Journal of Neurophysiology

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Temporal Properties of Posterior Parietal Neuron Discharges During Working Memory and Passive Viewing

Frederik C. Joelving, Albert Compte, Christos Constantinidis


Working memory is mediated by the discharges of neurons in a distributed network of brain areas. It was recently suggested that enhanced rhythmicity in neuronal activity may be critical for sustaining remembered information. To test whether working memory is characterized by unique temporal discharge patterns, we analyzed the autocorrelograms and power spectra of spike trains recorded from the posterior parietal cortex of monkeys performing a visuospatial working-memory task. We compared the intervals of active memory maintenance and fixation and repeated the same analysis in spike trains from monkeys never trained to perform any kind of memory task. The most salient effect we observed was a decrease of power in the 5- to 10-Hz frequency range during the presentation of visual stimuli. This pattern was observed both in the working-memory condition and the control condition, although it was more prominent in the former, where it persisted after cue presentation when the monkeys actively remembered the spatial location of the stimulus. Low-frequency power suppression resulted from relative refractory periods that were significantly longer in the working-memory condition and presumably emerged from local-circuit inhibition. We also detected a spectral peak in the 15- to 20-Hz range, although this was more prominent during fixation than during the stimulus and working-memory periods. Our results are in line with previous reports in prefrontal cortex and indicate that unique temporal patterns of single-neuron firing characterize persistent delay activity, although these do not involve the appearance of enhanced oscillations.


The cognitive capacity for sustaining and manipulating information that is not available to the senses is commonly referred to as working memory. Although originally thought of as an exclusive property of the prefrontal cortex, it is now well established that multiple brain areas are activated by working memory (Constantinidis and Procyk 2004). For example, visuospatial working memory recruits the posterior parietal cortex (PPC), the end stage of the dorsal visual pathway (Felleman and Van Essen 1991). Early studies in nonhuman primates showed that cortical neurons in both prefrontal and posterior parietal cortex exhibit elevated firing rates during the delay periods of spatial working-memory tasks (Andersen et al. 1987; Constantinidis and Steinmetz 1996; Funahashi et al. 1989). Much effort has gone into investigating the mechanisms mediating this sustained neuronal activity as a means of understanding spatial working memory (Constantinidis and Wang 2004). Recent reports also suggested that temporal patterns in neural activity may be implicated in the maintenance of information in working memory. Human electroencephalography (EEG) studies indicate that coherent oscillations arise during working memory and correlate with mnemonic performance (Sarnthein et al. 1998; Tallon-Baudry et al. 2001). Significant oscillatory activity in the γ-frequency range (25–80 Hz) was also previously observed in local field potentials (LFPs) and single-neuron discharges in the monkey PPC during working memory (Pesaran et al. 2002). The increase of rhythmic activity was proposed as evidence for the involvement of a Hebbian mechanism, in which activity reverberates within a stimulus-selective cell assembly (Lee et al. 2005; Pesaran et al. 2002; Tallon-Baudry et al. 2004). The presence of reverberating activity would then allow persistent delay activity in the absence of sensory stimulation. Interestingly, strong synaptic coupling among excitatory and inhibitory neurons in computational models of the local cortical network easily generates γ-frequency oscillations (Brunel 2000; Brunel and Wang 2003; Geisler et al. 2005). Indeed, network models of reverberating activity for working memory are prone to oscillatory activity in this frequency range (Compte et al. 2000; Tegner et al. 2002; Wang 1999).

Despite the evidence that working memory and persistent activity might be associated with increased γ-frequency oscillations during mnemonic periods, a recent study failed to find significant rhythmicity in the spike trains of prefrontal neurons engaged in persistent activity during working memory (Compte et al. 2003). It is thus unclear whether distinct temporal patterns of discharges are a generalized property of working memory throughout the cortex. Differences in processing between cortical areas, in behavioral tasks, or in the sample selection and analysis methods might account for discrepancies between different studies. To address these issues, we analyzed discharges of neurons in area 7a of the PPC. This cortical area shows persistent activity during working-memory tasks to a degree similar to that in the prefrontal cortex and lateral intraparietal area (LIP) (Chafee and Goldman-Rakic 1998; Constantinidis and Steinmetz 1996). Our study sought to examine whether working memory is characterized by specific temporal firing patterns. As a control, we considered the temporal structure of discharges in monkeys naïve to training in working-memory tasks. These animals passively viewed visual stimuli identical to those used in the working-memory task, but lacking any behavioral significance. We also wished to examine the firing patterns in neurons that showed significant elevation of their mean firing rate during the working-memory interval and those that did not, but might still play a role in the maintenance of working memory by virtue of changes in the rhythmicity of their discharges. We used analysis methods virtually identical to those of Compte et al. (2003) to determine whether the prefrontal and parietal cortices differed in terms of temporal properties of spiking activity.


Neurophysiological experiments

Data for this analysis were obtained from two earlier studies (Constantinidis and Steinmetz 2001a, 2005). A detailed description of surgeries, training, and neurophysiological methods can be found there. The initial study recorded single-unit responses in area 7a of PPC from two monkeys (Macaca mulatta) performing a spatial version of a delayed match-to-sample task (Constantinidis and Steinmetz 2001a,b). The animals were required to pull a lever while maintaining fixation of a target on a screen, remember the location of a spatial cue, and release a lever when a subsequent stimulus was presented at the same location as the cue (Fig. 1, right). Delay intervals where only the fixation point was visible on the screen were intercalated between successive stimulus presentations. All task epochs lasted 500 ms. The stimuli consisted of 4° squares presented in one of nine locations on an invisible 3 × 3 grid of 25° size. During experiments, arrays of multiple stimuli were sometimes presented, although the present analysis involves data recorded only during single-stimulus presentations. We will refer to this experiment as the “working-memory condition.”

FIG. 1.

Diagrams of the behavioral tasks used in Constantinidis and Steinmetz (2005) and Constantinidis and Steinmetz (2001a,b). In the control condition (left), the monkey pulled back a lever at the beginning of each trial and fixated continuously on the central spot for 500 ms. A stimulus was then presented for 500 ms and followed by a “delay” period of equal length. Monkey had to release the lever when the fixation target disappeared after the delay. In the working-memory (WM) condition (right), the monkey was required to remember the cue location and hold the lever until a subsequent match stimulus appeared. A random number of 0–2 nonmatch stimuli intervened between the cue and match stimulus.

In the second study (Constantinidis and Steinmetz 2005), neuronal responses were recorded from area 7a of two monkeys passively viewing stimuli (Fig. 1, left). These animals were never trained in any task that required them to remember the visual stimuli. They were required only to maintain fixation and to pull a lever. While fixating, stimuli were flashed on the screen, identical in appearance to those used for the working-memory condition. Delay periods were present between successive stimulus appearances. As in the working-memory condition, all task epochs lasted 500 ms. At the end of a delay period the fixation point disappeared, which cued the monkeys to release the lever. We refer to this experiment as the “control condition.”

Neurophysiological recordings were performed with an array of seven quartz-coated platinum–iridium microelectrodes that could be advanced independently by a microdrive. Action potentials from individual neurons could be isolated by a differential-amplitude window discriminator. Action potential time stamps were digitized and stored with 0.1-ms resolution. The waveforms of individual neurons were not stored and further classification of neuron types based on waveform was not possible for this study.

Data analysis


Only neurons that exhibited selectivity for our visual stimuli were included in the analysis. We defined selectivity as significant modulation of firing rate during the cue-presentation period for stimuli appearing at the nine possible locations (one-way ANOVA, P < 0.05). We analyze neurons both with and without significantly enhanced activity during the delay period of our tasks. We refer to the former as neurons exhibiting delay tuning or delay-tuned neurons. To examine which neurons displayed delay tuning, we used a paired t-test (P < 0.05) to compare the firing rates during fixation and during the delay period after the appearance of a stimulus at the neuron's preferred location (see following text). For this comparison, we used only the last 300 ms of the delay period, to eliminate any long-latency stimulus responses or stimulus-off responses. Neurons whose average delay period firing rate was <4 Hz were excluded from analysis because these provided too few spikes to be analyzed (Compte et al. 2003). We established the directional preferences for each neuron independently for cue and delay periods based on the following measure: (rmax + rmin)/2, where rmax is the highest firing rate observed among all nine stimulus locations and rmin is the lowest. Stimuli that elicited activity above or below this value were defined as preferred and nonpreferred, respectively.


We subjected the spike trains of each neuron to power spectrum analysis using the methods described in detail elsewhere (Compte et al. 2003). Briefly, spike data were first segmented in windows of duration T = 500 ms corresponding to each task epoch. The short duration of the data segments facilitated a stationarity assumption. Our methods can also be applied to nonstationary signals, but interpretation of the results is more difficult, especially at low frequencies. These spike trains {tj, j = 1, …, N} were then conditioned using the first four orthogonal Slepian-taper functions hk(t) (k = 1, 2, 3, 4), the Fourier transforms Hk(f) of which had a half bandwidth of 4 Hz. Slepian tapers are functions that maximize the energy in a given time–frequency interval, so they reduce the bias of the direct spectral estimator (Percival and Walden 1993). By averaging together spectra from data conditioned with orthogonal tapers, we obtain a well-controlled spectral estimate Math(1) with reduced variance (Jarvis and Mitra 2001). A power spectrum I(f) was calculated separately for each trial, then normalized by the expected power of a Poisson spike train of equal firing rate, and ultimately all spectra representing the same task period were averaged together (Jarvis and Mitra 2001). The variance of the normalized spectra was calculated using a jackknife method over trials (Thomson and Chave 1991). This method provides a robust estimator of the variance of the spectrum, even in the presence of nonstationarities. Our analysis did not address frequencies <5 Hz given the length of the time window, which was dictated in part by the duration of the stimulus presentation and delay intervals in the experiment.


We calculated the autocorrelogram of a spike train as the histogram of the time intervals between any two spikes, from which the shuffle predictor was subtracted (the shuffle predictor was obtained as the average cross-correlogram of spike trains corresponding to different trials) and the result was normalized to the SD of the shuffle predictor at each time lag (Aertsen et al. 1989). Thus the autocorrelogram is expressed in units of the shuffle predictor SDs.

Individual poststimulus time histograms (PSTHs) were computed for the neuron's preferred stimulus in 10-ms bins. The population PSTH was smoothed by averaging over three adjacent bins.


We classified cells according to their firing patterns as described in Compte et al. (2003). Two measures were used to classify the temporal pattern of discharges, based on the shape of the spike train's autocorrelogram and its power spectrum. An index A was defined as the height of the central autocorrelogram bins corresponding to time lags <5 ms. A spike train was categorized as bursty if A > 1 (>1 SD higher than the shuffle predictor), refractory if A < −1, and Poisson-like if −1 < A < 1. Similarly, neurons were classified based on the shape of their power spectrum. A neuron was defined as bursty if it exhibited a spectral peak that exceeded the expected Poisson power value by >1 SD; the neuron was defined as refractory if it exhibited a spectral trough that deviated from the expected spectrum by >1 SD; otherwise, the neuron was defined as Poisson-like.

The autocorrelogram and power spectrum criteria were used in conjunction, labeling spike trains as bursty if they exhibited both a power spectrum peak and a value of A > 1. This classification is based on the observation that bursty firing is associated with broad spectral peaks, even in the absence of oscillations (Bair et al. 1994). We classified spike trains as refractory if they had a spectral trough and A < −1 and as Poisson-like if they did not display significant spectral structures and −1 < A < 1. In addition, we classified spike trains as oscillatory when their power spectra exceeded 1 SD in the 10- to 25-Hz range and A < 1. This criterion may underestimate the number of oscillatory neurons because neurons exhibiting both a large proportion of short interspike intervals (ISIs) and oscillations are primarily classified as bursty.

Spike train simulations

To study the effects of nonstationarities and refractory periods on our spectral estimator we produced computer-generated spike trains and performed the power spectrum analysis described above. We simulated the effects of an absolute refractory period by generating Poisson-distributed spikes at a given firing rate λ and enlarging each ISI by 2 ms. So, in any small interval of time Δt after the absolute refractory period (over which the probability of a spike occurring is zero) the occurrence of a spike has probability λΔt. Such simulations produce exponentially decaying ISI histograms with a probability gap <2 ms. The effects of nonstationary firing rate were simulated by varying the value of λ as a function of time (Fig. 7). Spike trains with a relative refractory period were simulated by “canceling” spikes generated with the Poisson-distributed algorithm. Each spike was confirmed in the train only if its distance to the last accepted spike was longer than a randomly selected time window. The duration of these refractory windows was independently drawn at each spike from a probability distribution that dropped linearly to 0 over an interval of length L. Spike trains with relative refractory periods are characterized by a smooth ISI histogram that rises fast to reach a maximum (typically below L) and subsequently falls off exponentially. Thus ISIs shorter than L are penalized but not banned altogether. Simulations with a combination of an absolute and relative refractory period were also performed. Analysis of simulated spike trains was performed in 0.5 windows, as for the experimental data.

All data analysis and statistical testing were performed using the Matlab software package (The MathWorks, Natick, MA).



Activity from 170 neurons with visual responses and significant selectivity for spatial location (ANOVA test, P < 0.05) was recorded from two monkeys required only to maintain fixation and passively view stimuli without behavioral significance (control condition in Fig. 1, left). Additionally, recordings were collected from 202 selective neurons in the working-memory condition from two monkeys trained to perform a spatial version of the delayed-match-to-sample task (Fig. 1, right). In both sets of behavioral protocols, the first three phases of visual stimulation were identical (Fig. 1) and only the internal behavioral state of the monkeys differed. We restricted our analysis to neural responses recorded during these periods: baseline fixation, cue presentation, and the delay period after the offset of the cue.

Mean firing rates during the delay period

We first sought to identify neurons with significant elevation of their mean firing rate during the delay period, after the offset of the cue. We refer to these as “delay-tuned neurons.” A total of 14% (24/170) of the neurons in the control condition sustained a discharge rate that was significantly higher than baseline fixation at the preferred location (two-tailed paired t-test, P < 0.05). The number of delay-tuned neurons was significantly higher in the working-memory condition (χ2 test, P < 0.01), where it constituted 26% (53/202) of the neurons. There were no significant differences in the proportion of delay-tuned neurons between monkeys within each condition (χ2 test, P > 0.08). We examined the modulation of discharge rate among delay-tuned neurons by plotting population PSTHs (Fig. 2). The rate associated with the stimulus evoking the best delay-period response is plotted for each neuron. The response latency after cue presentation was about 50 ms shorter in the working-memory condition than in the control condition. Additionally, delay-period discharges were maintained at a higher level at the end of the delay period, whereas firing rate in the control condition appeared to decay faster, approaching the average baseline rate by the end of the delay period.

FIG. 2.

Population poststimulus time histograms (PSTHs) of neurons from both task conditions with significant delay activity. Results are shown for each neuron's preferred location. Task epochs are indicated on the x-axis. Average firing rates during fixation are shown as dashed horizontal lines (control: 8.4 spikes/s; WM: 10.5 spikes/s).

Neuronal discharge patterns

We next examined the temporal patterns of spiking activity for each condition and task epoch and classified these as either Poisson, refractory, or “bursty” based on their power spectrum and autocorrelogram (see methods). In doing this, we sought to address whether specific discharge patterns characterized working memory and whether neuronal discharge patterns were fixed for each neuron, or varied across task epochs. The most common pattern in the control condition (observed by 51% of all neurons in at least one task epoch) conformed to a Poisson distribution, where the timing of individual spikes is independent of each other, resulting in a flat autocorrelogram and power spectrum. Figure 3A presents an example of a neuron with predominantly Poisson-like discharge patterns and consequently little temporal structure in the autocorrelogram, except for the absolute refractory period; as expected, the ISI histogram for this unit decayed exponentially [Kolmogorov–Smirnov (K-S) test for goodness-of-fit, P > 0.6].

FIG. 3.

Examples of 4 neurons exhibiting one of the different discharge patterns in our classification: Poisson (A, from the control condition), refractory (B, from the working-memory condition), bursty (C, from the control condition), and oscillatory (D, from the working-memory condition). Each row displays discharge pattern in the epoch indicated (fixation, preferred cue, and preferred delay). Columns show 1) sample raster plots (each horizontal line represents one trial); 2) PSTHs (y-axis: spikes/s); 3) interspike interval histograms (ISIs; y-axis: percentage of total intervals); 4) normalized autocorrelograms, after subtracting the shuffle predictor and dividing by its SD; and 5) power spectra with associated error lines (±1 SD) normalized to the expected power of a Poisson spike train with the same rate.

The refractory firing pattern (Fig. 3B) was the second most frequent in the control condition (32% of all neurons exhibited such a pattern during at least one task epoch). This firing pattern was characterized by a trough in the ISI histogram, indicating a decreased spiking probability ≤20 ms after a spike has been fired. The shape of the ISI histogram deviated significantly from an exponential model (K-S test for goodness-of-fit, P < 10−5). The diminished firing probability produced a broad central depression in the autocorrelogram and a low-frequency (5- to 10-Hz) trough in the power spectrum. The relationship between a refractory period and a low-frequency spectral trough appears counterintuitive; one might expect that a refractory period of <20 ms would lead to a decrease in power in frequencies >50 Hz (because spikes are less likely to occur at high frequencies) and a concomitant increase of spectral power at frequencies below the inverse of the refractory period. However, this occurs for only very high firing rates. At rates significantly lower than the inverse of the refractory period, the spike train is still highly irregular and has contributions from many frequencies. Because the probability of firing is decreased immediately after a spike, the autocorrelation function presents a dip around zero-lag and its Fourier transform, the power spectrum, has correspondingly suppressed power at low frequencies; this phenomenon was previously described by Bair et al. (1994).

We also observed “bursty” discharging in our database, where action potentials were clustered in groups of two or more within a few milliseconds (Fig. 3C). In the control condition, 28% of all neurons showed this type of firing in at least one task epoch. The ISI histogram for these units displayed a high peak near zero (corresponding to a central peak in the autocorrelogram) and a long tail. As shown by Bair et al. (1994), bursting also causes a broad peak in the spike-train power spectrum between 0 and 50 Hz. Importantly, this spectral increase occurs even in the complete absence of oscillations, as when bursts are Poisson distributed.

In addition, we identified neurons that displayed rhythmic oscillations in the β-frequency range (12–25 Hz; Fig. 3D). We did not observe significant oscillations >20 Hz. For these spike discharges (occurring in 11% of neurons in at least one task epoch in the control condition), spike interdependence pro-duced oscillations in the autocorrelogram and a narrow peak in the power spectrum, which was clearly different from that associated with bursting.

These four types of discharge patterns were also observed in the working-memory condition, although a dominance of Poisson spike trains was not present there. Instead, 47% of all neurons exhibited refractory firing in at least one task epoch, whereas Poisson, bursty, and rhythmic firing patterns were observed in 39, 29, and 21% of neurons in some epochs of the task, respectively.

We then analyzed the incidence of these discharge patterns in our database across the various epochs of the task (Table 1). For the control condition, Poisson-like spiking activity was most frequent in the fixation epoch, whereas refractory discharges were prevalent in the cue epoch. Similar trends were observed in the working-memory condition with the additional effect that an increased incidence of refractoriness persisted in the delay period, after the extinction of the visual cue (Table 1). This suggests that many neurons modified their spiking statistics in a task-dependent manner. We analyzed the number of neurons that changed spiking pattern between task epochs. The most frequent transition was a change from a Poisson firing pattern in the fixation period to a refractory firing pattern in the cue and delay periods and a disappearance of oscillatory activity after the cue presentation (Fig. 4). Figure 4A shows an example of a neuron displaying a discharge pattern that did not deviate significantly from the Poisson distribution during the fixation epoch, but turned refractory during the cue epoch. In Fig. 4B, an oscillatory discharge pattern in the fixation period disappeared during the cue presentation.

FIG. 4.

Examples of neurons that displayed different discharge patterns between task epochs (both from the working-memory condition). Conventions are the same as for Fig. 3. A: this neuron exhibited discharge pattern that did not deviate significantly from Poisson in the fixation period (although a slight trend of oscillatory firing in the 15- to 20-Hz range is visible in the power spectrum). Same neuron exhibited refractory firing during the cue presentation, characterized by a significant spectral trough in the 5- to 10-Hz range. B: another neuron displayed a rhythmic discharge pattern during the fixation period, which disappeared during the cue period.

View this table:

Distribution of neuronal firing patterns

Power spectra of spiking activity

The increased incidence of discharge patterns differing significantly from the Poisson spectrum in some task epochs could, in principle, be accounted for by firing-rate increases rather than a change in the magnitude of spectral power. This is because the variance of the spike count of a Poisson spike train grows linearly with the rate r, so its SD is proportional to Math. Because we normalized power spectra by their mean firing rate, our statistical thresholds, which detect changes from the mean by a number of SDs, will tend to decrease with firing rate as Math/r ∼ 1/Math. We thus sought to determine how the mean spectra were modulated by the task across epochs and conditions and also whether working memory was associated with increased rhythmicity at specific frequency bands. To this end, we averaged the normalized power spectra of all neurons. We observed two salient structures in the population power spectra (Fig. 5): a low-frequency trough between 5 and 10 Hz (θ- and α-frequency range) and a peak between 15 and 20 Hz (β-frequency range).

FIG. 5.

Population spike-train power spectra from both conditions. Individual power spectra are normalized by dividing with the power of a Poisson train with the same firing rate (dashed horizontal line). Shaded areas represent 2 SE. We focused our analysis on the spectral trough between 5 and 10 Hz (indicated on the spectrum for preferred cues) and the peak between 15 and 20 Hz (indicated on the fixation spectrum), which displayed significant modulation throughout the task.

The low-frequency trough was most pronounced during the appearance of the cue. In both conditions, power in the 5- to 10-Hz range was significantly reduced during cue presentation compared with the fixation period (paired t-test, P < 10−5; see Fig. 6). Spectral power was normalized by firing rate, but because the cue presentation was also characterized by a large, phasic increase in firing rate we wanted to ensure that the spectral trough was not somehow related to this nonstationarity. For this reason, we performed two additional analyses. First, we repeated the spectral analysis for a time window beginning 200 ms after the onset of the cue, which omitted the sharp transient. A significant decrease in 5- to 10-Hz power was present in that time interval as well (paired t-test, P < 10−5). Second, we simulated the power spectrum of a Poisson process with an absolute refractory period and with nonstationary firing rate rising from 10 to >50 Hz (Fig. 7). No decrease in 5- to 10-Hz spectral power was observed in this simulation compared with a stationary process.

FIG. 6.

Averaged spectral power in selected frequency bands (5–10 and 15–20 Hz) shown for each condition and task epoch. Left, control condition; right, working-memory condition. Asterisks indicate significant differences in an epoch compared with fixation (t-test, P < 10−5).

FIG. 7.

Numerical simulations illustrating the effects of nonstationarities on the power spectrum estimation. A: PSTH and normalized power spectrum of simulated inhomogeneous Poisson spike trains and normalized power spectrum of a Poisson process with a 2-ms absolute refractory period and a time-varying firing rate, rising from 10 to 50 spikes/s. B: same for a homogeneous Poisson process with stationary firing rate of 30 spikes/s. No significant differences in spectral power were evident between the 2 simulations. Shaded bar indicates the 5- to 10-Hz range.

The spectral trough continued to be significant in the delay period of the working-memory condition, while the monkey remembered the location of the cue (paired t-test, P < 10−5). This effect was observed in the power spectra of both monkeys tested in the working-memory condition. In contrast, the spectral trough disappeared in the delay period of the control condition, when the animal was not required to remember the cue, and power in the 5- to 10-Hz range returned to the expected value of a Poisson process. Power in this spectral range thus did not differ significantly between the fixation and delay periods in the control condition (paired t-test, P > 0.8). Neither monkey tested in the control condition exhibited a spectral trough in the delay period. We used multivariate ANOVA to compare the 5- to 10-Hz power values across monkeys and conditions. The analysis showed no significant differences between individual monkeys within each condition, but a significant difference between the working-memory and control condition (P < 10−5).

The second systematic deviation from the Poisson power spectrum we observed in our neuronal recordings was a peak in the 15- to 20-Hz range. This was most pronounced in the fixation period, before the appearance of a stimulus (Fig. 5; see also individual neuron example in Fig. 4B). Power in the 15- to 20-Hz range was dramatically reduced from its fixation-period level at cue presentation both in the control and working-memory conditions (paired t-test, P < 10−5; see Fig. 6). However, the β-frequency peak returned in the delay period after offset of the cue, but in the working-memory condition β-power remained significantly lower than the fixation-period level (paired t-test, P < 10−5). The appearance of rhythmic oscillations was characterized by some variability between monkeys; a spectral peak above the expected Poisson power was observed in only two monkeys (one from each condition).

Comparing the quantitative spectral results in Fig. 5 with the numerical incidence of discharge patterns in the database across the task epochs (Table 1), we observe the same trends in the power content in the 5- to 10-Hz range and the incidence of refractory discharges in both task conditions. This is also true when considering the 15- to 20-Hz power content and the combined incidence of bursty and oscillatory discharges, which both act to increase power in this band. Thus the spectral effects observed at the population level indicate that neurons do indeed change their firing pattern (as shown in Fig. 4) as well as quantitatively modulate their temporal pattern of firing in the course of the task (as shown in Fig. 3, BD). Significant changes in spectral power between task epochs (e.g., intertrial- and stimulus-presentation intervals) were also reported in Bair et al. (1994), although that study emphasized the relative absence of spectral modulation for different stimuli presented in the receptive field.

Temporal properties of neurons with and without enhanced delay-period activity

The above results demonstrated that working memory is characterized by changes both in the mean discharge rate and in the temporal pattern of discharging in certain neurons. We set out to investigate how the two effects interacted by examining separately the average power spectra of neurons with and without significant elevation of discharge rate through the delay period. Overall, we observed no systematic differences in the position of the spectral trough and peak between neurons with and without delay tuning in either condition. The most salient difference we found was that delay-tuned neurons exhibited a deeper low-frequency trough during the delay period (Fig. 8). However, because of the small number of such neurons, the difference in the 5- to 10-Hz power between neurons with and without delay tuning only marginally approached significance (t-test, P < 0.03 in the control; P < 0.07 in the working-memory condition). No significant difference was observed between delay-tuned neurons and neurons without such tuning for the 15- to 20-Hz peak during the delay period, in either the control (t-test, P > 0.5) or working-memory condition (t-test, P > 0.1). Finally, no evidence of increased gamma power was present among delay-tuned neurons. The mean normalized power (±2 SE) in the 25- to 80-Hz range during the delay period was 0.92 ± 0.06 for the working-memory condition and 0.94 ± 0.07 for the control condition.

FIG. 8.

Population spectral power in the 5- to 10-Hz range (low-frequency trough) for neurons with significant increase in the mean rate of discharges over the delay period (delay-tuned), or not. Results are plotted separately for the control (left) and working-memory condition (right). Only data from the best cue location and after delay period are shown. Note that spectral power during the delay period remains at cue level in delay-tuned neurons, whereas this is not the case for neurons without delay tuning.

We also compared the distribution of discharge patterns within delay-tuned cells and cells without delay tuning. Although bursting was proposed as a mechanism of maintaining persistent activity, this discharge pattern was much less frequent among delay-tuned neurons than that among neurons without delay tuning; in the working-memory condition only 1/53 (2%) of delay-tuned neurons exhibited bursty behavior in the cue period and 4/53 (8%) in the delay period. Among cells without delay tuning, 11 and 16% showed bursty discharging during the cue and delay periods, respectively. The opposite trend was true for refractory discharging, which was more prevalent among neurons with elevated delay period activity. In the working-memory condition, 55% of delay-tuned neurons displayed a refractory discharge pattern during cue presentation and 40% in the delay period. The corresponding numbers for cells without delay tuning were 41 and 23%, respectively. In the control condition, the highest incidence of bursting was observed for neurons without delay activity and refractory discharging was more frequent among delay-tuned neurons here as well.

Spectral properties of activity to nonpreferred stimuli

The analysis of spectral properties we have reported so far involved discharges after presentation of preferred cues. It is possible, however, that neurons that did not alter their discharge rate in response to a particular stimulus might still exhibit changes in their temporal patterns of discharges. We therefore analyzed the spectral responses to nonpreferred cues, which did not produce a significant rate increase from baseline, to examine whether these properties were stimulus dependent (Fig. 9).

FIG. 9.

Population power spectra for neuronal discharges to nonpreferred stimuli. Conventions are the same as in Fig. 5.

In the control condition, nonpreferred stimuli produced little modulation of the power spectrum compared with the baseline fixation period. There was no significant decrease in power in the 5- to 10-Hz range in either the cue or the delay period (paired t-test, P > 0.1). The low-frequency power during the cue presentation was significantly suppressed for preferred compared with nonpreferred stimuli (paired t-test, P < 10−5), although this effect was not observed in the delay period (P > 0.05). There was a slight decrease of the 15- to 20-Hz peak during the presentation of nonpreferred cues compared with fixation, which just reached statistical significance (paired t-test, P < 0.01).

In the working-memory condition, appearance of a nonpreferred cue produced a significant decrease in 5- to 10-Hz power (paired t-test, P < 10−5). This was similar to the effect that a preferred cue had, but was significantly weaker for nonpreferred cues (paired t-test, P < 10−5). However, it disappeared in the delay period (paired t-test, P > 0.3) as opposed to the delay period after a preferred stimulus. Unlike in the control condition, the difference in low-frequency power for preferred and nonpreferred stimuli remained significant during the delay period (paired t-test, P < 10−5). The 15- to 20-Hz peak that was present in the fixation period was significantly reduced during appearance of a nonpreferred cue (paired t-test, P < 10−5).

Relation between spectral features and firing rate

The modulation of low-frequency power content, in a comparison of neurons with and without delay tuning and preferred and nonpreferred cues presented above, suggests that this spectral feature might be directly related to firing rate. Indeed, neurons with refractory discharging tended to have higher firing rates than did nonrefractory units in both the control condition (17.8 vs. 10.0 spikes/s; t-test, P < 10−5) and the working-memory condition (23.6 vs. 11.5 spikes/s; t-test, P < 10−5).

To understand the effect of firing rate on spectral power, we performed a number of simulations. We first sought to examine whether the presence of a 2-ms absolute refractory period followed by a 3-ms relative refractory period (simulating the refractory periods of action potential generation) might be responsible for the troughs in spectral power we observed at conditions associated with higher mean firing rate. Our results demonstrated that although spectral power in the 5- to 10-Hz range decreases as a function of firing rate in the presence of such refractory periods, a significant deviation from the expected Poisson spectrum by our criterion of statistical significance does not appear for rates as high as 80 spikes/s (Fig. 10A). This result indicates that appearance of significant spectral troughs cannot be explained simply by the refractory period of action potential generation. We then considered the effects of longer, relative refractory periods, such as those arising from hyperpolarization by inhibitory postsynaptic potentials or afterhyperpolarization. Our simulations suggested that refractory periods in the order of 20 ms could account for the shape of ISI histograms as well as significant troughs in spectral power similar to those we observed (Fig. 10B). Both sets of simulations showed that the magnitude of the spectral power in the 5- to 10-Hz range decreased monotonically as a function of firing rate and produced a straight line when power was plotted in a logarithmic axis, with a slope increasing as a function of the duration of refractory periods (Fig. 10, A and B).

FIG. 10.

A: simulations of spike trains with a 2-ms absolute followed by a 3-ms relative refractory period. Rasters, ISI histograms, and normalized power spectra are shown, using the same conventions as for Fig. 3. Top, middle, and bottom rows were generated with a firing rate of 10, 30, and 80 spikes/s, respectively. Right: average normalized spectral power in the 5- to 10-Hz band as a function of firing rate. A straight line indicates a logarithmic relationship. B: simulations of spike trains with an 18-ms relative refractory period in addition to the 2-ms absolute refractory period.

Given the relationship between spectral power and firing rate in the presence of refractory periods, we sought to determine whether there were differences in spectral troughs between epochs and conditions that could not be accounted for by changes in the firing rate of neurons with comparable refractory periods. We therefore transformed the spectral power of each neuron in the 5- to 10-Hz band by computing its logarithm and scaling by its firing rate. In our simulations, this quantity is constant for spike trains of equal refractory periods irrespective of firing rate (Fig. 11), so by applying it to our data we discounted the predicted rate dependency. We then performed a two-way ANOVA, using the experimental conditions (control and working memory) and epochs (fixation, cue, delay) as independent factors. The test indicated a significant difference between working memory and control spectral power (P < 10−5), even though the effect of firing rate was discounted (Fig. 12A ). There was also a marginally significant main effect of epoch (P < 0.05). Post hoc comparisons revealed no significant difference between monkeys in either the control condition or the working-memory condition. We reached the same conclusions by plotting the spectral power of monkeys tested in the working-memory and control conditions, grouped by firing rate (Fig. 12B): at each firing rate level, spectral power in the 5- to 10-Hz range was lower for the working-memory condition, a difference that was consistent between monkeys. These results indicate that the length or magnitude of refractory firing may be dynamically modulated during the presentation of a stimulus and during active working-memory maintenance compared with a control condition.

FIG. 11.

Simulated power for Poisson spike trains generated with different refractory periods. Log-transformed, normalized spectral power in the 5- to 10-Hz range scaled by firing rate is shown, representing the slope of the curves shown in the right panels of Fig. 10, and therefore being constant at different firing rates. Simulations were performed with an absolute and relative refractory period of total length equal to 5 ms (as in Fig. 10A) and 10, 15, and 20 ms (as in Fig. 10B).

FIG. 12.

A: log-transformed power in the 5- to 10-Hz range, scaled by firing rate as in Fig. 11 is shown separately for each task epoch and monkey. Curves denoted WM #1 and #2 plot data from the two subjects tested in the working-memory condition. Curves denoted Control #1 and #2, from the control condition. Graph indicates that differences in spectral power are present between conditions, even if the data are transformed to discount the expected effect of firing rate on spectral power. B: normalized spectral power in the 5- to 10-Hz band is plotted separately for each monkey and for all task epochs. Each data point represents the average of all neurons with firing rates in the range indicated on the x-axis. Fewer than 5 neurons with firing rate >40 spikes/s were recorded from 2 monkeys (one in each condition) and the corresponding averages have been omitted from the plot. Error bars represent SE in both panels.


We have analyzed neuronal discharges in area 7a of the posterior parietal cortex during a spatial working-memory task. We contrasted the discharge patterns from this task with recordings from monkeys that had never been trained in a working-memory task, but were required to passively view the same stimuli. Our analysis revealed that neuronal discharge patterns and firing rates were clearly modulated by the tasks. A population of posterior parietal neurons exhibited significantly elevated mean firing rates during working memory. Persistent firing was not present exclusively during working memory, although we did observe a quantitative difference between conditions in the percentage of neurons exhibiting such activity. Discharge patterns during working memory were characterized by a decrease in spectral power in the 5- to 10-Hz range, which correlated closely with the firing rate. This was associated with a relative refractory period of about 20 ms after the discharge of an action potential. Bursting behavior, in contrast, was not enhanced during working memory. We observed limited rhythmic discharging in the spike trains of posterior parietal 7a neurons. Oscillations were found in the β-frequency range and were most pronounced during the fixation period, before the appearance of a stimulus.

Firing rate increases associated with working memory

A persistent elevation of firing rate after the offset of a stimulus is commonly interpreted as a sign of active working-memory maintenance. The posterior parietal cortex has been known to exhibit persistent discharges during the execution of tasks that engage spatial working memory (Constantinidis and Steinmetz 1996; Gnadt and Andersen 1988). Our current results indicated that a population of area 7a neurons exhibited sustained discharges after the offset of the stimulus, even in monkeys who did not perform the working-memory task and were in fact never trained to assign behavioral relevance to any of the stimuli. This does not mean, however, that the monkeys would not be able to recall the stimuli if required to. Under natural conditions, humans are certainly able to recall sensory information that has been unavailable over a few seconds, even if not cued ahead of time. There is no reason to believe that monkeys do not possess this capacity. Our data indicate that a population of posterior parietal neurons continues to encode visuospatial information after the offset of a stimulus.

At the same time, our results demonstrated that executing a working-memory task produces quantitative changes in the discharge rate after a stimulus presentation. In the working-memory condition, a significantly higher percentage of neurons remained active after the cue offset and their activity decayed less over the delay interval. In that sense, our results suggest that willful maintenance of information in working memory does produce modulation in the mean discharge rate of posterior parietal neurons—in addition to modulation of temporal patterns. Therefore posterior parietal activity cannot be considered entirely passive or reflexive as studies in area LIP have also suggested (Sereno and Amador 2006).

We should note that differences between the naïve and trained state in firing rate and temporal discharge patterns (discussed in the following section) were observed in different monkeys. It is thus possible that anatomical differences in the areas sampled in each experiment may account for these results. Although we cannot rule out this possibility, we believe it is unlikely. The recording areas in each animal were verified by anatomical labeling after the end of recordings (fluorescent-dye marking of selected electrode tracks and marker pins localizing the center of the recording cylinders). Electrode penetrations localized outside of area 7a were excluded from further analysis. Multiple penetrations were performed, covering a large part of area 7a in each animal with an array of multiple electrodes positioned at a new location every day. No apparent anatomical localization of persistent discharges in a subregion of area 7a was evident in our database, or in previous studies. A large diversity of neuronal response profiles was reported in area 7a (reviewed in Constantinidis and Procyk 2004), although our randomized and unbiased sampling of a large number of sites provides the best possible assurance that the reported differences were ascribed to the training state rather than to the anatomical localization.

Low-frequency suppression of spectral power and refractory firing

The most significant and robust deviation of parietal spike trains from a Poisson-like discharge pattern was a decrease in the spectral power over the 5- to 10-Hz frequency range. This effect was observed during the appearance of a cue in both the control and working-memory conditions. However, the 5- to 10-Hz spectral suppression persisted into the delay period of only the working-memory condition. A spectral suppression in this frequency range was reported before in both prefrontal and parietal cortices (Compte et al. 2003; Pesaran et al. 2002). Our results demonstrate that it is a distinguishing property of active working-memory maintenance.

The low-frequency spectral suppression is related to a relative refractory period in neuronal spiking activity that may be otherwise Poisson-distributed and the suppression becomes more pronounced at higher firing rates (Bair et al. 1994). Whereas changes in spectral power in the 5- to 10-Hz band in the course of the task could be following rate modulations (as in our simulations of refractory Poisson spike trains in Fig. 10), our results show that this simple explanation cannot account for changes between control and WM monkeys (Fig. 12). It thus appears that at least one mechanism underlying the refractory period of area 7a neurons is accentuated in monkeys trained for a working-memory task.

A number of studies suggested that refractory firing patterns primarily characterize inhibitory interneurons (Compte et al. 2003; Constantinidis and Goldman-Rakic 2002; Csicsvari et al. 1999). Notably, Compte et al. (2003) reported that most of refractory spike trains recorded in the prefrontal cortex during a working-memory task were associated with fast-spiking (FS) units, exhibiting a narrow action potential waveform and high baseline firing rate. These features match the electrophysiological attributes of chandelier and basket interneurons (Krimer et al. 2005). One anatomical substrate that could account for refractory firing patterns was recently described in cortical interneurons: the existence of autapses, or synapses of an interneuron onto itself (Bacci et al. 2003, 2005). A discharge by an FS neuron will cause its own inhibition and a decrease in the probability of discharging another action potential immediately thereafter.

Our current results suggest that refractory patterns can be dynamically modulated and are thus unlikely to constitute fixed neuronal properties. One possibility that could account for the modulation that we observed is that refractory firing and a concomitant decrease of spectral power in the 5- to 10-Hz band is generated by feedback synaptic inhibition. Recurrent inhibition was previously hypothesized to play an important role in the local circuit engaged in working memory, including firing rate control (Amit and Brunel 1997; Latham and Nirenberg 2004; Wang 1999), neuronal tuning (Brunel and Wang 2001; Compte et al. 2000; Rao et al. 1999, 2000), and task sequencing (Constantinidis et al. 2002). Our results raise the possibility that FS interneurons shape not only the mean discharge rates of cortical neurons, but their spiking patterns as well. This interpretation does not rule out other potential mechanisms for the generation of refractory firing, such as intrinsic hyperpolarization.

Bursting and working memory

Bursts have long been hypothesized to be an efficient means for neurons to entrain other neurons into coordinated firing (Bair et al. 1994; Crick 1984; Lisman 1997). This could be particularly useful in the association cortex, where bursty firing may contribute to synaptic reverberations through the activation of short-term facilitation (Bair et al. 1994; Compte et al. 2003; Hempel et al. 2000). However, our data speak against this hypothesis. Among the 53 cells exhibiting enhanced delay activity in the WM condition, only one displayed bursty behavior during presentation of its preferred cue, which is where short-term facilitation would be expected to be induced if relevant for mnemonic performance. Furthermore, the incidence of bursty firing was generally not increased in the WM condition compared with the control and was consistently lower among delay-tuned neurons than that among neurons not displaying delay tuning. Bursting therefore seems an unlikely candidate for generating persistent activity in the posterior parietal cortex during working memory.

Rhythmic spiking

The original motivation for this study was to examine, in a controlled design, the hypothesis that sustained neuronal activity during working memory is associated with enhanced rhythmicity in neuronal spiking activity. We particularly sought to examine whether parietal activity is characterized by increased rhythmicity in the γ-frequency range. However, no such oscillations were observed in the spike trains of area 7a neurons. Task-modulated β oscillations (15–20 Hz), on the other hand, were a common yet inconsistent feature of neuronal discharge patterns in this area and were predominantly observed during the fixation period. Because oscillations were present to at least the same extent during precue fixation as that during the delay period, they were unlikely to be causally related to memory-specific reverberations.

A number of previous studies documented increased β-frequency oscillations in spiking activity and local field potentials in several cortical areas before the appearance of a behavioral cue, when a monkey is not executing a movement but is in an elevated state of alertness (Baker et al. 1997; Cardoso de Oliveira et al. 1997; Liang et al. 2002; Murthy and Fetz 1996; Sanes and Donoghue 1993). In fact, studies that do report γ-frequency oscillations during the processing of attended sensory stimuli also note a simultaneous decrease of β-frequency spectral power, which was elevated in the interval before the appearance of a stimulus (Fries et al. 2001). It appears that the sudden presentation of a stimulus upsets network dynamics and desynchronizes neural activity in the β-frequency range.

Comparison of prefrontal and parietal discharge patterns

We have shown that rhythmic neuronal firing at the single neuron level is not a characteristic sui generis of active maintenance of visuospatial information in memory, which is in line with earlier results from the prefrontal cortex (Compte et al. 2003). The temporal properties of posterior parietal spike trains resembled those of the prefrontal cortex in that they both exhibited a spectral trough in the 5- to 10-Hz range. This appeared during the cue presentation and persisted during the delay period, particularly for neurons that also exhibited significant sustained delay-period activity. A spectral peak in the 15- to 20-Hz range was not documented in the prefrontal data, although it was observed in one of the monkeys with prefrontal recordings (see Fig. 5 of Compte et al. 2003).

On the other hand, our results are in contrast with those reported by Pesaran et al. (2002) in area LIP of the posterior parietal cortex, despite using essentially identical analysis methods. Whereas that study found a γ-band peak specific for the memory period, we found neither γ-band oscillations nor oscillations at other frequencies showing specificity for the mnemonic delay. The reasons for this discrepancy are not immediately obvious. Anatomical location could be a consideration. Area LIP is more closely involved than area 7a with representation of saccadic eye movements (Barash et al. 1991; Shibutani et al. 1984) and the oculomotor-delayed-response task used by Pesaran and colleagues does not allow a distinction between motor planning and retrospective memory. The observed γ oscillations might therefore reflect saccade-coupled activity, which would explain their absence in our study. Marked differences in temporal properties of spike-train spectra were recently reported for adjacent parietal areas such as the parietal reach area and area 5 (Buneo et al. 2003). We should also note that the analysis by Pesaran and colleagues (2002) relied on a smaller (n = 40) sample of neurons, 70% of which exhibited significant mean-rate increases in the delay period of the task.

Despite the findings reported here and elsewhere (Compte et al. 2003), population-scale oscillations may still be supported by nonrhythmic firing in single units when the number of participating neurons is sufficiently large, so that individual units may “lock in” at different times (Brunel 2000; Brunel and Wang 2003; Csicsvari et al. 1999; Eckhorn and Obermueller 1993; Geisler et al. 2005). Further investigation of the relationship between spiking activity and local field potentials during working memory will prove essential for bridging the gap between persistent activity at the single-neuron and population levels.


This work was supported by awards from the Whitehall Foundation to C. Constantinidis and the Denmark–America Foundation to F. C. Joelving. A. Compte acknowledges support from the Spanish Ministry of Education and Science (Program Ramón y Cajal and BFI2002-02378), the European Regional Development Fund, and the Volkswagen Foundation.


We thank M. Steinmetz for help with the neurophysiological experiments that provided data for this analysis and X.-J. Wang, E. Salinas, and T. Meyer for valuable comments on the manuscript.

Present address of A. Compte: Institut d'Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), Carrer Villarroel 170, 08036 Barcelona, Spain.


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