Top-down signals transmitted from prefrontal to parietal neurons reflect the executive control of cognition

Network representation of rule-dependent categories

Neural signals reflecting the spatial category of the sample as a function of the categorization rule provided a neurophysiological correlate of executive control over a spatial cognitive process. Rule-dependent and category-selective neural activity was distributed to neurons in both prefrontal and posterior parietal cortex. This included populations of neurons in both cortical areas with activity differentiating the categories ‘above’ and ‘below’ under the vertical but not the horizontal categorization rule, as well as neurons with activity differentiating the categories ‘left’ and ‘right’ in a similarly rule-dependent fashion (Supplementary Fig. 2).. Neural signals coding rule-dependent categories did not encode the spatial position of the sample stimulus or the orientation of the category boundary (because the signal was a joint function of the two randomly associated task variables, and was therefore dissociated from either of them considered individually). Rule-dependent category signals emerged after the presentation of the rule-cue (Supplementary Fig. 2), when enough information had been provided in the trial to assign the sample to a rule-dependent category unambiguously.

To quantify the information about spatial categories that could be decoded from the pattern of activity in prefrontal and parietal neuronal populations, we applied pattern classification to firing rates in the two cortical areas measured in a sequence of 50 ms time bins throughout the trial. To compare decoding accuracy between cortical areas, we accumulated counts of accurate and erroneous category decoding (on a per bin and trial basis) over the interval from the onset of the rule cue to the onset of the first choice stimulus, and then tested the resulting distributions of dichotomous data using the z-test of proportions. The accuracy of decoding vertical categories was significantly greater when based on activity patterns in prefrontal cortex than in parietal cortex, both when decoding was based on the activity of neural ensembles (groups of neurons recorded simultaneously; Fig. 1f; p < 10⁻⁸, z = 6.41, n = 23,088) and neural populations (accumulating significant neurons across recording sessions; Fig. 1g; p < 10⁻¹⁵, z = 8.15, n = 3224). (Filled circles in Fig. 1f–i indicate individual time bins in which decoding accuracy varied significantly across cortical areas, z-test of proportions, p < 0.05).Decoding the horizontal category of the sample on horizontal rule trials was, in contrast, significantly more accurate when based on neuronal activity patterns in parietal than prefrontal cortex, both at the ensemble level (Fig. 1h; p < 0.02, z = 2.79, n = 33,644) and the population level (Fig. 1i; p < 0.03, z = 1.98, n = 4940). However, the differences in decoding accuracy between cortical areas were smaller in this case (compare Fig. 1h,i to 1f,g).

We in addition compared the strength of vertical and horizontal category signals within each cortical area. Vertical decoding accuracy was significantly greater than horizontal decoding accuracy, both when based on neuronal activity in parietal cortex (Supplementary Fig. 3a,b; ensembles: p < 10⁻¹⁰, z = 6.70, n = 28,340; population: p <0.02, z = 2.26, n = 4056) and in prefrontal cortex (Supplementary Fig. 3c,d; ensembles: p < 10⁻⁵⁰, z = 15.00, n = 28,392; population: p < 10⁻³⁵, z = 12.54, n = 4108). These results are evidence that the cortical representation of vertical categories was stronger than the cortical representation of horizontal categories.

Measuring signal transmission between cortical areas

To determine whether neural signals coding rule-dependent spatial categories were transmitted between prefrontal and parietal neurons during the trial, we evaluated whether rapid fluctuations in the strength of these signals were correlated between cortical areas over time. To measure the strength of category signals, we utilized the time series of posterior probabilities provided by the decoding analysis (as greater posterior probabilities correspond to more certain category membership based on neuronal activity). We then determined if the time series of posterior probabilities in the two cortical areas were significantly correlated at different lags.

To illustrate the analytical approach, we consider hypothetical ensembles in prefrontal and parietal cortex, each of which contains two category-selective neurons (Fig. 2). The activity state of each ensemble can be represented by a point in a corresponding two-dimensional rate space (with the firing rate of each neuron along the horizontal or vertical axis). The evolving pattern of activity in each ensemble is captured by the sequence of firing rate measurements in the two neurons, comprising a trajectory through the rate space (Fig. 2a,b; arrows). The correct spatial category for this example trial, based on the visual stimuli presented, is ‘below’. As the firing rates of neurons 1 and 2 fluctuate over time, the pattern of ensemble activity in each time bin of this trial (Fig. 2a,b; open circles) gets closer to (or farther from) the mean pattern of activity associated the category ‘below’ in the training data. (Activity on training trials is used to define the mean and covariance of activity patterns associated with each category in the analysis). Distances in the rate space (Fig. 2a,b; dashed lines) are converted to posterior probabilities (Fig. 2a,b) under the assumption that the distribution of activity patterns is multivariate Gaussian within each category (shorter distances in the rate space corresponding to greater probabilities of category membership). Note that for simplicity we illustrate the mean activity patterns for categories (Fig. 2a,b; black dots) as remaining fixed over bins. In the transmission analysis we adopted, we recomputed the mean and covariance of activity patterns associated with spatial categories within each time bin.

We evaluated whether the time series of posterior probabilities in the two cortical areas were correlated at different lags. For that purpose, we regressed the time series of posterior probabilities in one cortical area on the posterior probability time series in the other, keeping the two time series in temporal register (lag 0), or shifting one time series relative to the other by a variable number of time bins (lags 1 to 8). Before performing the regression analysis, we prewhitened the posterior probability time series to make them stationary over time and eliminate autocorrelation (Supplementary Figs. 4, 5). This is advantageous because computing the cross correlation of time series that themselves contain strong time trends or are strongly autocorrelated can inflate estimates of cross correlation^19-21. After pre-whitening, we slid a 500 ms window (10 bins) through the trial in 50 ms time steps, aggregated values over trials and ensembles at each time step such that we maintained the pairing of data in parietal and prefrontal cortex to simultaneously recorded neurons in the two areas, and performed the regression using the posterior probability values in the window at each time step. This produced a time-varying estimate of signal transmission between cortical areas throughout the trial. We used the F-statistic associated with the regression at each time step to index the strength of the relationship.

Top-down transmission of rule-dependent category signals

We applied this analytical approach to separately evaluate the directional transmission of signals coding vertical and horizontal categories at a lag of 1 time bin between the decoding data in the two cortical areas, and found that vertical category signals were selectively transmitted in a top-down direction from prefrontal to posterior parietal neurons (Fig. 3a; red). The F-statistic associated with top-down transmission first exceeded the significance threshold (Fig. 3a, horizontal dashed line) approximately 250 ms after the onset of the rule cue in the trial, when neural activity in both cortical areas started to exhibit differential activity as a function of the rule-dependent spatial category of the sample stimulus (Supplementary Fig. 2). Transmission of vertical category signals in the bottom-up direction, from parietal to prefrontal neurons, was significantly weaker (Fig. 3a; blue; black dots indicate significant difference between top-down and bottom-up transmission, p < 0.05, in a permutation test). There was little evidence of significant transmission of horizontal category signals between prefrontal and parietal cortex in either direction (Fig. 3b), perhaps as a result of the significantly weaker neural signals coding horizontal categories in this network (Supplementary Fig. 3).

Transmission reflects real-time interactions between areas

We found that our ability to detect network transmission using this method depended on the simultaneity of neural recording, as one would predict if our analysis captured physiological interaction between cortical areas in real time. We performed a bootstrap analysis in which we shuffled trials to break the simultaneity of neural activity in prefrontal and parietal cortex. In the shuffling, we kept the posterior probability time series intact, did not disrupt the relation between neural activity and spatial category, and maintained the grouping of neurons into simultaneously recorded ensembles. We found that breaking the simultaneity of activity in the two cortical areas was sufficient to destroy detected network transmission between them. Namely, the significance of top-down transmission as reflected by the time course of F statistics obtained using the original data (Fig. 4a; solid red line) far exceeded the 95^th percentile of the bootstrap distribution of F statistics derived from the trial shuffled data (Fig. 4a; solid purple line; note the close approximation of the 95^th percentile of the bootstrap distribution to the significance threshold for the F-statistic). This indicates that the temporal covariation in category signals that we observed did not reflect common activation of parietal and prefrontal neurons by the visual stimuli in the task, because in that case trial-shuffling would be predicted to have little effect.

To further confirm that interactions between cortical areas reflected transmission of category signals specifically and not merely coactivation of the two areas, we repeated the transmission analysis using the mean level of activity in each ensemble (averaged over neurons). In this analysis, we employed the mean ensemble firing rate instead of the posterior probability associated with the correct spatial category in each time bin. We failed to detect evidence of significant transmission in this case (Fig. 4a–d; dashed red and blue lines). This provides some insight into the aspect of neuronal activation that supported signal transmission. Namely, the pattern of activity over neurons within an ensemble had to be evaluated to detect signal transmission between cortical areas, and not just the overall level of activity within the ensemble. Taking the average ensemble rate as a proxy for more global measures of neural activity within a small volume of cortex (such as the local field potential, or BOLD signal), the implication is that resolving the information communicated between prefrontal cortex and connected areas requires resolving activity at the level of single neurons.

The pattern of top-down transmission of vertical category signals was robust when we relaxed our inclusion criterion to include more ensembles and neurons (Supplementary Fig. 6)., We further investigated the potential influence of signals coding the spatial position of the sample (rather than its spatial category) on the transmission results we obtained. First, we quantified the effect of sample position on category-selective activity. If category neurons were systematically tuned to the retinocentric locations of sample stimuli, one would predict that differences in their firing rate for sample positions that were next to one another would be smaller than for sample positions that were farther apart, within each neuron's preferred category. This was not the case (Supplementary Fig. 7). Next, we examined the influence on vertical category signal transmission of including, or excluding, category-selective neurons that also exhibited selectivity for sample position earlier in the trial. Top-down transmission of vertical category signals was not augmented by the inclusion of category-selective neurons in which activity also varied significantly as a function sample position (Supplementary Fig. 8). This is evidence that the transmission of category signals between prefrontal and parietal neurons was not strongly influenced by signals encoding the spatial position of the sample.

We also evaluated the transmission of neural signals coding the categorization rule, and the spatial position of the sample. We found evidence that rule signals were transmitted in a top-down direction from prefrontal to parietal neurons (Supplementary Fig. 9b), based on the activity of neurons that varied as a function of the rule only, and not spatial category. Evaluating neural signals coding the position of the sample in parietal and prefrontal cortex,we found evidence that position signals covaried strongly and significantly between cortical areas at lag 0 (Supplementary Fig. 9c), an effect which peaked in the delay period following the offset of the sample stimulus.(Our analysis had limited ability to resolve transmission earlier in the trial during the cue period, when feedforward transmission might be expected, because data had to be aggregated over a sequence of bins longer than the cue period before transmission could be detected.)

Transmission involves negative feedback

The transmission analysis revealed that vertical category signals in one cortical area could either drive or suppress vertical category signals in the other. When we evaluated top-down transmission of vertical category signals at a lag of 1 time bin, the resulting regression coefficients were positive (Fig. 5a,c; black). This provided evidence that prefrontal vertical category signals drove parietal vertical category signals, in the sense that lagged changes in the reliability of category representation in the two areas were in the same direction, with prefrontal cortex leading.

When we evaluated bottom-up transmission of vertical category signals at lag 1, we found the converse. In this case the resulting regression coefficients were predominantly negative, and stronger category signals in parietal cortex predicted weaker category signals in prefrontal cortex one time bin later (Fig. 5b,c; gray).This suggests that top-down signal transmission from prefrontal cortex to target cortical areas may operate under the control of negative feedback.

Transmission has a restricted temporal extent

We repeated the transmission analysis evaluating interactions between cortical areas at a broader range of temporal lags from 0 to 8 time bins (0 to 400 ms). The time course of F-statistics associated with top-down transmission far exceeded the threshold for significance at lags 1 and 3 (Fig 6a), but remained very near that threshold at other lags, providing the strongest evidence for top-down interactions occurring at 50 and 150 ms respectively. When we evaluated the magnitude and sign of the regression coefficients associated with transmission as a function of lag, we found that the sign of top-down interactions flipped from a significantly positive mean regression coefficient at lag 1 (Fig. 6c; asterisk indicates significantly positive coefficient at lag 1, sign test, p < 10⁻⁵) to a significantly negative mean coefficient at lag 3 (Fig. 6c; asterisk indicates a significantly negative coefficient at lag 3, sign test, p < 0.001).The inversion in the sign from earlier positive to later negative top-down effects could sharpen the interaction between cortical areas in time, effectively increasing the temporal resolution of transmission. Bottom-up interactions were comparatively weak (Fig. 6b), and the mean regression coefficient was negative over a broader time range, specifically lag 1 (Fig. 6d; sign test, p < 0.01) and lag 4 (sign test, p < 0.001).

Transmission varies with behavioral performance

We investigated whether the strength of vertical category signal transmission varied as a function of behavioral performance. Rather than comparing signal transmission on correct and error trials (as relatively few error trials were available), we divided successfully performed vertical categorization trials into two groups differentiated on the basis of whether monkeys had earned a comparatively large or small proportion of reward under the vertical categorization rule in the recent past. (Trials were split into high and low recent reward groups based on whether the number of rewards earned under the vertical categorization rule in the past 10 trials was above or below the median value over all trials). Recent reward provided a behavioral metric analogous in some respects to local fractional income, a parameter which influences neural signals in parietal area LIP during a decision making task²². Top-down transmission of vertical category signals was significantly more reliable on high in comparison to low recent reward trials (Fig. 7a, filled circles indicate time bins with a significant difference in transmission strength across reward conditions in a permutation test). We did not see evidence of bottom-up transmission in this analysis (Fig. 7b; most likely because of the reduction in statistical power associated with dividing the trials available for each analysis in half). The residual posterior probability time series obtained by fitting an ARIMA (autoregressive, integrative, moving average) model to the decoding data on high and low recent reward trials essentially overlapped (Supplementary Fig. 10).It was not likely therefore that differences in the reliability of vertical category signal transmission on high and low recent reward trials could be attributed to differences in the strength of neural signals coding vertical categories under the two reward conditions.

Behavioral paradigm

We developed a DYnamic Spatial Categorization (DYSC) task that required monkeys to flexibly categorize the same set of visual stimuli according to alternative grouping criteria, or categorization rules¹⁸ (Fig. 1). Trials began with the presentation of a gaze fixation target at the center of the display. Monkeys had to maintain gaze within 2.5° of this target throughout the trial. After an initial fixation period, a circular sample stimulus (0.25–0.5° diameter) was presented for 400 ms at an eccentricity of 13° (Fig. 1a, b; ‘Sample’). The sample position was selected pseudorandomly from a circular array of positions (Fig. 1c, d). A delay period (Fig. 1a, b; ‘Delay 1’; 900 ms) followed the offset of the sample, after which a rule cue was presented (Fig. 1a, b; ‘Rule cue’; 400 ms). The rule cue was a line that bisected the sample array in either a vertical or horizontal orientation and served as a category boundary. When the rule cue was a vertical line it instructed the horizontal categorization rule, and divided the circular sample array into the spatial categories ‘left’ and ‘right’ on opposite sides of the boundary (Fig. 1a, c). In this case, the horizontal coordinate of the sample position was critical to computing the spatial category it belonged to, whereas the vertical coordinate was irrelevant to category membership. When the rule cue was a horizontal line it instructed the vertical (above/below) categorization rule, requiring monkeys to reassign the same set of sample positions to a new set of spatial categories (Fig. 1b, d; ‘above’ and ‘below’). In this case, the vertical coordinate of the sample position determined category membership whereas the horizontal coordinate was irrelevant. In the data included in this report, Monkey 1 performed the DYSC task while the categorization rule was randomized over trials. Monkey 2 performed the DYSC task in blocks of random length from 7 to 12 trials. After the rule cue disappeared, a second delay period followed (Fig. 1a, b; ‘Delay 2’ 900 ms). Following the second delay, two choice stimuli (circular, 0.25–0.5° diameter) appeared sequentially (Fig. 1a, b; ‘Choice 1’, ‘Choice 2’; 700 ms each). One choice was located in the same spatial category as the sample (the match), by virtue of being on the same side of the category boundary as the sample on that trial. The other choice was located in the opposite spatial category (the nonmatch). The order of choice presentation (match and nonmatch) was randomized over trials (the boundary was not visible during the choice sequence). Monkeys responded by controlling when they depressed a single response key (a pedal with their foot) in relation to the randomized choice sequence. The outcome of the trial (correct/incorrect) was dictated by the timing of the motor response relative to the choice sequence; movement direction did not vary. If the choice stimulus that was visible at the time of the motor response matched the spatial category of the sample, defined by the sample location and the orientation of the rule cue, the monkey was rewarded with a drop of juice.

Neuronal Database

We conducted neural recording in Brodmann's area 7a in posterior parietal cortex and areas 46 and 9 in dorsolateral prefrontal cortex in two male Rhesus macaque monkeys (Macaca mulatta; 5–8 kg). We simultaneously recorded the spiking activity of small ensembles of prefrontal and posterior parietal neurons consisting of ∼15–25 individually isolated cells in each cortical area using two16-electrode Eckhorn Microdrive matrices, one positioned over each cortical area (Thomas Recording, Giessen, Germany). The electrodes controlled by each matrix could be advanced through the dura and into the brain independently under computer control to isolate the action potentials of distinct sets of simultaneously recorded neurons (ensembles). We typically recorded the electrical activity of 2–3 neural ensembles per day. The waveforms of single neurons were isolated online by two operators working in parallel. Additional details of surgery and neural recording have been reported previously¹⁸. The results reported in this study are based on the electrical activity of 1360 isolated cortical neurons, including 666 neurons in parietal cortex, and 694 cells in prefrontal cortex. We did not perform a priori power analyses to determine sample size. (Little prior information was available on which to base an estimate of effect sizes relating to transmission of task-related signals between cortical areas).Rather, we obtained as large a sample of neurons as was practically feasible given technical constraints of acute single neuron recording and the necessity of isolating task-related activity in two cortical areas concurrently. All neurons encountered and isolated were recorded without preselection (i.e. blindly).By necessity, transmission analyses were performed on neurons identified as carrying specific task-related signals in a prior ANOVA (below), so experimenters were not blinded with respect to neuronal type after this stage in the analysis. All surgical and animal care procedures conformed to the Principles of Laboratory Animal Care of the NIH and protocols approved by the Animal Care and Use Committees of the University of Minnesota and the Minneapolis Veterans Affairs Medical Center.

ANCOVA-based selection of simultaneously recorded neurons for transmission analysis

To quantify the transmission of information between cortical areas, we first applied analysis of covariance (ANCOVA) to identify the subsets of neurons within each ensemble that exhibited activity varying significantly as a function of rule-dependent spatial category. The dependent variable in the ANCOVA was the firing rate of each neuron averaged over the ‘Rule cue’ and following ‘Delay 2’task periods (Fig. 1a, b). The factors in the ANCOVA were horizontal category (left/right), vertical category (above/below), and the categorization rule (horizontal/vertical); along with the interactions between rule and both horizontal and vertical category. For this analysis, we coded the horizontal and vertical categories of the sample stimulus each trial as a function of the sample's location in the stimulus array regardless of the rule in force. We included the firing rate averaged over the preceding Sample and Delay 1 periods (Fig. 1) each trial as a covariate in the analysis. This allowed us to evaluate the influence of rule-dependent category on firing rate apart from any carryover influence of the position of the sample stimulus. To conduct the transmission analysis, we selected neurons that exhibited rule-dependent, category-selective activity, as indicated by a significant interaction between the categorization rule, and either the horizontal or vertical category factors (p < 0.05).

Supplementary Figure 4a illustrates two groups of simultaneously recorded neurons in parietal and prefrontal cortex, subsets of which have activity relating significantly to vertical categories (colored circles). We defined a neural ensemble to be a group of simultaneously recorded neurons within a cortical area with category-selective activity under the same categorization rule. For example, an ensemble might consist of 3 prefrontal neurons each of which was preferentially activated to represent the vertical categories ‘above’ and ‘below’, or 2 parietal neurons both of which were preferentially activated to represent the horizontal categories ‘left’ or ‘right’. We evaluated transmission between neural ensembles in prefrontal and parietal cortex that (1) were recorded simultaneously in the two cortical areas, and (2) contained a minimum number neurons with activity significantly related to vertical categories in both cortical areas, or horizontal categories in both cortical areas. Restricting the analysis to ensembles containing a minimum number of cells with activity encoding spatial categories along the same spatial axis (horizontal or vertical) involved a tradeoff between the minimum numbers of category-selective neurons each ensemble had to contain to be included, and the number of ensembles available for analysis. We performed the analysis requiring that simultaneously recorded ensembles in prefrontal and parietal cortex both contain a minimum of either 1 or 2 significantly category-selective neurons with activity relating to spatial categories along the same spatial axis (horizontal or vertical). Due to the constraints of random sampling, the number of ensembles containing larger numbers of simultaneously recorded neurons encoding the same sets of spatial categories waslimited.

The main results of this paper are based on application of the more stringent criterion (minimum of 2 significant neurons simultaneously recorded in each of the two areas), which yielded a total of 22 simultaneously recorded ensembles containing 63 task-related neurons. Transmission analysis of vertical category signals was based on decoding obtained from 32 vertical category-selective neurons. These neurons were simultaneously recorded in 5 parietal ensembles (containing 18 significant neurons) and 5 prefrontal ensembles (containing 14 significant neurons). Transmission analysis of horizontal category signals was based on the activity of 31 neurons, segregated into 6 parietal ensembles (15 neurons) and 6 prefrontal ensembles (16 neurons). However, we relaxed the inclusion criteria and repeated the transmission analyses requiring that ensembles include a minimum one significant category-selective neuron along the same spatial axis (horizontal or vertical) in both cortical areas. Using this criterion, results of the transmission analysis were based on 52 neuronal ensembles containing a total of 108 neurons. For vertical categories, the analysis was based on 15 parietal ensembles (35 neurons) and 15 prefrontal ensembles (27 neurons). For horizontal categories, the analysis was based on 11 parietal ensembles (23 neurons) and 11 prefrontal ensembles (23 neurons).

Decoding rule-dependent categories from ensemble activity in prefrontal and parietal cortex

To characterize the transmission of cognitive signals between prefrontal and parietal neurons, we first applied a pattern classification analysis to decode spatial category from the pattern of firing rates observed in neural ensembles (Fig. 2; Supplementary Fig. 4). To capture temporal variation in category signals over the course of the trial, we applied the decoding analysis to ensemble activity patterns measured in a sequence of 50 ms time bins. At each time step, the output of the decoding algorithm provided the posterior probabilities that the sample stimulus belonged to each of the two alternative spatial categories possible under the current rule based on the pattern of firing rates over neurons observed. The posterior probability quantifies the confidence of each category assignment based on neural activity, and therefore indicates the strength with which neural activity patterns encode categories. For the transmission analysis, we used the posterior probabilities associated with the correct spatial category each trial, as defined by the sample and rule cue shown. In addition, we restricted the analysis to the half of the trials in the set for which the category preference of the neurons being analyzed was relevant to the behavioral choice the monkeys had to make. For example, when decoding the vertical categories ‘above’ and ‘below’, we selected neurons with activity significantly influenced by the interaction between rule and vertical category, and then used their activity to decode the vertical category of the sample on trials when the vertical categorization rule was in force.

To perform the decoding analysis, we constructed an ensemble rate vector capturing a snapshot of activity within a short 150 ms time window. The ensemble rate vector within the time window was constructed by concatenating the firing rate of each significant category-selective neuron in the ensemble measured within three consecutive 50 ms time bins. We then advanced this 150 ms window through the trial in 50 ms steps, and decoded category at each time step to produce a decoding time course of posterior probabilities. This time course measured rapid variation in signal strength over time (Figs. 1f–i; Fig. 2; Supplementary Fig. 3b).

We applied a linear discriminant pattern classification algorithm (the ‘classify’ function in the Matlab Statistical Toolbox; The MathWorks, Natick, MA) to compute the posterior probabilities associated with each spatial category. We performed this analysis using 5-fold cross validation. At each time point, we trained the classifier using 4/5 of trials (the training set). Using the training data, we computed the mean and covariance of the ensemble activity vectors associated with each of the two alternative categories under the current categorization rule. These values provided the free parameters of classification functions modeling the distribution of activity patterns associated with each category as a multivariate Gaussian distribution. We then used the classification functions to decode spatial categories from the ensemble rate vectors observed on the remaining 1/5 of trials (the test set). For each time bin in each test trial, the classification functions computed the distance between the ensemble rate vector and the means of the two Gaussian distributions in the rate space that were associated with the two spatial categories in the training data (Fig. 2a, b). The functions then converted these distances to posterior probabilities that the sample belonged to each category based on the activity pattern observed (Fig. 2c, d). We used the classification functions defined by neuronal activity within a single time bin to classify trials based on activity in that same time bin. We retrained the classifier to perform the classification in each subsequent time bin. We classified successive 1/5 of trials, using the remaining trials as training data, until all trials were classified. The time series of posterior probabilities captured variation in the strength of signals coding rule-dependent categories during individual trials in each cortical area (Fig. 2c, d; Supplementary Fig. 4b), enabling us to evaluate correlation in these signals over time (below).

We evaluated whether differences in decoding accuracy in parietal and prefrontal cortex were significant using the z-test of proportions applied to counts of accurate and inaccurate decoding of spatial category over trials in individual time bins, or accumulated over the time bins between the onset of the rule cue and first choice stimuli.

ARIMA preprocessing of decoding time series

We then sought to determine whether short term fluctuations in the time series of posterior probabilities in one cortical area preceded and predicted lagged fluctuations in the time series in the other cortical area, providing evidence that a neural signal specifically encoding rule-dependent categories had been transmitted (directly or indirectly) from parietal to prefrontal cortex. Estimates of cross-correlation between any two time series are biased and inflated in the case that the times series are themselves autocorrelated or nonstationary^19-21. In this case, the internal regularity of the time series increases the degree to which they appear to be interdependent. To obtain estimates of interaction between cortical areas that were relatively free of these concerns, we applied a transformation developed by Box, Jenkins, Granger, and others^{19, 20} to the posterior probability time series, in order to remove their autocorrelation and make then stationary. For that purpose, we fit an ARIMA (auto-regressive, integrative, moving average) model (of order 10, 2, 2) to the time series of posterior probabilities in each cortical area, using the ‘armax’ function of the System Identification Toolbox in Matlab. ARIMA models are linear models that predict each value in a time series as a weighted sum of prior values and also prior errors in prediction, after differencing the time series to improve stationarity. Models of order 10, 2, 2 first difference the time series twice, then fit regression coefficients to the 10 prior values of the series and the two prior errors in estimation that provide the best estimate of each value in the series. The order of the ARIMA model employed was selected on the basis of preliminary testing as this order effectively eliminated autocorrelation in the data (Supplementary Fig. 5).

Linear regression analysis of preprocessed decoding time series to detect network transmission

We then applied a regression analysis to evaluate whether the residual posterior probability time series capturing rapid fluctuations in the strength of category signals significantly covaried in prefrontal and parietal cortex (Supplementary Fig. 4d). To evaluate top-down transmission, we regressed the posterior probability in each time bin of the parietal series onto the posterior probability bin in the prefrontal series shifted earlier by a variable lag of from 0 to 8 time bins (Supplementary Fig. 4d, left; the analysis at lag 1 is shown predicting each value of the parietal time series at time t as a function of the value of the prefrontal time series at time t–1). To evaluate bottom-up transmission, we did the converse, and regressed the posterior probability in each time bin in the prefrontal series onto the p268robability in a prior time bin in the parietal series shifted earlier by a variable lag of from 0 to 8 time bins (Supplementary Fig. 4d, right shows an example at lag 1). To evaluate changes in the strength of transmission over time, we advanced a sliding 500 ms window (consisting of 10 consecutive 50 ms bins) in 50 ms steps through the posterior probability time series in the two cortical areas, accumulated the posterior probabilities within the window over trials and ensembles, and then performed the regression analysis on these accumulated data at each time step. The resulting time series of the F statistic associated with the sliding window regression provided a time-resolved measure of signal transmission between the two cortical areas. We plotted the F statistic at each time step at the leading edge of this sliding window. In order to compare transmission and decoding results directly, the decoding time courses in Figure 3 were likewise averaged within a sliding window of 10 successive bins.

Bootstrap test of significance of transmission results

Transmission of category signals reflecting real-time physiological interaction between prefrontal and parietal cortex should only be detected in the case that the neural activity used for the analysis was recorded simultaneously in the two cortical areas. It was therefore important to show that transmission was not detected between prefrontal and parietal cortex when the analysis was based on neural signals recorded at different times in the two areas. To make that determination, we repeated the transmission analysis after shuffling trials in a bootstrap procedure in which we kept the residual posterior probability time series produced by the decoding and ARIMA steps intact. In the shuffling we also kept neurons grouped into the same simultaneously recorded ensembles within each area that we had in the original analysis. Finally, we constrained the shuffling so that the spatial category associated with each posterior probability time series did not change as a consequence of the shuffling. Thus, trial shuffling broke the simultaneity of neural activity in prefrontal and parietal cortex but did not otherwise modify the posterior probability time series entered in the transmission analysis. The results of the transmission analysis after the trial-shuffling procedure estimated the degree of detected transmission that could be attributed to spurious factors, such as an artifact of the analysis, or parallel entrainment of population activity in prefrontal and parietal cortex to behavioral events, for example. We performed the regression analysis after shuffling posterior probabilities over trials in each time bin 500 times generating a distribution of F-statistics and regression coefficients corresponding to the null hypothesis that detected transmission reflected spurious factors, rather than actual signal transmission between simultaneously recorded neurons. We considered transmission between prefrontal and parietal cortex to be significant at a given time bin if the F-statistic or regression coefficient derived from the original neural data recorded simultaneously in the two cortical areas exceeded the 95^th percentile of the bootstrap distribution of the same statistic derived from the trial shuffled data in that bin.

In addition, we tested the significance of the difference between top-down and bottom-up transmission of category signals by shuffling posterior probability time series across cortical areas (100 iterations) and repeating the transmission analysis. Differences between the strength of top-down and bottom-up signal transmission were considered significant if the difference in the associated F-statistics derived from the original data exceeded the 95^th percentile of the differences in F-statistics associated with top-down and bottom-up transmission in the bootstrap distribution.

Modulation of transmission by reward history

We investigated whether transmission of category signals varied as a function of behavioral performance. We did not undertake a comparison of category signal transmission between cortical areas on error and correct trials since few error trials were available, and the difference in statistical power to detect transmission between areas would confound interpretation of the outcome of the analysis. Rather we compared the strength of category signal transmission between two groups of trials of equal size, differentiated on the basis on whether a given categorization rule had been rewarded with relatively high or low frequency within the last 10 trials. For each trial, we counted the number of trials within the last 10 trials that were rewarded under a given categorization rule. We divided trials into high recent reward and low recent reward groups based on whether the number of rewards earned under a given categorization rule within the previous 10 trials was above or below the median value of rewards for this rule, over all trials. We then performed the lagged regression separately using high and low recent reward trial subsets (Fig. 7), and a larger sliding window of 1000 ms (20 bins). We evaluated whether differences between transmission on high and low recent reward trials was significant by determining whether the difference in F-statistics associated with the two reward conditions in each time bin exceeded the 95^th percentile of differences obtained in a bootstrap distribution after shuffling trials across reward status.