Putative cell-type-specific multiregional mode in Posterior Parietal Cortex during coordinated visual behavior

Summary

In the reach and saccade regions of the posterior parietal cortex (PPC), multiregional communication depends on the timing of neuronal activity with respect to beta-frequency (10 – 30 Hz) local field potential (LFP) activity, termed dual coherence. Neural coherence is believed to reflect neural excitability, whereby spiking tends to occur at a particular phase of LFP activity, but the mechanisms of multiregional dual coherence remain unknown. Here, we investigate dual coherence in the PPC of non-human primates performing eye-hand movements. We computationally model dual coherence in terms of multiregional neural excitability and show that one latent component, a multiregional mode, reflects shared excitability across distributed PPC populations. Analyzing the power in the multiregional mode with respect to different putative cell-types reveals significant modulations with spiking of putative pyramidal neurons and not inhibitory interneurons. These results suggest a specific role for pyramidal neurons in dual coherence supporting multiregional communication in PPC.

eTOC Blurb

Khazali et al. introduced a novel network analysis that extracts shared excitability from recordings of local field potentials distributed across different brain regions. The results suggest that shared excitability in the posterior parietal cortex correlates with the motor control of coordinated eye-hand movements and interacts with specific neuronal cell-types.

Introduction

Neural coherence characterizes neural population dynamics by measuring correlations between the timing of spikes emitted by a neuron, and the fluctuations of populations as measured by local field potential (LFP) activity, as well as correlations in the timing of LFP activity at different sites, and correlations in spike timing between neurons. Cell-type specificity is a widespread feature of neuronal coherence measured as spike-field coherence (SFC). Studies of visual-spatial attention in macaque visual area V4 have shown that putative interneurons display stronger SFC with different phase preferences¹, and stronger attentional modulation than putative pyramidal neurons². In ferret prefrontal cortex, inhibitory postsynaptic potentials (IPSPs) between neighboring neurons are more synchronized³. IPSPs are important in controlling the timing and probability of pyramidal cell firing³. Neural population dynamics in general, and neural coherence in particular reflect the interplay of excitation and inhibition^4,5. Therefore, understanding the cell-type specificity of neuronal coherence is important to better understanding the biological basis of distributed neuronal dynamics.

The mechanisms of flexible behavior, such as decision making, learning, attention and movement planning arise from neural interactions across multiple brain regions, and neural coherence has also been implicated in multiregional communication^6–12. Recent work characterizes multiregional communication in terms of ‘dual coherence’ by measuring correlations in spike timing between nearby LFP activity recorded in the same region as the spiking neuron and LFP activity recorded remotely by an electrode in another brain region ^13,14. In the reach and saccade systems of the posterior parietal cortex (PPC), neurons are more likely to fire spikes coherently with LFPs recorded across both regions, locally and remotely, than with LFPs in one region or another¹⁴. Furthermore, dual-coherent neuron spiking better encodes behavioral computations such as decisions and movement plans, highlighting behavioral relevance.

Cortical projection neurons are mainly pyramidal neurons while cortical interneurons are mainly local circuit neurons. Since different biological cell-types serve different anatomical roles, cell-type-specific multiregional coherence may yield insight into multiregional communication. Long-range afferent fibers make stronger excitatory connections onto interneurons than principal cells ensuring that even minimal levels of afferent input generate inhibition in cortical circuits ¹⁵. Moreover, GABAergic interneurons are recruited when excitation is generated locally and when received from distant sites ¹⁶. Therefore, the role of different cell types in distributed networks likely differs between local and remote populations of neurons.

The role different cell-types play in multiregional communication, however, remains unclear as cell-type-specific multiregional coherence has not been previously investigated. We therefore developed a computational model of multiregional coherence involving cell-type-specific afferent input to local neural population excitability and cell-type-specific local recurrent signal contributions to population excitability. We then analyzed experimental observations of cell-type-specific multiregional coherence during coordinated visual behavior to reveal novel multiregional mechanisms of coordinated movement planning. Our results show that neuronal cell types may play specific roles in the properties of local and remote coherence, as described by ‘multiregional modes’. Conceptually, multiregional modes are defined as the shared excitability between the local and remote populations. The results indicate that multiregional communication may reflect cell-type-specific mechanisms in the control of coordinated visual behavior.

Results

Multiregional coherence model

We first consider a single-region model (Fig 1A and see STAR Methods) which generates coherent neural activity because each neuron fires spikes according to local neuronal excitability in proportion to the sum of two types of synaptic inputs. The first type of synaptic input reflects neural activity that results from synchronized excitability that is measured by recordings of LFP activity, and gives rise to neural coherence¹⁷. The second type of input reflects neural activity that arises from unsynchronized, sparse, firing of individual neurons within the neural population. As a result, the second input does not necessarily contribute to LFP activity.

Figure 1. Illustration of how coherent neural activity affects neuron spike timing.

A. Model of local coherent activity of a neuron and spike timing. i) At the presynaptic level, both sparse activities that are not well presented in the population activity, and coherent activities that are dominant, can affect the cellular excitability of a neuron. ii) The influence on spike timing depends on the sum of synaptic weights on the total input signal of the neuron. Synaptic influence depends on the cell-type of the receiving neuron. iii) Model results for two example neurons, an interneuron (red) and a pyramidal neuron (blue). The interneuron receives heavy coherent input and low sparse input. The pyramidal neuron receives less coherent input. Coherent activity influences spike timing for the interneuron more than the pyramidal neuron leading to higher spike-field coherence for the interneuron. Note that spike-field coherence in the model peaks around the beta frequency band (10–30 Hz), by design (see STAR Methods). B. The influence of multiregional coherent activity on neuronal spike timing. Note that for simplicity we do not present sparse activity. i) Coherent activity can be either purely local (private local - purple) or can be influenced by interactions with other areas (green and orange). ii) Interactions can have different modes associated with local circuit output or with local neurons receiving signal from a remote area. iii) Model results for three neurons each receiving one mode of coherent activity. Purple: The neuron receives only local inputs. Therefore, spike timing is coherent with local activity. Orange: The neuron receives local inputs that are completely correlated with activity in another region (remote), by the projected output from the orange neuron, with no private local inputs. Therefore, the spike timing is coherent with the activity in the local and remote regions, which we call multiregional coherent. Green: The neuron receives inputs that are associated with signals arriving from remote origin. Therefore, the output of the neuron interacts with the surrounding neurons too and therefore is coherent with local and remote activity.

We simulated spiking and LFP activity from the model for neurons that are strongly coupled to local population input or to sparse, unsynchronized input (Fig 1Aii, see STAR Methods). As expected, neurons fire spikes coherently when they are strongly coupled to local synchronized population input compared to the sparse input (Fig 1Aiii red). Neurons that are coupled to the sparse input and are relatively weakly coupled to local synchronized population input do not fire spikes coherently (Fig 1Aiii blue).

To understand multiregional coherence, we next consider a multiregional model containing a local region and a remote region whose neurons experience local and remote neuronal excitability (Fig 1B and see STAR Methods). Fig 1Bi illustrates the multiregional model for three neuronal cell-types. One cell-type fires spikes due to input from a multiregional mode, a second cell-type fires spikes due to input from another multiregional mode and a third cell-type fires spikes only due to the private local component of excitability.

We infer the multiregional modes by examining correlations in local population activity measured by LFP activity in the local region, and remote population activity measured by LFP activity in the remote population. This step stands on our definition of the multiregional modes as a shared excitability between local and remote populations. High shared excitability leads to high LFP correlation and low shared excitability leads to low LFP correlation. We then simulated spiking and LFP activity for neurons that are strongly coupled to either one or other of the multiregional modes, or to the private local component (Fig 1Bii, see STAR Methods). As expected, neurons that only experience the local mode fire spikes coherently with the activity of the local population and not the remote population (Fig 1Biii purple). In contrast, neurons that are coupled to the either multiregional mode fire spikes coherently with activity of both local and remote populations (Fig 1Biii green and orange). Therefore, the multiregional model expresses properties of local and remote coherence.

Coordinated visual behavior and dual coherence in PPC

We next analyzed neuronal spike trains simultaneously recorded with LFP activities from different electrodes within and between medial and lateral banks of intraparietal sulcus (IPS, see STAR Methods and Figs 2A,B). Recorded neurons showed a firing pattern similar to previous work (Fig 2C) ^{13,14,18–21}. When evaluating the neurons that were recorded the responsive LFP activity (Fano factor > 0.2, see STAR Methods) ~80% of neurons fired coherently with either local (N = 344; 69%), remote (N = 282; 56%) or both LFPs (dual coherent neurons n = 203; 41%). Local and remote SFC had similar profiles to each other, which elevated in beta band (10–30 Hz). Across the population, local SFC was higher than remote SFC in the band 1–70 Hz for both baseline and delay epochs; p < 0.05; permutation test with cluster correction; Fig 2D, Fig S1 and STAR Methods).

Figure 2. Neural response and multiregional SFC during the task.

A. Illustration of the free choice task. Each monkey was instructed to touched and fixated the green and red squares for time intervals with various lengths, respectively. Then two different targets, associated with different rewards, were presented. Each monkey was then instructed to either reach, look, or reach and look at one target after Go-cue, green and red squares switch to gray. Green, red and yellow targets were associated with reach, saccade or reach and saccade respectively. B. Illustration of the constrained task. Each monkey was instructed to look or reach and look to a remembered target position after the Go-cue. C. Illustration of the recording sites on the medial and lateral banks of posterior parietal cortex (PPC). The lower panels plot the mean firing rate of PPC neurons during the task, with the shaded area being the standard error of the mean (SEM), aligned to Target-on cue (left panel) and to Go-cue (right panel). D. The average spike-field coherence (SFC) of PPC neurons. SFC for each neuron was calculated with local (dark gray) and remote (light gray) during the 500 ms preceding the Target-on cue (Baseline; left panel) and during the 500 ms preceding Go-cue (Delay; right panel) periods. Shaded areas represent the 95% confidence interval (CI). Note that both SFCs are having similar profile, peaking in beta band and local SFC has significantly higher magnitude than remote SFC during baseline and delay condition for all frequencies under (70 Hz), applying a cluster correction to correct for multiple comparisons of permutation test (p < 0.05).

Estimating the multiregional mode

Understanding how a neuron fires spikes coherently with local and remote population activity is important to understanding multiregional communication in PPC. Therefore, we next examined whether multiregional modes exist and how they might support the generation of dual SFC. We selected 464 recording sessions that included spiking activity from a neuron recorded simultaneously with local and remote LFPs, (Spike-Field-Field, SFF sessions). We first examined the correlation between local and remote LFPs. Local and remote LFP activity were correlated indicating the presence of a shared signal due to a multiregional mode. Importantly, correlations in local and remote LFP activity varied trial-by-trial. On trials when we observed high correlation between local and remote LFPs (e.g. Pearson correlation coefficient, r > 0.9 Fig S2A) the shared signal amplitude was large and the multiregional mode was active. On trials when we observed low correlation between local and remote LFPs (e.g. r < 0.3 Fig S2A), the shared signal amplitude was low and the multiregional mode was inactive.

To estimate whether the multiregional mode was active or inactive, we quantified the shared signal between local and remote LFPs. The multiregional mode depends on the correlation between local and remote LFPs and the time lag between them (Fig S2B, C). The multiregional mode estimation process therefore started with filtering LFP then correcting for the time lag between LFPs before estimating the multiregional mode for that given trial (See STAR Methods and Fig 3A). Time lags varied trial-by-trial in the same session, consistent with a different phase shift on different sessions. By shifting the recordings according to the time lag on each session, we effectively studied the magnitude component of LFP correlation independent of the phase difference.

Figure 3. Estimating the multiregional mode.

A. Three trials from an example recording. The trials are presented in three rows, each row has two sub-rows. The first sub-row presents local and remote LFPs (black and purple respectively) in time. The second, plots LFPs against each other in a spread plot. Column 1 shows the raw LFP activity. Column 2 shows the beta band LFPs after filtering. Column 3 shows the LFPs after aligning remote to local. Column four shows the estimated common mode using singular value decomposition (SVD). The three trials had 14, 30 and 15 ms lags respectively. B. Correlation between local and remote LFP activity during the example recording in A. Each point represents activity for one trial. i: Correlation before alignment. ii: Correlation after alignment. Lags are concentrated around zero after the alignment. C. Correlation between local and remote LFP activity during another example recording. Conventions as in B. D. Histogram of the average lag of each session before alignment. E: Histogram of the average lag after alignment. Correlation at zero lag demonstrates a successful alignment procedure. F. Histogram of the rotation angles for all trials in the example recordings in A and B. G Histogram of average rotation angles for all recordings. Note that all angles are in the same angular quadrant. H. Illustration of the sorting procedure for one third of the trials with high r (active mode - red) and low r (inactive- blue). i: Scatter plot of the correlation against the lag after alignment. ii: Histograms after normalizing correlation for active (red) and inactive (blue) mode trials from each session across all sessions. I. Normalized power difference between the sorted trials (active – inactive mode) across all sessions for the multiregional mode (i), remote (ii) and local (iii) activity. Note that the power is higher for trials with active mode compared with the inactive mode. * p<0.05; ** p<0.01; *** p<0.001; permutation test.

Since LFP activity fluctuated trial-by-trial, correcting for time lags did not eliminate the correlation, and yielded positive correlations because corrected local and remote LFPs were in phase (Fig 3A and Fig S2B). Recording sites had different distributions of time lags before alignment with some time lags scattered (Fig 3B) and others concentrated (Fig 3C). Average time lag was 0 – 30 ms (Fig 3D). After correcting for the time lags trial-by-trial, we confirmed the time lags became concentrated around zero (Fig 3B-D). Finally, we examined the rotation angle of the single value decomposition (SVD) algorithm. The rotation angle can represent the angle of the slope between the data points of local and remote LFPs. The fact that the rotation angle was located in the first quadrant for all trials of the example session (Fig 3F), means that according to the method the LFPs had always positive correlation. This was also true for the averaged angles of all recorded sessions (Fig 3G).

Dual coherence and the multiregional mode

Estimating the multiregional mode allows us to examine population excitability across different brain regions. We defined trials where the multiregional mode was active/inactive as the third of all trials with the highest/lowest correlation. (Fig 3H-i,). As expected, in the example session, trials with an active multiregional mode had high correlation (0.49 ± 0.08; mean ± std) and trials with inactive common mode had low correlation (0.18 ± 0.05; mean ± std). The normalized mean population correlation was significantly higher for active (0.7 ± 0.043; mean ± std) than inactive trials (0.3 ± 0.043; p<0.001; mean ± std; permutation test; Fig 3H-ii). As expected, the normalized power of local LFP, remote LFP and the multiregional mode was higher during active trials than inactive trials $\frac{active trials - inactive trials }{active trials + inactive trials}=0.046\pm 0.006$; 0.055 ± 0.007; 0.16 ± 0.05; mean ± 95% CI, respectively, with significant effect p < 0.001; one-group t-test; Fig 3I).

The multiregional mode represents the shared excitability between local and remote populations, so we should observe changes in SFC on trials when the multiregional mode is active compared with trials when the multiregional mode is inactive. Since different neuronal cell-types have different relationships to local SFC ^1,22–24, different cell-types may display different relationships to the multiregional mode.

Spike waveform classification yields four neuronal populations

Based on the averaged extracellular spike waveform, we sorted PPC neurons into four classes (very narrow spiking (vNS): n=99 neurons. moderately narrow spiking (mNS): n = 51. moderately broad spiking (mBS): n = 152 neurons. very broad spiking (vBS): n = 146; see STAR Methods, Fig 4A, B). We confirmed that class borders identified the same results with four clear clusters in each monkey (Fig S3). Previous work has suggested that narrow spike (NS) waveforms are generated by interneurons and wide spikes are generated by pyramidal neurons ^25–27. These studies have demonstrated that NS have higher firing rates than broad spike neurons (BS). Our analysis replicated these results. During the baseline epoch, vNS or mNS neurons had a higher firing rate than either mBS or vBS neurons and mBS neurons had a higher firing rate than vBS neurons (vNS: 13 ± 1.3 Hz (mean ± SEM). mNS: 14.4 ± 1.9 Hz. mBS: 9.2 ± 0.7 Hz. vBS: 7 ± 0.5 Hz. p < 0.05; permutation test false discovery rate (FDR) corrected; Fig 4C). Activity across task epochs demonstrated a consistent firing rate difference (Fig S4A). The populations also differed in the baseline inter-spike-interval (ISI) coefficient of variation (CV). vNS CV (1.46 ± 0.032; mean ± SEM) was higher than either mBS (1.36 ± 0.024; mean ± SEM) or vBS (1.36 ± 0.021; mean ± SEM; p < 0.01; permutation test FDR corrected, Fig 4D). mNS CV (1.36 ± 0.046; mean ± SEM) was not significantly different from any other group. Larger CV indicates that vNS neuron spiking was more irregular than the other cell-types. Thus, NS neurons may reflect putative subclasses of interneurons, and BS neurons may reflect putative subclasses of pyramidal neurons.

Figure 4. Neurons with different biophysical properties have different neural coherence.

A. Presents a typical spike waveform of a PPC neuron with trough-peak width in (black) on top of the average spike waveform of all recorded neurons. Colors are assigned based on trough-peak width sorting as in B. B. Trough-peak width histogram demonstrating at least 4 populations of neurons based on Hartigan’s dip test and K-means clustering. Gray areas in between the clusters represent neurons that were not pooled to any population to avoid overlapping between clusters. Red: Neurons with very narrow spikes vNS; Pink: neurons with second narrowest spikes, mNS; Light blue: neurons with wider spikes mBS; Dark blue: neurons with widest spikes vBS. C. Mean firing rate during baseline of each clustered neuron against its trough- peak width. The firing rate of vNS and mNS neurons is significantly higher than either mBS or vBS neurons. mBS neuron firing is higher than vBS neuron firing. D. Mean inter-spike interval during baseline of each clustered neuron against its trough-peak width. Note that vNS and mNS neuron firing displays significantly shorter inter-spike intervals than either mBS or vBS, and mBS neuron firing has a shorter interval than vBS neuron firing. * denotes p < 0.05; ** denotes p < 0.01; *** denotes p < 0.001 (permutation test). E-i. Average spike field coherence (SFC) for each of the neuronal populations in PPC. SFC was calculated with local beta band LFP (upper panels) and remote beta band LFP (lower panels) during the last 200 ms of the baseline period. Shaded areas: 95% confidence interval (CI). Note that local SFC is higher than the remote in beta band. There is no difference in local SFC magnitude, averaged at the peak beta frequency (16.5 – 22.5Hz), across cell-types but the difference is significant in remote (p < 0.05; Kruskal Wallis). E-ii. Histograms of the SFC magnitude, averaged at the peak beta frequency (16.5 – 22.5Hz), for each cell-type. The mean and standard deviation of the SFC of each cell-type is indicated by a neighboring circle and line with the corresponding color. Remote SFC magnitude was significantly higher for vBS compared to all other neurons pooled together, and compared to mBS but not vNS or mNS (p < 0.05; permutation with false discovery rate for multi comparison correction). F-i. Schematic illustrating a spike train with a preferred SFC phase. F-ii. Explaining the binning procedure of the SFC preferred phase. We used eight phase bins centered at 0° and every 45° with a width of 60° to count the number of spikes in each bin. F-iii and iv. Normalized polar histogram plotting histograms of two neural populations, F-iii. Each neuron prefers a different SFC locking phase; and F-iv. Each neuron prefers the same SFC locking-phase. Open circles: vector resultant when not significant. Filled circles: Vector resultant when significant (p < 0.05 Rayleigh test). Arc: 95% confidence interval of the preferred phase. G. Preferred local SFC phase (upper raw) and remote SFC phase (lower raw) across the population. For local SFC, all populations preferred one phase (p < 0.05 Rayleigh test) except mNS which did not have a preferred phase (p > 0.05 Rayleigh test). For remote SFC, vBS alone had a significant preferred phase (p < 0.05 Rayleigh test). mNS and mBS had a biphasic preference (p < 0.05 Rayleigh test). vBS is the only population with a preferred phase for local and remote SFC. H: The vector resultant of each neuron population for local (i) and remote (ii) SFC. The preferred phases differ across different populations for the local SFC but not for remote SFC (p < 0.05; one-way ANOVA).

Neurons with wide spike waveforms are coherent with multiregional LFPs

We next examined whether different putative cell-types differ in their coupling to multiregional LFP activity. We calculated the averaged magnitude of local and remote SFC of each putative cell-type and evaluated the preferred LFP phase. Before evaluating SFC magnitude, we first eliminated the firing rate difference across the cell-types by decimation (see STAR Methods, Fig S5A). When examining SFC of each putative cell-type, we observed no difference in local SFC magnitude across cell-types when examining either the effect across all cell-types or by pairwise testing (Local SFC magnitude: vNS = 0.051 ± 0.0043 (mean ± SEM). mNS = 0.061 ± 0.009. mBS = 0.05 ± 0.0037. vBS = 0.058 ± 0.0036. p = 0.17; Kruskal Wallis test and pairwise permutation test, Fig 4E-ii). By contrast, remote SFC significantly differed across cell-types (p = 0.014; Kruskal Wallis test) with vBS neurons displaying the highest remote SFC (0.038 ± 0.0027; mean ± SEM) compared with the other cell-types (vNS: 0.033 ± 0.0024, mNS: 0.031 ± 0.0039 and mBS: 0.029± 0.0024, respectively). vBS neuron remote SFC magnitude was significantly higher than that of all other neurons pooled together (p = 0.023; pairwise permutation test). When comparing vBS neuron SFC with SFC of each cell-type alone, vBS neuron SFC was significantly higher than mBS neuron SFC but not than SFC of either vNS or mNS neurons (p = 0.029; pairwise permutation test FDR corrected, Fig 4E-ii). We also compared multiregional SFC across all cell-types (Fig S4B), which showed a significant effect (p = 0.005; Kruskal Wallis test). Similar to local SFC, mNS neurons showed on average the highest multiregional SFC (0.055 ± 0.0059; mean ± SEM) and then (vBS: 0.053 ± 0.0031. vNS: 0.048 ± 0.038. mBS: 0.40±0.0031).

We also analyzed the spike preferred LFP phase in the beta band (~17Hz). We examined whether neurons tended to fire at a specific LFP phase as a function of their cell-type (See STAR Methods and Fig 4F). The spikes of three out of four putative cell-types displayed timing tuned around a preferred phase of local LFP (vNS with140.6 ± 18.7° mean preferred LFP phase ± confidence interval (CI); mBS: 170 ± 14.1°; and vBS: 135.6 ± 16.0°; p < 0.05 Rayleigh test; Fig 4G upper raw). One cell-type, vBS neurons, fired spikes with a preferred remote LFP phase (vBS= 9.3 ± 16.9°; p < 0.05 Rayleigh test; Fig 4G, lower raw). mNS and mBS neurons showed a biphasic preference (mNS: 26.2 and 206.2 ± 27.5° and mBS: 21.9 and 201.9 ±16.2°; biphasic p < 0.05 Rayleigh test). The effect of cell-type on the preferred LFP phase was significant for local but remote LFP (p < 0.05; one-way ANOVA. Fig 4H-i and ii). Notably, these results identify vBS neurons as the most prominent cell-type with the highest remote SFC and with preferred local and remote LFP phase. While mBS neurons had low remote SFC, mBS neuron spiking showed reliable phase-locking for both local (monophasic) and remote SFC (biphasic).

Multiregional mode modulates SFC for specific cell-types

To further investigate the relationship between the multiregional mode and dual SFC, we examined vBS neuron spiking to ask whether the interaction between vBS neuron spiking and the mode differs when the mode is active and inactive (Fig 5A).

Figure 5. The concept of the multiregional mode.

A. Relationship of the multiregional mode with local and remote SFC. We plot three trials when the multiregional model is active and three trials when it is inactive. For each trial, we plot local and remote LFPs, the multiregional mode and spike trains of a vBS neuron. B. The normalized power difference between the sorted trials (active – inactive mode) across all sessions that recorded vBS neurons. Note that the power is higher for trials with active mode as to inactive mode. * p < 0.05; ** p < 0.01; *** p < 0.001; permutation test. C. SFC with estimated multiregional mode (left), remote LFP (middle) and local LFP (right). SFC of one vBS neuron (upper). SFC during inactive mode (light) and active mode (dark). Note that all SFCs of this neuron modulated significantly based on the status of the mode 200ms before Target-on cue. When pooling all vBS neurons, SFC was significantly higher during active mode at the peak (~16.5–22.5 Hz, p < 0.05 and p < 0.001; permutation test; for multiregional mode and remote field, respectively). 95% confidence interval (shaded).

The power of the multiregional mode as well as local and remote LFP activity power was significantly higher during active states (Fig 5B; p=1.0·e-34, 3.0·e-19, 1.0·e-16 for multiregional mode, local and remote LFP respectively; t-test one sample). Therefore, if the multiregional mode is linked to dual SFC generation, dual SFC should vary with multiregional mode status. Thus, we estimated SFC of vBS spikes with multiregional mode during active and inactive trials. Multiregional mode SFC was significantly higher for active trials than for inactive trials at the peak of the beta band (16.5–22.5 Hz), tested during the 200 ms preceding Target-on cue (SFC for active mode: 0.0642 ± 0.0039; mean ± SEM, and for inactive: 0.054 ± 0.0029; p = 0.042 permutation test; Fig 5C). This modulation is stable for most of the baseline and not just the last 200 ms (Fig S4C). This result reflects a change in the spike timing with the multiregional mode, and is not due to systematic increase in the firing rate of vBS during trials when the mode is active compared to inactive ( mean ± std = −0.046 ± 0.87 Hz; p = 0.59 t-test one sample; Fig S5B,C). other cell types did not show systematic change in their firing rate with multiregional mode status (−0.014 ± 0.75, −0.02 ± 0.96, −0.041 ± 0.56; p = 0.85, 0.13, 0.39; t-test one sample for vNS, mNS, mBS, respectively; Fig S5B,C).

Our analysis suggests that the multiregional mode is the main link which estimates the interaction between vBS neurons and remote LFP. Hence, we expected modulation of remote SFC following the modulation of multiregional SFC. This was the case. Remote SFC of vBS was significantly higher during active mode (SFC for active mode: 0.053 ± 0.0033; mean ± SEM, and for inactive: 0.04 ± 0.0022; p= 9.0·e-4 permutation test; Fig 5C). In contrast, vBS neuron interaction with local LFP is not necessarily dependent on the multiregional mode because they can interact directly through private local routing of information. Thus, the effect of the mode status could be limited on local SFC. That was the case. vBS local SFC did not modulate significantly (SFC for active mode: 0.069 ± 0.0042; mean ± SEM; and inactive mode: 0.06 ± 0.0036; p = 0.11; permutation test) although it was modulated with similar modulation pattern seen in remote SFC. Thus, modulation of remote SFC magnitude of vBS neurons is directly dependent on the multiregional mode status.

We then analyzed mBS, vNS and mNS neurons. mBS neurons were coherent with multiregional mode, and local and remote fields similar to vBS neurons. mBS SFC with the multiregional mode and remote LFP modulated significantly with mode status (multiregional SFC for active mode: 0.054 ± 0.0035; mean ± SEM; and for inactive: 0.046 ± 0.0026; p = 0.044 permutation test; Fig 6; and of remote SFC for active mode: 0.045 ± 0.003 and for inactive: 0.035 ± 0.0022; p = 0.004 permutation test: Fig S6). mBS local SFC was not significantly modulated by mode status although it showed similar modulation pattern to remote SFC (SFC for active mode: 0.061 ± 0.0041; mean ± SEM; and inactive mode = 0.051 ± 0.0032; p = 0.065; permutation test). When examining SFC of vNS and mNS neurons, multiregional SFC for vNS and mNS neurons was not modulated significantly by mode status (vNS and mNS SFC respectively for active mode: 0.057 ± 0.0039 and 0.065 ± 0.0056; mean ± SEM; and for inactive mode = 0.05 ± 0.0034 and 0.054 ± 0.0064; p = 0.16 and 0.22; permutation test, Fig 6 middle and right panels). Thus, the mode is coherent with putative pyramidal neurons (BS neurons) and not with putative interneurons (NS neurons). Remote SFC for mNS neurons was significantly modulated by mode status but not vNS neuron SFC (vNS and mNS SFC respectively for active mode: 0.047 ± 0.0034 and 0.049 ± 0.0043; mean ± SEM; and for inactive mode = 0.04 ± 0.003 and 0.034 ± 0.0023; p = 0.07 and 0.003; permutation test; Fig S6). Local SFC for NS neurons was not modulated by the mode status (vNS and mNS neuron SFC respectively for active mode= 0.61 ± 0.0043 and 0.069 ± 0.0058; and for inactive mode= 0.053 ± 0.0038 and 0.066 ± 0.0065; p = 0.18 and 0.7; permutation test; Fig S6). Modulation of BS neuron response to the multiregional mode status reflected genuine differences in the response properties, namely lower SFC variance as compared to NS neurons (see STAR Methods). Modeling the results showed the interaction was simulated by high/low coupling for BS/NS with the multiregional mode (see STAR Methods, Table 1 and Fig 7).

Figure 6. State-dependent Multiregional mode SFC modulations across mBS, vNS and mNS cell types.

A. The normalized power difference for the multiregional mode between active and inactive mode. Each column represents a putative cell-type (mBS, vNS, and mNS) from left to right, respectively. Active mode trials display higher multiregional mode power compared to inactive mode trials for all three cell-types (p < 0.001 permutation test). B. Multiregional mode SFC for active trials (dark) and inactive trials (light). Multiregional mode SFC was significantly higher only for the mBS cell-type (~16.5– 22.5 Hz, p < 0.05; permutation test). * p < 0.05; ** p < 0.01; *** p < 0.001; permutation test.

Table1.

Multiregional coherence model variables used to run the simulation

Variables/Cell-type	vNS	mNS	mBS	vBS
$\mathit{\beta \_i}$	0.2	0.2	0.2	0.2
$\mathit{\beta \_a}$	0.15	0.15	0.15	0.15
$\mathit{\beta 1}$	0.15	0.15	0.15	0.15
$\mathit{\gamma 1}$	0.006	0.006	0.006	0.006
$\mathit{\gamma 2}$	0.005	0.007	0.018	0.018

Figure 7. Modeling multiregional SFC for Broad Spiking neurons.

Model-based SFC for multiregional mode (top row), remote LFP (middle row) and local LFP (bottom row) for mBS neurons (left column) and vBS neurons (right column). Active trials (dark). Inactive trials (light). Multiregional mode SFC and remote SFC significantly differs between active and inactive trials (p < 0.05; permutation test at ~16.5– 22.5 Hz). Local SFC was not significantly different between active and inactive trials. * p < 0.05; ** p < 0.01; *** p < 0.001; permutation test.

Behavioral relevance of the multiregional mode

We next examined whether the multiregional mode is linked to behavior, specifically eye-hand coordination. Since the multiregional mode reflects correlated activity between both banks, we expected that multiregional mode power was related to coordinated movement. To test this prediction, we sorted the trials based on their reaction time and compared the power modulation between them. We compared neural activity around the time of target onset and the Go-cue for the 33% of the trials which had the fastest reach reaction time with 33% of the trials which had the slowest reaction time. We calculated the power modulation index (PMI) for each session by subtracting the average power of slow trials from fast trials divided by their sum (see STAR Methods). PMI of eye-hand coordination movements was significantly lower than zero, indicating higher power for slow trials (p < 0.05 t-test one sample with discovery rate correction Fig 8A,B). In contrast, saccade alone trials did not show any clear power difference between fast and slow trials (Fig 8C). Thus, the multiregional mode power was significantly lower for fast trials compared to slow trials just for coordinated movements and not for saccades made alone. We also analyzed trials involving a coordinated saccade and reach movement toward the preferred direction of the recorded neuron (Fig 8D) and the null direction (Fig 8E). The PMI of the preferred direction showed similar modulation to that for all directions in Fig 8B. PMI was significantly lower than zero across all time points of the first epoch, (p < 0.05 t-test one sample with discovery rate correction, at the second epoch) but not for the null direction trials. Thus, multiregional mode power is correlated with the timing and direction of coordinated eye-hand movements, but not eye movements alone. Moreover, the power of both banks LFP did not modulate with coordinated movement reaction time (Fig S8). Thus, power correlation with coordinated movement control is specific to the multiregional mode and not for the lateral LFP or medial LFP alone.

Figure 8. Multiregional mode and eye-hand coordination.

A. Time course of the multiregional mode centered at Go-cue. An example of a fast trial (orange) and a slow trial (blue) from the same session. Note that the fast trial has lower peak to peak fluctuation than the slow trial. B. Power modulation index (PMI) for each session and for all directions sampled by 100 ms width bins (~ two beta cycles) with moving steps of 50ms. Each brown dot represents the PMI of one recording session at one 100 ms interval in two time periods, the first centered at Target-on and the second at Go-cue. The shaded line shows the averaged PMI across all sessions with block design (n = 33, black line) with CI of 95% (brown shadow). PMI was significantly lower than zero for most time points in both epochs. The averaged PMI was (first epoch: −0.14 ± 0.11; mean ± 95%CI; centered at Target-on with p = 0.015 t-test one sample with discovery rate correction, and second epoch: −0.13 ± 0.1 with p = 0.017) indicating a consistent higher multiregional power for slow trials than fast trials. C. same as B but for saccade alone, with the same number of sessions as in B (n = 33). Note that PMI was not significantly lower than zero at any point of time. The averaged PMI was (first epoch: −0.003 ± 0.012 with p = 0.63; mean ± 95%CI; with p = 0.18, and second epoch: −0.005 ± 0.012 with p = 0.45). D same as B but for preferred direction. PMI was significantly lower than zero during the whole first epoch and was almost significant for the second epoch. The averaged PMI was (first epoch: −0.17 ± 0.11; mean ± 95%CI; with p = 0.006, and second epoch: −0.11 ± 0.1 with p = 0.04). E same as B but for null direction. PMI was not significantly lower than zero at any point of time. The averaged PMI was (first epoch: −0.003 ± 0.1; mean ± 95%CI; with p=0.95, and second epoch: −0.014 ± 0.09 with p = 0.77). ---- indicates p < 0.05; t-test one sample with discovery rate correction.

Discussion

Here, we developed a model of SFC to examine how local recurrent excitability and long-range inputs influence neuronal spike generation. This model can be applied to neuronal interactions within one region and across multiple regions. We focused on neurons that interact with multiregional excitability that manifests as dual coherence. Dual coherent neurons are neurons which emit spikes whose timing is correlated with multiregional LFPs. Such neurons have been shown to be recruited rapidly in PPC during decision making tasks that involve visually guided behavior¹⁴. Coherent neurons also contain information about the reaction time of coordinated eye hand movements ⁷.

In our analysis, we estimated the common excitability across multiple regions by estimating the shared signal across LFPs recorded across the PPC. The shared signal, which we term the multiregional mode, allowed us to explore the relationship between the activity at different regions and the spike timing of dual coherent neurons. We estimated the multiregional model after correcting for the influence of potential lags between different LFPs. This corrective procedure was necessary to estimate the mode and its power in order to detect whether the mode was active or inactive, as well as the interaction with neuronal spiking. We found that the multiregional mode was behaviorally-relevant because the power modulated with the reaction time of eye hand coordinated movement and not eye alone movement. This result suggests the involvement of the multiregional mode in neural communication between the lateral and medial banks, which is needed during coordinated eye and hand movement. In contrast, we observe low or no involvement of the multiregional mode when mainly just one bank is supporting one effector movement, as in eye movement alone. We also showed that multiregional mode power increased with longer reaction time for the preferred but not the null direction, movement directions with maximum and minimum firing rate of the recorded neuron. This result is in line with other work that shows coherent neurons in PPC predict movement timing during coordinated eye hand movements ^7,13. Thus, the mode contains multiregional, motor control features that are associated with the timing and direction of upcoming coordinated movement. Similar beta power correlation with the movement reaction time has been reported in human MEG ²⁸ and EEG ^29,30. Our results add additional insights regarding the significance of beta-band activity to motor planning and control and show that the modulation of beta power reflects movement features of multiple-effectors, supported by distinct cortical regions.

Another important feature of the multiregional mode is how it relates network dynamics to individual neuron spiking. The mode was coherent with different neurons in both banks of the PPC, yet this coherence varied for different specific-putative-cell-types. Our classification procedure represented mBS and vBS, as two different neuronal classes with potentially different biophysical and coherence characteristics which strengthened/weakened their coherence with the multiregional mode when the mode status became active/inactive. Thus, multiregional mode was most coherent with putative pyramidal neurons, which may have specific morphology, providing long apical dendrites and axons projecting to distal regions ³¹. In contrast, putative interneurons, neurons with narrow spikes did have significant coherence with the multiregional mode but did not vary when the mode was active or inactive. These findings are in alignment with several previous studies that argue the somatic-apical dendrite axis forms dipoles in pyramidal neurons which are important to beta events ^31–33. Thus, pyramidal neuron spiking activity is strongly associated with beta events and may be a consequence of the coincident arrival of inputs to dendritic and somatic synaptic from diverse distant sources, and involves interneurons at different parts of the pyramidal neuron body ^33,34. Related work shows putative pyramidal and interneurons in the anterior cingulate and lateral prefrontal cortex (ACC/PFC) fire bursts of spikes that are synchronized with long-range LFPs in the beta band during shifts of attention²⁷. The same populations of neurons increase in local beta power around bursts of putative interneurons and in earlier phases of putative pyramidal neuron bursts ²⁶. In contrast to these reports, our analysis summarizes beta band excitability across several regions in one variable, the multiregional mode, and suggests a differential role for BS and NS neurons in maintaining multiregional communication.

Our proposed multiregional coherence model was able to replicate observed multiregional cell-type-specific coherence by varying a single variable. By varying the coupling coefficient of cell-types with the multiregional mode, the modulation of recorded LFPs was significant across active and inactive mode status for all recording sessions. Thus, the differences we observed in the modulation of multiregional coherence across different cell-types could not be due to the power modulation of the LFP activity. In our simulation, we generated the LFP activity from recordings, keeping the construction procedure of the simulated fields similar across cell-types. The model successfully generated modulated SFC between BS neurons and the multiregional mode due to reliable coupling coefficient.

Based on our computational model, changing remote SFC implies a significant change in the multiregional mode SFC. However, our data showed that, for mNS neurons, remote SFC but not multiregional SFC significantly varied with multiregional mode status. A parsimonious explanation of our observations is that other multiregional modes may exist. Multiple modes are usually needed to explain neural population dynamics ^35–38. Therefore, while narrow spiking linked multiregional modes must be secondary to the multiregional mode we estimated, mNS neurons may be coupled strongly with other modes, which lead to modulations in remote narrow spiking SFC. In addition, the existence of multiregional modes that are purely cell-type-specific seems unlikely because pyramidal and interneurons operate closely together in local microcircuits. We indeed observed a tendency toward NS multiregional SFC modulation with the estimated mode. BS neuron remote SFC modulation was also larger than that predicted from the multiregional mode alone, consistent with the contribution of other modes. Such scenarios might represent excitatory-inhibitory interplay in cortical-cortical interactions during flexible behavior ^4,5. Finally, we show that our results cannot simply be explained by volume conduction phenomena or variations in LFP signal-to-noise ratio (see START Methods).

In conclusion, this study provides novel evidence for a multiregional excitability latent component that is behaviorally relevant and interacts differently with specific putative cell-types.

STAR METHODS Text

RESOURCE AVAILABILITY

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the Lead Contact, Bijan Pesaran ( pesaran@upenn.edu )

Materials availability

The study did not generate new unique reagents

Data and code availability

• The electrophysiological and behavioral data reported this study have been deposited at: Figshare. The DOI is listed in the key resources table.

• All original code to analyze the electrophysiological and behavioral data and perform the numerical simulations has been deposited at Figshare and is publicly available as of the date of publication. DOIs are listed in the key resources table.

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

KEY RESOURCES TABLE

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Experimental data and code	Custom software and experimental data	https://doi.org/10.6084/m9.figshare.22056806.v2
Experimental models: Organisms/strains
Rhesus macaque (Macaca mulatta)	Covance and Charles River Laboratories	N/A
Software and algorithms
MATLAB R2017	Mathworks	https://www.mathworks.com/products/matlab.html
FSL	Analysis Group, FMRIB, Oxford, UK	https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/
Other
Microelectrodes 0.7–1.4 MΩ impedance	Alpha Omega single electrodes	https://www.alphaomega-eng.com/
Neural recordings and amplifier for monkeys R and C	NSpike NDAQ system, Harvard Instrumentation	http://nspike.sourceforge.net/#Overview
Neural recordings and amplifier for monkeys J and H	TDT Electronics, Alachua, FL	https://www.tdt.com/
Touch screen	ELO Touch Systems	https://www.elotouch.com/
Eye tracking	ISCAN, MA	http://iscaninc.com
Task controller	Custom LabView software with a real-time embedded system NI PXI-8820	https://www.ni.com/en-us/shop/labview.html

Experimental model and subject details

Data from four adult male rhesus monkeys (Macaca mulatta) were used in this study. Data from Monkey M1 and Monkey M2 were previously reported by Dean et al., 2012. Data from Monkey M3 and Monkey M4 were previously reported by Wong et al., 2016. All surgical and animal care procedures were done in accordance with National Institute of Health guidelines and were approved by the New York University Animal Care and Use Committee.

METHOD DETAILS

Experimental preparation

Each monkey was first implanted with an MRI-compatible head cap under general anesthesia. The head caps contained a head post to allow head restraint during training and experimental testing. We obtained a structural MRI to guide the placement of a recording chamber over the posterior parietal cortex within 1mm, using (BrainSight, Rogue Research, Canada) on 3 monkeys (M1–3). Monkey M4 did not have MRI scans due to the existence of iron in the soft tissue. Therefore, we placed the recording chamber according to stereotaxic coordinates over 7 P, 13 l and verified the anatomical localization based on the functional responses at different transdural penetration depths from the cortical surface. All experimental testing was conducted under controlled water and during light cycle access.

Behavioral tasks

Monkeys M3 and Monkey M4 each performed four behavioral tasks, one center-out task and three variants of a choice task, to earn fluid rewards. Each monkey was trained to make reach movements to green targets, saccade movements to red targets and coordinated reach-and-saccade movements to yellow targets. Each monkey performed first the coordinated reach-and-saccade. Subsequently, three variants of a two-armed-bandit choice task were performed. To reach, each animal used the contralateral arm to the hemisphere over which the recording chamber was implanted. The three choice tasks, reach-alone, saccade-alone and coordinated saccade-and-reach, were randomly-interleaved. Monkeys M1 and M2 performed two center-out tasks: a randomly-interleaved memory saccade-alone and memory coordinated saccade-and-reach.

For all tasks, each trial started by the illumination of red and green squares, side-by-side at the center of the display (2° visual angle on a side, green on left). Each monkey then made a saccade and fixated at the red square, and reached and touched the green square for a baseline line period (500–800 ms, uniformly distributed). A square target was then illuminated briefly in the visual periphery (eccentricity 10° visual angle, one of eight possible locations) and the monkeys were trained to maintain fixation and touch for an instructed delay period (1,000–1,500 ms, uniformly distributed). After this time, the central targets were extinguished, cueing each monkey to make a saccade alone if the peripheral target was red, or to make a combined reach-and-saccade when the target was yellow. In the choice tasks, two yellow targets (a triangle and circle) were presented, after baseline period at similar eccentricity as in the center out task. One target was placed in the direction of the response field and the other placed in diametrically opposed direction. The shape of the targets were assigned randomly independent of the response field. Each monkey had to choose one of the targets to perform either saccade-and-reach, reach-alone or saccade-alone after the 1,000–1,500 ms delay period based on the peripheral targets color as mentioned above. Each monkey was given a fluid reward of volume determined by the target chosen.

Spike preprocessing and sorting

We obtained spike waveforms from broadband neural recordings by first band-pass filtering to the raw neural waveforms from 0.3 to 6.6 kHz (multitaper projection filter settings: time duration = 0.01 s, frequency bandwidth = 3,000 Hz, center frequency = 3.3 kHz). We then selected 1.6 ms duration sections of the filtered signal that passed 3.5 std threshold below the mean filtered signal. The spike waveform was then projected into a three-dimensional principal component feature space on a moving 100 s time window if they showed robust estimate of the std. k-mean unsupervised clustering algorithm to sort the spike waveform in clusters. We manually then merged the clusters that showed a clear separation from the multiunit noise.

Electrophysiology recordings

The recordings were taken from 699 medial bank sites (M1: 396, M2:211, M3:74, M4:18) and 780 lateral bank sites (M1: 467, M2: 243, M3:50, M4:20; Fig 2C). The recordings included spiking activity of 656 neurons that 502 of them were (M1: 288 neurons, M2: 153, M3: 39, M4: 22) simultaneously recorded with LFP activities at 1001 sites (M1: 575 sites, M2: 303, M3: 85, M4: 38).

Criterion for unit acceptance

We included all well isolated units that were recorded for more than 150 trials of any of the tasks in SFC analysis. For the spike LFP locking phase analysis we included just the significantly SFC units applied 100ms before Target-on in the baseline (permutation test, P < 0.05).

LFP preprocessing

We included LFP activities recorded within 100 μm of a site that has a neuronal action potential to ensure that these activities were recorded from IPS banks and not the sulcus or white matter. We obtained the LFP activity by low-pass filtering of the broadband recording at 400 Hz (multitaper projection filter settings: time duration = 0.025 s, frequency bandwidth = 400 Hz, center frequency = 0 Hz) and by down-sampling the activity to 1 kHz from 30 kHz.

QUANTIFICATION AND STATISTICAL ANALYSIS

Spike-field coherence analysis

Spike-field coherence (SFC) was estimated using multitaper methods with ±10 Hz frequency smoothing with sliding windows of 500 ms. Since each neuronal action potential was recorded with several LFP activities from different electrodes, we chose LFP activity that had the highest Fano-factor across trials to estimate SFC. To test whether SFC was significant, we tested the magnitude of the SFC at a frequency window of 15–20 Hz against a null hypothesis that there was no SFC using a permutation test (at least 10,000 permutations). The null distribution was regenerated by shuffling the order of trials for the spiking data compared to the LFP data. This destroyed the dynamic relationship between spiking and LFP data. For either baseline or delay period, SFC was tested 200 ms before Target-on cue onset and Go-cue respectively.

We classified a neuron as coherent if the neuron fired spikes coherently with either LFP during the 200 ms period preceding Target-on (p < 0.05; permutation test). We sorted SFC in two groups, (local) for spike-field pairs on electrodes within the same bank (n = 502) and (remote) from two banks (n = 499). So, a given neuron could have one spike-field session or two. In the case of having several local or several remote LFPs recorded with a neuron, we chose the one local and remote LFP that had the highest Fano-Factor of the delay period across trials, applied on the raw LFP. We chose this criteria because the Fano-Factor value indicated the LFP modulation due to the task and position of the targets. We included in the analysis LFPs that had a Fano-factor of at least 0.2 or more. We excluded any neurons that had firing rate less than 2 Hz from SFC analysis.

Estimating cell-types preferred LFP phase

We applied spikes preferred LFP phase analysis without aligning remote LFP to local LFP because the alignment process affects remote LFP relation to spike timing. We generated normalized polar histograms for each putative cell-type. The histogram described spike firing probability at each LFP phase. We used eight phase bins centered at 0 and every 45° step with a width of 60°. When a neural population prefers to spike at a certain LFP phase, the normalized histogram peaks at that phase otherwise the population does not prefer a phase (Fig 4F). We did not calculate the phase preference of the spikes with respect to the multiregional mode because the mode estimation was performed after aligning LFPs in time trial-by-trial, rendering spike phase preference uninterpretable.

Decimation

Estimating SFC is affected by the number of spikes emitted during the time interval of the estimation. To address this concern, we decimated firing rate differences before estimating SFC by removing some spikes from the neurons that have high firing rate. We deleted spikes with a probability that was calculated by the ratio between the firing rate of the given neuron and 6 Hz. 6 Hz was the average firing rate of vBS neurons which had on average the lowest firing rate between the four clusters. This process eliminated the firing rate difference across cell-types successfully (decimated firing rate of for vNS: 4.6 ± 2.8 Hz; mean ± std; mNS: 5.5 ± 3.2 Hz; mBS: 4.0 ± 2.6 Hz, vBS: 4.6 ± 3.1 Hz; Kruskalwallis p = 0.22; Fig S5A).

Clustering different cell types

The clustering procedure was applied on the normalized average spike waveform. We normalized the spike wave form by dividing it by the action potential amplitude, the difference between trough and peak. The time interval between the normalized tough and peak indicated half of the spike width. We applied the Hartigan-Dip test to test whether the distribution of spike widths is unimodal or not. The dip test demonstrated that the neuronal population is at least bimodal and we used the modal interval, lower and upper borders of the isolated unimodal population, to estimate the initial borders between the neuronal clusters. We used these borders to divide the neuronal population and applied the same test again on the new two separated parts. We repeated this procedure until we reached unimodal outcomes. We reached five unimodal clusters and we analyzed just four because the fifth had an insufficient number of neurons (n = 27) to be analyzed. We repeated the clustering process by a second method, using K-mean clustering. We provided the K-mean algorithm by the number of clusters resulting from the first step. The K-mean is an unsupervised clustering method that provides strongly overlapping clusters, centroids and borders at Hartigan Dip method. Finally, we removed the neurons, which were located around the cluster’s borders to avoid any overlap between the populations. Specifically, we removed any neuron, which was in a bin that had lower than 10 neurons and was between two clusters. If the bins, which are located between the clusters, had more than 10 neurons, we removed the neurons in the lowest bin resulting with the following 4 clusters: very narrow spiking (vNS): 0.27 ± 0.041 ms; mean ± std, n=99 neurons. moderately narrow spiking (mNS): 0.44 ± 0.018 ms; n = 51 neurons. moderately broad spiking (mBS): 0.60 ± 0.022 ms; n = 152 neurons. very broad spiking (vBS): 0.75 ± 0.026 ms; n = 146, Fig 4A, B.

Multiregional coherence model

We use the concept of neural excitability to model when neurons fire spikes and investigate cell-type-specific multiregional coherence. In the model, neurons tend to fire spikes when they receive depolarizing synaptic input that increases their excitability. At times when neuronal excitability is high, the probability of a neuron to fire a spike is high. When excitability is low, the probability of spiking is low. In this sense, neuronal excitability captures statistical properties of neuronal firing and corresponds to the conditional intensity function for a point process¹⁸. Furthermore, we model the cell-type effect on the spike properties by associating different neuronal excitability with different cell types. This is biologically plausible since different cell-types receive different synaptic inputs from locally recurrent connections and afferent multiregional inputs. The model can be simplified to a single-region model (Fig 1A), which generates spiking activity of each neuron according to Local_neuronal_exc(i)(t). Local_neuronal_exc(i)(t) is a proportion to the sum of two types of synaptic inputs (see eq1). The multiregional coherence model uses the neural population excitability to model the probability of a neuron to fire spikes.

$${\mathit{P}}_{\mathit{spike}}\text{(}\mathit{i})(\mathit{t}\text{)}=\mathbf{\gamma }\cdot {\mathit{e}}^{Local\_population\_exc(i)(t)},\mathbf{\gamma }=\frac{1}{mean (e(Local\_population\_exc(i)(t)))}$$ Eq1

$${\mathit{P}}_{\mathit{spike}}(\mathit{i})(\mathit{t})=\mathbf{\gamma }\cdot {\mathit{e}}^{Sparse(i)(t)+\alpha (i)\cdot Local\_population\_exc(t)}=\mathbf{\gamma }\cdot {\mathit{e}}^{Sparse (i)(t)}{\mathit{e}}^{Local\_population\_ext(i)(t)}$$

$${\mathit{P}}_{\mathit{spike}}(\mathit{i})(\mathit{t})=\mathit{Firing\_rate}(\mathit{i})(\mathit{t}) \mathbf{\gamma }\cdot {\mathit{e}}^{Local\_population\_ext(i)(t)}$$

$${\mathit{P}}_{\mathit{spike}}(\mathit{i})(\mathit{t})=\mathit{Firing\_rate}(\mathit{i})(\mathit{t})\cdot \mathbf{\gamma }\cdot {\mathit{e}}^{\alpha (i)\times Local\_population\_ ext(t)}$$

The first input reflects synchronized excitability that is measured by recordings of LFP activity, Local_population(t)¹¹. The second input reflects neural activity that arises from unsynchronized, sparse firing of individual neurons, Sparse (t). Therefore Sparse(t) does not contribute to LFP activity. Therefore the model can simulate spiking and LFP activity for neurons that are strongly coupled to local population input and weakly to sparse, or weakly to local population input and strongly to sparse (Fig 1Aii). By that, the model can generate neurons with high SFC (Fig 1Aiii red) and neurons with low SFC (Fig 1Aiii blue). We used coupling coefficient ${\mathit{\alpha }}_{(\mathit{i})}$ to define the input strength from Local_population(t) to the neuron excitability Local_population_exc(i)(t). Coupling coefficient ${\mathit{\alpha }}_{(\mathit{i})}$= 0.01 to simulate SFC of (Fig 1Aiii red) compared to the sparse(t) coupling coefficient =1.0·e⁻⁴. These coupling coefficients were reversed for SFC of (Fig 1Aiii blue). Note that we adjusted the sparse coupling coefficient here just for illustration. Since the relative sum of these two inputs governs the coherence, adjusting just ${\mathit{\alpha }}_{(\mathit{i})}$ without having any coupling coefficient for Sparse(t), was sufficient to capture SFC, (see eq1) . Another important difference between Local_population(t) and Sparse(t) is that SFC is mainly present in the beta-frequency band (Fig 2D). Therefore, we restricted the coherent activity in our model to beta-frequency band, in contrast to Sparse(t). Mathematically, the probability to fire a spike from a neuron at certain point of time t, $P_{\mathit{spike}}\left(i\right)\left(t\right)$can be nonlinearly described by Local_population_exc(i)(t) as an input (see eq1), with $\mathit{\gamma }$ being normalizing coefficient. The average firing rate for a given neuron across all trials, Firing_rate(i)(t), resulted from mechanisms that are not presented in trial-by-trial LFP fluctuation because these fluctuations are largely canceled out by the averaging. Based on eq1, Sparse(t) that reaches an individual neuron Sparse(i)(t) contributes nonlinearly to the probability of that neuron to fire a spike, $e^{Sparse\left(i\right)(t)}$. Since $e^{Sparse\left(i\right)(t)}$ do not contribute to LFP, we approximated it to equal Firing_rate(i)(t). Since both Firing_rate(i)(t) and Sparse(i)(t) cannot generate SFC, their contribution is unexplained variability in the SFC. SFC is generated just though the contribution of Local_population_exc(t) to Local_population_exc(i)(t) through the coupling coefficient ${\mathit{\alpha }}_{(\mathit{i})}$, which might differ from neuronal cell-type to another. Hence, SFC is dependent of Local_population_exc(t) power too. Fig 1A shows an example of one neuron (red) that receives large Local_population_exc(t) contribution due to high ${\mathit{\alpha }}_{(\mathit{i})}$ = 0.01 as compared to for the sparse(t) coupling coefficient =1.0·e10⁻⁴. This resulted with higher SFC (Fig 1Aiii) in red as compared to SFC in blue for a neuron that had these coupling coefficients reversed. Note that we adjusted the sparse coupling coefficient here just for illustration and we kept it constant for all neurons for our simulation.

We further assume that neuronal excitability in the local population can be decomposed into local components and multiregional components. The local components of neuronal excitability in the local population are private and, by definition, uncorrelated with activity in the remote population. Put another way, correlated local components of excitability are, by definition, multiregional components. Hence, multiregional components are shared between local and remote populations and can generate correlated activity patterns. Each neuron also experiences sparse input that does not generate coherent dynamics.

To simulate multiregional coherence we fed the neurons with neural excitability, which sourced from local and remote regions (Fig 1B). This meant that neuronal excitability in the local population could be decomposed into local components and multiregional components. The local components are private and uncorrelated with activity in the remote population, private_local(t). The multiregional components are shared excitability between local and remote populations and can generate correlated patterns in local and remote LFPs. Therefore, multiregional components reflected the neurons ability to fire spikes coherently with remote area, because the neurons received local-remote shared excitability through these components. Each neuron also experiences sparse input that does not generate coherent dynamics. Fig 1Bi illustrates three neurons. One fires spikes due to input from one of the multiregional modes, multiregional_mode1(t), and another neuron fires due to another multiregional_mode2(t). A third neuron fires spikes only due to the private local component of excitability. The first and second neurons are dual coherent because they receive multiregional modes as input. Each multiregional mode might be associated with a specific cell-type reflecting differences in how different cell types send and receive signals from local and remote regions. To simulate dual coherence, we estimated one multiregional mode by applying Single Value Decomposition (SVD) algorithm on local population activity measured by local LFP activity, LFP_local(t), and remote population activity measured by remote LFP activity, LFP_remote(t). Since our experiment included two LFPs, we could not estimate more than one mode. Yet we used the estimated mode to simulate the second by simply shuffling the trial’s order. We used multiregional_mode2(t) just for demonstrating how several modes can work in parallel and we did not use it to explain our data. We then simulated LFP activity as the relative sum of multiregional mode 1, mode 2 and private local excitability for LFP_local(t) (see eq2).

$$\mathit{LFP\_local}(\mathit{t})=\mathit{\beta }\mathit{\text{1}}\cdot \mathit{private\_local}(\mathit{t})+\mathit{\beta }\mathit{\text{2}}\cdot \mathit{multiregional\; mode}\mathit{\text{1}}(\mathit{t})+\mathit{\beta }\mathit{\text{3}}\cdot \mathit{multiregional\; mode}\mathit{\text{2}}(\mathit{t})$$ Eq2

$$\mathit{LFP\_remote}\left(\mathit{t}\right)=\mathit{\beta }\mathit{\text{2}}·\mathit{multiregional\_mode}\mathit{\text{1}}\left(\mathit{t}\right)\mathit{}+\mathit{\beta }\mathit{\text{3}}·\mathit{multiregional\_mode}\mathit{\text{2}}(\mathit{t})$$ Eq3

$$\mathit{Multiregional\_mode}\left(\mathit{t}\right)=\mathit{\beta \_a}·\mathit{multiregional\_mode\_a}\left(\mathit{t}\right)\mathit{}+\mathit{\beta \_i}·\mathit{multiregional\_mode\_i}\left(\mathit{t}\right)$$ Eq4

$${\mathit{P}}_{\mathit{spike}}(\mathit{i})(\mathit{t})=\mathit{Firing\_rate}(\mathit{i})(\mathit{t})\cdot \mathbf{\gamma }\cdot {\mathit{e}}^{(y1(i)\times private\_local(t)+y2(i)\times multiregional\_mode 1(t)+y3(i)\times multiregional\_mode2(t))}$$ Eq5

LFP_remote(t) was simulated as the relative sum of the multiregional modes 1 and 2 (see eq3). We neglected private remote excitability for simplicity and because it does not reach the synapses of the simulated neuron. Note the multiregional_mode1 and 2 consist of two components, one inactive multiregional_mode_i(t) and it represents the minimum power of the mode and one active multiregional_mode_a(t) and it gets added to the inactive when the power of the mode increase (see eq4). The contributions of private_local(t) and multiregional modes, defined by $\mathbf{\beta }$ coefficients, were kept constant across all recording sessions. By this construction, LFP_local(t) had higher power than LFP_remote(t) which is not necessarily true for all recording sessions but this was a secondary issue because the model wanted to simulate SFC and not the LFPs themselves. Neurons are strongly coupled to either one of the multiregional modes or to the private local component depending on the coupling coefficients $\mathit{Y}\left(\mathit{i}\right)$ (see eq5), which vary from neuron to neuron based on their cell-type (Fig 1Bii). So neurons that only experience private_local(t) fired spikes coherently with the activity of the local population and not the remote population (Fig 1Biii purple; ${\mathit{Y}}_{\mathit{\text{1}}}\left(\mathit{i}\right)$= 0.015 for private_local; ${\mathit{Y}}_{\mathit{\text{2}}}\left(\mathit{i}\right)$= 0 and ${\mathit{Y}}_{\mathit{\text{3}}}\left(\mathit{i}\right)$ = 0 for multiregional_mode1 and 2). In contrast, neurons that are coupled to either multiregional mode fired spikes coherently with activity of both local and remote populations (Fig 1Biii green; ${\mathit{Y}}_{\mathit{1}}\left(\mathit{i}\right)$= 0.0 for private_local; ${\mathit{Y}}_{\mathit{\text{2}}}\left(\mathit{i}\right)$= 0.035 and ${\mathit{Y}}_{\mathit{\text{1}}}\left(\mathit{i}\right)$ = 0 for multiregional_mode1; and orange ${\mathit{Y}}_{\mathit{1}}\left(\mathit{i}\right)$ = 0.0 for private_local; ${\mathit{Y}}_{\mathit{\text{2}}}\left(\mathit{i}\right)$= 0.0 and ${\mathit{Y}}_{\mathbf{\text{3}}}\left(\mathit{i}\right)$ = 0.045 for multiregional_mode2). Therefore, the multiregional model expresses properties of local and remote coherence, presenting an example of dual coherence. Similar to the SFC in a single region, multiregional SFC is dependent on the strength of the coupling coefficients $\mathit{Y}\left(\mathit{i}\right)$ and multiregional mode power. In this framework, multiregional coherence can be generated by multiregional modes and their contributions to neuronal excitability from local and remote populations. Such cell-type-specific multiregional coherence may be consistent with other differences in how different cell types send and receive signals from local and remote populations of neurons.

Simulation

We ran the simulation for every recorded BS and NS neuron individually with the exception that BS had stronger coupling to the generated multiregional mode. We limited the strong coupling to BS neurons because they were the only to show modulation of their multiregional SFC based on the mode status (active or inactive). So we estimated the multiregional mode first by applying SVD algorithm on aligned and filtered beta-band local LFP and remote LFP, which were recorded together with the neuron. We then generated a new mode by shuffling the trials of the estimated mode of each session. As a result, the generated mode had similar temporal structure as the estimated mode with a peak in the beta band. We simulated the active and inactive status of the mode by generating the mode from two components: active, multiregional_mode_a(t) and inactive, multiregional_mode_i(t) (see above). When the status was active, the mode consisted of both components and when it was inactive, the mode consisted of just multiregional_mode_i(t). By this construction we guaranteed a power difference between active and inactive in favor of the active status. We generated private_local(t) by shuffling the trials of the estimated mode a second time. Therefore, the time frequency structure of private_local(t) and multiregional_mode1(t) were similar. We set the multiregional_mode2 (t) to zero. We adjusted the model parameters intuitively until we reached the same simulated SFC performance as the recorded data (Fig 7). Since BS neurons were set to have high coupling coefficient,their multiregional SFC got modulated based on the mode status (mBS: 0.051 ± 0.027 and vBS: 0.052 ± 0.036 during active mode; mean ± std; and mBS: 0.038 ± 0.019 and vBS: 0.04 ± 0.028 during inactive mode; p < 0.05 permutation test; Table 1 and Fig 7 upper row). Since the multiregional SFC of BS neurons was modulated by the mode status that resulted in modulating their remote SFC similarly to the experimental data (mBS: 0.05 ± 0.027; mean ± std, and vBS: 0.052 ± 0.035 during active mode, and mBS: 0.038 ± 0.019 and vBS: 0.04 ± 0.028 during inactive mode; p < 0.05 permutation test; Fig 7 middle row). No significant local SFC modulation was generated because of the contribution of the private local field to the excitability input. Such contribution reduced the influence of the multiregional mode on local SFC modulation (Local SFC: mBS: 0.081 ± 0.043; vBS: 0.085 ± 0.058 for active mode. mBS: 0.073 ± 0.044; vBS: 0.083 ± 0.058 for inactive mode; mean ± std. p>0.05 permutation test; Fig 7 lower row). The modeled multiregional SFC for NS neurons did not significantly vary between active and inactive trials (vNS: 0.035 ± 0.018; mean ± std, and mNS: 0.033 ± 0.014 during active mode, and vNS: 0.031 ± 0.017 and mNS: 0.033 ± 0.017 during inactive mode; p > 0.05 permutation test). Examining the model parameters demonstrated that this was due to the low coupling coefficient (Table 1 and Fig S7). These simulation show that the different coupling between the multiregional mode and different cell-types can explain differences in the multiregional SFC of different cell-types.

Criterion for rejecting primary volume conduction effect

We tested the results generated by our methods against the effect of volume conduction, applying three different criteria: 1 – Volume conduction contamination of the signals does not suggest the presence of lags between LFPs. The lags varied on trial-by-trial basis and across different sessions while volume conduction must be instantaneous. 2 - Volume conduction contamination of the signals does not suggest the behavioral relevant effect of the modulation of the estimated mode power. 3- Volume conduction contamination of the signals does not suggest to have SFC between single neurons and the estimated mode. The mode was significantly coherent with single neurons located at both banks. Volume conduction cannot by definition influence the spikes firing of individual neurons. Additionally, the mode coherence modulated reliably with putative pyramidal neurons, demonstrating another biological relevance of the mode. Each of these pieces of evidence served as clear criteria by its own for the robustness of our results against volume conduction influence.

Criterion for rejecting primary signal-to-noise-ration effect

We tested the results generated by our methods against the effect of variations in LFP signal-to-noise ratio. This concern was mitigated due to the results of the following tests: 1- We find that there was no systematic increase of the firing rate of all recorded neurons when the multiregional mode switched from inactive to active, although the power of all fields increased. Thus, the increase in the power should not affect SFC unless the timing of the spikes gets more synchronized with the LFP during the power increase. 2- When multiregional mode changed from inactive to active, local LFP power modulated significantly but the local SFC did not increase significantly. This examination demonstrates LFP power can change without changes in SFC. 3- If the SFC changes were due to the changes in the LFP power and signal-to-noise ratio and were not due to changes in the coherence of spiking with the LFP, then we should observe the same changes in SFC across cell types. This examination shows that the changes we observe in the remote SFC and the multiregional SFC when the multiregional mode is active and inactive differ across cell types. This result is not consistent with a primary role for changes in LFP power in our SFC results. 4- Multiregional mode beta power correlated with reaction times during coordinated eye-hand behavior but the modulation of medial and temporal LFP beta power did not. This demonstrates the behaviorally-relevant changes in multiregional mode activity are not simply due to changes in either LFP activity, a scenario one expects during primary signal-to-noise ratio effect on our results.

Quantifying dual coherence prevalence in PPC banks

Dual coherent neurons were more prevalent (41%; Lateral = 52%. Medial = 48%) than local only neurons (20%; Lateral = 70%. Medial = 30%), remote only neurons (9%; Lateral = 69%. Medial = 31%) and not coherent neurons (18%; Lateral = 73%. Medial = 27%). The prevalence of each form of coherence on each bank was similar (Dual: 54% of medial bank neurons, 35% of lateral bank neurons. Local only: 20% of medial bank neurons, 25% of lateral bank neurons. Remote only: 10% of medial bank neurons, 13% of lateral bank neurons. Not coherent: 16% of medial bank neurons, 27% of lateral bank neurons). We examined whether dual coherent neurons demonstrated similar coherence features as the total population to justify the beta mode extraction for dual coherent neurons. Dual coherent neurons showed that local SFC was higher than remote SFC (1–75 Hz for both baseline and delay; p < 0.05; permutation test with cluster correction; Fig S1). During baseline and delay epochs, local SFC and remote SFC peaked with similar frequencies but different magnitudes (Local SFC - Baseline peak: 22.9 ± 0.9 Hz (mean ± standard error of the mean (SEM)) and magnitude: 0.089 ± 0.003 (mean ± SEM). Delay peak: 23.2 ± 1 Hz, and magnitude: 0.088 ± 0.003. Remote SFC - Baseline peak: 25.2 ± 1.2 Hz and magnitude: 0.069 ± 0.002. Delay peak: 24.1 ± 1.1 Hz and magnitude 0.068 ± 0.002). There was no significant difference between the peak frequency of local and remote SFC for either baseline or delay periods (p > 0.05; rank-sum test).

Validating our the statistics of SFC modulation against the effect of different sample sizes

We specifically controlled whether the difference in the statistical significance across neuron classes is simply related to the application of an arbitrary threshold, reflects differences in sample sizes, or reflects genuine differences in the response properties. In SFC analysis, we have cell-type samples with different sizes: vNS=93 neurons; mNS=47; mBS=103; vBS=98. When we pool vBS and mBS neurons and test whether there is a change in multiregional SFC with the change in multiregional mode activity was highly significant (p=0.005). However, when we pool vNS and mNS neurons to give a larger sample, we still do not obtain a significant difference (p=0.07) even though there are 140 neurons in the pool. To further ensure that sample size is not contributing to any difference we report, we applied the following bootstrapping analysis: We first pooled the BS neurons (201 neurons) and NS neurons (140 neurons). We then estimated SFC from 100 randomly chosen neurons from each pool without replacement and tested whether their multiregional SFC increased significantly or not between active and inactive. We then repeated this procedure 1000 times. We found that BS neurons are 5 times more likely to show significant differences (~500 times) as compared to NS neurons (~100 times). The generated p values from this procedure are significantly smaller for BS as compared to NS, p=1·e-53 two sample t-test. This emphasizes how the properties of multiregional SFC differ between BS and NS neurons. Interestingly, this procedure reveals why there is a significant difference. The standard deviation values for the difference in multiregional SFC generated by this procedure were smaller for BS (mean ± std= 0.028±0.0016 for inactive mode and 0.038 ± 0.0029 for active mode) than NS neurons (0.038 ± 0.0029 for inactive mode and 0.039 ± 0.0019 for active mode). The difference in standard deviation values was significantly different between NS and BS neurons (p= 3·e-322 and p = 1·e-22, two sample t-test comparing inactive and active). Thus, our analysis indicates that BS neurons have a more consistent multiregional SFC during active and inactive mode trials as compared to NS neurons and that this increased reliability of BS neuron multiregional SFC is why there is an increase in statistical significance. In contrast, the increase in NS neuron multiregional SFC during active mode trials is not different because NS neuron multiregional SFC is unreliable. This result is consistent with other observations demonstrating consistent and stable multiregional SFC for BS neurons in time (vBS: 1000 ms before Target-on, and mBS: 500 ms before Target-on), unlike the modulation observed for mNS and vNS neurons.

Since multiregional SFC modulation reflects similar features for remote SFC. Applying the same bootstrapping procedure, BS neurons were 8 times more likely to show significant increase in remote SFC (336 times out of 1000) during active mode than in NS neurons (t-test two samples, threshold = 0.001). We found that the standard deviation of BS neurons (mean ± std = 0.022 ± 0.002 for inactive mode and 0.032 ± 0.003 for active mode) was smaller than for NS neurons (0.026 ± 0.002 and 0.032 ± 0.002), and significantly different for both (p=8.4·e-7, p=3.0·e-308, t-test two samples for inactive and active).

Quantifying and correcting for the lags between local and remote LFP

We examined the lag effect of identical sinusoidal signal oscillating in beta band ~17 Hz, a 3 ms time lag reduces the correlation to 0.94 (Fig S2C). A 14.5 ms time lag, equivalent to a phase lag of 90 degrees, reduces r to zero. If the time lag increases, r becomes negative reaching −1 at a time lag of 29 ms. Consequently, the Pearson correlation coefficient may not detect genuinely correlated sinusoidal signals in the presence of a time lag. Since we are interested in estimating the content of the multiregional mode independent of the time for activity to propagate between recording sites, we corrected the time lags. We corrected time lags by aligning remote LFP to local LFP, on a trial-by-trial basis, according to the time shift that gave the highest correlation coefficient, r, between them. The optimal shift was estimated by the cross-correlation function between the two LFPs, with 40 ms as a maximum shift allowed between them for each trial. The procedure of estimating the lag on each trial from the correlation of the band-pass filtered signal is akin to estimating the phase of the LFP coherence. The multiregional mode estimation process therefore started with filtering LFP recordings by multi-taper bandpass filtering to preserve the beta-frequency band (10–30 Hz) component. The beta band component represents the dominant part of SFC as shown above (Fig 2D and Fig S1). Finally, the lag was corrected by shifting the remote LFP by the optimal shift obtained by the cross-correlation function.

Quantifying the behavioral relevance of the multiregional mode

We sorted the trials to fast trials: for the 33% of the trials which had the fastest reach reaction time and slow trials: for the 33% of the trials which had the slowest reaction time. We compared the power of the neural activity around the time of target onset and the Go-cue. We calculated the power modulation index (PMI) for each session by subtracting the average power of slow trials from fast trials divided by their sum for a time window of 100 ms moved in 50 ms steps (Fig 8). When PMI was negative, slow trials had higher power than fast trials, and vice versa for positive PMI. To build comparable results, our analysis was applied on recorded sessions of block design, allowing us to compare PMIs of different movement types before target onset, because the monkeys knew the movement type before the target onset. We calculated PMI for eye and hand coordinated movements, and saccade alone movements (Fig 8B, C). The same analysis was repeated but just on the trials in which the monkeys coordinated saccade and reach movements toward the preferred direction of the recorded neuron (Fig 8D) defined by the maximum firing rate associated with the movement direction, as well as on the trials in which the monkeys moved toward the neuron’s null direction (Fig 8E) defined by the minimum firing rate associated with the movement direction.

Highlights.

• Multiregional modes reflect shared excitability across posterior parietal cortex.

• Multiregional coherence of putative pyramidal neurons modulates with mode power.

• Pyramidal neurons may play a specific role in multiregional communication.

• Multiregional mode power correlates with coordinated movement.