist after
its extinction (see, however, Shu et al., 2003), the long
duration of active states indicates the possible implication
of a nontrivial persistence mechanism. Also, it is indeed a
case where the system appears to make regular transitions between two states of quasi-stability (this is described in detail in the model by Compte et al. (2003c)), so
that probably multistability, the hallmark of working memory in attractor network models, underlies this phenomenon. It is nonetheless also true that the system is far from
being a satisfactory experimental model for persistent activity in working memory: Firstly, oscillatory activity per se
is conceptually very far from stimulus-reactive systems like
the ones necessary for working memory. The slice cannot
be stopped oscillating and yet conserve stimulus-triggered
upstates. Upstates are generated periodically and spontaneously and therefore they tell us about the inner conditions of the system, rather than about external contingencies. Secondly, it lacks selectivity. When the slice enters
an active state (“upstate”), this propagates to all neurons in
the slice (Fig. 4A.4) and it does not remain restricted to a
subset of them, so it does not appear to engage subpopulations selectively. Thirdly, the downstate in this preparation is practically quiescent, while spontaneous activity in
cortical neurons in the alert animal is sizable and very
variable (Compte et al., 2003a). In the context of attractor
3: Experimental tests for persistent activity
mechanisms in vitro
Experimental research on the physiological mechanisms
of working memory has to be done necessarily with inva-
A. Compte / Neuroscience 139 (2006) 135–151
145
Fig. 4. Illustration of in vitro experiments related to the cellular and synaptic mechanisms of persistent activity. (A) The oscillating acute slice of
(Sanchez-Vives and McCormick (2000)) shows recurring events of synchronized network firing (“upstates”) as demonstrated by simultaneous
extracellular (A.1) and intracellular (A.2) recordings. These upstates remain upon neuronal hyperpolarization revealing that they are generated through
incoming barrages of postsynaptic potentials (A.3). Array extracellular recordings show that the upstate propagates horizontally through the slice and
it recruits most neuronal tissue (A.4). Copyright by Nature. (B) In organotypic prefrontal cortex (PFC)-ventral tegmental area (VTA) co-cultures,
spontaneously occurring episodes of synaptically sustained activity are also observed (B.1) in close similarity to the slowly oscillating slice (Seamans
et al. (2003)). In PFC–VTA– hippocampal co-cultures, CA1 stimulation also produces prolonged firing in PFC cortical neurons (B.2 left) which is
synaptically sustained through NMDA receptors (see bath application of APV in B.2 right). Voltage clamp experiments (B.2 lower graphs) reveal a slow
inward current (gray line) that is blocked by NMDA antagonists. Reproduced by permission of Oxford University Press. (C) Simultaneous calcium
imaging (C.1) and intracellular recording (C.2) in a mouse visual cortex slice show that in periods of increased network synchrony (two different
snapshots shown in left and right columns) network activations as revealed by calcium increases (C.1 red dots) correspond to persistent firing (upstate)
of neurons in the network (Cossart et al. (2003)): the neuron recorded in C.2 is indicated by the black arrow in C.1, so that when calcium signals are
not increased for this cell no firing activity is observed electrophysiologically (left), while the opposite occurs when robust calcium transients are
associated to the neuron (right). Copyright by Nature. (D) A hybrid experimental– computational approach to analyzing the conditions for persistent
activity (Fellous and Sejnowski (2003)) shows that injecting into the recorded neuron a mixed barrage of excitatory and inhibitory background synaptic
conductances in dynamic clamp, together with a short series of random excitatory and inhibitory postsynaptic potential trains following each spike of
the neuron (reactive clamp, simulating the local network feedback) is able to replicate in vivo-like persistent activity (D.1). However, a minority of
strongly adapting neuron were unable to fire persistently (D.2). Reproduced by permission of Oxford University Press.
networks these differences can indicate that the slice network lies in a very different dynamical regime than the in
vivo circuit. It is, for instance, possible that the upstate in
the slice corresponds more closely to the low-rate spontaneous activity in vivo than to the persistent activity state in
working memory, while the downstate is a third possible
state associated with anesthesia or sleep (Steriade et al.,
1999; Steriade, 2000). Still, it remains a fascinating issue
to learn about the mechanisms of synaptically sustained
activity in the slice and test the hypotheses formulated by
attractor network models of persistent activity, with the
ultimate objective of drawing conclusions to be tested in
awake behaving animals. Oscillating slices in vitro, are
therefore possible experimental test beds of mechanisms
for unselective multistability, rate control, reset of activity,
and firing statistics in sustained states; but they are not
well suited to address issues like selectivity, spontaneous
activity, distraction, line attractors, etc.
So far, research in the slowly oscillating slice has produced a wealth of informative data related to the cellular and synaptic mechanisms of reverberatory activity
(Sanchez-Vives and McCormick, 2000; Shu et al., 2003;
Compte et al., 2003c; McCormick et al., 2003; Silberberg
et al., 2004). On the one hand, experiments have convincingly established that these activated states are synaptically maintained through barrages of NMDAR- and
AMPAR-mediated excitatory postsynaptic currents temporally superimposed on barrages of inhibitory postsynaptic
146
A. Compte / Neuroscience 139 (2006) 135–151
currents (Sanchez-Vives and McCormick, 2000; Shu et al.,
2003; see also Fig. 4A.3). This is the first functional confirmation that dense reciprocal connectivity in the cortical
local circuit, in near-physiological conditions, is potent
enough to sustain reverberatory activity, which is all the
more remarkable for in an acute cortical slice a significant
fraction of connections and presynaptic partners have
been drastically pruned. The functional substrate for the
reverberation hypothesis of working memory is therefore
present in the local cortical circuit. On the other hand,
inhibition has been shown to follow excitation closely,
keeping a stable degree of depolarization (Shu et al.,
2003). Thus, inhibition is likely implementing the rate control mechanism that we have described in the previous
section to avoid runaway excitation in reverberatory conditions. Experiments have also shown that excitatory
pulses to the slice can switch off an active upstate (Shu et
al., 2003), lending support either to massive inhibitory
recruitment by external input during the upstate (see Sec.
1.2 above) or else to a synchrony-based reset mechanism
(see Sec. 1.1 above).
The mechanism that underlies the selectivity of most
working memory network models is strong inhibitory inputs
to neurons that do not belong to the active ensemble of the
network (Sec. 1.2, but see Lisman et al., 1998). What
these experiments demonstrate is that surround inhibitory
connectivity in the slowly oscillating cortical slice is not
strong enough to maintain localized activity, for it systematically spreads along the slice (Sanchez-Vives and McCormick, 2000). This questions the role of strong inhibitory
feedback in selectivity formation. It is however possible
that these surround inhibitory mechanisms require the third
dimension of the cortical tissue, which is truncated in the
slice; or else that neuromodulation in vivo reshapes the
spatial synaptic balance with respect to the in vitro situation so as to ensure robust selectivity during persistent
activity through inhibitory interactions. Alternatively, selectivity producing surround inhibitory mechanisms might be
evoked only for stronger activated cortical states than seen
in vitro, in line with the idea that what one sees as an
activated state in these slices is to be associated rather to
the spontaneous activity state than to the mnemonic state
of working memory systems.
As for the implication of NMDARs in the maintenance
of persistent activity in the slice, current experiments are
not conclusive. On the one hand, both AMPARs and
NMDARs seem to be necessary for the maintenance of
this activity (Sanchez-Vives and McCormick, 2000). Also,
the fact that oscillatory activity in the beta– gamma band is
often seen in field recordings during the upstates and not
the downstates of the slow oscillations (Compte et al.,
2003b) supports the implication of a long-time-constant
mechanism, possibly NMDAR-mediated currents, in the
stability of persistent activity based on the indirect theoretical arguments laid down above (Sec. 1.3). However, it
remains to be explicitly shown in the experiment whether
NMDARs participate in the reverberation of the upstate by
any of the means detailed in Sec. 1.3, rather than just as
bulk excitatory drive substitutable by AMPAR-mediated
synaptic currents.
The active periods of the slow oscillation in the in vitro
preparation also reveal that synaptically sustained neuronal activity is very variable: the average coefficient of variation measured for upstate activity by (Shu et al., 2003) is
similar to the one observed in vivo during working memory
(Compte et al., 2003a). As explained in Sec. 2.1, generating a high coefficient of variation in the persistent activity
state is a problem for current attractor models of persistent
activity. Since activity in the slice is known to be based on
reverberation, the fact that high variability is observed in
the slice indicates that both the reverberation hypothesis
and highly irregular activity must be compatible. Further
experimental research will surely help us understand what
kind of additional mechanisms are involved in making synaptically sustained persistent activity in this preparation so
variable.
3.2: Membrane voltage bistability in organotypic cultured slices. A similar network dynamics can be observed in organotypic cultured slices (Plenz and Aertsen,
1996; Seamans et al., 2003; McCormick and Aptowicz,
2004). Because of the similarity with the activity in the
slowly oscillating acute slice described above (see Fig.
4B), the same caveats are in order, regarding the usage of
this experimental model to investigate the cellular and
synaptic mechanisms of persistent activity (see subsection
3.1). This preparation, in contrast to the slowly oscillating
slice, does not strictly correspond to the structure of an
adult cortex but as a bonus its connectivity is not as truncated as in acute slices, since it grows new connections on
the experimenter’s plate. Therefore, these slices might be
more easily brought to reverberate than acute slices (Seamans et al., 2003). An interesting thing about this preparation is the fact that one can grow slices from different
brain regions together, and as they grow they tend to
connect to each other in ways similar to how they are
linked in situ. This provides a good experimental tool to
explore neuromodulatory mechanisms of persistent activity (Seamans et al., 2003). These experiments have suggested so far that NMDAR-mediated synaptic currents
have a predominant role in the maintenance phase of the
upstate (Fig. 4B.2), rather than in its initiation, and the
critical aspect for this seems to be their long decay time
constant (Seamans et al., 2003).
3.3: Calcium imaging and recordings in immature visual cortical slices. This in vitro preparation also evidences the spontaneous emergence of synaptically-sustained long-lasting activity in neocortical slices, but of a
qualitatively different nature than the experiments above.
Slices of visual cortex of juvenile mice in their late postnatal development are maintained in standard ACSF solution
while calcium transients are recorded with two-photon imaging (Mao et al., 2001; Cossart et al., 2003). A few
neurons in the slice are spontaneously active, and they
engage occasionally in collective, synchronous firing (Fig.
4C.1). Simultaneous intracellular recordings show that during these periods of synchronous fluorescence changes,
A. Compte / Neuroscience 139 (2006) 135–151
most coactive neurons undergo a membrane voltage transition to a stably elevated membrane potential (“upstate,”
see Fig. 4C.2). This upstate can be as long as 30 s, and
when it is suprathreshold neuronal firing is around 20 Hz.
In addition, upstate transition frequency is drastically reduced when glutamate receptors are blocked and totally
eliminated after additional blockade of GABAergic transmission (Cossart et al., 2003). All in all, this evidences
again the ability of the neocortical circuitry to sustain activity over long time periods through synaptic reverberation. As I discussed in 3.1 above, the association of this
type of activity to persistent activity in working memory is
debatable because these episodic periods of increased
synchrony occur spontaneously, revealing the internal dynamics of the tissue rather than informative aspects about
the environment, and they are followed by periods of practically total quiescence, very rare in vivo. In addition, in this
preparation GABAergic transmission appears to have an
excitatory character, in contrast to in situ conditions in the
cortex. However, in this case only a small fraction of neurons participates in this persistent activity as opposed to
the oscillating slice experiments above, where the whole
network was recruited during each upstate of the oscillation (Fig. 4A.4). The sparsity of active neural populations is
a feature of persistent activity in working memory and it is
the base on which stimulus selectivity can be built. These
spontaneous, reverberating upstates have therefore the
potentiality of being selective, which the previously discussed in vitro experiments lack (subsections 3.1 and 3.2).
The mechanisms for this selectivity are still unknown. Attractor networks have typically invoked inhibition to generate selectivity (see Sec. 1.2). Alternatively, it could rely on
the voltage dependency of NMDA channels, as proposed
by Lisman et al. (1998). Also, it could be subserved by very
sparse neuronal connectivity such that synaptically connected neurons conform essentially independent cell assemblies (in line with synfire chains: Abeles, 1991). Notice
however that individual cells have been seen to participate
in more than one activation ensemble (Cossart et al.
(2003). Whether one of these mechanisms is actually engaged in this preparation or it is a different one that restrains persistent activity within a small subpopulation of
the network, is an open issue that can be explored experimentally.
3.4: Dynamic and “reactive” clamp in the slice.
Recently, a new in vitro experiment has been proposed
where one can carry out hybrid experimental–theoretical
investigations on the cellular and synaptic mechanisms of
persistent activity (Fellous and Sejnowski, 2003). One
records intracellularly from a cell in a cortical slice while
simultaneously injecting two different sources of synthetically generated synaptic inputs by means of a dynamic
clamp setup: on the one hand, continuous Poisson trains
of excitatory and inhibitory conductance openings are simulated to represent the input that a cell in vivo presumably
receives from neurons from outside the local circuit; the
second source of input simulates feedback from the local
circuit by injecting a short Poisson train of AMPAR,
147
NMDAR and GABAA-receptor conductance openings each
time that the recorded neuron fires one action potential
(“reactive clamp”). With appropriate parameters for these
inputs, recorded neurons can often be made to display
bistability between a quiescent state and a low-rate persistent firing state (see Fig. 4D.1; Fellous and Sejnowski,
2003). This experiment cannot test the existence of an
actual connectivity or synaptic substrate for persistent activity (since both are bypassed by the simulation part of the
experiment), but it can test computational hypotheses
against a real neuron and determine how intrinsic mechanisms influence the dynamics. One conclusion of the experiment of Fellous and Sejnowski (2003), for instance, is
that neurons with strong spike-frequency adaptation are
unable to be brought into bistability (Fig. 4D.2), as models
showed (see Sec. 2.3). A careful examination of the conditions for this persistent activity could help establish, for
instance, how high the NMDA-to-AMPA ratio in the feedback needs to be to sustain robust persistent activity, and
whether the value of the NMDA-to-AMPA ratio in different
cells correlates with the magnitude of a possible intrinsic
afterdepolarization (as suggested by Tegner et al. (2002)).
This experiment could also be used to implement inhibition-dominated conditions in the local circuit in spontaneous activity and compare the conditions for stable persistent activity there with the case of excitation-dominated
recurrence (which is the case in Fellous and Sejnowski
(2003)). As it was also the case in the previous experiments discussed, persistent activity in this in vitro preparation is quite variable (though lower than in vivo), with a
coefficient of variation approaching 1. Here, however, everything is known regarding connectivity and synapses,
and the critical feature for this high variability is the built-in
exact balance between excitation and inhibition (Tsodyks
and Sejnowski, 1995; van Vreeswijk and Sompolinsky,
1996), in line with the microcolumnar model by Renart
(2000).
3.5: Models and in vitro experiments. As outlined in
the previous sections, several in vitro experiments are now
available that can be used to investigate some of the
issues discussed here, but not all, regarding the reverberatory hypothesis for persistent activity in working memory.
In the coming years, this exciting field of research will see
close cooperation between modeling and in vitro electrophysiology that will address some of the open issues in
current theoretical models of persistent activity. I want to
emphasize that these conclusions must be taken with caution, as the activity observed in vitro is episodic rather than
truly persistent and their mechanisms might therefore differ. Eventually, the consistent findings of models and in
vitro experiments will have to be tested against recordings
in awake behaving animals in order to determine whether
these reverberatory mechanisms are indeed at play in the
brain during working memory tasks.
In vitro experiments have already given ample evidence of the existence in the cortical circuitry of a reverberatory substrate that can underlie synaptically-based
persistent activity. Some of the issues that this joint com-
148
A. Compte / Neuroscience 139 (2006) 135–151
Table 1. Reference table identifying computational issues (first column), mechanisms implicated (second column) by different biophysical models
(third column) and experiments in vitro providing some support to the presence of the mechanism in the cortical circuit or to the involvement of the
mechanism in addressing the corresponding issue (fourth column)
Issue
Mechanism
Model references
Supporting experiments
in vitro
Maintenance of persistent
activity
Excitatory reverberation in the
local circuit
Amari (1977); Hopfield (1982)
Intrinsic cellular mechanismsa
Booth and Rinzel (1995); Camperi
and Wang (1998); Loewenstein
and Sompolinsky (2003)
Sanchez-Vives and
McCormick (2000); Cossart
et al. (2003)
Egorov et al. (2002)
Strong inhibition in the local
circuit
Amit and Treves (1989);
Buhmann (1989); Rubin and
Sompolinsky (1989)
NMDAR saturation
Fransén and Lansner (1995);
Wang (1999)
Wang (1999); Miller et al. (2003)
Low-rate persistent activity
Short-term synaptic depressiona
Non-silent spontaneous activity
Inhibition-dominated recurrence
Amit and Treves (1989); Amit
(1995); Amit and Brunel (1997)
Selectivity during persistent
activity
Cross-inhibition
NMDAR voltage-dependence
Fast Hebbian learninga
Amit and Brunel (1997)
Lisman et al. (1998)
Sandberg et al. (2003)
Stability against oscillations
NMDARs in recurrence
Strong inhibition to i-cells
Dynamics of spike generationa
Slow inward current
Wang (1999, 2001)
Hansel and Mato (2001)
Gutkin et al. (2001)
Tegner et al. (2002)
Reset of persistent activity
External excitatory input . . .
. . . recruits massive inhibition
. . . synchronizes activity
Seamans et al. (2003)
Shu et al. (2003)
Compte et al. (2000); Brunel and
Wang (2001)
Gutkin et al. (2001)
High CV in persistent activity
Fluctuation driven persistent
firing with excitatory-inhibitory
balance
Renart (2000); Renart et al.
(2003a)
Line attractor robustness
Homeostatic mechanisms
Discrete bistable units
Neuronal bistability
Noisy external inputs
Renart et al. (2003b)
Koulakov et al. (2002); Goldman
et al. (2003)
Camperi and Wang (1998)
Laing and Longtin (2001)
Strong external noisy input
Laing and Chow (2001)
Stability to spike-frequency
adaptation
Sanchez-Vives and
McCormick (2000); Shu et
al. (2003); Seamans et al.
(2003)
Fellous and Sejnowski (2003)
Entries in the table are indexed by the computational issue involved (first column), rather than by the mechanism implicated (as is done in the text)
to help the reader find its way in both directions.
a
Not discussed in the text.
putational– experimental approach should be able to settle
in the future are: (1) cortical inhibition dominance: can an
inhibition-dominated regimen be observed experimentally?
if so, how does it compare with the models that implement
it and to the excitation-dominated regimens? (2) selectivity:
can strong surround inhibition be observed such that selectivity is maintained during persistent activity? (3)
NMDARs: are NMDARs really indispensable for synaptically sustained activity in vitro? (4) activity variability: what
is missing in network models to be able to have as variable
a persistent activity as seen in vitro?
CONCLUSIONS
I have reviewed here the principal cellular and synaptic
mechanisms of working memory that network attractor
models of persistent activity have put forward to date. Most
of these mechanisms revolve around three ideas: strong
reverberation, strong inhibitory feedback, and NMDARmediated recurrent connections, each one playing one or
several possible roles in the generation, maintenance or
stability of persistent activity in working memory (see Sec.
1 and Table 1). At present, attractor models of recurrently
A. Compte / Neuroscience 139 (2006) 135–151
generated persistent activity face a number of challenges,
notably the structural lack of robustness of models based
on line attractors and the high variability of firing observed
during persistent activity in working memory tasks. Despite
these weaknesses, attractor models are currently the best
formulated framework for persistent activity generation and
they raise very specific and testable predictions that will
surely be the focus of much experimental attention in the
coming years. For this reason, I have also reviewed here
the current in vitro experimental models for synapticallysustained persistent activity: their strengths, weaknesses,
findings and prospects (see Sec. 3) in the hope that both
experimenters and modelers will find this useful in following this rapidly developing field of research.
The attractor hypothesis for persistent activity has
driven all computational research on persistent activity and
working memory up to now, but recently there has been
increased interest in the fact that typical neuronal firing in
working memory tasks includes very significant temporal
dynamics, and this suggests that maybe a framework beyond fixed-point attractors might be more appropriate to
understand working memory (see also Durstewitz and
Seamans in this issue; Brody et al., 2003; Ikegaya et al.,
2004). Such a formal framework is presently lacking, but
intense research in this direction is under way that will
probably yield exciting insights both biologically and
theoretically.
Acknowledgments—I gratefully acknowledge Alfonso Renart,
Maria V. Sanchez-Vives, Miguel Maravall and Alfonso Fairén for
helpful comments on the manuscript. Supported by the Spanish
Ministry of Education and Science, by the European Regional
Development Fund, and by the Volkswagen Foundation.
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(Accepted 3 June 2005)
(Available online 6 December 2005)