Subjects and preparatory surgery

Data was collected from three awake, behaving male rhesus monkeys (Macaca Mulatta, F, H, S), weighing between 5.6 Kg and 11.9 Kg. Monkeys were first implanted with a MRI-compatible head post (Rogue Research) and trained on the experimental paradigm until they were thoroughly familiar with the task. We then performed a second surgery to implant a 2-cm circular recording chamber (Crist Instrument, IAC series) on the contralateral side of the reaching right arm of monkeys H and F. Chamber placement was guided stereotaxically and centered at posterior 7 mm, lateral 5 mm in monkey F. For monkey H, we placed the chamber in a position that maximized access to the medial bank of the intraparietal sulcus as confirmed by Brainsight, a neuro-navigation system (Rogue Research); surgery plan images centered on the targeted area are shown in Fig 1D. We secured the chamber in place with MRI-compatible ceramic screws (Rogue Research) and Simplex P bone cement (Stryker, Hamilton, ON, Canada). Monkey S was implanted with two 16-channel micro-electrode arrays (MicroProbe, Gaithersburg, MD) each in areas MIP and PMd of the left hemisphere (64 channels in total). Micro-electrode array locations were planned using Brainsight, by first registering sulcal markers (the intraparietal sulcus) to a stereotaxic atlas registered to the animal’s structural MRI. During surgery, a motion-capture system using skull-referenced fiducial points was used to precisely locate the planned array implantation site (Rogue Research). In both acute and chronic recording setups, we recorded from deep within the sulcus (2-8mm for single electrode recordings, 3-6mm for micro-electrode arrays) to exclusively target area MIP. The electrode depth measurements were made using a stereotaxic atlas registered to each animal’s structural MRI. The approximate anatomical location of chronic microelectrode array implantation is shown in Fig 1C. Additional surgical and experimental procedure details are reported elsewhere [29]. All surgical and experimental procedures complied with the Canadian Council of Animal Care guidelines and were approved by the McGill Animal Care Committee. Monkeys were weighed and their health and growth monitored daily. Animals were also pair-housed and had constant access to exercise via a jungle gym on all days, including experimental days. Each monkey had its own recording schedule that ensured that experiments started at the same time every session. Monkeys were given fresh fruits in the lab after all completed sessions.

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Fig 1.

(A) Variable amplitude memory reach task. To initiate a trial, monkeys had to touch a central green circular target and visually fixate a red target located in the center of a touch screen for 500ms (fixation). A cue (circular green target) was then flashed in the periphery for 300ms indicating the target of the upcoming reach. A randomized delay period followed (memory period: 1.1–1.7 s) during which monkeys had to maintain the visual fixation and the hand contact established in the fixation period. The central green target was then extinguished instructing the monkeys to reach to the location indicated by the cue flash. Monkeys had to touch the screen within a 2.5 cm circle centered on the target for 400ms without breaking visual fixation. If successful, monkeys were rewarded with juice. (B) Target configurations. Monkeys reached to targets in two different configurations. In Task 1, targets were arranged at two amplitudes along each of four equally distributed directions. In Task 2, targets were at three amplitudes in each of 16 equally spaced directions, slightly offset from a perfectly radial configuration to maximally use the touchscreen area. (C) Electrophysiological recording anatomy. The approximate anatomical location of chronic microelectrode array implantation is shown for MIP and PMd. (D) Structural MRI with surgery plan targeting area MIP in one monkey. The intra-parietal sulcus (IPS) is marked for anatomical reference. The cross-hairs indicate the center of the targeted location, and the ticks represent the boundary of the cortical surface of interest.

https://doi.org/10.1371/journal.pone.0182519.g001

The monkeys performed the experiment in a dimly lit Faraday chamber. Each animal was seated in a chair within arm’s reach (~45cm) of a touch screen (ELO Touch, California) that was coupled to a monitor. The only light in the chamber emanated from visual cues displayed on the monitor and the monitor’s low ambient output. Monkeys reached the touch screen through an opening in the chair on the side of their reaching hand (right arm in all animals). The non-reaching hand was obstructed. The monitor and touchscreen were on the fronto-parallel plane, within arm’s reach of the animal. Behavior was controlled by a real time system (LabVIEW RT, National Instruments). Eye position was monitored with an infrared reflection camera (ISCAN, Boston) and hand position was monitored using the acoustic touch screen.

The single unit recording procedure is reported in detail elsewhere [29]. Briefly, extracellular recordings in monkeys F and H were performed with a single channel from a multichannel micromanipulator system (NAN Drive, NAN Instruments). Before each recording session, a 23-gauge stainless steel guide tube containing a 120-mm tungsten microelectrode (FHC, Pl/Ir impedance: 1 MΩ) was placed over the appropriate cortical location (in the XY plane) and lowered onto the dura mater surface. Thus the guide tube served as the electrical ground. The electrode was then lowered into the cortex to a desired depth ranging from 2 to 8 mm and left to rest from 15 to 60 min before any subsequent movements. All neurons that could be isolated and stabilized were recorded. Single-/multi-channel recordings were filtered (250Hz– 8000 Hz for spikes) and amplified using commercially available systems (Plexon Inc, Texas). Each channel was digitized (at sampling rates of 40 kHz for spikes) and continuously recorded to disk for further analysis. Spike waveforms were sorted online using a manual-sorting method (Plexon Inc.), and offline using custom software (MATLAB) before being visually inspected.

Behavioral task and datasets

We trained the monkeys on the memory reach task, illustrated in Fig 1A, for several months before collecting data. To initiate a trial, monkeys had to touch a central green circular target and visually fixate a red target located in the center of a touch screen for 500ms (fixation). A cue (circular green target) was then flashed in the periphery for 300ms indicating the target of the upcoming reach. A randomized delay period followed (memory period: 1.1–1.7 s, uniformly distributed) during which monkeys had to maintain the visual fixation and hand contact established in the fixation period. The central green target was then extinguished, instructing the monkeys to reach to the location indicated by the cue flash. Monkeys had to touch the screen within a 2.5 cm circle centered on the target for 400ms without breaking visual fixation. If successful, monkeys were rewarded with juice.

We used two different reach target configurations (see Fig 1B): Task 1 consisted of targets at two amplitudes along each of four equally distributed directions, while Task 2 consisted of targets at three amplitudes in each of 16 equally spaced directions. The reach targets subtended the near periphery (±12.5 degrees of visual angle for Task 1 and ±25 degrees of visual angle for Task 2). Reach targets in Task 2 were slightly offset from a perfectly radial configuration to maximally use the touchscreen area (see Fig 1B right panel). We first recorded 93 MIP neurons while monkeys F and H reached to targets in Task 1. Using chronically implanted micro-electrode arrays, we recorded 39 MIP neurons and 42 PMd neurons from monkey S performing Task 1. In order to characterize the spatial response patterns of neurons, we recorded an additional dataset of 58 MIP neurons and 52 PMD neurons in one session of monkey S reaching to targets in Task 2 (see Fig 1B). Three out of these 48 targets were omitted due to insufficient number of trials. In total, we collected 42 (30) trials per target for Task 1, and 10 (1) trials per target for Task 2 (median and interquartile range).

In total, 190 MIP neurons (33, 60, and 97 from monkeys F, H, and S respectively) and 94 PMd neurons (from monkey S) were recorded. We analyzed the firing rates of these neurons in four different trial epochs (cue, early-memory, late-memory, movement) of length 500ms. We defined the criterion for task-relatedness as significantly different spiking activity during at least one of these four trial epochs relative to a baseline epoch (p < 0.05/4, t-test with Bonferroni correction for multiple comparisons); importantly, this criterion for task-related neurons is not based on tuning properties such as selectivity for amplitude or direction. Based on this task-relatedness criterion and a threshold on firing rates (>1Hz in at least one of the four trial epochs considered), 152 MIP neurons and 68 PMd neurons were selected for analysis in the current study. Data and analyses are made available on a public repository: https://github.com/RishiRajalingham/musallam_plos2017.

Analysis

We computed firing rates in four trial different epochs, of 500ms bins aligned to trial events: Cue (C): [0ms, 500ms] after target cue onset; Early-Memory (EM): [200ms, 700ms] after target cue offset; Late-Memory (LM): [-700ms, -200ms] before go signal; Reaction and Motion Time (RT/MT): [0ms, 500ms] after go signal. The early and late memory period epochs (EM and LM) were temporally offset from cue offsets to avoid contamination by visual and preparatory movement signals respectively. As such, the early and late memory period epochs could overlap slightly, with an average overlap of 0ms. The RT/MT epoch overlapped substantially with the reaching movement, as the monkeys’ reaction times (time from go signal to start of hand movement) and motion times (time from start of hand movement to target acquisition) were 276ms (±29ms) and 186ms (±38ms) respectively. As such, the reach and gaze positions were spatially dissociated during this epoch.

Single unit analyses

We examined the modulation of neuronal firing rate by the instructed reach amplitude and direction. To assess significant modulation in firing rate due to these task variables, we used multivariate (2-way) fixed-effect ANOVAs with interaction of firing rate with direction and amplitude as factors. ANOVAs were approximately balanced, as the factors (reach target direction and amplitude) were sampled from a uniform distribution. To further assess significant modulation by amplitude in each direction separately, we used unpaired t-tests between firing rate distributions in small and large amplitude trials. When testing for significant effects in at least one of the four epochs of interest, we adjusted the significance threshold (Bonferroni correction) to counter problems of multiple comparisons. When testing significance of a one-group proportion against chance (e.g. proportion of neurons with significant amplitude modulation per area), we used a one-tailed binomial test. We use the convention of denoting p < 0.05 as *, p < 0.01 as ** and p < 0.001 as *** throughout.

Response field characterization

In order to characterize the spatial response fields of neurons, we examined the firing rate of neurons recorded as monkey S reached to 3 amplitudes in each of 16 directions. We first mapped targets to Cartesian coordinates and used linear interpolation to estimate the firing response at each point in a Cartesian grid (11x11 bins, spanning 14cm x 14cm). The interpolation procedure simply estimates neuronal responses for arbitrary target locations within the experimentally measured reach target space, using a spatial smoothness prior on firing rates. We quantitatively characterized the interpolated response patterns by measuring the eccentricity of the peak response coordinate. Additionally, we measured the response field width, defined as the square root of the spatial area containing the top quartile of responses. Both response field eccentricity and width were converted to degrees of visual angle, based on a 45cm eye-to-screen distance.

Response field modeling

To quantitatively test several alternative hypotheses of neuronal encoding, we constructed and tested the goodness of fit of several computational models (see Table 1, Fig 2). Our primary goal was to uncover models of neuronal response patterns with good generalization accuracy, i.e. models that accurately capture the data without over-fitting it, such that they can generalize to new, unseen data. To this end, we used cross-validated accuracy, wherein a fixed learned model is explicitly tested on held-out data [30]. This metric directly measure a model’s generalization ability rather than estimate it indirectly based on model parsimony, as is the case with measures such as Akaike’s information criterion (AIC) or Bayesian information criterion (BIC) [30]. Moreover, AIC and BIC metrics do not apply in a cross-validation scheme, as all cross-validated models are fixed (have zero free parameters) with respect to the test data [30]. The models and the procedure used to estimate their goodness of fit with the neuronal data are described in detail below, fully characterized in Table 1, and illustrated conceptually in Fig 2.

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Table 1. Description of all computational models tested, with mathematical characterizations, explicitly stated optimization parameters and constraints.

https://doi.org/10.1371/journal.pone.0182519.t001

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Fig 2. Response field characterization and modeling.

For an example PMd neuron, the response field characterization procedure is shown. Color scale indicates firing rate response. The mean firing rate response to each reach target (left panel) is used to interpolate the two-dimensional spatial response pattern (middle panel). This interpolated response pattern is then used to fit computational encoding models of neuronal responses. Model response patterns for each of the tested models (corresponding to models 1–5) are shown below.

https://doi.org/10.1371/journal.pone.0182519.g002

For each neuron and each epoch, we first split the trials into two halves. From these two disjoint sets of trials, we estimated two response patterns N1 and N2 using linear interpolation as described above. The interpolated response patterns were mid-range normalized () to map onto [0,1]. The Pearson correlation between N1 and N2 is the neuronal internal consistency, a measure of the reliability of the neuronal response pattern estimated across disjoint sets of observations. This value corresponds to a noise ceiling of the neuronal data, as it is measured relative to the neuron’s best possible model, namely itself. From each response pattern, we solved for the model parameters with constrained non-linear least-squares minimization (see Table 1 for parameters and parameter constraints), resulting in two model response patterns M1 and M2. The Pearson correlation between N1 and M2 (and between N2 and M1) is the cross-validated correlation (ϱ_neuron,model), as it compares the neuronal response pattern to the prediction from a model fitted on different sets of observations (trials). This cross-validation procedure is crucial to ensure that model fits do not reflect over-fitting. For each neuron and each epoch, we repeated this procedure 50 times with random resampling of trial split-halves to estimate average values for correlation values. For brevity, we refer to the cross-validated correlation between model and neuronal response patterns as the model consistency. Using this method, we tested the consistency of several models that each map a two-dimensional point x = (x, y) = (θ, r) to a scalar normalized firing rate value FR(x). As with the neuronal response patterns, the model response patterns were mid-range normalized () to map onto [0,1].

All five tested models are listed in Table 1 and visualized for an example neuron in Fig 2. We tested for directional tuning using both cosine and Von Mises functions, parameterized by preferred direction angle and width (concentration parameter). For each of these, we tested either a pure directional tuning, or directional tuning with a linear amplitude gain (parameterized by a gain k). The resulting four model equations are shown in Table 1 (Models 1–4). We also tested a model of position tuning (see Model 5 in Table 1), consisting of a 2D Gaussian function, characterized by parameters μ and Σ denoting the two-dimensional center and width of the Gaussian respectively. This model corresponds to a smooth response field that fires maximally at a particular location in reach space. Example response patterns for each of these models is shown in Fig 2.

We modeled the response patterns of all task-related neurons recorded under Task 2, separately for each epoch. As noted above, the models were fitted and/or optimized using only the training data, and subsequently tested on held-out testing data to measure model consistency. Importantly, this cross-validation procedure avoids the problem of over-fitting, (where excessively complex models, i.e. models with large number of parameters, fit the noise in the data). By always measuring model consistency on held-out data, we ensure that differences in consistencies across models are not due to their ability to over-fit (i.e. number of parameters).

Neuronal spatial response patterns

Together, these results indicate that the direction and amplitude of a reach target in space conjointly modulate neuronal activity in MIP and PMd. The interaction between amplitude and direction suggests a possible encoding of the position of a target as a coordinate in visual space, rather than a representation of direction and/or amplitude. These different encoding hypotheses are not optimally differentiated using the sparse reach target configuration in Task 1. In order to do so, we characterized the response patterns of task-related neurons in MIP and PMD simultaneously recorded while one monkey performed reaches to a dense spatial sampling of targets (16 directions x 3 amplitudes, referred to as Task 2). We analyzed the spatial response patterns of neurons using the procedure (described in Methods) illustrated in Fig 2. Briefly, the average firing rates of neurons in response to reaches to the different targets were used to interpolate and characterize their spatial response patterns in a 2D fronto-parallel plane, for each neuron and each epoch. To test our encoding hypotheses, we compared the cross-validated goodness of fit (consistency) of several alternative computational models with respect to the interpolated response patterns of single neurons. Fig 6 shows spatial response patterns for two example neurons, one from each area, for all epochs considered. The measured average firing rates at spatial positions of the reach target are shown (colored circles) overlaid on the interpolated spatial response pattern. We first qualitatively observe that neurons exhibit reliable spatially tuned responses in both areas. Further, these example response patterns suggest that neurons are not simply modulated by target direction alone, but rather seem to encode particular regions of reach-space in each epoch. As previously shown (see Fig 5B), response fields typically peaked in the periphery. Quantitatively, the eccentricities of the peak response locations were not different between MIP and PMd (MIP: 16.04° ± 0.43°; PMd: 16.05° ± 0.44°, mean ± SE, pooling across epochs). Response field widths were slightly but significantly larger in MIP than in PMd (MIP: 11.28° ± 0.07°; PMd: 10.89° ± 0.09°, p < 1e-4, unpaired t-test, see Methods). We additionally observe that the spatial response patterns of neurons can vary across epochs. However, these temporal dynamics were considered beyond the scope of the current study.

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Fig 6. Example spatial response patterns.

Each row shows the spatial response patterns of an example neuron, for each epoch considered. One example neuron from each area is shown. The measured average firing rates at spatial positions of the reach target are plotted (colored circles) overlaid on the interpolated spatial response pattern (11x11 colored maps), using the same color scale. Warmer colors indicate higher firing rates. For visualization purposes, the interpolated spatial response patterns have been slightly smoothed, using a two-dimensional Gaussian kernel of width 0.5 bins.

https://doi.org/10.1371/journal.pone.0182519.g006

To quantitatively test alternative encoding hypotheses of neuronal responses, we asked how well several alternative computational encoding models could predict the observed neuronal responses. The tested encoding models, ranging from cosine directional tuning to Gaussian position encoding, are mathematically described in Table 1 and illustrated with example model fits in Fig 2. The large number of targets in Task 2, and corresponding small number of trials per target condition, could result in a relatively noisy estimate of average neuronal firing rate for each target. We measured this noise ceiling via the neuronal internal consistency (the correlation between neuronal response patterns estimated from disjoint split halves of the data). Importantly, the entire modeling procedure was cross-validated: the model training and testing were done on separate disjoint halves of the data (see Methods for detailed description of modeling procedure). Cross-validation ensures that differences in consistencies across models are not due to their ability to over-fit (i.e. are not due to differences in number of parameters).

For each of the five tested models, we computed a consistency value for each task-related neuron recorded under Task 2 and for each epoch. Fig 7A shows the resulting distribution of model consistencies over neuronal samples (mean ± SE) for each model. First, we observe that all models capture a relatively large proportion of the replicable variance in neuronal responses (i.e. the model consistencies are relatively close to the noise ceiling of the data). However, we observe a significant improvement in model consistency for the Gaussian position encoding model (model 5), relative to null models of direction and amplitude tuning (models 1–4). Fig 7B shows this quantitative comparison for each pairwise combination of models. Each panel (row i, column j) directly compares two models (model #i vs. model #j), and each point in the panel’s scatter plot corresponds to the models’ consistency to a particular neuronal response pattern. The dashed unity line corresponds to equal consistency across these two models. The p-value obtained from a two-tailed signed rank test comparing the distributions of correlations between models i and j is shown in the panel title, and model pairs with statistically significant differences are highlighted in grey. We observe that the Gaussian position-encoding model (#5) significantly outperforms all other models. In particular, these comparisons suggest that for a subset of neurons (points along the identity line), the consistencies of direction and position encoding models are largely indistinguishable, whereas for a sizeable proportion of neurons, the position-encoding model (model #5) vastly out-performs the direction-encoding model (see points above the unity line). Taken together, these results suggest that a simple Gaussian position-encoding model most accurately captures the response patterns of task-related neurons in MIP.

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Fig 7.

(A) Model Consistency. For each of the five tested models, the resulting distribution of model consistencies over all task-related MIP neurons and all epochs (mean ± SE) is shown for each model. The gray horizontal bar corresponds to the noise ceiling (internal consistency of the neuronal response patterns, mean ± SE). (B) Quantitative comparison for each pairwise combination of models. Each panel (row i, column j) directly compares two models (model #i vs. model #j), and each point in the panel’s scatter plot corresponds to a particular neuronal response pattern in MIP. The dashed unity line corresponds to equal consistency across these two models. The p-value obtained from a two-tailed signed rank test comparing the distributions of correlations between models i and j is shown in the panel title, and model pairs with statistically significant differences are highlighted in grey. (C, D) Identical to (A,B) for task-related neurons in PMd.

https://doi.org/10.1371/journal.pone.0182519.g007

Fig 7C and 7D repeat this procedure for task-related PMd neurons, with very similar results. However, both cosine direction-encoding (model 1) and Gaussian position-encoding (model 5) accurately capture the neuronal response patterns, significantly better than all other models, but these data do not have the power to distinguish between these two models.

Representation of reach amplitude and direction in MIP

In this work, we tested the hypothesis that the reach amplitude is represented in the activity of neurons, during movement planning and execution, in sensory-motor integration area MIP, a sub-region of the parietal reach region. Previous work has examined the neuronal representation of the in-plane depth of reaches in neighboring and overlapping reach-related posterior parietal areas [11–13, 31]. Here, we found that neurons in MIP, similarly to PMd, conjointly represent the intended reach direction and amplitude, in a manner consistent with encoding of the remembered location of the reach goal.

Similar to previous findings in motor and premotor cortices [4, 20], our results highlight an under-representation of reach amplitude relative to reach direction in movement planning signals; the number of neurons with significant modulation by reach amplitude is approximately one third of the corresponding number for reach direction. Such a comparison may not be valid given that the two variables were not matched in dynamic range: while the full range of reach directions in the fronto-parallel plane were presented, the tested reach targets extended a limited range of amplitudes. However, the observed differences in representation of direction and amplitude are reflected in the reaching behavior. Psychophysical experiments in humans show that subjects make greater errors in the extent of a reach compared to the direction [32], and that the initial kinematics of a movement do not perfectly predict movement amplitude without the inclusion of compensatory adjustments [33]. These behavioral data point towards a poorer representation of reach amplitude, relative to direction, in the movement plan. However, reach amplitude must be represented in the neuronal motor plan, because the visual stimuli defining the reach goal no longer exist in the external environment in the context of memory-guided reaches. As such, the modest neuronal modulation of movement planning signals by amplitude observed both here and in previous studies is consistent with the behavioral output.

We focused our analyses on neuronal activity in MIP (152 task-related neurons in monkeys H, F, S), and recorded from PMd (68 task-related neurons in monkey S) for direct cross-area comparisons. We did not observe any idiosyncratic behavioral or neuronal signatures in monkey S and, importantly, multi-electrode recordings in monkey S simultaneously sampled from both MIP and PMd in each session, thus eliminating the possibility of experimental variance that selectively affects one brain area, and maximizing power for direct comparisons. Furthermore, our recordings in PMd largely replicate previously reported findings characterizing this area, namely that the activity of PMd neurons is modulated by an interaction of reach direction and amplitude [20], and likely to represent the instructed target location [34]. Thus, we argue that this data has sufficient power to support inferences about the representation of reach goal amplitude in MIP, as compared to PMd.

Neurophysiological recording sites were targeted for area MIP based on a stereotaxic definition. Recording chambers for acute recordings were placed sufficiently posterior (-7) such that area 5 is restricted to the gyral surface, and our electrode penetrations were deep enough (2-8mm) to exclusively target putative area MIP. For chronic array recordings, we used long and staggered electrodes (3-6mm), thus restricting the recording sites to deep within the sulcus at the planned location. Using a neuro-navigation system (Brainsight), we were able to precisely register the stereotaxic atlas to individual subject structural MRI scans (for monkey H, S) for targeting and surgery planning. However, the boundary between MIP and neighboring cortical area 5 is not stereotaxically well defined, and the denominations are not always consistent across studies [35]. In this study, we did not perform histological validation of recording site locations, which may help differentiate these two neighboring areas [36], but rather rely on stereotaxic planning to claim that recordings targeted area MIP.

We trained monkeys to perform memory-guided reaches in order to investigate the representation of reach direction and amplitude in movement planning signals, independently of visual responses. We observed that monkeys accurately reached to the remembered target, with an average (± SEM) error of 1.91° (± 0.05°); this suggests that closed-loop visual feedback, while likely extremely useful [37–39], may not be necessary for making correct reaching movements, especially in the domain of highly trained movements. We found that a modest but significant proportion of neurons in MIP and PMd modulate their movement planning activity based on both the direction and the amplitude of the forthcoming reach, suggesting that these neuronal representations may causally support accurate memory-guided reaching behavior. Furthermore, we speculate that these same representations may contribute to planning and executing visually-guided reaches [40].

We examined the representation of reach direction and amplitude at various epochs within a memory reach trial. It is important to note that the cue epoch (C) overlaps with the visual stimulus, whereas the movement epoch (RT/MT) overlaps with a hand movement. The observed selectivity to reach target direction and amplitude during the former (C) could reflect visual response selectivity. Likewise, the selectivity during the latter (RT/MT) could reflect a representation of the hand position. Moreover, since we did not vary eye position (monkeys held gaze fixation throughout the trial), these data do not provide evidence for or against an eye-centered representation, i.e. a representation of the reach goal or hand position relative to the center of gaze.

Finally, we found a bias in the representation of reach space in our recorded neuron population, with systematically stronger response for planned reaches to large amplitudes (see Fig 4). Importantly, this response bias does not necessarily suggest that the periphery is better represented; indeed, the high-dimensional neuronal population can accurately represent both central and peripheral reach targets without having a substantial proportion of individual units respond with high firing rates to these targets. Additionally, this finding may depend on our choice of reach targets positions, where the observed peak locations correspond to ceiling effects from insufficient spatial sampling. However, in this work, we used reach targets with eccentricities at near practical limits (to subtend the entire touchscreen surface for Task 2), comparable or greater in extent relative to previous similar work [20, 41–44]. Including more peripheral targets may be useful to make accurate inferences about response field properties beyond the examined range of reaching movements.

Spatial response fields

We found strong evidence for a conjoint encoding of reach direction and amplitude; neurons in both areas exhibited significant modulation of movement planning activity by reach amplitude in some but not all reach directions. In particular, a dense sampling of reach targets revealed that neurons in both areas exhibit reliable spatial response patterns that are best predicted by a position-encoding model rather than a number of alternative direction and amplitude encoding models. Interestingly, this internal representation of the instructed reach target is highly consistent with previously observed sensory representations in the posterior parietal cortex [45–47], as well as corresponding response fields for saccadic movement plans.

The differences in model consistencies were not simply due to the complexity of models (i.e. the number of parameters), as models were evaluated in a cross-validation scheme. Importantly, the relatively high consistency of a Gaussian position-encoding model is not at odds with the relatively small proportions of neurons with significant modulation by amplitude, as compared to reach direction (~one third the population size). Indeed, for a large subset of neurons, both direction- and position-encoding models equally captured the neuronal response patterns (points along the unity line in Fig 7B and 7D), suggesting that this simple Gaussian model may concisely and accurately capture the response patterns of all (both amplitude-modulated and not) task-related neurons. Alternatively, it is possible that there exist two distinct populations of neurons that are best captured by two different models; however, our current data do not strongly suggest such heterogeneity.