Neuronal representation of saccadic error in macaque posterior parietal cortex (PPC)

Yang Zhou; Yining Liu; Haidong Lu; Si Wu; Mingsha Zhang

doi:10.7554/eLife.10912

. 2016 Apr 20;5:e10912. doi: 10.7554/eLife.10912

Neuronal representation of saccadic error in macaque posterior parietal cortex (PPC)

Yang Zhou ^1,^2,³, Yining Liu ⁴, Haidong Lu ¹, Si Wu ¹, Mingsha Zhang ^1,^*

Editor: Wolfram Schultz⁵

PMCID: PMC4865368 PMID: 27097103

Abstract

Motor control, motor learning, self-recognition, and spatial perception all critically depend on the comparison of motor intention to the actually executed movement. Despite our knowledge that the brainstem-cerebellum plays an important role in motor error detection and motor learning, the involvement of neocortex remains largely unclear. Here, we report the neuronal computation and representation of saccadic error in macaque posterior parietal cortex (PPC). Neurons with persistent pre- and post-saccadic response (PPS) represent the intended end-position of saccade; neurons with late post-saccadic response (LPS) represent the actual end-position of saccade. Remarkably, after the arrival of the LPS signal, the PPS neurons’ activity becomes highly correlated with the discrepancy between intended and actual end-position, and with the probability of making secondary (corrective) saccades. Thus, this neuronal computation might underlie the formation of saccadic error signals in PPC for speeding up saccadic learning and leading the occurrence of secondary saccade.

DOI: http://dx.doi.org/10.7554/eLife.10912.001

Research Organism: Rhesus macaque

Introduction

Interacting accurately with the environment is critical for an animal’s survival. However, a noticeable fact is that the executed actions are not always perfectly matched with the intended (desired) ones, but have errors. This is true even for very well trained actions (Shadmehr et al., 2010). Therefore, the brain must evolve efficient mechanisms to detect the motor errors between the intended and the executed actions for motor control, motor learning, spatial perception, and other motor-related cognitive functions.

The executed motor actions can be encoded by two types of signals in the brain: the internal movement-related signals (e.g., efference copy/corollary discharge) (Helmholtz, 1925; Sherrington, 1918) and the external sensory signals (e.g., proprioception) (Wang et al., 2007). In self-originated movements, the internal signals predict the displacement of motor effector (Crapse and Sommer, 2008; Duhamel et al., 1992; Helmholtz, 1925; Sommer and Wurtz, 2002; Sperry, 1950), whereas the external sensory signals inform its actual position (Fuchs and Kornhuber, 1969; Sherrington, 1918). Because the emergence of the sensory information lags the execution of the movement, it is believed that the motor errors in high velocity movements, such as saccades, are calculated by relying heavily on the internal signals (Kawato, 1999; Robinson, 1975; Shadmehr and Krakauer, 2008; Shadmehr et al., 2010; Wolpert et al., 1995). Over the past three decades, the online control of saccades as well as saccadic learning can, in principle, be fully explained by the well-established models that reflect the properties of the brainstem-cerebellum machinery for saccades (Barash et al., 1999; Catz et al., 2005; Dash and Thier, 2014; Ito, 1970; Kawato et al., 2003; Nowak et al., 2007; Pasalar et al., 2006; Robinson, 1975; Shadmehr and Krakauer, 2008; Shadmehr et al., 2010; Stein, 2009; Wolpert et al., 1998). However, up to date, whether neocortex is also involved in saccadic error detection is largely unknown.

We recently recorded the activity of a single neuron from posterior parietal cortex (PPC) of two monkeys while they were performing oculomotor tasks. Unexpectedly, we found the neuronal computation and representation of the saccadic error. One group of PPC neurons discharged persistently before and after saccades (PPS neurons). Another group of PPC neurons discharged purely post-saccadically (LPS neurons), starting to discharge ~70 ms after the completion of the saccade. A correlation analysis between the neuronal discharge and the end-position of the saccades suggested that the PPS neurons represented the intended end-position of the saccade (i.e., the location of the visual target) whereas the LPS neurons represented the actual end-position of the saccade. The PPS neurons started to decay their activities shortly after the increase of LPS neurons’ activities, fitting the temporal request for comparing the motor intention and sensory input (Figure 1A). Furthermore, the activity of the PPS neurons shortly after the arrival of the LPS signal was highly correlated with the magnitude of saccadic error and the probability of making a secondary saccade. Interestingly, the activity level of PPS neurons during this period resembled the subtraction between the intended and the actual end-position signals.

Figure 1. — (A) The proposed temporal sequence for comparison of the intended and the actual position signals. The intended signal raises up before the initiation of movement and lasts after the arrival of the external sensory signals. The external sensory signal raises up after the start of movement. The comparison occurs after the convergence of these two signals (marked by the dashed rectangle). The error signal is generated after the comparison. (B) Spatial-cue delayed saccade task (SCS). Horizontal direction trials: target is 10° in eccentricity. Oblique direction trials: target is 13° in eccentricity. (C) Memory-guided saccade task (MGS). (D) Color-cue delayed saccade task (CCS).

**DOI:** http://dx.doi.org/10.7554/eLife.10912.002

Taken together, our results showed that the PPS neurons in PPC behaved like an error detector that computed the saccadic error by comparing the intended and the actual saccade end-position signals. This error signal might be used for speeding up saccadic learning and predicting the occurrence of secondary saccade.

Results

The main behavioral task in the present study is named as spatial-cue delayed saccade task (SCS, Figure 1B). In this task, monkeys chose one from two identical visual stimuli (left versus right visual field) as the saccadic target, based on the position of an additional visual cue either appearing to the left or right of the visual field. The memory-guided saccade task (MGS, Figure 1C) was used to find the lateral intraparietal area (LIP) based on its physiological signature: neurons discharged persistently throughout the memory interval (Andersen and Buneo, 2002; Snyder et al., 1997; Zhang and Barash, 2004). In total, we recorded 753 neurons, in which 377 out of 753 neurons showed significant pre-saccadic activity (pre-saccadic neurons) whereas 107 neurons showed significant pure post-saccadic activity (post-saccadic neurons). The neuronal data shown here were recorded from the same holes (0.5 mm in diameter for each hole and 0.5 mm between two holes) of a recording grid in which we recorded persistent response neurons in the MGS task. The reconstructed recording sites show that all neurons, but one, were recorded within a small area of 3x4 mm² in monkey B and 3x3 mm² in monkey D. Therefore, the neurons shown in this study were probably recorded mostly from the LIP. We identified a group of pre-saccadic response neurons (89 out of 377) that discharged persistently in both pre- and post-saccadic intervals (PPS) when saccades were directed to the response fields (preferred direction). We also identified another 27 neurons with late post-saccadic responses (LPS).

The perisaccadic activity of PPS neurons reflects the intended end-position of saccade

The activity of an example PPS neuron in the spatial-cue delayed saccade (SCS) is shown in Figure 2A. In the preferred direction (black), the neuron started to increase in activity ~200 ms prior to the initiation of the saccade, and reached peak activity at ~100 ms after the end of the saccade. Then it started to decay in activity. Similar firing pattern was seen in the population activity of 89 PPS neurons (Figure 2B). On average, the activity of PPS neurons started to decay at ~74.8 ms (STD = 33.1) after the completion of the saccade.

Figure 2—figure supplement 1. — (A) The activity of an example PPS neuron in the SCS task. Averaged spike density with the 95% confidence interval (shaded area) in the preferred (black) and null direction (grey) are shown in the upper panel, whereas the horizontal and vertical eye traces are shown in the lower panel. (B) The averaged population activity of 89 PPS neurons (69 neurons from monkey B, 20 neurons from monkey DT). (C) Comparison of each neuron’s activity between trials that saccades directed to the left or right target. Symbols represent the activity of single neurons. The horizontal and vertical bars represent the standard error of the mean (SEM) of pre-saccadic activity (-200~0 ms from saccade start). The filled dots denote that the activity is significantly different between left and right saccades (p<0.05, Wilcoxon test). (D) The correlation between perisaccadic activities (-150~100 ms after saccade end) of single PPS neurons (n = 55) and the end-position of the horizontal saccades. Each dot represents the correlation coefficient value of a single neuron. The histograms in horizontal and vertical axis represent the distribution of correlation coefficient and p value, respectively. (m: mean, p: p value, n: number of neurons).

**DOI:** http://dx.doi.org/10.7554/eLife.10912.003

The pre-saccadic activity of the PPS neurons was strongly correlated with the direction of saccades. The relationship between the pre-saccadic activity (-200~0 ms before saccade start) and the direction of saccades (left versus right) is shown in Figure 2C. All but seven neurons had significantly higher activity (p<0.05, Wilcoxon test) in the preferred direction than in the non-preferred one. We further analyzed the correlation between the early post-saccadic activity (0–100 ms after saccade end) and the pre-saccadic activity of PPS neurons. The distribution of correlation coefficient values based on single trial analysis of 89 PPS neurons is shown in Figure 2—figure supplement 1. The results show that the pre-saccadic and the early post-saccadic activities were significantly and positively correlated in 34 of 89 neurons (p<0.05, t-test), and this correlation was also observed in the population data (mean r = 0.2151, p<0.001, paired t-test). Such results imply that the early post-saccadic activity of PPS neurons might encode similar information as the pre-saccadic activity did. Therefore, we introduced an epoch, the perisaccadic interval (-150~100 ms of saccade end), pooling the pre- and the early post-saccadic intervals.

We then assessed whether the perisaccadic activity of PPS neurons consistently encoded the actual post-saccadic eye position. To do so, we analyzed the correlation between the perisaccadic activity and the end-position of saccade for each PPS neuron on single trial basis. 55 out of 62 PPS neurons were recorded with enough trials (>30 trials in the preferred direction) that allowed us to make the correlation analysis when the monkeys performed the horizontal SCS task (Figure 1B). Overall, the correlation coefficient values of these 55 PPS neurons were symmetrically distributed around zero (Figure 2D, mean r = 0.0132, p=0.5242, paired t-test), suggesting that their responses are not directly encoding the actual end-position of saccades. On a single neuron level, most PPS neurons (45 out of 55) were uncorrelated with the end-position of saccades, with the remaining 10 neurons reaching statistical significance (p<0.05) but having inconsistent mixed positive and negative correlation: 4 were negatively correlated and 6 positively. Similar results were observed in 24 out of 27 PPS neurons that had enough trials for correlation analysis in the oblique SCS task (Figure 1B). There was no significant correlation between the perisaccadic activity and the end-position of saccade either in the horizontal (Figure 2—figure supplement 2A, mean r = −0.0209, p=0.4240, paired t-test) or in the vertical (Figure 2—figure supplement 2A, mean r=0.0170, p=0.5245, paired t-test) direction of saccade end-positions. These results indicated that the perisaccadic activity of PPS neurons does not likely encode the actual end-position of saccades. However, results are consistent if PPS does code for the intended end-position of the saccade.

There might be other factors that could possibly affect the early post-saccadic activity of PPS neurons. For instance, since the saccadic targets remained on until the end of a trial in the SCS task (Figure 1B), it is possible that the early post-saccadic activity of PPS neurons reflected the foveal visual stimulation, which followed the change in gaze direction from the central fixation point to the saccadic target. However, we found that during the MGS task, the same PPS neurons were not visually responsive during the visual feedback after finishing saccades (Figure 2—figure supplement 3). Note that in the MGS task, the target reappeared (‘feedback on’ in Figure 1C) after the saccade (273 ms in average). The absence of a visual response during the MGS feedback stimulus suggests that the perisaccadic activity of PPS neurons was not a foveal visual response.

Moreover, the observed variation in the perisaccadic activity for preferred and non-preferred directions cannot be caused by different reward signals. This is because the reward was identical between trials to either the preferred or the non-preferred direction. Thus, the discharge difference between preferred and non-preferred direction (e.g., Figure 2B–D) cannot be due to the level of reward.

The intended end-position was encoded by the relative change, rather than the absolute firing rate, of the perisaccadic activity of PPS neurons

Was the intended end-position signal task specific? We examined this question by comparing the activity of the same neuron in two different tasks. In both the SCS and MGS tasks, the monkeys made horizontal saccades to the same target locations. The firing patterns of PPS neurons were similar between two tasks, but the absolute firing rate differed between tasks (Figure 2—figure supplement 4A–B). While the absolute firing rate was significantly higher in the SCS task than that in the MGS task (Figure 2—figure supplement 4C, in population level, p<0.001, paired t-test), the relative change in activity, comparing the perisaccadic interval (-150~100 ms of saccade end) with the interval of 100~300 ms before saccade onset, was very similar between two tasks (Figure 2—figure supplement 4D, in population level, p=0.2887, paired t-test). Such results suggested that the intended end-position was not task specific and it might be more reliably encoded by the relative change of activity of PPS neurons.

The activity of LPS neurons reflects the actual end-position of saccade

In addition to the PPS neurons, we also recorded a group of neurons which started to discharge with a relatively long delay after saccade completion (LPS neurons, mean = 70.9 ms, STD = 31.3 ms). The activity of an example LPS neuron in the SCS task is shown in Figure 3A, and the population activity of 27 such neurons is shown in Figure 3B. The activity of LPS neurons was spatially tuned. Comparing the post-saccadic activities (25~225 ms after saccade end) of individual LPS neurons between trials in which saccades were directed to the opposite directions, all but two LPS neurons showed stronger activities in one direction than in the other (Figure 3C, p<0.05, Wilcoxon test). We then assessed the possibility that the activity of LPS neurons could consistently encode the actual end-position of saccades. If single LPS neurons code (at least partly) linearly for the end-position, one would expect a significant correlation of their activity with the random jitter in the actual saccadic end-position. If the code were consistent across single LPS neurons, we would expect a consistent bias of the correlation in one direction (negative or positive). Thus, we analyzed the correlation between the activities of LPS neurons and the end-position of saccades on a single-trial basis. 22 of 24 LPS neurons were recorded with enough trials (>30 trials in the preferred direction) when the monkeys performed the horizontal saccades. Indeed, we found that the distribution of the correlation coefficient values of these 22 LPS neurons was significantly biased to the positive direction (Figure 3D, mean r = 0.1237, p=0.0074, paired t-test). On a single neuron basis, we found that 18 out of 22 LPS neurons tended to be positively correlated with the end-position of saccades, with 5 reaching statistical significance (p<0.05). Taken together, although subject to noise on a single neuron basis, our results show that, in contrast to the PPS neurons, the activity of LPS neurons was positively correlated with the actual end-position of saccades.

Figure 3—figure supplement 1. — (A) The activity of an example LPS neuron in the SCS task. Averaged spike density with 95% confidence interval (shaded area) in the preferred (black) and null direction (grey) are shown in the upper panel, whereas the horizontal and vertical eye traces are shown in the lower panel. (B) The averaged population activity of 27 LPS neurons. (C) Comparison of single neuron’s activity between trials that saccades directed to the left or right target. Symbols represent the activity of signal neurons. The horizontal and vertical bars represent the standard error of the mean (SEM) of post-saccadic activity (25–225 ms after saccade onset). The filled dots denote that the activity is significantly different between left and right saccade (p<0.05, Wilcoxon test). (D) The correlation between postsaccadic activity (25~125 ms after saccade offset) of single LPS neurons (n = 22) with horizontal post-saccadic eye position when monkey made horizontal saccades. Each dot represents the correlation result of a single neuron. The horizontal and vertical histograms represent the distribution of correlation coefficient or p value, respectively.

**DOI:** http://dx.doi.org/10.7554/eLife.10912.008

Furthermore, unlike the PPS neurons, the LPS neurons showed similar post-saccadic activity between different tasks (Figure 3—figure supplement 1A: example neuron; Figure 3—figure supplement 1B: population neurons). Both the absolute firing rate (Figure 3—figure supplement 1C, in population, p=0.6526, paired t-test) and the relative change of the normalized post-saccadic activity (Figure 3—figure supplement 1D, in population, p=0.7262, paired t-test) were similar between the two tasks. Such task-independent activity further supports the notion that LPS neurons might encode the actual end-position of saccades.

The PPS neurons behaved like a comparator to estimate the discrepancy between the intended and the actual end-positions of saccade

We first assessed the possibility that the activities of PPS and LPS neurons fitted the temporal request for the comparison between intended and executed action (Figure 1A). To do so, we superimposed the population activities of PPS and LPS neurons to directly compare their temporal characteristics (Figure 4A). We proposed the middle point of the activity change as an index to represent the temporal feature of neural activity. On average, the LPS neurons started to increase their activity 25 ms before the decay of PPS neurons, indicating the temporal overlap of the PPS and LPS signals in PPC.

Figure 4. — (A) The temporal relationship between the activities of two types of neurons. The averaged activity with a 95% confidence interval of PPS neurons (black, n = 89) and LPS neurons (red, n = 27) was superimposed. The black and red vertical lines marked the time of the middle point of activity change for PPS neurons and LPS neurons, respectively. (**B-C**) The mean activity of LPS neurons (B) (n = 24) and PPS neurons (C) (n = 55) in three subsets of trials that were grouped based on the post-saccadic eye position in the horizontal meridian. The inserted histogram represents the distribution of post-saccadic eye position in the horizontal meridian. Colored curves represent the population activity of trials that have same color in the inserted histogram. The solid rectangle in (B) marks the postsaccadic period which was used for the analysis in (D), while the dashed and solid rectangles in (C) mark the perisaccadic internal used in (D) and post-subtraction interval used in (E), respectively. (D) The correlations of the late post-saccadic activity (25~125 ms after saccade offset) of LPS neurons (red) and perisaccadic activity (-150~100 ms relative to saccade offset) of PPS neurons (black) with post-saccadic eye position in the horizontal meridian. The colored dots represent the normalized activity of correlated trials for two types of neurons, respectively. The colored lines represent the regression linear fitting of correlated activity. The black and red bars in the bottom and top represent the trial number of each group. (E) The correlation between the post-subtraction activity (150~350 after saccade offset) of PPS neurons and the horizontal postsaccadic eye position. The larger the difference between the postsaccadic eye position and target location, the greater the post-subtracted activity in both undershoot and overshoot saccades. (F) The correlation between post-subtraction activity (150~350 ms after saccade offset) of single PPS neuron (n = 55) with saccadic error (distance between post-saccadic eye position and target position in horizontal meridian). Each dot represents the correlation result of a single neuron. The horizontal and vertical histogram represents the distribution of correlation coefficient or p value, respectively. (G) The post-subtraction activity fits well with the absolute difference between intended and real eye position signals. The blue and red lines represent the linear fitting of normalized perisaccadic activity of PPS neurons (blue, intended eye position signal) and post-saccadic activity of LPS neurons (red, actual end-position signal) with horizontal post-saccadic eye positions, respectively. The black lines represent the linear fitting of post-subtraction activity of PPS neurons with horizontal post-saccadic eye positions. The pink dashed line represents the regression fitting of the absolute subtraction result between the post-saccadic activity of LPS neurons and the perisaccadic response of PPS neurons.

**DOI:** http://dx.doi.org/10.7554/eLife.10912.010

Figure 4—figure supplement 1. — (A) The temporal relationship between the activities of two types of neurons. The averaged activity with a 95% confidence interval of PPS neurons (black, n = 89) and LPS neurons (red, n = 27) was superimposed. The black and red vertical lines marked the time of the middle point of activity change for PPS neurons and LPS neurons, respectively. (**B-C**) The mean activity of LPS neurons (B) (n = 24) and PPS neurons (C) (n = 55) in three subsets of trials that were grouped based on the post-saccadic eye position in the horizontal meridian. The inserted histogram represents the distribution of post-saccadic eye position in the horizontal meridian. Colored curves represent the population activity of trials that have same color in the inserted histogram. The solid rectangle in (B) marks the postsaccadic period which was used for the analysis in (D), while the dashed and solid rectangles in (C) mark the perisaccadic internal used in (D) and post-subtraction interval used in (E), respectively. (D) The correlations of the late post-saccadic activity (25~125 ms after saccade offset) of LPS neurons (red) and perisaccadic activity (-150~100 ms relative to saccade offset) of PPS neurons (black) with post-saccadic eye position in the horizontal meridian. The colored dots represent the normalized activity of correlated trials for two types of neurons, respectively. The colored lines represent the regression linear fitting of correlated activity. The black and red bars in the bottom and top represent the trial number of each group. (E) The correlation between the post-subtraction activity (150~350 after saccade offset) of PPS neurons and the horizontal postsaccadic eye position. The larger the difference between the postsaccadic eye position and target location, the greater the post-subtracted activity in both undershoot and overshoot saccades. (F) The correlation between post-subtraction activity (150~350 ms after saccade offset) of single PPS neuron (n = 55) with saccadic error (distance between post-saccadic eye position and target position in horizontal meridian). Each dot represents the correlation result of a single neuron. The horizontal and vertical histogram represents the distribution of correlation coefficient or p value, respectively. (G) The post-subtraction activity fits well with the absolute difference between intended and real eye position signals. The blue and red lines represent the linear fitting of normalized perisaccadic activity of PPS neurons (blue, intended eye position signal) and post-saccadic activity of LPS neurons (red, actual end-position signal) with horizontal post-saccadic eye positions, respectively. The black lines represent the linear fitting of post-subtraction activity of PPS neurons with horizontal post-saccadic eye positions. The pink dashed line represents the regression fitting of the absolute subtraction result between the post-saccadic activity of LPS neurons and the perisaccadic response of PPS neurons.

**DOI:** http://dx.doi.org/10.7554/eLife.10912.010

Then, we analyzed whether and how the activities of the PPS and LPS neurons correlated with the monkeys’ saccadic eye movements. We grouped the trials into different subsets based on the end-position of saccade in the horizontal meridian when the monkeys made horizontal saccades to the same target in the SCS task. The activities of three example subsets of trials are shown in Figure 4B for LPS neurons and in Figure 4C for PPS neurons. Notably, the activities of LPS neurons differed among subsets shortly after the increase in their activities (Figure 4B, within solid rectangle) and remained separated for at least 300 ms (about end of the trial). On the other hand, the perisaccadic activities of PPS neurons were similar among different subsets (Figure 4C, within dashed rectangle) but differed after the rise of the LPS neurons’ activity (within solid rectangle).

To more systematically analyze the correlation between neuronal activities and the end-positions of saccade, trials were grouped into 6 subsets for LPS neurons and 16 subsets for PPS neurons, based on the horizontal end-position of saccade. The averaged post-saccadic activity (25~125 ms after saccade end) of the LPS neurons was positively correlated with the end-position of saccade (Figure 4D, red, r = 0.9791, p=0.0006, t-test). In contrast, the perisaccadic activity of PPS neurons (-150~100 ms to saccade end) did not vary among different end-positions of saccades (Figure 4D, black, r = -0.1355, p=0.6168, t-test). However, shortly after the arrival of the late post-saccadic activity of LPS neurons (150–350 ms after saccade end), the discharge level of the PPS neurons varied among different subsets of trials (Figure 4C, within solid rectangle); that is, the farther away the end-position of saccades is from the location of saccadic target, the higher the activity of PPS neurons.

Strikingly, in a late post-saccadic interval (150–350 ms after the saccade end), the normalized activities of PPS neurons were highly correlated with the end-position of saccade and showed a parabolic distribution (Figure 4E, black dots) with the lowest activity when saccades ended near the target location (10°). Data from hypometric (amplitude < 10°) and hypermetric (amplitude > 10°) saccades were nicely fitted with different regressions (Figure 4E, black lines). The correlation analysis between single PPS neuron activity and the magnitude of saccadic error (difference between the saccadic end-position and the target position) further confirmed this result. While 12 out of 55 PPS neurons showed negative correlation (2 neurons reached statistically significant level), 43 out of 55 neurons showed positive correlation, and 19 neurons reached statistically significant level (p<0.05, t-test). Overall, the population correlation data showed a significant positive correlation with the magnitude of saccadic error (Figure 4F, mean r = 0.155, p<0.0001, paired t-test).

How did PPS neurons compare the intended and actual end-position signals? A simple mathematic model to estimate the congruence of two signals could be derived via subtraction. To make these two signals comparable, we set the activity in trials with saccades ending at target location (no saccadic error) as a reference condition for both PPS and LPS neurons. Then, for trials with saccades ending at other locations, their activities were normalized by subtracting the activity in the reference condition (Figure 4G, blue and red lines). Consistent with the subtraction model, the absolute difference between the two regression fittings of normalized activities of PPS and LPS neurons (Figure 4G, purple dashed lines) clearly overlapped with the activity of PPS neurons in the late post-saccadic interval (150–350 ms after saccade end) (Figure 4G, black lines). Moreover, the correlation between population activities of PPS neurons in the late post-saccadic interval and the magnitude of saccadic errors was significantly higher (p=0.0314, paired t-test) than the correlation with the end-position of saccade (mean r = 0.1134). It was also significantly higher (p=0.0023, paired t-test) than the correlation with the saccade amplitude (mean r = 0.0898). Thus, the level of the post-subtraction activity of PPS neurons was correlated positively with the discrepancy (error) between the intended (target location) and the actual end-position of saccade. However, the post-subtraction activity did not differentiate whether the error was from a hypometric or a hypermetric saccade.

To examine whether the chosen window (150–350 ms after the saccade end) for error presentation was merely coincidental, we analyzed the correlation between post-subtraction activity of PPS neurons and saccadic errors by using a 100 ms sliding window with a step of 10 ms. The sliding window started at 0 ms and stopped at 450 ms after saccade end. As shown in Figure 4—figure supplement 1, the population post-subtraction activity showed significant positive correlation with saccade error in a relatively long interval (120–380 ms after saccade end). In particular, during 150–300 ms the correlation was significantly positive (mean r > 0.1) and stable. Therefore, our results suggested that the PPS neurons might estimate the congruence between intended and actual end-position of saccades through subtracting the actual signal from intention signal.

A similar correlation between post-subtraction activity of PPS neurons and saccadic error was obtained in oblique trials of the SCS task (Figure 1B, with target 13° eccentricity) (Figure 4—figure supplement 2A–C) and in another task (CCS, Figure 2C, with target 10° eccentricity) (Figure 4—figure supplement 3A–C).

The post-subtraction activity of PPS neurons was highly correlated with the probability of a secondary saccade

Finally, we examined whether the post-subtraction activity was correlated with the monkey’s corrective behavior. In 1009 out of 4090 trials, the monkeys made a secondary (corrective) saccade following the primary saccade. The majority of the secondary saccades (851 of 1009) were directed toward the saccade target. We found that the probability of making a secondary saccade was reduced following the reduction of the primary saccadic error (Figure 5A). Also, the post-subtraction activity of PPS neurons was positively correlated with the probability of making a secondary saccade (Figure 5B, r = 0.8289, p=0.0001 t-test). Furthermore, when comparing trials with and without a secondary saccade, the post-subtraction activity was significantly higher in the trials with a secondary saccade (Figure 5C and Figure 5D). The positive correlation between the post-subtraction activity of PPS neurons and the probability of making a secondary saccade was also observed in the color-cue delayed saccade task (Figure 4—figure supplement 1D–E) and in the oblique saccade of the SCS task (Figure 4—figure supplement 2D–E).

Figure 5. — (A) The correlation between the probability of making corrective saccades and the post-saccadic eye position. Data showed the lower the saccadic accuracy, the higher the secondary saccade ratio. Two black lines represent the linear fittings of undershoot and overshoot saccades, respectively. (B) Correlation between the post-subtraction activity and the occurrence of a secondary saccade. The data groups were the same as in panel (A). (C) The average activity in trials with and without corrective saccades. Among trials with similar horizontal post-saccadic eye position, the post-subtraction activity was higher in trials with secondary saccades (solid curves) than in trials without secondary saccades (dashed curves). (D) The comparison of the activity between trials with and without secondary saccades. All data sets show that trials with secondary saccades have higher post-subtraction activity. The length of the bars under each data point represents the trial number in each group (red: trials with corrective saccade; black: trials without corrective saccade). Asterisks indicate the following: *p<0.05, **p<0.01, ***p<0.001 (Wilcoxon test).

**DOI:** http://dx.doi.org/10.7554/eLife.10912.014

The PPS and LPS neurons were intermixed in PPC

To examine how PPS and LPS neurons were distributed in PPC, we reconstructed the recording sites of individual neurons in a three-dimensional coordinate map for each monkey (Figure 6). Neurons were recorded from a 2 cm diameter recording chamber. The recording chamber was implanted under the stereotactic position, centered at 13 mm lateral to the middle sagittal line, and 3 mm posterior to the middle coronal line for monkey B; and at 13.5 mm lateral to the middle sagittal line and 4 mm posterior to the middle coronal line for monkey D. In the reconstructed map, the X and Y coordinates were relative to the center of the recording chamber of each monkey. Data showed that the distributions of the PPS and LPS neurons largely overlapped in both monkeys. Such intermingled distributions of PPS and LPS neurons indicated that PPS and LPS were recorded from the same area of PPC, suggesting the functional interaction between the two types of neurons is possible.

Figure 6. — The distributions of two groups of neurons based on recording site are shown for both monkeys (A, B). Each circle represents one single neuron. The black and red stars mark the averaged center positions for PPS and LPS neurons, respectively. The mean distances between the PPS and LPS neurons are 1.78 mm and 1.0727 mm for monkey B and monkey D, respectively. The X and Y coordinates are relative to the center of the recording chamber.

**DOI:** http://dx.doi.org/10.7554/eLife.10912.015

Discussion

In the present study, we reported two groups of PPC neurons, which encoded the intended and the actual end-positions of saccade, respectively, and the difference between the two signals was highly correlated with the saccade error and with the possibility of making a secondary saccade.

In the experiment, the monkeys were trained intensively to make a saccade to a small target (0.2°) within a 3° checking window. The saccadic target remained visible in the SCS and CCS tasks (Figure 1B, D) while the monkeys made saccades. More importantly, the end-positions of saccades for rewarded trials were distributed closely around the target as a Gaussian-like distribution with STD = 0.49°. Thus, it is reasonable to assume that monkeys did intend to make saccades to the target location. Here, we found a group of PPC neurons that discharged persistently in both pre- and post-saccadic epochs (PPS neurons). Although this perisaccadic activity exhibited significant difference between left and right saccades (Figure 2A–C), it was not correlated with the actual end-position of saccade (Figure 4D, black). Therefore, we propose that the perisaccadic activity of PPS neurons represented the intended end-position of saccade (i.e., the location of the saccadic target) (Steenrod et al., 2013).

Another group of neurons is marked by late post saccadic activity (LPS). The activity of these neurons rises ~70 ms after saccade completion (Figure 3B). Such late post-saccadic activity unlikely represents the efference copy that emerges before the initiation of saccade (Helmholtz, 1925; Sherrington, 1918). In contrast, the temporal profile of this LPS activity is very similar to the extraocular proprioceptive response reported previously (Prevosto et al., 2009; Wang et al., 2007). Moreover, for the following reasons, we believe that the activity of LPS neurons represents more likely the extraocular proprioceptive signal rather than the visual signal. Firstly, the LPS neurons did not have visual responses in all three oculomotor tasks. Secondly, when aligning the activity of LPS neurons at ‘feedback on’ in the MGS task (Figure 1C), the activity increased even before the time of feedback stimulus onset. Thirdly, we previously reported that the extraocular proprioceptive signal rose up in the primary somatosensory cortex ~30 ms after the end of saccade (Wang et al., 2007). In our case, the LPS neurons started to discharge ~70 ms after saccade (Figure 4A–B), indicating that the LPS neurons might encode an extraocular proprioceptive signal (Genovesio et al., 2007).

More interestingly, we found that the PPS neurons in PPC behaved like a comparator that calculated the difference between the intended and actual end-position of saccade. The post-subtraction activity of PPS neurons was correlated highly with the magnitude of saccadic error and with the probability of making a secondary saccade. Considering the fact that PPC is not directly involved in the control of saccadic eye movement (Li et al., 1999; Thier and Andersen, 1998; Wardak et al., 2002), the saccadic error signal in PPC might function differently from the error signal that drives the premotor circuitry for saccade in the brainstem. One possible function may be the programming of a secondary saccade in case of the primary saccade missing the target. Our data show that the comparison between the intended and the actual end-position of saccade starts in PPC ~70 ms after the end of the primary saccade (Figure 4A–C), which is too late to influence the primary saccade but is early enough to control the secondary saccade (the latter has a latency of ~154 ms in average). Therefore, this parietal error signal may reflect the next of programming a secondary saccade, a possibility that is suggested by the correlation between secondary saccade probability and the post-subtraction activity of PPS neurons. In contrast, the brainstem-cerebellum models do not explain how a secondary saccade is planned.

The widely studied short-term saccadic adaptation may be fully explained by the brainstem-cerebellum machinery. Nevertheless, the cortical error representation can still be useful, for instance, for certain features of adaptation that go beyond the standard short-term adaptation. In parallel to short-term adaptation, a long-term adaptation (i.e., the post-adaptation effect lasting for days) is present (Barash et al., 1999; Robinson et al., 2006), and the neural basis for the long-term adaptations remains unclear. There is evidence for meta-learning, that is, short-term adaptation becoming more rapid with repeated training (Kojima et al., 2004; Wong and Shelhamer, 2011); there are even contentions of ‘cognitive’ modulation of short-term saccadic adaptation (Cotti et al., 2009; Srimal and Curtis, 2010). The cortical error representation observed in the present study may have to do with any of these processes.

Another phenomenon is that a saccade can be elicited either by the sudden appearance of an external stimulus (reactive saccade) or by an endogenous cue (voluntary saccade). The cumulative evidence has shown that the saccadic adaptation of reactive and voluntary saccades involves different mechanisms and partially separated neural circuitries (Cotti et al., 2009; Deubel, 1995; Erkelens and Hulleman, 1993; Gaveau et al., 2005; Hopp and Fuchs, 2010; Panouilleres et al., 2014; Zimmermann and Lappe, 2009). While the brainstem-cerebellum circuitry plays a crucial role in the adaptation of reactive saccades (Barash et al., 1999; Hopp and Fuchs, 2004; Optican and Robinson, 1980; Panouilleres et al., 2015; Robinson et al., 2002; Takagi et al., 1998), PPC is highly involved in the adaptation of voluntary saccade (Gerardin et al., 2012; Panouilleres et al., 2014). The parietal error signal found in the present study might contribute to the latter.

Recent studies have shown that comparison between motor intention and proprioception is critical for motor learning (Desmurget and Grafton, 2000; Panouilleres et al., 2015; Wolpert et al., 2011; Wolpert and Ghahramani, 2000) and motor-related cognitive functions, such as motor awareness (Berti and Pia, 2006; Fink et al., 1999; Haggard, 2005) and self-recognition (Haggard, 2008; Jeannerod, 2003; Knoblich, 2002; van den Bos and Jeannerod, 2002). A line of evidence suggests that PPC of primates plays an important role in the comparison between motor intention and proprioception (Gerardin et al., 2012; Panouilleres et al., 2015). Clinical studies also found that patients with lesions in PPC frequently exhibit difficulties in evaluating and comparing the intended and actual positions for awareness of self-movement (Haarmeier et al., 1997; Sirigu et al., 1999), for maintaining and updating an internal representation of action state (Kawato and Wolpert, 1998), and for motor error correction (Pisella et al., 2000). Here, our study adds the neuronal evidence for motor error computation in PPC.

Materials and methods

Animal preparation

Two male rhesus monkeys (6–8 kg, 6–7 years old) participated in the present study. They were housed in separate cages in a large room with a 12 hr light/dark cycle. The horizontal and vertical eye position signals were recorded using the scleral eye coil technique (Crist Instrument Sclera), and data were sampled at 1 kHz. Before training, each monkey was surgically implanted with a head post and two eye coils. After training in all three oculomotor tasks, a recording chamber was implanted above PPC of the right hemisphere for chronic electrophysiological recording. All experimental and surgical procedures were standard and approved by the Animal Care Committee of Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences; Animal Care and Ethics Committee of Beijing Normal University.

Behavior tasks

Visual stimuli were projected (View sonic, PJD7383) onto a large screen that was placed 80 cm in front of the monkeys’ eyes. We used a QNX computer to control the visual display and to run the real-time data acquisition system (REX; NIH, Bethesda, MD).

Spatial-cue delayed saccade task (SCS, Figure 1B)

There were two versions of the SCS task: horizontal (with target at 10° eccentricity) and oblique (with target at 13° eccentricity) directions of saccadic targets. During training and data collection, the two versions were presented in separate sessions. Trials began with a central fixation point (FP) that appeared in the center of the screen. The monkeys were required to keep their fixation on this point for as long as it was on the screen. Next, 500 ms after the monkey achieved central fixation, two identical dots (targets) appeared simultaneously, one on the left and one on the right of the fixation point. These two dots remained visible until the end of the trial. 400 ms after the appearance of the two dots, a visual cue randomly flashed for 200 ms in one of 24 locations on the screen. Another 400 ms after the visual cue offset, the central fixation point disappeared. The monkeys needed to make a saccade to the dot that was on the same side of the visual field as the visual cue appeared.

During the daily training, monkeys were always encouraged to make a saccade to the target as accurately as possible. We used a small check window (3°) to check monkeys’ post saccadic eye position for every trial. In addition, the saccadic target was very small (0.2°) in order to avoid a wide variation of the saccade end points. In fact, the end points of saccades in both monkeys showed narrow Gaussian-like distribution that was centered near the target location (mean = 9.6615 degree, STD = 0.4894 degree). Thus, our monkeys were striving for the exact position of the target in the tasks.

Memory-guided saccade task (MGS, Figure 1C)

Trials began with the appearance of a fixation point (FP) at the center of the screen. Monkeys needed to fixate on the FP for as long as it was on. After 500 ms, a visual target briefly appeared (200 ms) at one of eight potential locations that were evenly spaced and positioned at equal eccentricity (10°). Monkeys had to maintain central fixation until the fixation point offset and then had to make a single saccade toward the memorized target location. Afterwards, a visual stimulus appeared in the same location of the target as the visual feedback.

Color-cue delayed saccade task (CCS, Figure 1D)

Trials began with the appearance of a fixation point (FP) at the center of the screen. Monkeys needed to fixate on FP for as long as it was on. After 500 ms, two visual stimuli with different colors (one red and one green) appeared simultaneously, and 600 ms later, the fixation point disappeared and monkeys needed to make a saccade to the red stimulus.

Neuronal recording

We used a micromanipulator (NAN Instruments) to drive the glass-covered tungsten microelectrodes (~1 MΩ), guided by a gauged stainless steel guide tube, down into the cortex to record activity in single neurons. Neural signals were conventionally amplified (Alpha Omega MCP Plus8) and then filtered through 300~3000 HZ (Krohn-Hite Model 3384). We used a QNX computer to run a real-time neuronal analysis system (MEX; NIH, Bethesda, MD) to sort the spiking signals based on the amplitude and waveform of spikes.

Behavioral data analysis

Criteria for saccades: The start and end of a saccade were determined using a threshold for velocity- and template-matching criteria. The start of a saccade was defined as the time when the velocity exceeded 30°/s, and the end of a saccade was defined as the point at which the velocity became less than 10% of the peak velocity. Furthermore, trials were only included for further analysis if they fitted the following criteria: (1) the saccade duration was 10 to 100 ms; (2) the saccadic endpoint was within a 5° window that was centered at the saccade target; (3) the saccadic amplitude was larger than 4°; and (4) the saccadic latency was shorter than 500 ms. Furthermore, we set different criteria for secondary saccade analysis: (1) the saccade duration was longer than 5 ms; (2) the minimum velocity for saccade onset was 8°/s; (3) the saccadic amplitude was larger than 0.2°; and (4) the secondary saccade occurred at least 100 ms after the end of the first large saccade. It has been reported that in human subjects, up to 20% of secondary saccades were not directed to the saccade target. These secondary saccades were also considered as secondary saccades (Morel et al., 2011). Therefore, we included all secondary saccades for further analysis. Furthermore, we defined the average eye position during 0–20 ms after the saccade offset as the saccade end point.

Neuronal data analysis

Classification of recorded neurons

We defined a neuron as a pre- and post-saccadic response neuron if its activity fitted the following criteria: (1) the mean activity during the pre-saccadic interval (0–200 ms before the saccade onset) in the preferred direction was significantly greater than the mean activity in the baseline interval (0~500 ms after fixation onset) (p<0.01, paired t-test); (2) at least 5 out of 10 bins (bin width = 20 ms) during the pre-saccadic interval had significantly higher activity than the mean activity in the baseline interval (p<0.05, paired t-test); (3) the mean activity during the pre-saccadic interval in the preferred direction was significantly greater than the mean activity during the pre-saccadic interval in the non-preferred direction (p<0.01, Wilcoxon test); and (4) the decay of activity was later than 35 ms after the saccade completion. In total, we isolated 380 neurons that significantly increased in activity before saccade initiation in the SCS task. Among them, 89 neurons were classified as pre- and post-saccadic response neurons.

We defined the late post-saccadic response neurons according to the following criteria: (1) the mean activity during the pre-saccadic interval was not significantly different from the mean activity in the baseline interval (p>0.05, paired t test); (2) the mean activity from 150 ms before the saccade completion was neither significantly different from the mean activity at baseline nor the mean activity in the non-preferred direction (p>0.05, Wilcoxon test); (3) the mean activity in one of two post-saccadic intervals (0~200 ms or 100~300 ms after saccade completion) was significantly greater than the mean activity at the baseline and the mean post-saccadic activity in the non-preferred direction (p<0.05, Wilcoxon test); (4) in at least 2 of 4 bins (bin width = 50 ms), the post-saccadic activity was significantly greater than that at the baseline interval; and (5) the increase in the time of post-saccadic activity was longer than 35 ms after the saccade completion. In the SCS task, 110 neurons exhibited significant post-saccadic activity. Among them, 27 were classified as late post-saccadic response neurons.

Data shown in Figure 2 and Figure 2—figure supplement 1–2 and Figure 4—figure supplement 1 includes all neurons that fitted the above criteria. Data shown in Figure 4C–H and Figure 5 includes neurons with enough trials (>30 trials) in the preferred direction (55 out of 62 for pre- and post-saccadic response neurons, 19 out of 24 for late post-saccadic response neurons). Also, data shown in Figure 4—figure supplement 1–2 includes neurons with enough trials in the preferred direction (in Figure 4—figure supplement 2, trials > 20; in Figure 4—figure supplement 3, trials > 30).

Method for determining the decay of pre-saccadic activity

Because the pre-saccadic activity decreased exponentially mostly around the time of the saccade, we employed an exponential function to fit the mean activity of each neuron to determine the optimal decay time. Specifically, we used the following method: (1) Calculating the mean spike density of each neuron in the preferred direction using a Gaussian kernel function (σ = 5 ms) and then selecting a time interval (200 ms before the saccade onset to 300 ms after the saccade onset, alignment at saccade onset; 250 ms before saccade completion to 250 ms after saccade completion, alignment at the saccade completion) for further analysis; (2) Using a small moving window (bin width = 20 ms, step = 1 ms) to determine the peak activity point, which was selected as the start point for the exponential fitting; (3) The end point for the exponential fitting was defined as the lowest activity after the peak activity point; (4) Because neurons discharged with large variations, we defined a period of peak activity fluctuation, which contained the activity decay time. This period ran from the peak activity point to a point after which the activity was lower than the peak activity by 2 STE, or 80% of peak activity; (5) Using an exponential function (y = A(1)*e(x/A(2))+A(3)) to fit the spike density function starting from each time point within the fluctuation period to the end point. The start point of the best fit, which had the minimum mean square residual error, was the activity decay time.

Method for determining the increase in post-saccadic activity

We also used the exponential fitting method to determine the optimal increase in the time of post-saccadic activity: (1) using the same method as mentioned in the previous section to calculate the mean spike density function in the preferred direction, selecting the time interval for further analysis, and finding the peak activity; (2) finding the bin with the lowest activity before the peak point; (3) defining the fluctuation period of lowest point as the lowest activity point to the last bin in which the activity was lower than 2 STE above the mean activity of the lowest activity or 2 STE above the mean activity of baseline; (4) the start point with the best exponential fit was the increasing time points of post-saccadic activity.

Statistic functions used in analyzing neuronal activity

Two standard statistic functions were used in the present study (t-test and Wilcoxon test). The normalized single neuron’s activity was calculated by using the baseline activity (100~500 ms after fixation point onset) to divide the activity throughout the trial.

Choosing different temporal windows to analyze different signals

We chose a time window to analyze a signal based on its biological meaning and the model framework. For instance, the actual saccade end-position signal (proprioceptive input) usually reaches the cortex with a delay of ~30 ms after a saccade completion (Wang et al., 2007; Xu et al., 2012). Since the monkeys might make secondary saccades at ~250 ms after the primary saccades, we chose a window, 25–125 ms after saccade completion, to study the actual saccade end-position signal. The intended saccade end-position signal should appear before saccade initiation and last until the arrival of the actual eye position signal. Thus we chose a time window from 150 ms before to 100 ms after the saccade end to study the intentional signal. Finally, the error signal should be generated after the comparison of internal and external signals, we chose a window (150–350ms after the saccade completion) for error signal analysis. Although varying the time interval may quantitatively change the results slightly, it will not change the major conclusions qualitatively.

Acknowledgements

We thank Prof. Michael E Goldberg and Dr. Malte Rasch for their helpful suggestions and comments. We thank IDG/ McGovern Institute for Brain Research at Beijing Normal University for the grant support.

Funding Statement

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Funding Information

This paper was supported by the following grants:

Ministry of Science and Technology of the People's Republic of China 2011CBA00406 to Mingsha Zhang.
National Natural Science Foundation of China 31471069 to Mingsha Zhang.
National Natural Science Foundation of China 91432109 to Mingsha Zhang.

Additional information

Competing interests

The authors declare that no competing interests exist.

Author contributions

YZ, Designed the experiments, Trained monkeys and collected the behavioral and neuronal data, Ana.

YL, Trained monkeys and collected the behavioral and neuronal data, Conception and design, Analysis and interpretation of data.

HL, Drafting or revising the article, Contributed unpublished essential data or reagents.

SW, Conception and design, Analysis and interpretation of data, Drafting or revising the article.

MZ, Designed the experiments, Supervised the experiments, Analysis and interpretation of data, Drafting or revising the article.

Ethics

Animal experimentation: Two male rhesus monkeys (6-8 kg, 6-7 years old) were involved in the present study. They were housed in separate cages in a large room with 12 hours light/dark cycle. The horizontal and vertical eye positions signals were recorded using the scleral eye coil technique (Crist Instrument Sclera), and data were sampled at 1 kHz. Before training, each monkey was surgically implanted with a head post and two eye coils. After training in three oculomotor tasks, a recording chamber was implanted above the posterior parietal cortex of the right hemisphere for chronic electrophysiological recording. All experimental and surgical procedures were standard and approved by the Animal Care Committee of Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences (Project number ER-SIBS-221112P); Animal Care and Ethics Committee of Beijing Normal University. (Project number IACUC (BNU) - NKLCNL 2013-09).

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eLife. 2016 Apr 20;5:e10912. doi: 10.7554/eLife.10912.018

Decision letter

Editor: Wolfram Schultz¹

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

[Editors’ note: a previous version of this study was rejected after peer review, but the authors submitted for reconsideration. The previous decision letter after peer review is shown below.]

Thank you for choosing to send your work entitled "Neural representation of the computation of motor error by single neurons in the parietal cortex" for consideration at eLife. Your full submission has been evaluated by Eve Marder (Senior editor), a Reviewing editor, and three peer reviewers, and the decision was reached after discussions between the reviewers. Based on our discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife at this point. However, if you would be able to address all issues raised by the reviewers in a satisfactory manner, we might consider a resubmission, although we cannot guarantee renewed refereeing by the same or other reviewers nor ultimate acceptance of your manuscript.

We identified the following main problems (for details and other issues, please see the appended reviews):

1) There were major problems with the design of the study (explicit control of errors, reviewer 1). While this cannot be changed at this point, it would be mandatory to reevaluate the interpretation of these data.

2) There were major issues in the style and clarity of the text, including the description of hypotheses, and the English (all three reviewers).

3) There were major problems with data analysis and interpretation. These include, but are not limited to, the distinction of different neuronal types in LIP which was felt to be particularly important (reviewer 3).

Reviewer #1:

This manuscript addresses an important issue in motor control, evaluating at the neuronal level for the presence and integration of prediction and feedback signals in LIP neurons during saccades. These signals are critical to the operation of a forward internal model and computing sensory prediction errors. The study uses three types of delayed saccade paradigms, spatial-cue delayed (SCS), memory-guided saccades (MGS) and color-cue delayed saccades (CCS), focusing on the relation between neurons firing both before and after the saccade and neurons that fire after the saccade.

While interesting, the manuscript has major problems with the presentation, analysis and interpretations. The result leaves a reviewer confused and uncertain exactly what was done, the results and their implications. First is the paradigm. The critical arguments need to be based on the undershooting or overshooting of the target. However, the paradigm was not designed to produce these events, instead the study attempts to obtain that information based on the natural variation in saccade end point position. The analysis assumes that the monkey is always striving for the exact center of the target and, therefore the presaccadic firing does not vary with position but this is a big assumption and needs evidence to support. Without this implicit assumption, the critical analyses in Figure 5 break down. The study would be more convincing if position errors were explicitly controlled.

The second major problem is the presentation. The study ignores the cerebellum and cerebellum-like literature on sensory prediction error processing. These include the many psychophysical, imaging and patient studies showing that the cerebellum is critical to sensory prediction errors by Shadmehr, Krakauer, and Diedrichsen (see papers such (Diedrichsen et al., 2005; Izawa et al., 2012; Krakauer and Shadmehr, 2006; Shadmehr et al., 2010) (Tseng et al., 2007) as well as single cell studies by Sawtell (Kennedy et al., 2014; Requarth et al., 2014) and Ebner (Popa et al., 2012; Popa et al., 2014). Also the presentation of the Results is dominated by description and discussing of supplementary figures. This is somewhat distracting, in some cases the claims are not clear or the supplementary results are not that crucial. In the Methods, three paradigms were used. However, no data is presented from the color-cue delayed saccade paradigm.

The third major problem is the analyses and problematic use of statistics. Many claims are based on one-sided t-tests. The vast majority of statisticians agree that one-sided tests should only be used if the alternative is physically impossible. This is not the case here and should not be used. Also, the use of 95% confidence intervals as a measure of population variability is not an appropriate measure nor is SEM a good measure. Instead, standard deviation is a much more appropriate measure of variability and should be used. Also, the single cell analyses in Figure 5, F, G and H that relate p-values to the correlation coefficients are problematic. First, obviously p-values and the correlation coefficient are highly related and will have somewhat of a bell-shaped profile. This is not informative. Second, performing secondary level statistics on correlation coefficients is not good statistical practice.

References:

Diedrichsen J, Hashambhoy Y, Rane T, Shadmehr R (2005) Neural correlates of reach errors. J Neurosci 25:9919-9931.

Izawa J, Criscimagna-Hemminger SE, Shadmehr R (2012) Cerebellar contributions to reach adaptation and learning sensory consequences of action. J Neurosci 32:4230-4239.

Kennedy A, Wayne G, Kaifosh P, Alvina K, Abbott LF, Sawtell NB (2014) A temporal basis for predicting the sensory consequences of motor commands in an electric fish. Nat Neurosci.

Krakauer JW, Shadmehr R (2006) Consolidation of motor memory. Trends Neurosci 29:58-64.

Popa LS, Hewitt AL, Ebner TJ (2014) The cerebellum for jocks and nerds alike. Front Syst Neurosci 8:1-13.

Popa LS, Hewitt AL, Ebner TJ (2012) Predictive and feedback performance errors are signaled in the simple spike discharge of individual Purkinje cells. J Neurosci 32:15345-15358.

Requarth T, Kaifosh P, Sawtell NB (2014) A role for mixed corollary discharge and proprioceptive signals in predicting the sensory consequences of movements. J Neurosci 34:16103-16116.

Shadmehr R, Smith MA, Krakauer JW (2010) Error correction, sensory prediction, and adaptation in motor control. Annu Rev Neurosci 33:89-108.

Tseng YW, Diedrichsen J, Krakauer JW, Shadmehr R, Bastian AJ (2007) Sensory prediction errors drive cerebellum-dependent adaptation of reaching. J Neurophysiol 98:54-62.

Reviewer #2:

This manuscript addresses the question of how the error between predictive and actual motor signals are represented in LIP. They propose that one population of neurons 'pre- and post-saccadic neurons' encode the desired target location and another the 'postsaccadic neurons' encode the actual target location, and that the difference between the signals of these two populations encodes the error signal. They also propose that larger error signal correlates with greater probability of corrective saccades.

The hypothesis is well described in Figure 1 and the experimental methods are well executed. However, the writing of the manuscript leaves much to be desired. It is often not clear what question is being addressed. Figures are described but what hypothesis is being addressed is left to be inferred by the reader; it would be extremely helpful to first state the hypothesis or prediction at the beginning of each section/paragraph and then describe the data. One important shortcoming is the lack of clarity regarding how the subtracted responses are computed; this is essential for the reader to understand the central tenet of this manuscript. I suspect that all this could be fixed with the help of an experienced writer. As it is, I found it difficult to read and therefore difficult to evaluate. However, if the writing is clarified and the data support the claims made, then it could be a highly impactful paper.

Comments:

Many English usage errors. e.g. Introduction, first paragraph: ‘…challenged by evidence that indicates…’, subsection “The activity of pre- and postsaccadic response neurons reflects the internal signals to predict the required future eye position”, end of first paragraph: should be “…postsaccadic activity decayed…”? At the start of the second paragraph of the aforementioned subsection: impending?

In the subsection “The activity of pre- and postsaccadic response neurons reflects the internal signals to predict the required future eye position”, second paragraph: 'in one direction than the other'. Do you mean in the preferred vs. non-preferred direction? Or do you mean in the left direction in the left saccade trials? Figure 3C: are all of these 89 from left saccade trials?

In the subsection “The activity of pre- and postsaccadic response neurons reflects the internal signals to predict the required future eye position”, second paragraph: unclear what the point of this paragraph is. Is it trying to say that pre and postsaccadic activity typically correlated so both could be relevant signal?

In the subsection “The activity of pre- and postsaccadic response neurons reflects the internal signals to predict the required future eye position”, third paragraph: not clear why you are comparing postsaccadic SCS with foveal visual response in MGS. Is this the rationale? "One consideration we excluded is the possibility that the postsaccadic activity is induced by visual stimulation. If so, then one would expect to see response to foveal visual response in the MGS task." However, this rationale is still not very strong. One could have weak visual response that is potentiated more in the SCS task than MGS task.

In the subsection “The activity of pre- and postsaccadic response neurons reflects the internal signals to predict the required future eye position”, third paragraph: 'post-subtracted activity': what exactly is being subtracted from what? It would be helpful to delineated what portions of response from which neurons fit into the hypothesis outlined in Figure 1.

This is really difficult to parse: 'between the perisaccadic activity of the pre- and post-saccadic neurons and postsaccadic activity of the late postsaccadic response neurons'. Perhaps it would be helpful to shorten 'pre- and post-saccadic neurons' to something like PPS neurons.

It is not clear what the color cue task was used for.

Reviewer #3:

The manuscript at question addresses the role of efference copy (=corollary discharge) and proprioceptive information in movement control. The model system considered is visually guided saccades and the hypothesis, the authors present is that parietal area LIP has access to both efference copy information and proprioceptive feedback and moreover, that a particular class of neurons, dubbed presaccadic-postsaccadic (=perisaccadic) response neurons represents the difference between the two. This difference is thought to serve as an error signal, responsible for subsequent corrective movements.

This argument is based on the distinction of two pools of neurons found in areas LIP of rhesus monkeys. One pool involves neurons which start to fire after a saccade, assumed to represent the acquired eye position after a saccade, reflecting proprioceptive feedback. The second pool consists of neurons with perisaccadic responses thought to represent a prediction of the eye position. The major result is that the late activity of perisaccadic neurons seems to correspond to the difference between their early (presaccadic) response and the discharge of the postsaccadic neurons. Moreover, this difference measure and the late perisaccadic responses thought to represent the difference show an intriguing dependence on the final eye position. The dependence shows a minimum for the ideal position (i.e., for an eye position corresponding to target position) and increases with increasing deviation from this ideal in both directions. This result is intriguing! The dependence found is the one of an error representation suitable to drive corrections and eventually learning. Actually, it seems too specific to be an adventitious consequence of the many assumptions the authors have to make on their way to this particular result, assumptions whose biological significance one may question. Nevertheless, I am not fully convinced that the conclusions drawn are justified and, moreover, that the conceptual framework presented is viable. What are my concerns?

Differentiation of 2 groups of neurons: The authors separate 2 groups basically only based on differences in the amount of presaccadic activity. Yet, this is not sufficient to conclude that neurons falling on either side of the cut off chosen are qualitatively different. The problem associated with this approach can be easily demonstrated by considering the distribution of saccade errors discussed in Figure 5, a distribution which is parsed by the authors into a number of error classes. Here they could as well have concluded that saccades found in distinct error classes are qualitatively different. Yet, they assume a continuous distribution. What is needed in order to justify the assumption of separate populations is a rigorous statistical approach (e.g., a cluster analysis), based on many more parameters.

Non-visual vs. visual basis of responses: independent of the question if the assumption of two neuronal pools is justified or not, I doubt that the interpretation of presaccadic activity is really as unambiguous as claimed by the authors. For instance, the neuron shown in Figure 3—figure supplement 2 shows a strong build-up of presaccadic activity with a clear peak at the time of the saccade when tested in the SCS paradigm but very little in the MGS paradigm, although probably in both tasks saccades having similar metric were carried out. The major difference between the two is the fact that in the SCS, but not in the MGS paradigm, the saccade target was available all the time. In other words, I would assume that the peripheral visual cue (based on the target) must have contributed significantly to the response in the SCS task. Independent of this specific interpretation: why should a response component, which – according to the authors – reflects the prediction of the saccade-based change in eye position should differentiate between paradigms? Further: why should an efference copy related discharge show the conspicuous build up plus peak associated with the saccade? And why should it begin such a long time before the saccade? My admittedly very subjective intuition is that such profiles reflect an intention and not an efference copy.

Tuning for eye position (change): If the presaccadic response component of the perisaccadic neurons and the responses of postsaccadic neurons reflected the predicted and experienced saccades, one would expect to see a clear reflection of saccade metrics. The paper does not provide any pertinent information: Do the authors find a tuning for the amplitude of the saccade vector and/or eye position? I think that a clear tuning must be demanded. Moreover, one would like to see that postsaccadic response neurons can be activated by passive eye movements.

Response windows: in order to quantify responses and the subtraction measure, the authors define windows without providing any justification for their specific choices. As they assume that the activity of perisaccadic neurons in the late window reflects the subtraction, nature would have to choose the windows like the authors unless the result were independent of the exact choice of windows. This question relates to the more general one of wiring: is there any biological basis for supporting the assumption that the output of postsaccadic neurons could be subtracted from the discharge of perisaccadic neurons? For instance, could it be that postsaccadic neurons are actually interneurons, potentially revealed by different spike waveforms and discharge statistics?

Conceptual concerns: I think that the conceptual framework presented in the Introduction and the Discussion suffers from a lack of clarity and rigor as to the role of parietal cortex in comparing an efference copy and actual eye position. I would guess that probably any oculomotor physiologist believes in the one or the other variant of Robinson saccade model in which the predicted momentary eye position is compared with the desired endpoint position and the difference is driving the saccade. Furthermore, the prediction is continuously updated based on error information, probably by cerebellar signals. This is a brainstem model with the superior colliculus representing the highest level. The neurons representing the prediction (i.e., the efference copy) in this model are the PPRF short-lead burst neurons whose discharge is precisely correlated with saccade kinematics, with a precision of msec. This model works perfectly without involving cortex, which would only disturb because of the unpleasant delays it would contribute. What I am trying to say is that in order to drive saccades, there is no need for the comparison of efference copy and actual eye position at the level of LIP. Such a comparison may take place, yet, the raison d´etre (e.g. perceptual purposes?) the authors have in mind should be presented much more clearly. As yet, I do not see a compelling concept and I do not see a need for control purposes.

[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]

Thank you for resubmitting your work entitled "Neuronal representation of the motor errors in macaque posterior parietal cortex" for further consideration at eLife. Your revised article has been favorably evaluated by Eve Marder (Senior editor), a Reviewing editor, and three reviewers. The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:

We apologize for the delay in this decision, which was caused by extensive discussions among the editors and reviewers. Basically, one of the reviewers is strongly supportive of publication, one more negative, and the last midway between. Consequently, there are some remaining concerns that you will need to address in the text before a final decision can be made.

1) If evidence is obtained without a prior working hypothesis – one should at least try to discuss the findings in relation to dominating concepts a posteriori and try to argue why the latter may be insufficient, wrong or whatever. However, to use the standard model to justify the experiments is weak. Please rework the text with this perspective in mind.

2) You assume a specific subtractive mechanism. This requires a specific anatomical relationship and it implies continuous interactions. However, there is no evidence that the strong anatomical assumption is met. You searched in large parts of posterior parietal cortex, ignoring well-defined anatomical boundaries. Secondly, the assumption of error representation is based on the selection of rather arbitrary time windows. Please address in the Discussion whether the assumed error representation could be a serendipitous finding consolidated by later work. However, it might well be an artifact of the many non-substantiated assumptions made.

Specific comments for your attention:

It is still somewhat of a challenge to get at the robustness of the data. For example, in Figure 5F, 18 out of 55 PPS neurons showed a significant position correlation with saccadic error and the population ρ is 0.13. Therefore, less than 2% of the firing variability is error-related. Is this sufficient encoding for the argument? Another example is in Figure 4D in which the correlation between post-saccadic activity of single LPS neurons and eye position is 0.10, or 0.01% of the variability. However, that is an issue best decided by the wider scientific community.

Reviewer #2 was the most critical. We are including his/her review in entirety for context above.

"A major earlier criticism related to the identification of 2 categories of neurons, which seemed arbitrary. My concern had been that the two groups of neurons might actually be extreme fractions drawn from a continuous distribution. The fact that the two groups can be separated convincingly by a cluster analysis resolves this doubt. Yet, the result does not mean that these two groups of neurons are in positions allowing them to entertain the subtractive interaction the authors try to advocate. Where are the LPS and the PPS neurons located – are they intermingled, are they found in non-overlapping regions of posterior parietal cortex, perhaps even in different layers, is there any evidence for the kind of connection between them needed to support the suggested subtractive interaction between LPS and PPS neurons? All we learn is that these neurons were recorded from posterior parietal cortex. This is a large regions consisting of a number of well-defined areas. In other words, when I concluded – after having read the previous version of the manuscript – that the authors had studied one of these areas, area LIP, I was obviously wrong. I think what is missing is experimental data addressing the exact anatomical position and the question of the existence of true physiological interactions between LPS and PPS – e.g. based on multielectrode recordings that would allow the authors to look for functional interactions between simultaneously recorded PPS and LPS. Hence, my concern remains that the seeming representation of the error by the subtraction of the two may be an artifact of the many assumptions made like the pretty arbitrary choices of time windows, the choice of saccade amplitude classes etc. For instance, I do not see any a priori reason why the assumed subtractive comparison should be confined to the two time windows chosen by the authors. If the assumed subtractive interaction between PPS and LPS were more than wishful thinking it would be in any case continuous… Moreover, if the population difference really reflected the saccade error, it should represent the error independent of the amplitude of the primary saccade (at least to some extent…). However, unfortunately, also this is not shown. Hence, I would say that the suggested subtractive interaction is a possibility but as yet far from being grounded on a solid experimental footing.

Unfortunately, also my criticism of the guiding concept and its presentation has not been addressed convincingly. Actually, I feel a bit guilty having drawn the author's attention to work on the cerebellum in processing motor errors and adjusting motor behavior. The reason is that considerations of the cerebellum now take a lot of space in both the Introduction and the Discussion, yet without really contributing to the question why – in the first place – there may be need for a parietal representation of saccadic errors. My original point had been that the Robinson saccade model and any of the many alternatives we have seen over the years work successfully with an internal feedback circuit controlling saccades, circuitry that is purely subcortical. The desired saccade amplitude is represented by the SC – and perhaps LIP etc. Yet, I do not see why the desired saccade amplitude representation in cortex requires error feedback. The authors are mixing up the need to adapt the efference copy in a forward model based on sensory feedback and the question if there are any consequences for the original saccade plan. I am not saying that there cannot be a reason why cortex may want to be informed about the execution of the saccade plan. But all the evidence argues against a role in the online control of saccades. The authors need a clear concept – e.g. related to differences between short term and long-term learning, metalearning etc. Convincing considerations in this direction are completely lacking. I do not think that lengthy – and partially fallacious – considerations of motor error representations in cerebellar cortex can compensate this deficiency.

A few further concrete remarks:

In the third paragraph of the subsection “The perisaccadic activity of PPS neurons reflects the intended eye position”, correlations between perisaccadic activity and postsaccadic position are being presented. Why analyze the horizontal and vertical components independently?

In the first paragraph of the subsection “The activity of LPS neurons reflects extraocular proprioceptive signals”: the distribution is clearly skewed. Hence, a t-test is not applicable.

In the second paragraph of the subsection “The activity of LPS neurons reflects extraocular proprioceptive signals”: the latency of LPS responses is on average 70.9 ms relative to the completion of the saccade. If we add a saccade duration of 30-40 msec, this would mean that the assumed proprioceptive signal would arrive more than 100msec after the beginning of the muscle contraction. I am not convinced that the assumption of a proprioceptive signal is justified. This is way too late for a standard proprioceptive signal and suggests something visual.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Neuronal representation of the motor errors in macaque posterior parietal cortex" for further consideration at eLife. Your revised article has been evaluated by Eve Marder (Senior editor), a Reviewing editor, and two of the original and very experienced reviewers.

The manuscript has been improved but there are substantial remaining issues that need to be addressed before acceptance, as follows:

As you will see, the first referee, who has seen the paper several times before, continues to have major issues that would normally lead to a rejection of the paper. However, at this advanced stage of the refereeing process, we would like to give you a chance to publish your interesting data, provided you can follow this referee's arguments. Specifically, the referee makes very clear and simple suggestions for a final revision (under the title 'Suggestion'). Provided that you are willing and able to follow these suggestions, and do not introduce new points that might give rise to new issues, we would invite you to do this revision, after which we need to make a final decision about acceptance for publication or not. Ordinarily at this point we would only provide a summary of what remains to be done, but we think you might be curious to see the reviewer's reasoning, as well as his/her suggestions.

Reviewer #2:

Let me stress that I very much appreciate the efforts of the authors to improve the manuscript taking comments and criticism into account. However, unfortunately also this now third version of the paper is still far from being flawless. Actually, while some problems have been fixed new ones have been added and the conceptual framework offered is still very poor.

Improved:

The authors now provide reasonable arguments that they may have recorded from LIP, although they should be a bit more cautious when drawing this conclusion in the first paragraph of the Results. I would suggest to add the qualifier”probably mostly recorded…" They moreover provide evidence that the two types of neurons (PPS and LPS neurons) were found intermingled. I agree that this may make functional interactions between the two more likely. Yet again, I would phrase this possibility more cautiously.

They also have taken the criticism that the correlation between the postsaccadic error and the subtraction signal may be a fortunate artifact of the time windows chosen. They now show that this result is also obtained if the time windows are changed to some extent. This is an improvement.

Remaining or new problems:

Unfortunately, the problem that the range of target eccentricities tested is limited to 10deg and the range of saccade amplitudes explored therefore being very small remains (see below).

In the first paragraph of the subsection “The activity of LPS neurons reflects extraocular proprioceptive signals“, we learn that only 5 out of 22 LPS neurons showed significant correlations between their discharge and saccade amplitudes. This is not a compelling argument for an interest in saccade amplitudes. Only if they had varied target eccentricity (which they did not do) they might have been able to clarify if LPS neurons indeed encode amplitude as claimed. In any case, the next step in the argument is again confusing: in the population they find negative as well as positive correlations with a bias for the latter. This is the basis of the conclusion that the population encodes eye position. The implication of this conclusion is that negative correlations would not be compatible with position encoding, which is not correct. Neurons can encode information in multiple ways, linearly or non-linearly.

Conceptual framework propagated in the Abstract, the Introduction and the Discussion.

Much of what we read in these sections deals with the roles of efference copy signals and the need for proprioceptive feedback. The authors provide evidence for a signal – based on their LPS neurons – that may reflect eye position. Yet, the data does not allow one to decide whether this eye position signal is based on efference copy or proprioceptive feedback. However, already the Abstract talks about the latter. This is simply not correct. I agree that a proprioceptive signal may be possible or even likely in view of its demonstration elsewhere in parietal cortex. Yet, others have provided clear evidence for efference copy signals in posterior parietal cortex (e.g. the Andersen lab for reaching). From my point of view the authors should not make claims that are not justified and discuss the pros and cons honestly in the Discussion. In the Abstract and Introduction though they should be more neutral and use phrases such as eye position related etc. Actually dwelling on the nature of this signal in the Discussion would be much more valuable than the endless pages on motor errors and the role of the cerebellum in the Discussion and already earlier in the Introduction, sentences that do not contribute anything to an understanding of their findings and rather have the flavor of a poor – and occasionally simply wrong – review of a literature that they may not have fully understood. For instance, now we read in the Introduction that error encoding in parietal cortex may be needed in order to deal with the”different state of the extraocular muscles". Well, this is exactly one of the well-established functions of a cerebellar forward model that is able to adjust the cerebellum-dependent efference copy in models of saccade control. And the adjustment is based on the climbing fibre system providing information on the error drawn from the SC as shown convincingly for instance by work coming from the Fuchs lab in Seattle. No need for parietal cortex.

Suggestion:

Why not simply write a very short Introduction in which the authors clearly say that the online control of saccades as well as saccadic learning can in principle be fully explained by well-established computational models that reflect the properties of the brainstem-cerebellum machinery for saccades. No need to go into any details here. Then the authors might say that they studied parietal cortex and unexpectedly found an encoding of eye position and the saccade error. In the Discussion – after a short summary of the major finding and a discussion of the question of the nature of their eye position signal (efference copy vs. proprioception) they could then offer as an explanation of this unexpected finding that parietal cortex may be needed to encode the metrics of the secondary saccade, i.e. the correction saccade. After all, they show that the probability of corrective saccade is predicted by their parietal error signal… The brainstem models I alluded to do not explain how the secondary saccade is planned which is why a cortical contribution might indeed help. However, the authors should carefully check if the timing would be appropriate to encode a secondary saccade whose latency is very short. A second (not exclusive) idea may be that parietal error information might be used to speed up saccadic learning. We know that an understanding of the task and the resulting saccadic errors may help to update the internal image of the target allowing the subject to generate a more appropriate saccade next time. The consequence is that saccadic behavior may change from one trial to the next, rather than requiring many hundred trials if this knowledge is not available.

As said this is a suggestion made in an attempt to help the authors. I very much hope that they will be willing to follow this advice to avoid confusing readers with irrelevant and in many cases false information and ideas.

Reviewer #3:

The authors have adequately responded to the reviewers’ comments and have satisfied me. I have no further comments.

eLife. 2016 Apr 20;5:e10912. doi: 10.7554/eLife.10912.019

Author response

[Editors’ note: the author responses to the first round of peer review follow.]

Reviewer #1:

[…] While interesting, the manuscript has major problems with the presentation, analysis and interpretations. The result leaves a reviewer confused and uncertain exactly what was done, the results and their implications. First is the paradigm. The critical arguments need to be based on the undershooting or overshooting of the target. However, the paradigm was not designed to produce these events, instead the study attempts to obtain that information based on the natural variation in saccade end point position.

Here, we studied the neuronal representation of the comparison between intended and real eye position signals for saccadic error computation. As reviewer 1 mentioned, the study was carried out under natural saccadic eye movements, rather than adaptive saccades (undershooting or overshooting to target). We think that there are at least two advantages comparing natural saccades to adaptive saccades. (1) In natural saccades, the intended eye position is matched with the location of saccadic target because the target is a static goal for an impending saccade. In contrast, the location of saccadic target is displaced after the initiation of a saccade in the adaptive saccades. Therefore, it is not clear whether the intended saccade directs to the pre-saccadic target or the post-saccadic target. (2) In the real life, we make much more nature saccades than adaptive saccades. Thus, studying the neuronal representation of saccadic error computation under nature saccade condition will shed light on understanding the neuronal computation of motor errors.

The analysis assumes that the monkey is always striving for the exact center of the target and, therefore the presaccadic firing does not vary with position but this is a big assumption and needs evidence to support. Without this implicit assumption, the critical analyses in Figure 5 break down. The study would be more convincing if position errors were explicitly controlled. In the present study, saccadic target remained visible in SCS and CCS tasks (Figure 2A, C) while monkeys made saccades. Monkeys were intensively trained for years to make saccade to a small target (0.2°) within a 3° checking window. In fact, our behavioral data showed that the post-saccadic eye position of rewarded trials distributed around the target position similar as a Gaussian distribution (insert histogram in Figure 5B, C). Thus, we believe that, under SCS and CCS task conditions, monkeys intended to make saccades to the location of target. Consistently, we recorded a group of PPC neurons that persistently discharged in both pre- and post-saccadic epochs (PPS neurons), and this perisaccadic activity was not correlated with the real post-saccadic eye position (Figure 3D). Therefore, we proposed that the persistent perisaccadic activity of PPS neurons represented the intended eye position to the saccadic target.

This paragraph has been added in the Discussion section paragraph 6.

Yes. The cerebellum is an important center for generating sensory prediction errors. Such error signals in cerebellum play crucial role in real-time motor control and motor learning. However, it is not clear whether and how the error signals in cerebellum play a role in spatial cognition, such as spatial perception, self-recognition and motor awareness. Previous studies have found that the frontoparietal loop, in particular the posterior parietal cortex (PPC), is crucial for spatial perception, self-recognition and motor awareness. Therefore, we are testing an alternative hypothesis that the PPC is another center for generating the error signals.

Following the comments of the reviewer, we have made substantial changes in the current version of manuscript, including the conceptual model, data analysis and result representation. For instance, we discussed and compared the present study with previous cerebellum literatures in both Introduction and Discussion sections: Introduction paragraph 2, Discussion paragraph 2-4.

Also the presentation of the Results is dominated by description and discussing of supplementary figures. This is somewhat distracting, in some cases the claims are not clear or the supplementary results are not that crucial.

The presentation of the results has been reorganized.

In the Methods, three paradigms were used. However, no data is presented from the color-cue delayed saccade paradigm.

Data of the Color-cue delayed saccade task (CCS) are presented in Figure 5—figure supplement 1A–C.

Sorry for improperly using one-side t-test in the previous version. In the current version, we have changed data analysis by using two-sided t-test. As you can see in the revised text (Results section), even though the p value became little bit larger in two-sided t-test analysis than in one-side t-test analysis, the results did not change qualitatively.

Also, the use of 95% confidence intervals as a measure of population variability is not an appropriate measure nor is SEM a good measure. Instead, standard deviation is a much more appropriate measure of variability and should be used. Also, the single cell analyses in Figure 5, F, G and H that relate p-values to the correlation coefficients are problematic. First, obviously p-values and the correlation coefficient are highly related and will have somewhat of a bell-shaped profile. This is not informative. Second, performing secondary level statistics on correlation coefficients is not good statistical practice. We agree that the most appropriate measure of the population variability is the standard deviation (STD). However, since neuronal discharge varied vigorously among trials as well as among neurons, practically, 95% confidence intervals (1.96 * SEM) has been frequently used as a measure of population variability or the accuracy of the mean estimation previously (please see the listed publications below). Please note thatnone of the results were calculated based on the activity variance. Actually, we used the 95% confidence intervals to measure the accuracy of the mean estimation.

We agree that the p value and the correlation coefficient are highly related to an individual neuron with monkey’s postsaccadic eye position and the population distribution of a group of neurons will show a bell-shaped profile. The point is if the mean of the bell-shaped distribution of a group of neurons is significantly biased from 0 toward positive value, it means that the discharge of the majority neurons has positive correlation with the postsaccadic eye position.

List of literature using 95% confidence interval to measure the activity variability or the accuracy of the mean estimation:

“A prefrontal–thalamo–hippocampal circuit for goal-directed spatial navigation” (Nature 2015);

“Functional organization of excitatory synaptic strength in primary visual cortex” (Nature 2015);

“Distinct relationships of parietal and prefrontal cortices to evidence accumulation” (Nature 2015);

“Sensory stimulation shifts visual cortex from synchronous to asynchronous states” (Nature 2014);

“Top-Down Versus Bottom-Up Control of Attention in the Prefrontal and Posterior Parietal Cortices” (Science 2008);

“Free choice activates a decision circuit between frontal and parietal cortex” (Nature 2008);

Fourth, there are critical claims in the paper that do not agree with the data presented. In Figure 5D, the argument is made that the late post-saccadic activity is linearly related to horizontal eye position based on averaging and binning of the data. It is then claimed in Figure 5F that the same is true for individual cell firing (subsection “The pre- and postsaccadic response neurons behave like a subtraction operator that measure the discrepancy between predicted and actual eye position signals”, second paragraph). However, Figure 5F shows that the p-value for the vast majority of the cells is > 0.05. At best, 2 or 3 cells had a correlation coefficient that reached statistical significance. Furthermore, the correlation coefficients are equally distributed between positive and negative for the included cells in Figure 5F, yet there is an overall positive relationship between post-saccadic activity and position in Figure 5D. These discrepancies seem very hard to reconcile. While assessing the possibility of the late post-saccadic activity encoding the real post-saccadic eye position, we analyzed the correlation between the post-saccadic activity and the end point of saccade for each later postsaccadic response neurons (LPS) on single trial basis. 22 of 24 LPS neurons were recorded with enough trials (>= 30 trials in the preferred direction) in horizontal saccades. Although only 3 out of 22 individual neurons had a correlation coefficient that reached statistical significance (p<0.05), in population the distribution of the correlation coefficient values was significantly biased to the positive direction (Figure 4D, mean r = 0.1028, p=0.0087, paired t-test). Such positive correlation between neuronal activity and end point of saccades indicated that the LPS neurons might encode the real eye position.

Reviewer #2: This manuscript addresses the question of how the error between predictive and actual motor signals are represented in LIP. They propose that one population of neurons 'pre- and post-saccadic neurons' encode the desired target location and another the 'postsaccadic neurons' encode the actual target location, and that the difference between the signals of these two populations encodes the error signal. They also propose that larger error signal correlates with greater probability of corrective saccades. The hypothesis is well described in Figure 1 and the experimental methods are well executed. However, the writing of the manuscript leaves much to be desired. It is often not clear what question is being addressed. Figures are described but what hypothesis is being addressed is left to be inferred by the reader; it would be extremely helpful to first state the hypothesis or prediction at the beginning of each section/paragraph and then describe the data. One important shortcoming is the lack of clarity regarding how the subtracted responses are computed; this is essential for the reader to understand the central tenet of this manuscript. I suspect that all this could be fixed with the help of an experienced writer. As it is, I found it difficult to read and therefore difficult to evaluate. However, if the writing is clarified and the data support the claims made, then it could be a highly impactful paper.

Thanks very much for your kind comments and suggestions. We have changed the manuscript substantially according to your suggestions. Also, the current version of the manuscript was polished by an English speaker.

Comments:

Thanks; we have corrected these.

We have rewritten this passage to read: “activity in the preferred direction comparing with non-preferred direction”.

In this paragraph, we want to show that the pre-saccadic activity level and post-saccadic activity level of PPS neuron were highly correlated with each other. Such high correlation between them indicates that the activity in these two intervals might encode similar information.

In order to exclude the possibility that the postsaccadic activity of PPS neurons is evoked by the foveal visual stimulation, we compared the post-saccadic activity of PPS neurons in SCS with their foveal visual response in MGS. Previous studies have shown that the suddenly onset visual stimulus (salient) appearing in the RF of the LIP neuron will evoke much higher visual response than the situation that a saccade brings a persistent visual stimulus into LIP neuron’s RF. In our study, most of the LIP neurons did not show obvious visual response after foveal visual feedback onset in MGS. This result indicated that the strong post-saccadic response of peri-saccadic response neuron was not evoked by foveal visual stimulation.

We have changed the text accordingly.

Reviewer #3:

Thanks for your suggestion. We performed the cluster analysis, which showed that PPS and LPS neurons were separated (please see Author response image 1).

Author response image 1. — For each single neuron, the mean activity around the saccade (400 ms before, to 400 ms after saccade onset, time bin = 50 ms) was used in the analysis resulting in a 16-dim vector for each neuron. For simple illustration of the 16-dimensional space, we used linear Fisher’s discriminant dimension to project the space onto meaningful dimensions. The two clusters are shown in red and blue, respectively. The ellipses represent the standard deviation of two Gaussians. The clustering result fits our previous neuron grouping (LPS vs. PPS) very well, except that few PPS neurons (red dots, 7 neurons) were classified as in the same cluster as LPS neuron.

**DOI:** http://dx.doi.org/10.7554/eLife.10912.016

It is well known that the neuronal discharge is task dependent. Previous studies have reported that the pre-saccadic activity of LIP neurons is associated with many cognitive functions, such as spatial attention, saccadic intention, decision-making, etc. It is clear that the pre-saccadic activity in our data does not only represent the desired post-saccadic eye position. Also, the visual target definitely influences the neuron’s activity. Therefore, we claim that the intended eye position is one of the signals that are encoded by the perisaccadic activity of PPS neurons.

Further: why should an efference copy related discharge show the conspicuous build up plus peak associated with the saccade? And why should it begin such a long time before the saccade? My admittedly very subjective intuition is that such profiles reflect an intention and not an efference copy.

We have modified the abstract and Introduction accordingly.. In the previous version we interpreted the persistent pre- and post-saccadic activity as an internal position signal, which might mix intention and efference copy (corollary discharge). Now, we argue that the activity of PPS neurons represents intention for impending saccades, including the intended eye position.

Although we did not systematically test the spatial tuning of each neuron to saccade vector and eye position in detail, signal neuron’s activity in preferred and non-preferred direction was compared. Most neurons showed significant difference between these two direction. It indicated that both PPS and LPS neurons had spatial tuning with the post-saccadic eye position. Furthermore, the population activity of LPS neurons was significantly correlated with the real post-saccadic eye position (Figure 5), even though the range of eye position was not very large. We bet that the LPS neurons will be activated by passively moving of the eye.

We have changed paragraph 15 of the Materials and methods as per your suggestion.

Unfortunately, neuron activity was recorded by an old model of Α-Omega recording system, which did not record the spike wave.

We have edited the Introduction (paragraph 2) and Discussion (paragraph 2-4).

[Editors' note: the author responses to the re-review follow.]

The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:

Thank you very much for this important suggestion We added the following paragraph to the Introduction to emphasize the insufficiency of cerebellum internal models in motor error detection. Also, we significantly changed the conceptual model in Figure 1.

“However, the cerebellar internal models have disadvantages. Firstly, saccadic commands might be highly variable among saccades with same trajectary, due to the varied task context in which the saccades are made (Shadmehr et al., 2010). […] The involvement of PPC in the adaptaiton of purpose saccades suggests that, independent to cerebellum, there might be external error detector in PPC that compares saccadic plan with sensory feedback signals. Up to date, however, the cortical representation of such external error detection has not been identified.”

For the first question, we now present the reconstructed 3-dementional recording map for each monkey based on the recording sites in the Results section. Data of both monkeys show intermixed distribution between two types of neurons (Figure 7), which makes the interaction between them possible. In addition, the memory-guided saccade task (MGS, Figure 2B) was used to find the lateral intraparietal area (LIP) based on its biological activity signature: neurons discharged persistently throughout memory (delayed) interval (Andersen and Buneo, 2002; Snyder et al., 1997; Zhang and Barash, 2004). Neuronal data were recorded from the same holes (1 mm in diameter for each hole) of a recording grid in which we recorded persistent response neurons in MGS. The reconstructed recording sites show that all neurons but one were recorded within an area of 3x4 mm² (81 out of 81 neurons) in monkey B and 3x3 mm² (34 out of 35 neurons) in monkey D. Therefore, the PPS and PLS neurons were mostly recorded from LIP.

For the second question, to examine whether the selected window (150-350 ms after saccade end) for error presentation was purely arbitrary, we did a new analysis of the correlation between post-subtraction activity of PPS neurons and saccadic errors by using a 100 ms sliding window with step of 10 ms. The sliding window started at 0 ms and stopped at 450 ms after saccade end. As shown in a new figure (Figure 5—figure supplementary 1), in the population level the post-subtraction activity showed significant positive correlation with saccade error in a relative long interval (100-380 ms after saccade end), in particular in 120-310 ms the correlation was significantly positive (mean R > 0.1) and stable. This paragraph has been added in the Results section.

Also, the following paragraph has been added in the Discussion section, in which we propose future studies to assess the functional significance of the saccadic error signals in PPC:

“In the present study, we showed the correlation of neuronal activity in macaque PPC with the accuracy of primary saccades as well as with the occurrence of corrective (secondary) saccades. […] The positive results indicate that the error signals in PPC is not a simply readout from cerebellum or other oculomotor plant.”

Specific comments for your attention: It is still somewhat of a challenge to get at the robustness of the data. For example, in Figure 5F, 18 out of 55 PPS neurons showed a significant position correlation with saccadic error and the population ρ is 0.13. Therefore, less than 2% of the firing variability is error-related. Is this sufficient encoding for the argument? Another example is in Figure 4D in which the correlation between post-saccadic activity of single LPS neurons and eye position is 0.10, or 0.01% of the variability. However, that is an issue best decided by the wider scientific community. We reduced the minimum saccade amplitude of primary saccade from 6 degrees to 4 degrees, in order to include trials with large saccadic error. In Figure 5F, 43 out of 56 PPS neurons showed positive correlation between post-subtraction activity and saccadic error, and 19 of these neurons reached statistical significance. Although the averaged mean correlation coefficient (CC) was 0.155, the population post-subtraction activity of PPS neurons was highly correlated with saccadic error (cc = 0.9041, p<0.0001). We do realize that, in our data, the CC value of single PPS neuron’s activity and postsaccadic eye position was relatively low. One reason that caused the lower CC value was the low coding bandwidth of the spike count (discontinued in timing) in single trials compared with relatively continued saccadic errors.

Reviewer #2 was the most critical. We are including his/her review in entirety for context above.

To assess the anatomical relationship between PPS and LPS neurons, we now present the reconstructed 3-dementional recording map for each monkey based on the recording sites in the Results section. Data of both monkeys show intermixed distribution of two types of neurons (Figure 7), which makes the interaction between them possible. Please see our response to point 2 above.

Hence, my concern remains that the seeming representation of the error by the subtraction of the two may be an artifact of the many assumptions made like the pretty arbitrary choices of time windows, the choice of saccade amplitude classes etc. For instance, I do not see any a priori reason why the assumed subtractive comparison should be confined to the two time windows chosen by the authors. If the assumed subtractive interaction between PPS and LPS were more than wishful thinking it would be in any case continuous… Moreover, if the population difference really reflected the saccade error, it should represent the error independent of the amplitude of the primary saccade (at least to some extent…). However, unfortunately, also this is not shown. Hence, I would say that the suggested subtractive interaction is a possibility but as yet far from being grounded on a solid experimental footing. Theoretically, to render the comparison between saccadic plan and sensory feedback possible, the saccadic plan signal should rise up before the initiation of saccade and last until the arrival of the sensory signals after the completion of saccade (External error detector in Figure 1). Based on this assumption, if PPS neurons represent the intended eye position signal, the most important timing is the perisaccadic interval. Therefore, we chose a perisaccadic window (150 ms before to 100 ms after saccade end) to analyze the correlation between the activity of PPS neurons and saccadic errors. On the other hand, the generation of sensory feedback (actual eye position signal) is after the initiation of saccade. To make the comparison between intended and actual eye position signals possible, the comparison should be made before the fully declination of the activity of PPS neurons. Therefore, we selected a time window (25-125ms after saccade end) to analyze the correlation between actual eye position signal and saccadic errors. Although these two windows were chosen artificially, they did represent the critical timing of encoding the intended and actually eye position signals, respectively.

We totally agree that, in theory, there are many possible mathematic models for calculating the comparison of different signals. Here, we proposed a subtraction model for the comparison of intended and actual eye position signals is mainly due to two considerations: simplicity and accuracy. As shown in Figure 5G, the subtraction results between intended and actual eye position signals (purple dashed lines) are nicely overlapped with the activity of PPS neurons in a time interval of 150-350 ms after saccade end (black solid lines). Moreover, the subtraction results are linearly correlated with the end position of the primary saccade, i.e., the magnitude of saccadic errors: saccadic end points relative to the goal of saccades (10º) (Figure 5G). The magnitude of saccadic errors is highly depended on the end points of the primary saccades, but not dependent on the saccadic amplitudes.

To examine whether the selected window (150-350 ms after saccade end) for error presentation was merely arbitrary, we did a new analysis of the correlation between post-subtraction activity of PPS neurons and saccadic errors by using a 100 ms sliding window with step of 10 ms. The sliding window started at 0 ms and stopped at 450 ms after saccade end. As shown in a new figure (Figure 5—figure supplementary 1), in the population level the post-subtraction activity showed significant positive correlation with saccade error in a relative long interval (100-380 ms after saccade end), in particular in 120-310 ms the correlation was significantly positive (mean R > 0.1) and stable. This paragraph has been added in the Results section. We calculated the correlation between the chosen post-subtracted activity and saccade amplitude for each single neuron in the current manuscript. We found that the correlation of post-subtracted activity with saccade error (mean r = 0.1550) was significantly higher (p=0.0023, paired t-test) than the correlation with the saccade amplitude (mean r = 0.0898)

A few further concrete remarks: In the third paragraph of the subsection “The perisaccadic activity of PPS neurons reflects the intended eye position”, correlations between perisaccadic activity and postsaccadic position are being presented. Why analyze the horizontal and vertical components independently? There are two components, horizontal and vertical, for the postsaccadic eye position of each oblique saccade. Therefore, when we assessed the correlation between neuronal activity and postsaccadic eye position, we did the correlation coefficient analysis of neuronal activity with horizontal and vertical component, respectively. But, when we assessed the correlation between neuronal activity and saccadic errors, we analyzed the correlation coefficient between neuronal activity and the distance from postsaccadic eye position to target location.

In the fourth paragraph of the subsection “The perisaccadic activity of PPS neurons reflects the intended eye position”, the authors conclude that reward expectation was not correlated with the postsaccadic activity because the reward delivered did not change. Reward expectation also depends on internal processes that vary. Hence, this conclusion is not justified. We totally agree that the reward expectation is highly dependent on the internal processes that vary from time to time. However, in our case, because the quality and quantity of reward were identical between trials in which saccades directed to the preferred or the non-preferred direction of the neurons, the different perisaccadic activity of PPS neurons between two saccadic directions (Figure 3A–C) wouldn’t reflect the reward expectation. To make it clearer, we rewrote the following sentence to read:

“Moreover, the perisaccadic activity of PPS neurons was not correlated with reward expectation because the quality and quantity of the reward were identical between trials in which saccades directed to either the preferred or the non-preferred direction of neurons.”

In the subsection “The intended eye position was encoded by the relative change, rather than the absolute firing rate, of the perisaccadic activity of PPS neurons”, when comparing the results from the SCS and MGS task, the authors conclude that the”intended eye position was not task specific". This is based on comparing activity of PPS neurons in a narrow time window. However, there is no reason to assume that the monkey´s intention would have been confined to this window. And at earlier times the discharge was clearly very different. It has been known for long time that the discharge of neurons is highly modulated by the difficulty of the tasks (Boudreau et al., 2006; Chen et al., 2008). Indeed, we also found that the same neurons’ absulote firing rate differed remarkably between two tasks—CCS versus MGS (Figure 3—figure supplement 4A–C). Based on findings of previous studies, the presaccadic activity of PPC neurons has been associated with multiple cognitive functions, such as attention, intention, decision making, ect. Here, we ask a specific question whether the perisaccadic activity of PPC neurons represents the intended eye position of an impending saccade. If the answer is positive, we expect to see that the intended eye positon signal remains invariable between different tasks, as long as the saccadic trajactory is same. We found that, despite the alteration in the abslute firing rate of PPS neurons between two tasks, interestingly, relative activity changes during perisaccadic interval remained similar between two tasks (Figure 3—figure supplementary 4D). Therefore, we argue that:

“Thus, the intended eye position was not task specific and it might be more reliably encoded by the relative change of neural activity of PPS neurons, rather than their absolute firing rate.”

In the first paragraph of the subsection “The activity of LPS neurons reflects extraocular proprioceptive signals”, we read that only 6 out of 22 LPS neurons had a significant correlation with eye position. This is hard to reconcile with the obviously significant effects of eye position discussed later with respect to Figure 5. Any explanation? Due to the fact that the spiking activity of signal neurons is noise and the coding bandwidth of the spike count is low, the number of LPS neurons that show significant correlation with eye position is low in our data. Nonetheless, the population distribution of the correlation coefficient values was significantly biased to the positive direction (Figure 4D, mean r = 0.1237, p=0.0074, paired t-test). Such positive correlation between neuronal activity and end point of saccades indicated that the population activity of LPS neurons might encode the actual eye position.

In the first paragraph of the subsection “The activity of LPS neurons reflects extraocular proprioceptive signals”: the distribution is clearly skewed. Hence, a t-test is not applicable. In the current manuscript, we reduced the minimum saccade amplitude of primary saccade from 6 degree to 4 degree, in order to include trials with large saccade error. Now, the distribution of the CC values between post-subtraction activity and saccadic errors is not significantly different form normal distribution (p=0.2081, Kolmogorov-Smirnov test). In addition, we performed paired Wilcoxon test and the result was similar as the result of t-test.

There are two reasons for us to believe that the activity of LPS neurons represents extraocular proprioception, rather than vision. First, the LPS neurons did not have visual response in both SCS and MGS tasks (Author response image 2). Second, previous studies have reported that the latency of extraocular proprioceptive input in cortex is ~80 ms after the initiation of saccades (Nakamura et al., 1999; Wang et al., 2007).

Author response image 2. — Averaged spike density with SEM (shaded area) in the preferred (black) and null direction (grey) are shown separately.

**DOI:** http://dx.doi.org/10.7554/eLife.10912.017

[Editors' note: further revisions were requested prior to acceptance, as described below.]

The manuscript has been improved but there are substantial remaining issues that need to be addressed before acceptance, as follows:

Reviewer #2:

Improved:

Following the reviewer’s comment, we now added “probably” before “mostly recorded…”.

They moreover provide evidence that the two types of neurons (PPS and LPS neurons) were found intermingled. I agree that this may make functional interactions between the two more likely. Yet again, I would phrase this possibility more cautiously. We changed the sentence as follows: “Such intermingled distribution of PPS and LPS neurons indicated that PPS and LPS were recorded from the same area of the PPC, which may make functional interactions between the two types of neurons more likely.”

Remaining or new problems: Unfortunately, the problem that the range of target eccentricities tested is limited to 10deg and the range of saccade amplitudes explored therefore being very small remains (see below). Indeed, it is very unfortunate that we did not systematically test the neuronal activity with a larger range of the target eccentricities. Nevertheless, we also recorded the behavioral and neuronal data when monkeys made saccades to the visual targets in the oblique direction at 13° eccentricity in the SCS task. The correlation between the neuronal activity and the saccadic error during oblique saccades showed similar results as during horizontal saccades (with 10° eccentricity), as shown in Figure 4 and Figure 4—figure supplement 2. To make this point clearer, we added a new paradigm in Figure 1B to denote the oblique direction, and rewrite the description of SCS task as follows:

“Spatial-cue delayed saccade task (SCS, Figure 1B): There are two versions of the SCS task: horizontal (with target at 10° eccentricity) and oblique (with target at 13° eccentricity) During training and data collection, the two versions were presented in separate session…”

In the fourth paragraph of the subsection “The perisaccadic activity of PPS neurons reflects the intended eye position” the authors deal with the possibility that the early post-saccadic activity of PPS neurons may be a consequence of persistent foveal visual stimulation (first by the fixation spot, then by the fovealized cue/target). In order to show that this is not the case, they resort to a comparison with the memory saccade paradigm in which no peripheral saccade target is fovealized. However, rather than considering the saccade-related activity (which is non-visual) they look at the earlier visual response evoked in this paradigm. Why? I do not see that this addresses the aforementioned question. I would have looked at the saccade-related burst. I think that the reviewer’s problem arises from our unclear labeling of Figure 2—figure supplement 3 (have been modified in the revised figure). In the figure the memory-guided saccade activity is synchronized on the reappearance of the target (i.e., “feedback on” in Figure 1C), now at the fovea. There is no response at this time, although there was a presaccadic burst that ended before the reappearance of the foveal target. This indicates that the perisaccadic activity of the PPS neurons was not a foveal visual response.

The conclusion that the activity of PPS neurons is not correlated with reward is based by them on the fact that reward was constant. This is of course not justified. In order to figure out if reward levels have an impact they need to be varied. They may be allowed to conclude that discharge changes cannot not be due to changes of reward level (as it was constant). But this is not what is said. We are grateful to the reviewer for this comment. We now added: “Furthermore, the perisaccadic activity could not be a measure of expected reward. The reward was identical between trials in which saccades directed to either the preferred or the non-preferred direction of neurons. Therefore, the discharge difference between preferred and non-preferred direction (e.g., Figure 2B–D) cannot be due to the level of reward.”

“…we assessed the possibility whether the activity of LPS neurons could consistently encoding the actual end-position of saccades. If single LPS neurons code (at least partly) linearly for the end-position, one would expect a significant correlation of their activity with the random jitter in the actual saccadic end-position. […] Taken together, although subject to noise on a single neuron basis, our results show that, in contrast to the PPS neurons, LPS neurons' activity was positively correlated with the actual end-position of saccades.”

Conceptual framework propagated in the Abstract, the Introduction and the Discussion.

We now changed “proprioception” to “actual end-position of saccade” in the abstract and Introduction.

Actually dwelling on the nature of this signal in the Discussion would be much more valuable than the endless pages on motor errors and the role of the cerebellum in the Discussion and already earlier in the Introduction, sentences that do not contribute anything to an understanding of their findings and rather have the flavor of a poor – and occasionally simply wrong – review of a literature that they may not have fully understood. For instance, now we read in the Introduction that error encoding in parietal cortex may be needed in order to deal with the”different state of the extraocular muscles". Well, this is exactly one of the well-established functions of a cerebellar forward model that is able to adjust the cerebellum-dependent efference copy in models of saccade control. And the adjustment is based on the climbing fibre system providing information on the error drawn from the SC as shown convincingly for instance by work coming from the Fuchs lab in Seattle. No need for parietal cortex. We thank the reviewer for his/her helpful comments. We now discuss the nature of the eye position related signals in the Discussion section. We also removed the following from manuscript: “error encoding in parietal cortex may be needed in order to deal with the different state of the extraocular muscles".

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PERMALINK

Neuronal representation of saccadic error in macaque posterior parietal cortex (PPC)

Yang Zhou

Yining Liu

Haidong Lu

Si Wu

Mingsha Zhang

Roles

Abstract

Introduction

Figure 1. Conceptual model and behavioral paradigms.

Results

The perisaccadic activity of PPS neurons reflects the intended end-position of saccade

Figure 2. PPS neurons represent the intended end-position of saccades.

Figure 2—figure supplement 1. Correlation between single PPS neuron’s pre-saccadic and post-saccadic activity.

Figure 2—figure supplement 2. Correlation between the single PPS neuron’s perisaccadic activity and the end-position of saccade when monkey made oblique saccades.

Figure 2—figure supplement 3. The post-saccadic activity of PPS neurons is not evoked by foveal stimulation.

Figure 2—figure supplement 4. PPS neurons show a similar firing pattern but different rate between tasks.

The intended end-position was encoded by the relative change, rather than the absolute firing rate, of the perisaccadic activity of PPS neurons

The activity of LPS neurons reflects the actual end-position of saccade

Figure 3. LPS neurons represent the actual end-position of saccades.

Figure 3—figure supplement 1. LPS neurons discharged similarly in different tasks.

The PPS neurons behaved like a comparator to estimate the discrepancy between the intended and the actual end-positions of saccade

Figure 4. The integration between PPS and LPS neurons and the correlation with the end-position of saccades.

Figure 4—figure supplement 1. Averaged Pearson correlation coefficient (CC) analysis between post-subtraction activity of PPS neurons (n = 55) and saccadic errors for horizontal saccades in SCS task.

Figure 4—figure supplement 2. Correlation between post-subtraction activity and oblique saccadic errors.

Figure 4—figure supplement 3. Correlation between post-subtraction activity and horizontal saccades in color-cue delayed saccades.

The post-subtraction activity of PPS neurons was highly correlated with the probability of a secondary saccade

Figure 5. The correlation between the post-subtraction activity and the secondary saccades.

The PPS and LPS neurons were intermixed in PPC

Figure 6. The 3D distribution of the PPS and LPS neurons.

Discussion

Materials and methods

Animal preparation

Behavior tasks

Spatial-cue delayed saccade task (SCS, Figure 1B)

Memory-guided saccade task (MGS, Figure 1C)

Color-cue delayed saccade task (CCS, Figure 1D)

Neuronal recording

Behavioral data analysis

Neuronal data analysis

Classification of recorded neurons

Method for determining the decay of pre-saccadic activity

Method for determining the increase in post-saccadic activity

Statistic functions used in analyzing neuronal activity

Choosing different temporal windows to analyze different signals

Acknowledgements

Funding Statement

Funding Information

Additional information

Competing interests

Author contributions

Ethics

References

Decision letter

Roles

Author response

Author response image 1. We used Gaussian mixture model (neglecting covariance) to classify all neurons (LPS+PPS) into two groups by using expectation maximization.

Author response image 2. The averaged population activity of 27 LPS neurons in the SCS task.

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