## Abstract

Looking and reaching are controlled by different brain regions and are coordinated during natural behaviour^{1}. Understanding how flexible, natural behaviours such as coordinated looking and reaching are controlled depends on understanding how neurons in different regions of the brain communicate^{2}. Neural coherence in a gamma-frequency (40–90 Hz) band has been implicated in excitatory multiregional communication^{3}. Inhibitory control mechanisms are also required to flexibly control behaviour^{4}, but little is known about how neurons in one region transiently suppress individual neurons in another to support behaviour. How neuronal firing in a sender region transiently suppresses firing in a receiver region remains poorly understood. Here we study inhibitory communication during a flexible, natural behaviour, termed gaze anchoring, in which saccades are transiently inhibited by coordinated reaches. During gaze anchoring, we found that neurons in the reach region of the posterior parietal cortex can inhibit neuronal firing in the parietal saccade region to suppress eye movements and improve reach accuracy. Suppression is transient, only present around the coordinated reach, and greatest when reach neurons fire spikes with respect to beta-frequency (15–25 Hz) activity, not gamma-frequency activity. Our work provides evidence in the activity of single neurons for a novel mechanism of inhibitory communication in which beta-frequency neural coherence transiently inhibits multiregional communication to flexibly coordinate natural behaviour.

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## Data availability

Data for the current study are available on a GitHub repository: https://bitbucket.org/pesaranlab/doublestep/.

## Code availability

The MATLAB code for current study is available on a GitHub repository: https://bitbucket.org/pesaranlab/doublestep/.

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## Acknowledgements

We thank R. Comeau, S. Frey and B. Hynes for custom modifications to the BrainSight system, and N. Price, E. Zavitz, A. Charles and members of the Pesaran laboratory for helpful feedback. This work was supported, in part, by NIH T32 EY007136 (M.A.H.), ARC DE180100344 (M.A.H.), NHMRC APP1185442 (M.A.H.), NSF CAREER Award BCS-0955701 (B.P.), NEI R01-EY024067 (B.P.), the Army Research Office (B.P.), the Simons Foundation (B.P.), McKnight Scholar Award (B.P.), Sloan Research Fellowship (B.P.) and NIH R01-NS104923 (B.P.).

## Author information

### Authors and Affiliations

### Contributions

M.A.H. and B.P. conceptualized the project and designed the experiments. M.A.H. performed the experiments. M.A.H. and B.P. analysed the data and wrote the manuscript.

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The authors declare no competing interests.

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*Nature* thanks Martin Giese, Nicholas Hatsopoulos and Lawrence Snyder for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Extended data figures and tables

### Extended Data Fig. 1 Coordinated and independent movement tasks.

**a**, Reach and saccade double-step task (RS) and Saccade double-step task (SS), indicating hand (H) and eye (E) position at each epoch. Dashed lines indicate period of gaze-anchoring in the RS task, and temporally matched epochs in the SS task. The slowing of the second saccade reaction time (SSRT) was tied to the coordinated movement. **b**, The coordination of the first movement was established by the strong correlation between the reaction times for the reach and saccade in the first movement (Monkey 1 (M1): R = 0.34, slope = 0.21 ms/ms, p = 3 x 10^{−139}, Monkey 2 (M2): R = 0.45, slope = 0.25 ms/ms, p = 0, Pearson pairwise linear correlation). **c**, SSRT correlated with the difference between the reaction times of the reach and saccade in the first movement (M1: R = 0.20, slope = 0.26 ms/ms, p = 2 x 10^{−49}, M2: R = 0.22, slope = 0.39 ms/ms, p = 2 x 10^{−78}, Pearson pairwise linear correlation). **d**, Specifically, SSRT correlated with the reaction time of the reach (M1: R = 0.23, slope = 0.29 ms/ms, p = 4 x 10^{−63}, M2: R = 0.20, slope = 0.32 ms/ms, p = 2 x 10^{−65}, Pearson pairwise linear correlation). **e**, The SSRT was not dependent on the reaction time of the saccade in the RS task (M1: R = 0.05, slope = 0.09 ms/ms, p = 8 x 10^{−4}, M2: R = 0.006, slope = 0.02 ms/ms, p = 0.63, Pearson pairwise linear correlation). **f**, SSRT did not depend on the duration of the reach (M1: R = 0.07, slope = 0.08 ms/ms, p = 1 x 10^{−6}, M2: R = 0.001, slope = 0.002 ms/ms, p = 0.91, Pearson pairwise linear correlation). **g**, SSRT only weakly correlated with the SRT in the SS task (M1: R = 0.06, slope = 0.08 ms/ms, p = 1 x 10^{−3}, M2: R = 0.12, slope = 0.17 ms/ms, p = 7 x 10^{−13}, Pearson pairwise linear correlation). Therefore, the slowing of the SSRT was tied to coordinated movement, and primarily the timing of the reach. Monkey 1: RS task, n = 10,324 trials, SS task, n = 8,372 trials; Monkey 2: RS task, n = 12,840 trials, SS task n = 8,452 trials. All error bars show mean ± SEM.

### Extended Data Fig. 2 Anatomical locations of recordings.

Recording chambers were placed over the posterior parietal cortex of the hemisphere contralateral to the reaching arm. **a**, **b**, Whole brain MRI reconstructions and example coronal slice from Monkey 1 (**a**) and Monkey 2 (**b**). Chamber placement and electrode recording sites were registered to the structural MRI (BrainSight, Rogue Research). Recording regions for area LIP (blue) and PRR (black) are indicated by the shaded regions. Dashed lines indicate the plane of example coronal sections shown. Key sulcal landmarks, intraparietal sulcus (ips), lunate sulcus (lu) and superior temporal sulcus (sts), are also indicated.

### Extended Data Fig. 3 Phase of spike-*β*-LFP coherence in each cortical area.

**a**–**c**, Peri-reach (**a**), post-reach (**b**), and saccade (**c**) trials showing spike-LFP coherence between PRR spiking and PRR LFP phase (y-axis) and LIP LFP phase (x-axis) in the beta-band (\(\beta ,\) 20 Hz, colorscale: proportion of trials). Marginals show the proportion of trials as a function of phase in each area. **Peri-reach:** PRR \(\beta \)-LFP p = 2 x 10^{−49}, mean phase = 136 ± 75°; LIP \(\beta \)-LFP p = 8 x 10^{−5}, mean phase = 172 ± 79°, **Post-reach:** PRR \(\beta \)-LFP p = 4 x 10^{−57}, mean phase = 149 ± 74°, LIP \(\beta \)-LFP p = 0.02, mean phase = 164 ± 79°, **Saccade trials:** PRR \(\beta \)-LFP p = 2 x 10^{−52}, mean phase = 135 ± 73°, LIP \(\beta \)-LFP p = 2 x 10^{−52}, mean phase = 59 ± 78°, Rayleigh’s test of non-uniformity, circular mean ± SD phase). Black triangles indicate mean phase, stars indicate that the distribution is non-uniform (one star, p < 0.05; two stars, p < 0.01, exact p-values above). Peri-reach: n = 4814 trials, Post-reach: n = 2116 trials, Saccade: n = 3583 trials (same dataset shown in Figs. 2, 3). All error bars show mean ± SEM.

### Extended Data Fig. 4 Negative-log-likelihood and generalization errors for model fits.

**Second saccade reaction time: a**, Dual-phase negative-log-likelihood (NLL) = 25124; PRR-only phase NLL = 25158; LIP-only phase NLL = 25157; Null NLL = 25162; ∆NLL_{Dual-PRR} = 35; ∆NLL_{Dual-LIP} = 33, AIC test. **b**, Expected generalization error: Dual-coherent: 10.6 ms, R = 0.10; PRR-only: 12.5 ms, R = −0.05; LIP-only: 11.8 ms, R = 0.01; Null: 11.8 ms, where R = 1-(SSE_model/SSE_null). **Reach accuracy: c**, Dual-phase negative-log-likelihood (NLL)= 6462; PRR-only phase NLL = 6507; LIP-only phase NLL = 6511; Null NLL = 6512; ∆NLL_{Dual-PRR} = 45; ∆NLL_{Dual-LIP} = 49, AIC test. **d**, Expected generalization error: Dual-coherent: 0.18 deg, R = 0.20, PRR-only: 0.27 deg, R = −0.14, LIP-only: 0.24 deg, R = −0.02, Null: 0.24 deg). Non-parametric analyses: Peri-reach trials: SSRT: dual-coherent: resultant = 6.2 x 10^{−3}, p < 10^{−6}, LIP-only: p = 0.28, PRR-only: resultant = 2.3 x 10^{−6}, p = 0.02, RA: dual-coherent: resultant = 1.6 x 10^{−4}, p = 0. LIP-only: p = 0.33. PRR-only: resultant = 5.3 x 10^{−5},p = 1.6 x 10^{−3}. Post-reach trials for dual coherent phase: SSRT: resultant = 5.7 x 10^{−3},p = 0. post-reach RA: resultant = 2.1 x 10^{−4}, p = 1.2 x 10^{−3}. Saccade trials: SSRT: p = 0.89. Peri-reach: n = 4814 trials, Post-reach: n = 2116 trials, Saccade: n = 3583 trials (same dataset shown in Figs. 2, 3).

### Extended Data Fig. 5 Dual coherent *β*-LFP phase aligned to reach onset.

**a**, Second saccade reaction time (SSRT) against dual-coherent \(\beta \)-LFP phase for each RS task trial type (Peri-reach: light green. Post-reach: dark green) during the gaze anchoring epoch when aligned to reach onset, instead of second target onset. Solid lines present changes in SSRT fitted by von Mises function (peri-reach: p = 0, preferred phase = 41°. post-reach: p = 6 x 10^{−5}, preferred phase = 153°). Downward triangle presents the mean of the von-Mises fit dual-coherent \(\beta \)-LFP phase at maximum SSRT on peri-reach trials. **b**, **c**, Phase of spike-\(\beta \)-LFP coherence in each cortical area (PRR \(\beta \)-LFP coherence, y axis; LIP \(\beta \)-LFP coherence, x axis) and influence on SSRT (colorscale). Marginals show SSRT against \(\beta \)-LFP phase coherence in each area alone (Peri-reach: PRR-only p = 0.53, LIP-only p = 2 x 10^{−3}, preferred phase = 48°. Post-reach: PRR-only p = 0.53, LIP-only p = 0.48) . Dashed lines (**b**) indicate the corresponding dual-coherent phase shown by the downward triangle in (**a**). Note that confounds due to the onset of the Go cue were not a concern because the LFP phase calculation during gaze-anchoring epoch rarely overlapped cue delivery (3.7% of peri-reach trials, 0% of post-reach trials and 2.5% of saccade trials). All p-values report likelihood-ratio test. Peri-reach: n = 4814 trials, Post-reach: n = 2116 trials, Saccade: n = 3583 trials (same dataset shown in Figs. 2, 3). All error bars show mean ± SEM.

### Extended Data Fig. 6 *β*-LFP phase difference alone did not predict gaze anchoring.

The circular mean \(\beta \)-LFP phase was taken across the gaze-anchoring epoch, irrespective of spike timing. **a**, Mean phase difference of the \(\beta \)-LFP (20 Hz) across cortical areas for each task trial type (Saccade: pink. Peri-reach: light green. Post-reach: dark green). Solid lines present changes in SSRT fitted by von Mises function (Peri-reach: p = 0.23. Post-reach: p = 1 x 10^{−3}, preferred phase = 53°. Saccade: p = 0.83. likelihood-ratio test). **b**–**d**, Mean \(\beta \)-LFP phase in each cortical area (PRR \(\beta \)-LFP phase, y axis; LIP \(\beta \)-LFP phase x axis) and influence on SSRT (colorscale). Marginals show SSRT as a function of mean \(\beta \)-LFP phase in each area alone (Peri-reach: PRR-only p = 0.89, LIP-only p = 0.24. Post-reach: PRR-only p = 8 x 10^{−3}, preferred phase = 32° LIP-only p = 0.20. Saccade: PRR-only p = 8 x 10^{−4}, preferred phase = −143; LIP-only p = 0.12. likelihood-ratio test). **e**–**g**, \(\beta \)-LFP phase in PRR (y-axis) and LIP (x-axis, colorscale: proportion of trials). Downward triangles show the circular mean phase. Peri-reach: n = 4814 trials, Post-reach: n = 2116 trials, Saccade: n = 3583 trials (same dataset shown in Figs. 2, 3). All error bars show mean ± SEM.

### Extended Data Fig. 7 Spike timing dependence of dual coherent β-LFP phase.

**a**–**l**, For each trial, spike times were jittered according to a Gaussian distribution with standard deviation 2 ms (**a**–**c**), 5 ms (**d**–**f**), 10 ms (**g**–**i**) and 20 ms (**j**–**l**). Second saccade reaction time (SSRT) as a function of dual-coherent \(\beta \)-LFP phase for each task trial type (Saccade, pink; Peri-reach, light green; Post-reach, dark green) during the gaze anchoring epoch was recomputed with the jittered spike times. Solid lines present changes in SSRT fitted by von Mises function (**a**, Peri-reach: p = 1 x 10^{−13}, preferred phase = 82°. Post-reach: p = 5 x 10^{−5}, preferred phase = 126°. Saccade: p = 0.68. **d**, Peri-reach: p = 3 x 10^{−3}, preferred phase = 73°. Post-reach: p = 7 x 10^{−5}, preferred phase = 108°. Saccade: p = 0.23. **g**, Peri-reach: p = 0.22. Post-reach: p = 0.29. Saccade: p = 0.90. **j**, Peri-reach: p = 0.11. Post-reach: p = 1. Saccade: p = 0.38. likelihood-ratio test). For peri-reach trials, the phase of spike-\(\beta \)-LFP coherence in each cortical area were computed for the jittered spike times (PRR \(\beta \)-LFP coherence, y axis; LIP \(\beta \)-LFP coherence x axis) and influence on SSRT (colorscale). Marginals show SSRT as a function of \(\beta \)-LFP phase coherence in each area alone (**b**, PRR-only p = 0.10, LIP-only, p = 0.10, **e**, PRR-only p = 0.04, preferred phase = −127°, LIP-only, p = 0.47, **h**, PRR-only p = 0.68, LIP-only, p = 0.63, **k**, PRR-only p = 0.52, LIP-only, p = 0.71, likelihood-ratio test). Spike-LFP coherence between PRR spiking and each cortical area alone for jittered spike times on peri-reach trials (PRR LFP phase, y-axis, LIP LFP phase x-axis, colorscale: proportion of trials). Marginals show the proportion of trials as a function of phase in each area (**c**, PRR p = 2 x 10^{−47}, mean = 137°, LIP p = 8 x 10^{−4}, mean = 175°, **f**, PRR p = 2 x 10^{−31}, mean = 139°, LIP p = 1 x 10^{−3}, mean = 167°, **i**, PRR p = 3 x 10^{−10}, mean = 132°, LIP p = 0.04, mean = −140°, **l**, PRR p = 0.84, LIP p = 0.79, Rayleigh’s test of non-uniformity, circular mean phase). Black triangles indicate mean phase, stars indicate that the distribution is non-uniform (one star, p < 0.05; two stars, p < 0.01, exact p-values above). Peri-reach: n = 4814 trials, Post-reach: n = 2116 trials, Saccade: n = 3583 trials (same dataset shown in Figs. 2, 3). All error bars show mean ± SEM.

### Extended Data Fig. 8 Dual coherent *γ*-LFP phase.

Dual-coherent phase was calculated between PRR spiking and the \(\gamma \)-LFP phase (40 Hz) in each cortical area. **a**, Second saccade reaction time (SSRT) against dual-coherent \(\gamma \)-LFP phase for each RS task trial type (Peri-reach = light green; Post-reach = dark green). Solid lines present changes in SSRT fitted by von Mises function (Peri-reach: p = 8 x 10^{−4}, preferred phase = −6°. Post-reach: p = 0.04, preferred phase = 26°. Saccade: p = 0.1likelihood-ratio test). **b**–**d**, Mean \(\gamma \)-LFP phase in each cortical area (PRR \(\gamma \)-LFP phase, y axis; LIP \(\gamma \)-LFP phase x axis) and their influence on SSRT (colorscale). Marginals show SSRT against mean \(\gamma \)-LFP phase in each area alone (Peri-reach: PRR-only p = 0.55, LIP-only p = 0.02, preferred phase = 112°. Post-reach: PRR-only p = 0.02, preferred phase = −25°. LIP-only p = 4 x 10^{−6}, preferred phase = 78°. Saccade: PRR-only p = 0.13, LIP-only p = 0.04, preferred phase = 17°, likelihood-ratio test). **e**–**g**, \(\gamma \)-LFP phase in PRR (y-axis) and LIP (x-axis, colorscale: proportion of trials). Marginals show the proportion of trials against phase in each area (Peri-reach: PRR p = 4x10^{−23}, mean = −177°, LIP p = 0.02, mean = −125°. Post-reach: PRR p = 2 x 10^{−6}, mean = 148°, LIP p = 3 x 10^{−4}, mean = −159°. Saccade: PRR p = 1 x 10^{−4}, mean = 153°, LIP p = 0.33, Rayleigh’s test of non-uniformity). Black triangles indicate mean phase, stars indicate that the distribution is non-uniform (one star, p < 0.05; two stars, p < 0.01, exact p-values above). Peri-reach SSRT slowing with gamma-frequency phase was significantly reduced compared to that with beta-frequency dual-coherent phase (resultant = 2.9 x 10^{−3}, p = 1 x 10^{−4}. permutation test). Peri-reach: n = 4814 trials, Post-reach: n = 2116 trials, Saccade: n = 3583 trials (same dataset shown in Figs. 2, 3). All error bars show mean ± SEM.

### Extended Data Fig. 9 LIP-spike dual coherent *β*-LFP phase.

Dual-coherent phase was calculated between LIP spiking and the \(\beta \)-LFP phase (20 Hz) in each cortical area. **a**, Second saccade reaction time (SSRT) as a function of LIP dual-coherent \(\beta \)-LFP phase for each RS task trial type (peri-reach trials, light green; post-reach trials, dark green) and SS task trials (saccade trials). Solid lines present changes in SSRT fitted by von Mises function (peri-reach: p = 1 x 10^{−4}, preferred phase = −122°. post-reach: p = 0.21. saccade: p = 1 x 10^{−3}, preferred phase = −157°. likelihood-ratio test). SSRT varied with PRR-spike dual-coherent phase significantly more than with LIP-spike dual-coherent phase (resultant = 1.2 x 10^{−3}, p < 10^{−6}, permutation test). **b**–**d**, Mean LIP-spike \(\beta \)-LFP phase in each cortical area (PRR \(\beta \)-LFP phase, y axis; LIP \(\beta \)-LFP phase x axis) and their influence on SSRT (colorscale). Marginals show SSRT as a function of mean LIP-spike \(\beta \)-LFP phase in each area alone (Peri-reach: PRR-only p = 0.23. LIP-only p = 0.49. Post-reach: PRR-only p = 6 x 10^{−4}, preferred phase = 109°. LIP-only p = 0.48. Saccade: PRR-only p = 5 x 10^{−5} preferred phase = −25°. LIP-only p = 0, preferred phase = −142°, likelihood-ratio test). **e**–**g**, LIP-spike \(\beta \)-LFP phase in PRR (y-axis) and LIP (x-axis, colorscale: proportion of trials). Marginals show the proportion of trials as a function of phase in each area (Peri-reach: PRR: p = 2 x 10^{−5}, mean = 160°, LIP: p = 1 x 10^{−7}, mean = 97°. Post-reach: PRR p = 2 x 10^{−5}, mean = 11°, LIP p = 5 x 10^{−4}, mean = 67°. Saccade: PRR p = 2 x 10^{−5}, mean = 100°, LIP p = 4 x 10^{−12}, mean = 103°, Rayleigh’s test of non-uniformity, circular mean). Black triangles indicate mean phase, stars indicate that the distribution is non-uniform (one star, p < 0.05; two stars, p < 0.01, exact p-values above). Peri-reach: n = 7782 trials, Post-reach: n = 3604 trials, Saccade: n = 8603 trials. All error bars show mean ± SEM.

### Extended Data Fig. 10 Dual-coherent *β*-LFP phase is weakly correlated with PRR firing rate.

**a**–**c**, PRR firing rate and a function of dual-coherent \(\beta \)-LFP phase for each peri-reach (**a**), post-reach (**b**), and saccade (**c**) trials. Solid lines present changes in SSRT fitted by von Mises function (Peri-reach: p = 0, preferred phase = −121°. Post-reach: p = 0.23. Saccade: p = 0, preferred phase = 19°, likelihood-ratio test). Peri-reach: n = 4814 trials, Post-reach: n = 2116 trials, Saccade: n = 3583 trials (same dataset shown in Figs. 2, 3). All error bars show mean ± SEM.

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Hagan, M.A., Pesaran, B. Modulation of inhibitory communication coordinates looking and reaching.
*Nature* **604**, 708–713 (2022). https://doi.org/10.1038/s41586-022-04631-2

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DOI: https://doi.org/10.1038/s41586-022-04631-2

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