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This study is based on data from 71 mice (age > postnatal day (P)60, we used both male and female mice) (Supplementary Tables 1, 2). We used six transgenic mouse lines: PV-IRES-Cre45, Ai32 (Rosa-CAG-LSL-ChR2(H134R)-EYFP-WPRE, JAX 012569)46, VGAT–ChR2–EYFP32, Gad2-IRES-Cre (a gift from B. Zemelman), Ai35D (Rosa-CAG-LSL-Arch-GFP-WPRE, JAX 012735)46, and Olig3-Cre47. All procedures were in accordance with protocols approved by the Janelia Institutional Animal Care and Use Committee. Detailed information on water restriction, surgical procedures and behaviour have been published3, 28. All surgical procedures were carried out aseptically under 1–2% isoflurane anaesthesia. Buprenorphine HCl (0.1 mg kg−1, intraperitoneal injection; Bedford Laboratories) was used for postoperative analgesia. Ketoprofen (5 mg kg−1, subcutaneous injection; Fort Dodge Animal Health) was used at the time of surgery and postoperatively to reduce inflammation. After the surgery, mice were allowed free access to water for at least three days before the start of water restriction. Mice were housed in a 12:12 reverse light:dark cycle and behaviourally tested during the dark phase. A typical behavioural session lasted 1–2 h and mice obtained all of their water in the behaviour apparatus (approximately 1 ml per day; 0.3 ml was supplemented if mice drank less than 0.5 ml). On other days mice received 1 ml water per day. Mice were implanted with a titanium headpost28. For ALM photoinhibition, mice were implanted with a clear skull cap3. Optical fibres for photostimulation or cannulae for muscimol infusion were implanted during the headpost surgery or after behavioural training. Craniotomies for recording were made after behavioural training. All coordinates are given with respect to bregma (anterior–posterior (AP), medial–lateral (ML), dorso–ventral (DV)). A metal pole (diameter, 0.9 mm) was presented in one of two locations3, 28 (Fig. 1). The two pole locations were 8.58 mm apart along the anterior–posterior axis. The posterior pole position was 5 mm from the whisker pad. Whiskers made contacts with the object at both pole locations, more strongly in the posterior location. A two-spout lickport (4.5 mm between spouts) was used to record licking events and deliver water rewards. At the beginning of each trial, the pole moved within reach of the whiskers (0.2 s travel time) (Fig. 1a) for 1 s, after which it was retracted (0.2 s retraction time). The sample epoch (1.3 s total) was the time from onset of pole movement to 0.1 s after the pole started to retract (Fig. 1a). The delay epoch lasted for another 1.2 s after completion of pole retraction (1.3 s or 1.2 s total). An auditory ‘go’ cue separated the delay and the response epochs (pure tone, 3.4 kHz, 0.1 s). Licking early during the trial (‘lick early’ trials) was punished by an ‘alarm’ sound (siren buzzer, 0.05 s duration), followed by a timeout (1–1.2 s). After the go cue licking the correct lickport produced a water reward (approximately 3 μl); licking the incorrect lickport triggered a timeout (0–5 s). Trials in which mice did not lick within 1.5 s after the go cue (no response trials) were rare and typically occurred at the end of behavioural sessions. These no response and lick early trials were excluded from analyses (Figs 1, 2, 3, 4, 5, 6). The ALM (AP 2.5 mm, ML 1.5 mm, diameter 1.5 mm) is the cortical area that produced behavioural effects with photoinhibition during the delay epoch3, 24. For the thalamic reticular nucleus the coordinates were AP −0.7, ML 1.6, DV 3.7 − 3.3 mm, as retrograde labelling from the thal showed labelling in this sector of the thalamic reticular nucleus (Extended Data Fig. 9). Virus and tracer were injected through the thinned skull using a volumetric injection system (modified from Mo-10 Narishige)48. Glass pipettes (Drummond) were pulled and bevelled to a sharp tip (outer diameter around 20–30 μm), back-filled with mineral oil and front-loaded with viral suspension immediately before injection. The injection rate was 15 nl per min. See Supplementary Table 2 for description of viruses and injection coordinates used for each experiment. We used the following viruses and tracers: AAV2/1-CAG-EGFP (Penn vector Core, University of Pennsylvania), AAV2/10 CAG-flex-ChR2(H134R)-tdTomato (Penn vector Core, University of Pennsylvania), AAV1-CAG-mRuby2-Flag49, wheat germ agglutinin (WGA)–Alexa Fluor 555 (Thermo Fisher Scientific)50 (WGA–Alexa555) and Red RetroBeads (Lumafluor). For anterograde and retrograde anatomy27, 51 (Extended Data Figs 1, 8, 9) mice were perfused transcardially with PBS followed by 4% PFA/0.1 M PB. The brains were fixed overnight and transferred to 20% sucrose before sectioning on a freezing microtome. Coronal, 50-μm free-floating sections were processed using standard fluorescent immunohistochemical techniques. All sections were stained with NeuroTrace 435/455 Blue Fluorescent Nissl stain (Thermo Fisher Scientific, N21479). Slide-mounted sections were imaged on a Zeiss microscope with a Ludl motorized stage controlled with Neurolucida software (MBF Bioscience). Imaging was done with a 10× objective and a Hamamatsu Orca Flash 4 camera. Each coronal section was made up of 80–200 tiles merged with Neurolucida software. To reconstruct recording and photostimulation locations (Extended Data Figs 2, 4), mice were perfused transcardially with PBS followed by 4% PFA/0.1 M PB. The brains were fixed overnight and sectioned on a microtome at 100 μm thickness. Images were acquired on a macroscope (Olympus MVX10). Electrode tracks labelled with DiI were used to determine the recording locations. Tissue damage caused by optical fibres was used to determine photoinhibition locations. For cell counting (Extended Data Fig. 1d), neurons labelled with WGA–Alexa555 were detected using Neurolucida software (MBF Bioscience). The whole brain image stack was registered to the Allen Institute Common Coordinate Framework (CCF) of the mouse brain using a MATLAB-based script (Mike Economo, Janelia Farms). The coordinates of detected WGA–Alexa555 labelled neurons were counted in the brain structures annotated in the Allen reference atlas. We used Fluorender52 to create 3D-reconstructed images of anterograde and retrograde signals (Extended Data Fig. 1e). GFP signals and densities of retrogradely labelled cells were overlaid. Cell densities were based on the cell counts described above. For individual retrogradely labelled neurons, the number of other surrounding retrogradely labelled neurons within the ± 100-μm cube were counted to estimate cell density. Cannulas (26GA, PlasticsOne) were implanted bilaterally near the VM/VAL and control locations (Extended Data Fig. 3; cannula coordinates in Supplementary Table 1). An injection needle was inserted into the guiding cannula, projecting 1.7 mm beyond the cannula tip. Muscimol∙HBr (3–100 ng, Sigma-Aldrich) dissolved in 50 nl cortex buffer (125 mM NaCl, 5 mM KCl, 10 mM glucose, 10 mM HEPES, 2 mM MgSO , 2 mM CaCl , pH adjusted to 7.4) was injected through the volumetric injection system. The control solution was cortex buffer without muscimol. Control behaviour was paused after mice performed 120–200 trials in a session and muscimol was infused for 4.5 ± 0.7 min (mean ± s.d., n = 50), after which behaviour resumed. As the infusion step requires pausing behaviour, which by itself can increase behavioural variability, identical procedures were also performed without infusion. After the last session of muscimol infusion, fluorescent muscimol bodipy (100 ng in 100 nl DMSO) was infused and mice were perfused immediately. Fluorescence and tissue damage caused by the injection needle were used to identify muscimol infusion locations. Each muscimol concentration was tested once per injection site. For muscimol infusions near the VM/VAL, the ipsilateral bias lasted for the whole session (Extended Data Fig. 3b). After mice were released from head-fixation, ipsilateral circling was scored in the home cage. With the small dose of muscimol tested (1.8–5.9 ng), we did not observe circling (data not shown)53. Supplementary Table 1 provides coordinates and photostimulus powers for each experiment. Photoinhibition was used in 25% (Figs 1, 3a–f 6) or 25–50% (Figs 3g, 4) of the behavioural trials. To prevent mice from distinguishing photoinhibition trials from control trials using visual cues, a ‘masking flash’ (forty 1 ms pulses at 10 Hz) was delivered using 470 nm LEDs (Luxeon Star) near the eyes of the mice throughout the trial. Trimming whiskers prevents mice from performing this task3. Photostimuli from a 473 nm laser (Laser Quantum) were controlled by an acousto-optical modulator (AOM; Quanta Tech) and a shutter (Vincent Associates). Photoinhibition of the ALM was performed through the clear-skull cap (beam diameter at the skull: 400 μm at 4σ). We stimulated parvalbumin-positive interneurons in PV-IRES-Cre mice crossed with Ai32-reporter mice expressing ChR2 (Figs 1, 6 and Extended Data Figs 8, 10). Behavioural and electrophysiological experiments showed that photoinihibition in the PV-IRES-Cre × Ai32 mice was indistinguishable from the VGAT–ChR2–EYFP mice (data not shown)3. To silence the cortex during the delay epoch (Figs 1, 6 and Extended Data Figs 8, 10), we photostimulated for 1.3 s, including the 100 ms ramp, starting at the beginning of the epoch. Photoinhibition silences a cortical area of 1 mm radius (at half-maximum) through all cortical layers. We used 40 Hz photostimulation with a sinusoidal temporal profile (1.5 mW average power) and a 100-ms linear ramp during the laser offset (this reduced rebound neuronal activity)3. The light transmission through the intact skull is 50%3. See Supplementary Table 1 for the animals, coordinates and power used for each experiment. To silence the thalamus, the photostimuli were delivered through a 200-μm diameter optical fibre (Thorlabs). We used a continuous photostimulus with a 100-ms linear ramp at the offset (Figs 1d, 3, 4, 5). The photostimulus was applied for 1.2–1.3 s, including the 100-ms ramp, starting at the beginning of the delay epoch and terminating at the end of the delay epoch. Photoinhibition reduced activity (0.5–1.1 mm from the tip of the optical fibre) to 15.9 ± 9.3% (mean ± s.e.m., Extended Data Fig. 2d). On the basis of retrograde labelling (Extended Data Fig. 1), we silenced at least 16,558 ALM-projecting thalamic neurons. For M1 silencing, we silenced at least 26,599 ALM-projecting neurons within a 1 mm radius from the laser centre. In the contralateral ALM we silenced at least 38,062 neurons projecting to the recorded side of the ALM (Extended Data Fig. 1d). To silence the thalamus for behavioural experiments (Fig. 1) and current injection experiments (Extended Data Fig. 5), we avoided stimulating any uncharacterized GABAergic projection neurons. We expressed ChR2 selectively in the TRN, by injecting AAV2/10 CAG-flex-ChR2(H134R)-tdTomato into TRN of Gad2-IRES-Cre mice. We implanted an optical fibre over the VM/VAL, but other thalamic nuclei projecting to the ALM were also likely to have been affected (Extended Data Fig. 2). Recordings were made from the left hemisphere. Recording locations were deduced from electrode tracks (see ‘Histology’ and Extended Data Fig. 4). For ALM recordings, a small craniotomy (1 mm diameter) was made one day before the recording session3. Extracellular spikes were recorded using NeuroNexus silicon probes (A4x8-5 mm-100-200-177) or Janelia silicon probes (A2x32-8 mm-25-250-165). The 32- or 64-channel voltage signals were multiplexed, recorded on a PCI6133 board at 312.5 kHz or 400 kHz (National Instrument), and digitized at 14-bits. The signals were demultiplexed into the 32- or 64-voltage traces, sampled at 19,531.25 or 25,000 Hz, respectively, and stored for offline analyses. 3–5 recording sessions were obtained per craniotomy. Recording depth was inferred from manipulator readings and verified based on histology3. The craniotomy was filled with cortex buffer and the brain was not covered. The tissue was allowed to settle for at least 10 min before the recording started. For VM/VAL recordings, a small craniotomy was made over the dorsal medial somatosensory cortex (centre, bregma AP −1.5 mm, ML 1.8 mm). For optrode recording from the VM/VAL, we used NeuroNexus silicon optrodes (A4x8-5 mm-100-400-177 with a 105-μm diameter optical fibre placed 200 μm above recording sites on the inner right shank). For SNr recordings, a small craniotomy was made over the visual area (centre, bregma AP −3.5 mm, ML 3 mm). Electrodes were driven down about 4.5 mm to reach SNr. RetroBeads injected near the VM/VAL labelled SNr extensively in the caudal–rostral and medial–lateral directions54 (Extended Data Fig. 9). Our recording probes (spanning ML 600 μm) sampled a large region of the SNr (medial, lateral, rostral and caudal). The effects of ALM photoinhibition on SNr activity did not vary spatially and the data were pooled. Whole-cell recordings were made using pulled borosilicate glass (Sutter instrument)55. A small craniotomy (100–300 μm diameter) was created over the ALM or M1 (bregma AP 0.0 mm, ML 2.0 mm) under isofluorane anaesthesia and covered with cortex buffer during recording. Whole-cell patch pipettes (7–9 MΩ) were filled with internal solution (in mM): 135 K-gluconate, 4 KCl, 10 HEPES, 0.5 EGTA, 10 Na -phosphocreatine, 4 Mg-ATP, 0.4 Na -GTP and 0.3% Biocytin (293–303 mOsm, pH 7.3). The V was amplified (Multiclamp 700B, Molecular Devices) and sampled at 20 kHz using WaveSurfer (http://wavesurfer.janelia.org/). V were not corrected for liquid junction potential. After the recording the craniotomy was covered with Kwik-Cast (World Precision Instruments). Each animal was used for 2–3 recording sessions. Recordings were made from 350 to 850 μm below the pia. Neuronal responses to thalamic or cortical inactivation were similar across depths and were pooled for analysis. To obtain mean V dynamics of each neuron (Figs 3g, 4 and Extended Data Figs 5, 6), we clipped off action potentials. We found the point in the V where the derivative passed 3 s.d. from the baseline (kink). Baseline and s.d. were calculated from 2.5 ms to 1.5 ms before the spike peak. Points from −0.5 to 5 ms around the kink were interpolated. The s.e.m. of the V was estimated by bootstrapping. The action-potential threshold was defined as the difference between baseline V (0–0.5 s before onset of each behavioural trial) and the spike threshold. Whole-cell recordings with more than 20 behavioural trials were pooled to calculate action-potential thresholds and membrane time constants (n = 60). The onset of the V change after photoinhibition (Fig. 3g and Extended Data Fig. 6b, e, f) was the time when the V changed by more than 3 s.d. from the baseline. The baseline and s.d. were calculated from 20 ms before the photostimulus onset until 2 ms after onset of the photostimulation trials. A similar procedure was used to estimate the onset of V change after thalamus photoactivation (Extended Data Fig. 6c). The s.e.m. of the onsets was determined by bootstrapping. Behavioural performance was the fraction of correct trials, excluding lick early and no response trials. We separately computed the performance for contra and ipsi trials relative to the manipulation side (Fig. 1 and Extended Data Fig. 3). Behavioural effects of photoinhibition were quantified by comparing the performance with photoinhibition with control performance (Fig. 1c, d). Significance of the performance change was determined using Student’s t-test. Photoinhibition of the ALM or thalamus caused only small changes in lick early rates, no response rates and licking latency (Supplementary Information). The performance change due to muscimol silencing was computed as the fraction of correct trials after infusion (the 100 trials immediately after muscimol infusion) relative to the fraction of correct trials before muscimol infusion (the 100 trials right before muscimol infusion). Performance change in the muscimol condition was compared with that during the control condition. Significance was determined using Student’s t-test (Extended Data Fig. 3). Muscimol infusion did not increase the lick early rates (P > 0.1; paired t-test) and slightly increased the no response rate from 0 to 1% (that is, from no no response trial to one no response trial in a session, P = 0.02). Detailed spike sorting procedures have been described3. Recording depths were estimated from histology3 (Extended Data Fig. 4). The extracellular recording traces were band-pass filtered (300 Hz–6 kHz). Events that exceeded an amplitude threshold (4 s.d. of the background) were subjected to manual spike sorting to extract single units. For the low thalamus inactivation experiments (Fig. 5), spikes were sorted using JRclust (program by J. Jaeyoon Jun, APIG, Janelia Farm). Spikes were binned by 1 ms and averaged over 200 ms (Figs 2, 3, 5, 6). In the ALM, 1,214 single units were recorded across 57 behavioural sessions. Spike widths were computed as the trough-to-peak interval in the mean spike waveform. The distribution of spike widths was bimodal (Extended Data Fig. 4); units with width <0.4 ms were defined as putative fast-spiking neurons (166 out of 1,214) and units with width >0.6 ms as putative pyramidal neurons (1,006 out of 1,214). This classification was previously verified by optogenetic tagging of GABAergic neurons3. Units with intermediate spike widths (0.4–0.6 ms, 42 out of 1,214) were excluded from our analyses. We concentrated our analyses of the ALM on putative pyramidal neurons (Figs 2, 3, 5). In the thalamus, 790 single units were recorded across 73 behavioural sessions. Unit locations were determined from the locations of the relevant recording sites, which in turn were reconstructed from histology (Extended Data Fig. 4). All units were recorded in a narrow range of AP locations (between bregma −1 mm and −2 mm). We therefore overlaid units on one coronal section for spatial analysis (bregma −1.76, Fig. 6d). Neurons in the VM/VAL are excitatory. The distribution of spike widths was unimodal with a tail with short spike widths; this suggests that some units corresponded to GABAergic axons from the TRN or SNr56. Units with spike width >0.5 ms were selected as putative thalamic neurons (672 out of 790) and we concentrated our analyses on these neurons. However, our conclusions (Figs 2, 6) are valid if all the units were pooled. To select units in the VM/VAL we applied a stringent spatial criterion; units within 0.4 mm from the VM/VAL centre (determined from retrograde labelling experiments, Extended Data Fig. 1) were scored as VM/VAL neurons (313 out of 790). This criterion could be relaxed to 1.0 mm from the VM/VAL centre without changing our conclusions, as neurons within 1.0 mm from the VM/VAL centre showed robust inhibition (to 36% of control activity during the first 100 ms inhibition, also see Extended Data. Fig. 8b). Furthermore, randomly jittering neuron locations by 200 μm in the AP, ML and DV directions did not affect our conclusions. In the SNr, 227 single units were recorded across 23 behavioural sessions. SNr GABAergic neurons have narrower spike widths than dopaminergic neurons in the nearby substantia nigra pars compacta57. Units with spike trough-to-peak width <0.45 ms were selected as putative GABAergic neurons (spike width at half maximum, 0.143 ± 0.030 ms (mean ± s.d.), 181 out of 227). These units have high spike rates (40.9 ± 21.5 (mean ± s.d.), n = 181). For comparison, neurons with longer spike widths have lower spikes rates (23.4 ± 17.0 (mean ± s.d.), n = 46). We concentrated our analyses on putative GABAergic neurons. We used bootstrapping to test whether there were more neurons significantly down-modulated than up-modulated. The null hypothesis was that there were equal or more up-modulated neurons. In each round of bootstrapping, we replaced the original neurons with a re-sampled dataset. The number of down-modulated and up-modulated neurons were counted and compared. The P value was the fraction of times the bootstrapping produced a consistent result as the null hypothesis. Neurons were tested for trial-type selectivity during the sample, delay or response epochs by comparing spike counts during contra and ipsi trials (t-test, P < 0.05; Fig. 2 and Extended Data Fig. 10). Neurons that significantly differentiated trial types during any one of the trial epochs were deemed as selective (704 out of 1,006 in the ALM, 204 out of 295 in the VM/VAL, 152 out of 181 in the SNr). Neurons with selectivity during the sample or delay epochs were classified as having preparatory activity. Neurons with significant selectivity during the response epoch were classified as having peri-movement selectivity. Selective neurons were classified as contra-preferring or ipsi-preferring on the basis of their total spike counts across all three trial epochs27 (Fig. 2 and Extended Data Fig. 10). To compute contra-selectivity, we took the firing rate difference between the contra trials and ipsi trials for each neuron. The ipsi-selectivity was computed similarly. Only trials in which mice correctly reported pole locations were included to compute selectivity. For the peri-stimulus time histograms (PSTHs; Figs 3, 5, 6 (except the top panels in Figs 3b, 6b) and Extended Data Fig. 7), correct and incorrect trials were included, as photoinhibition reduced neural activity irrespective of the response outcomes. To analyse the effects of photoinhibition, units with at least 5 (Fig. 3, n = 314; Fig. 6, n = 201) or 25 (Fig. 5, n = 160) photoinhibition trials were selected. Bootstrapping was used to estimate s.e.m. (Figs 3, 6 and Extended Data Figs 2, 7, 8, 10). As the effect of photoinhibition began 10–20 ms after photostimulus, we used 20–120 ms after photostimulus onset to measure the amplitude of inactivation (Figs 3, 6 and Extended Data Fig. 10). For Figs 3c, 5b, 6c (top), both contra and ipsi trials were pooled to calculate mean spike rate. For Fig. 5c, neurons with spike rates higher than two spikes per second during both control and photoinhibition conditions were included (n = 73). The onset of inactivation was defined as the time when the V passed 3 s.d. of the control condition. The s.d. was calculated using the control condition during the delay epoch. Changing the duration used to calculate the s.d. did not change the estimate of onset latency. We also detected the onset by comparing the PSTHs during the photoinhibition and control conditions using a Student’s t-test, with consistent results. To estimate the s.e.m. of the inhibition onset, we randomly sampled neurons with replacement and used the bootstrapped dataset to compute the onset of photoinhibition. This procedure was repeated 1,000 times. The sample sizes are similar to sample sizes used in the field (more than 100 units per brain region). No statistical methods were used to determine sample size. We did not exclude any animal for data analysis. Trial types were randomly determined by a computer program. During spike sorting, experimenters cannot tell the trial type, so experimenters were blind to conditions. All comparisons using t-tests are two-sided. For the behavioural test of thalamus inhibition (Fig. 1), the data points are normally distributed (tested using Kolmogorov–Smirnov test). All bootstrapping was done over 1,000 or 10,000 iterations. Datasets will be shared at https://crcns.org/ in the NWB format58 (https://dx.doi.org/10.6080/K03F4MH2). All other data that support the findings of this study are available from the corresponding author upon reasonable request.

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Vgat-ires-Cre31, Sst-Cre32 and PV-Cre33 knock-in mice (The Jackson Laboratory, Bar Harbour) and C57BL/6 male mice, 10–25 weeks old, were used. Mice were housed under standard conditions in the animal facility and kept on a 12 h light/dark cycle. All procedures were performed in accordance with national and international guidelines, and were approved by the local health authority (Landesamt für Gesundheit und Soziales, Berlin) and the Stanford University Institutional Animal Care and Use Committee. Injections were performed as described previously22, 34. Mice were anaesthetized with isoflurane and placed in a stereotaxic head frame (David Kopf Instruments). A 34-gauge bevelled metal needle connected via a tube with a microsyringe pump (PHD Ultra, Harvard Apparatus) was used to infuse viruses at a rate of 100 nl min−1. After infusion, the needle was kept at the injection site for 10 min and then slowly withdrawn before the incision was sutured. Optogenetic constructs from K. Deisseroth, purchased from Penn Vector Core, UNC Gene Therapy Center Vector Core, or provided by K. Deisseroth, were used. For manipulations of the LS–LH pathway, Vgat-Cre mice were injected bilaterally in the LS (right: anterior-posterior (AP) 0.74, lateral (L) 0.38, ventral (V) 3.3; 3.1 mm; left: AP 0.62, L 0.33, V 3.45; 3.0 mm) with 0.3 μl per injection site of AAV2/5-Ef1a-DIO-ChETA(E123T/H13R)-eYFP-WPRE-hGH (Penn Vector Core, titre 1.75 × 1012 viral genomes (vg) per ml). Sst-Cre mice were injected bilaterally in the LS (right: AP 0.38, L 0.4, DV 3.0, 2.7 mm; left: AP 0.26, L 0.4, V 3.0, 2.5 mm) with 0.125–0.25 μl per injection site of AAV2/5-Ef1a-DIO-ChETA(E123T/H13R)-eYFP-WPRE-hGH, titre 1.75 × 1012 vg ml−1 (Penn Vector Core) or 0.2 μl per injection site of AAVdj-nEF-DIO-NpHR-TS-p2A-hChR2(H134R)-eYFP (eNPAC2.0, titre 6.1 × 1012 vg ml−1) or 0.125–0.2 μl per injection site of AAV2-EF1a-DIO-eYFP-WPRE-hGH (Penn Vector Core, titre 2 × 1012 vg ml−1). For manipulation of LH cells, Vgat-Cre mice were injected bilaterally in the LH (AP −1.5, L ±1, V 5.4 mm) with 0.3 μl per injection site of AAV2/5-Ef1a-DIO-ChETA(E123T/H13R)-eYFP-WPRE-hGH (Penn Vector Core) or 0.3 μl per injection site of AAVdj-nEF-DIO-NpHR-TS-p2A-hChR2(H134R)-eYFP (eNPAC2.0, titre 6.1 × 1012 vg ml−1) or 0.3 μl per injection site of AAV2-EF1a-DIO-eYFP-WPRE-hGH (Penn Vector Core, titre 2 × 1012 vg ml−1). For manipulations of the mPFC–LH pathway, mice were bilaterally injected in the mPFC (AP 1.70, L ±0.35, V 2.85 mm) with 0.25–0.5 μl per injection site of AAV2-CaMKIIa-hChR2(H134R)-eYFP (Penn Vector Core, titre 2.55 × 1012 vg ml−1) or 0.25–0.5 μl per injection site of AAV5-CaMKIIa-ChETA(E123T/H134R)-eYFP-WPRE-hGH (Penn Vector Core, titre 1.26 × 1013 vg ml−1), or 0.25–0.5 μl per injection site (AAVdj-hSyn-NpHR-TS-p2A-hChR2(H134R)-eYFP (eNPAC2.0, titre 2.9 × 1013 vg ml−1) or 0.5 μl per injection site of AAV2-CaMKIIa-eYFP (University of North Carolina Vector Core, titre 5 × 1012 vg ml−1). For CLARITY experiments, mice were injected in the mPFC (AP 2.0, L 0.3, V 2.6 mm) with 1 μl AAV8-CaMKIIa-eYFP-NRN. For synaptophysin imaging, 1 μl AAV8-CaMKIIa-synaptophysin-mCherry (7 × 1013), was injected in the mPFC (AP 2.0, L 0.3, V 2.6 mm). Optic fibre implants were fabricated from 100 μm diameter fibre (0.22 numerical aperture (NA), Thorlabs) and zirconia ferrules (Precision Fibre Products). For optogenetic manipulations of mPFC–LS pathway, mice were implanted with optic fibre implants on top of the LS (right, AP 0.1, L 0.25, V 2.25 mm, left, AP 0.5, L 0.3, V 2.7 mm). For optogenetic manipulations in the LH, optical fibres were bilaterally (for LS–LH and LH stimulation or inhibition) or unilaterally (LH stimulation combined with the LH silicon probe recordings) implanted above the LH (AP −1.6, L 1, V 4.8 mm). Arrays of single tungsten wires (40 μm, California Fine Wire Company), stationary implanted linear silicon probes (CM32, NeuroNexus Technologies), or movable probes (B32 or B64, NeuroNexus Technologies) mounted on a microdrive35 were implanted as described previously22, 26. The following coordinates were used for electrode implantations in the LS: AP 0–0.5, L 0.2–0.45, V 2.3–3.4 mm (B32 probes, B64 probes (mPFC–LS co-implantations), CM32, wire arrays); LH: AP −1.6, L 1, V 4.7 mm (B32 probes, B64 probe, wire arrays); mPFC: AP 1.4–1.9, L 0.3, V 3.0 mm (B64 probes (mPFC–LS co-implantations), wire arrays); dorsal hip: AP −2.1, L 1.6, V 1.5 mm (wire arrays), ventral hip: AP −3.16, L 2.5–3.5, V 4.0 mm (wire arrays). Reference and ground electrodes were miniature stainless-steel screws in the skull above the cerebellum. The implants were secured on the skull with dental acrylic. Electrodes were connected to operational amplifiers (HS-8, Neuralynx, or Noted BT) to eliminate cable movement artefacts. Electrophysiological signals were differentially amplified, band-pass filtered (1 Hz–10 kHz, Digital Lynx, Neuralynx) and acquired continuously at 32 kHz. A light-emitting diode was attached to the headset to track the mouse’s position (at 25 Hz). Timestamps of laser pulses were recorded together with electrophysiological signals. A 3-m-long fibreoptic patch cord with protective tubing (Thorlabs) was connected to a chronically implanted optical fibre with a zirconia sleeve (Precision Fibre Products), which allowed the mice to explore an enclosure freely or perform a behavioural task during optogenetic manipulations. Subjects were randomly assigned to the experimental conditions. For optogenetic stimulation, the patch cord was connected to a 473-nm diode-pumped solid-state laser (R471005FX, Laserglow Technologies) with an FC/PC adaptor. The laser output was controlled using a stimulus generator and MC_Stimulus software (Multichannel Systems). Optogenetic stimulation of LS–LH and mPFC–LS projections consisted of 5 ms blue (473 nm) light pulses, at 66.7 Hz or a control, non-gamma (theta) intensity-matched stimulation (167 Hz bursts of 4 ms pulses repeated at 9 Hz) with the light power output (during light-on parts of illumination cycles) of 10–25 mW from the tip of the patch cord measured with a power meter (PM100D, Thorlabs). Optogenetic stimulation of LH somata consisted of 5 ms blue (473 nm) light pulses, at 20 Hz, with light power output (during light-on parts of illumination cycles) of 10–25 mW from the tip of the patch cord. For bilateral optogenetic inhibition, optic fibre implants were connected via patch cords to a 593-nm diode-pumped solid-state laser (R591005FX, Laserglow Technologies) using a multimode fibre optic coupler (FCMM50-50A-FC, Thorlabs), continuous yellow light, approximately 20 mW from the tip of each patch cord. Duration of light delivery is described below for each type of behavioural experiment. For control experiments, mice expressing YFP in the same brain regions (mPFC or LS) were used, and optostimulation was performed as described above. For within-animal comparisons in sessions in which food intake was measured during LH stimulation (Extended Data Figs 2i, 8c, d, f), optic patch cords were connected to dummy ferrules, attached to the headset, and light of the same wavelength and power as during opsin-activating stimulation was delivered. Free-access feeding model. This was performed in a chamber similar to that described previously36 (Fig. 1a). Mice freely explored a custom two-chamber (30 × 50 × 20 cm) enclosure, which contained food and water in designated areas (each area 10 × 10 cm; see Fig. 1a). Food (Dustless Precision Pellets, 20 mg, Rodent Purified Diet, Bio Serv) was provided either in a food cup or in a pellet feeder (Coulbourn Instruments Pellet Feeder H14-23M; sampling rate 10 Hz, one nose poke led to the delivery of one food pellet). Before experiments, mice received these pellets in the homecage for at least 2 days, and were habituated to the behavioural setup for at least 3 days. Coordinates of 10 × 10 cm food, drinking, non-food corner zones and a control zone located in the non-food compartment were defined. Times of entering and leaving each zone were extracted from the mouse’s position-tracking data. An approach rate was defined as the distance between a position of the mouse and the centre of the food zone, the drinking zone or the control zone, divided by the time it took to enter a respective zone. For each experiment, a corner zone, one of which was a food zone, visited first after the onset of stimulation was detected. Latency to enter each zone was defined as the time between the beginning of optogenetic stimulation and the first entry of the mouse into a zone, with the mouse staying in the zone for at least 1 s. To account for differences in distances to a zone after the stimulation onset, in each experiment we have normalized the latency after stimulation onset to the average latency of entering the same zone from the same distance during the baseline. Duration of experimental sessions and optogenetic manipulations are described below. Optogenetic activation of LS –LH projections. Mice explored the enclosure for 30 min: 10 min before stimulation, 10 min during optogenetic stimulation, 10 min after stimulation. Blue light (473 nm) was bilaterally delivered over LS–LH projections, in 5 ms pulses at 66.7 Hz or using a control, non-gamma (theta) intensity-matched stimulation (167 Hz bursts of 4 ms pulses repeated at 9 Hz), with light power output of 10–25 mW. For brief gamma stimulation, 5 ms pulses at 66.7 Hz were delivered for 30 s, followed by a break of 2 min, during a 10 min period. Optogenetic inhibition of LS –LH projections during food approach. Mice explored the enclosure for 30 min. Each time the mouse crossed the border of a food-approach area (20 × 20 cm, marked as an orange dotted line on Extended Data Fig. 6e), continuous yellow (593 nm) light was bilaterally delivered over LS–LH projections. Light delivery stopped each time a mouse left the approach zone. Optogenetic activation of LS –LH projections during free-access to high-fat food. Mice explored the enclosure for 20 min. Blue light (473 nm) was bilaterally delivered over LS–LH projections, in 5 ms pulses at 66.7 Hz, with light power output of 10–25 mW. High-fat food pellets (Testdiet, 60% energy from fat) were weighted before and after the experiment, to calculate the amount of food (>5 mg) consumed per session. Optogenetic stimulation of LH cells. Mice explored the enclosure for 30 or 60 min: 10 or 20 min before stimulation, 10 or 20 min during optogenetic or control light stimulation, 10 or 20 min after stimulation, Dustless precision pellets (BioServ) were counted to measure the amount of food (>1 pellet) consumed per session. Blue light (473 nm) was delivered bilaterally, in 5 ms pulses at 20 Hz. Optogenetic inhibition of LH cells in food-deprived mice. Mice received approximately 2.5–3.0 g of standard chow daily; the mouse weight was controlled and weight loss did not exceed 10%. Dustless precision pellets (BioServ) were counted to measure the amount of food consumed by hungry mice (>3 pellets in baseline) per session. The experiments consisted of four epochs: 10 min light-on (optogenetic or control stimulation), 10 min light-off, 10 min light-on, and 10 min light-off. This was performed in a custom two-chamber enclosure similar to the one used for the free-feeding model (30 × 50 × 20 cm). One of the chambers contained a familiar object, whereas the other contained a new object. Before experiments, mice were habituated to the enclosure containing two objects, then for each experimental session one of the objects (new object) was replaced, whereas the object in the other chamber (familiar object) remained the same. Optogenetic stimulation started as the mouse was put in the enclosure. Mice freely explored the enclosure maximally for 2 min, otherwise a session was finished once the mouse visited both objects. Blue light (473 nm) was bilaterally delivered over LS–LH projections, in 5 ms pulses at 66.7 Hz, with light power output of 10–25 mW. Spatial non-matching to place testing on the T-maze was performed as described elsewhere37. The T-maze (start arm: 46 × 11 × 10 cm, choice arm: 80 × 11 × 10 cm; see Fig. 4p) was made of pieces of wood painted dark-grey. For spatial non-matching to place testing, each trial consisted of a sample run and a choice run. During the sample run, mice could run only to one arm (left or right, according to a pseudorandom sequence with equal numbers of left and right turns per session) because another arm was blocked by a wooden block. A reward (0.1 ml condensed milk or a 20 mg food pellet) was available in the food well at the end of the arm. After the sample run, mice stayed in another, familiar, enclosure for 10–15 s. The block was then removed, and mice were placed at the end of the start arm to perform the test run. Mice were rewarded for choosing the previously unvisited arm (that is, for alternating). For this test and all subsequent experiments, entry into an arm was defined as when a mouse had placed all four paws into the arm. Mice ran one trial at a time with inter-trial intervals of 3–5 min. Each mouse conducted 20–40 trials in total (10 trials per day). For a subset of experiments, mice were water-restricted and water was used as a reward instead of food. A number of slow (30–60 Hz) or fast (60–90 Hz) gamma-oscillation episodes (detected as described below) in the start or choice arm was normalized by dividing by the mean number of gamma events in each arm during the whole experiment. Optogenetic activation or inhibition of mPFC–LS projections in the T-maze. Optogenetic stimulation started as the mouse was put at the end of the start arm, and finished when the mouse reached the reward. Blue light was delivered on mPFC–LS projections in 5-ms pulses at 66.7 Hz, or in a non-gamma (theta) intensity-matched stimulation protocol, described above for free-feeding model. For inhibition, yellow light was delivered onto mPFC–LS projections continuously during the run. LFP was obtained by down-sampling of the wide-band signal to 1,250 Hz using Neurophysiological Data Manager38 (http://neurosuite.sourceforge.net/). Gamma oscillations were detected at 30–60 Hz, 60–90 Hz and, for the analysis shown in Extended Data Fig. 1i, 90–120 Hz, bandpass filtered, rectified and smoothed with a 15-ms window LFP signals. Events with amplitudes exceeding 2 s.d. above mean for at least 25 ms were detected13. The beginning and the end of oscillatory epochs were marked at points at which the amplitude fell below 1 s.d. Power spectral density and coherence were computed using the multitaper method (NW = 3). For the analysis of association between gamma power and approach rate, the cumulative power in the 30–60 and 60–90 Hz bands as well as the approach rate (see ‘Behavioural assays’) was computed, and for each 1-s recording epoch, gamma power was z-transformed. Values within 10 s before entry in the food or drinking zones were statistically evaluated. Current source density (CSD) maps (versus time and depth) were computed as previously described37, 39. LFP depth profiles, recorded using CM32 probes with the spatial sampling of 100 μm, were averaged using peak gamma oscillations detected in an LS channel as triggers. The second spatial derivative of the obtained voltage traces, that is, CSD, indicates locations of current sinks and sources in the extracellular space40. For the analysis of mPFC–LS and hippocampus–LS coherence, normalized current flow density in the LS was computed by subtraction of gamma-band filtered LFP signals, recorded by a pair of wire electrodes in the LS against a common screw-reference above cerebellum40, 41. Action potentials were detected in a high-pass filtered signal using NDManager16 (http://neurosuite.sourceforge.net/). Spike waveforms were extracted and represented by the first three principle components and by amplitudes of action potentials. Spike sorting was performed automatically using KlustaKwik42 (http://klusta-team.github.io/klustakwik/) followed by manual clusters adjustment using Klusters38. Isolation distance42 was computed for sorted units (LH: 101.5 ± 8.0, LS: 66.3 ± 4.6, mPFC: 56.3 ± 3.6). Phase of gamma oscillations was computed for signal epochs within detected gamma episodes as described elsewhere37, 43. In brief, 0° and 360° were assigned to troughs of each gamma cycle and 180° to a cycle peak, phases for each data sample between these points were computed using linear interpolation13, 37. Subsequently, gamma phases were obtained for data samples when action potentials were emitted, for each recorded neuron, and firing phase histograms were computed. A possible asymmetry of oscillation cycles leads to a different number of phase samples composing ascending and descending parts of the cycle and can bias firing phase histograms39. To prevent this, we tested uniformity of grand gamma phase distributions for each recording using the Rayleigh test and, if significantly non-uniform, computed a deviation of a grand phase histogram from uniformity, via division by the average across all bins. In such recordings, firing histograms were normalized by the corrected grand phase histogram37, 44, 45. Each firing phase histogram was normalized by its total number of spikes. Circular uniformity, mean phase and the resultant vector length were estimated for each histogram. Before averaging, individual histograms were convolved with the Gaussian kernel46 of size 0.65 s.d. Putative LH neurons were optogenetically identified based on rapid (<10 ms lags in laser pulse onset-triggered cross-correlations, computed with 1-ms bins) increase of firing after onset of laser pulses. Reliability of light-induced responses was estimated as a probability of the maximal light-induced spike count in a Poisson distribution computed for cross-correlogram (CCG) delays in the pre-pulse baseline26, 47. To estimate gamma-rhythmic responses of LH cells to LS–LH stimulation, a cross-correlation (CCG) with the times of LS–LH light stimulation was computed for each cell. To avoid spurious CCG peaks at the stimulation frequency, every second time stamp of light was used as a trigger. A reshuffled CCG was computed using light times shifted to a baseline, light-off, recording epoch. A power spectrum of the response of a cell was then obtained by subtracting the power spectrum of the reshuffled CCG from the power spectrum of the stimulation CCG. Firing of LH neurons in the free-access feeding model was evaluated as described elsewhere for quantification of positional firing37, 48. Firing maps were computed by dividing the number of spikes in a given spatial pixel (2 × 2 cm) by the time spent in this pixel. Periods of immobility (speed <3 cm s−1) were excluded from the analysis. Peak firing rate was defined as the maximum firing rate over all pixels in the environment. For calculation of food-zone preference (FZ-match index), the average firing rate of a cell in the food zone was divided by the average firing rate in a control zone of the same size (10 × 10 cm), located in the non-food compartment of the enclosure. For the analysis of firing during gamma oscillations, cells were split in ‘FZ-match’ or ‘FZ-mismatch’ groups based on an FZ-match index higher or lower than 1, respectively. For identification of LH cells, excited in response to LH or LS –LH optogenetic stimulation, the number of spikes (x) was computed for each 100-ms bin during the baseline (10 min) and within 3 s after stimulation onset. A distribution derived from the baseline was fitted to a Poisson distribution, and rate parameter λ was estimated. A bin with maximal count of spikes during stimulation was assigned to observed value x . P value was defined as P(x ≥ x ), in which x follows Pois(λ). The firing rate ratio (R) between 3 s baseline and stimulation epochs was computed for each stimulation epoch and then averaged across stimulation epochs. A cell was classified as excited if P < 0.05 and R > 1. Code is available from the corresponding authors upon request. Each statistical test was used according to the design of the experiment and the structure of the data. Two-group comparisons were performed using t-test, Mann–Whitney or Wilcoxon matched-pairs tests depending on the normality of a distribution. Assessment of effects in experiments involving several conditions was performed using ANOVA, followed, when appropriate, by Bonferroni (for pre-selected contrasts) or Tukey tests, adjusting for multiple comparisons. Grubbs’ test was used to exclude outlier points from behavioural datasets. Depending on the normality of a distribution, Pearson’s or Spearman’s correlations were computed. For group comparisons, two-tailed statistical tests were applied. Sample size was determined according to the accepted practice for the applied assays, no statistical methods were used to predetermine sample size. Conditions of the experiments were accounted during design of analysis algorithms, computations were subsequently performed blindly using automatic selection of data from a database. A detailed description of statistical analysis is provided in the statistical section of the Supplementary Information. Descriptive statistics are reported as mean ± s.e.m. Primary cultured neurons were prepared from the hippocampi of P Sprague–Dawley rat pups (Charles River Laboratories), as described previously49. CA1 and CA3 hippocampal regions were taken out and digested with 0.4 mg ml−1 papain (Worthington), and plated onto 12-mm glass coverslips that were pre-coated with 1:30 Matrigel (Beckton Dickinson Labware). Cultures were kept under neurobasal-A medium (Invitrogen) containing 1.25% FBS (HyClone), 4% B-27 supplement (Gibco), 2 mM glutamax (Gibco) and 2 mg ml−1 fluorodeoxyuridine (FUDR, Sigma) and plated at a density of 65,000 cells per well in 24-well plates. The plates were incubated at 37 °C in a humid incubator with a constant level of 5% CO . Cultured neurons were transfected at 6–10 days in vitro (DIV). A DNA–CaCl mix composed of the following was prepared for transfection per well: 1 μg of endotoxin-free DNA for recordings, 1.875 μl 2 M CaCl , and sterile H O for a total volume of 15 μl. Another 15 μl of twice-filtered HEPES-buffered saline (HBS, in mM: 50 HEPES, 1.5 Na HPO , 280 NaCl, pH 7.05 with NaOH) for each DNA–CaCl mix. This mix was incubated at room temperature for 20 min. In the meantime, the neuronal growth medium was removed from the wells and kept at 37 °C, and replaced with 400 μl pre-warmed minimal essential medium (MEM). After incubation of the DNA–CaCl –HBS mix was complete, the mix was then added dropwise into each well, and plates were incubated for 45–60 min at 37 °C. Once the transfection was complete, each well was washed three times with 1 ml of pre-warmed MEM. The MEM was then replaced with the original neuronal growth medium, and plates were placed into the culture incubator at 37 °C. Whole-cell patch-clamp recordings of cultured hippocampal neurons were performed 3–5 days after transfection with the construct AAVdj-hSyn-NpHR-TS-p2A-hChR2(H134R)-eYFP (eNPAC2.0). Expression of the construct was identified by eYFP fluorescence. The external recording medium was composed of the following (in mM): 125 NaCl, 2 KCl, 25 HEPES, 2 CaCl , 2 MgCl , 30 d-(+)-glucose. pH 7.3, with synaptic transmission blockers d-2-amino-5-phosphonovaleric acid (AP5; 25 μM), 2,3-dihydroxy-6-nitro-7-sulfamoyl-benzo[f]quinoxaline-2,3-dione (NBQX; 10 μM), and gabazine (10 μM). The intracellular recording solution contained (in mM): 130 potassium gluconate, 10 KCl, 10 HEPES, 10 EGTA and 2 MgCl . An upright microscope (BX61WI, Olympus) with infrared differential interference contrast (IR-DIC) was used for visualization and recording of the expressing neurons. A Spectra X Light engine (Lumencor) attached to the fluorescent port of the microscope was used for light application, for detecting eYFP expression and for blue or yellow light delivery for opsin activation. A 475/28 nm and a 586/20 nm filter (Chroma) were used for blue and yellow light respectively (Chroma). A power meter (ThorLabs) was used to measure the light power through the microscope objective, and light power density was set at 5 mW mm−1 (ref. 49). Recordings were obtained using a MultiClamp700B amplifier, 1440A Digidata digitizer, and pClamp10.3 software (Molecular Devices). Data were analysed with pClamp10.3 and SigmaPlot (SPSS). Photocurrent amplitudes at blue and yellow were measured at steady-state at the end of a 1-s light stimulation protocol. To measure spike inhibition probability at 586 nm, we first applied a 50–200 pA electrical current injection (depending on spike threshold of the recorded cell) to induce spiking in the expressing neurons. Spike inhibition probability was calculated as the percentage in which yellow light application inhibited spiking during the electrical current injection. To measure spike generation probability with blue light, we applied 5-ms width pulses of 475 nm light at 5 or 20 Hz frequency, and calculated the percentage of action potentials generated by the blue light pulse train. Series resistance was carefully monitored for stability throughout the recordings. To ensure accurate measurements of voltage-clamp recordings, data were incorporated for analysis only if the series resistance was below 25 MΩ and changed less than 20% throughout the recording. Standard whole-cell slice patch-clamp recordings were undertaken after slice preparation of at least 2-month-old mice. In brief, after gluing a block of brain with cyanoacrylate glue to the stage of a Campden Vibroslice, coronal brain slices of 250-μm thickness containing the LH were cut while immersed in ice-cold slicing solution. Slices were incubated for 1 h in artificial cerebrospinal fluid (ACSF) at 35 °C then transferred to a submerged-type recording chamber. Living neurons containing fluorescent markers were visualized in acute brain slices with an upright Olympus BX61WI microscope equipped with an oblique condenser and appropriate fluorescence filters. After identifying appropriate neurons by their fluorescence, oscillatory currents of 10 pA amplitude (30, 50, 70 and 100 Hz) were injected for 5 s to the cell during whole-cell patch-clamp recordings. Recordings of membrane potentials were analysed in MatLab. To record selectively from Vgat neurons, a cross between Vgat-ires-Cre and CAG-tdTomato mice33 was used. To target MCH-Cre neurons selectively, MCH-Cre mice were injected into the LH (1.3 mm caudal from bregma; ±0.95 mm lateral from midline; and 5.25 and 5.15 mm ventral from brain surface) with a Cre-dependent ChR-mCherry. For brain slice recordings, ACSF and ice-cold slicing solution were gassed with 95% O and 5% CO , and contained the following (in mM) ACSF: 125 NaCl, 2.5 KCl, 1 MgCl , 2 CaCl , 1.2 NaH PO , 21 NaHCO , 2 d-(+)-glucose, 0.1 Na+-pyruvate and 0.4 ascorbic acid. Slicing solution: 2.5 KCl, 1.3 NaH PO.H 0, 26.0 NaHCO , 213.3 sucrose, 10.0 d-(+)-glucose, 2.0 MgCl and 2.0 CaCl . For standard whole-cell recordings, pipettes were filled with intracellular solution containing the following (in mM): 120 K-gluconate, 10 KCl, 10 HEPES, 0.1 EGTA, 4 K ATP, 2 Na ATP, 0.3 Na GTP and 2 MgCl , pH 7.3 with KOH. Multitaper power spectra of voltage traces and of injected current traces were computed and divided, resulting in impedance spectra. Mean impedance at ±1.5 Hz around stimulation frequency was computed. Brain hemispheres were clarified using the CLARITY procedure as described elsewhere27. In brief, a brain hemisphere was fixed in hydrogel solution (4% PFA, 1% acrylamide/bis) for 72 h at 4 °C. After polymerization (37 °C, 4 h), the brain hemispheres were clarified in 8% SDS for 8 days (at 40 °C), then washed three times with PBST (0.2% Triton X-100) for a total of 24 h at 37 °C. Hemisphere images were acquired with the Ultramicroscope II (Lavision Biotec)27. Samples were mounted to a custom 3D printed holder using RapidClear Mounting Gel (Sunjin laboratory). Brains were imaged using a 2×/0.5 NA objective at 0.8× zoom using a single light sheet illuminating from the dorsal side of the sample. Z-step was set to 4 μm. Fourteen horizontal focal points were set to each imaging plane to create a homogeneous field of view. For synapsin staining the brains were cut, after CLARITY processing, into 1-mm-thick sections. Primary antibody: rabbit anti-synapsin (Cell Signaling, 5297), 1:400, in 0.3% PBST, room temperature, 24 h; secondary antibody: donkey anti-rabbit (Alexa 594, Jacksonimmuno), 1:200, in 0.3% PBST, room temperature, 24 h; then sections were refractive index-matched and mounted in RapidClear CLARITY-specific gel (Sunjin Laboratory). Sections were imaged at bregma = 0.5 using Olympus FV1200 confocal, 40×, 1.3 NA, oil objective, at 4× zoom. For synaptophysin imaging, brains expressing CaMKIIa-synaptophysin-mCherry in the mPFC were cut into 0.5-mm-thick section for CLARITY clearing and imaging. The sections were imaged at bregma = 0.5 using Olympus FV1200 confocal, 40×, 1.3 NA, oil objective, at 4× zoom. After completion of the experiments, mice were deeply anaesthetized and electrolytic lesions at selected recording sites were performed. Subsequently, the mice were perfused intracardially with saline followed by 4% paraformaldehyde in PBS and decapitated. Brains were fixed overnight in 4% paraformaldehyde, equilibrated in 1% PBS for an additional night and finally cut into 40 or 50 μm slices using an oscillating tissue slicer (EMS 4500, Electron Microscopy Science). Brain slices were mounted (Flouromount Aqueous Mounting Medium, Sigma-Aldrich). Images were taken using an Olympus BX 61 microscope (×2/0.06 NA, ×10/0.3 NA and ×20/0.5 NA, dry) or using a Leica DMI 6000 microscope (×20/0.7 NA, ×63/1.4 NA; oil-immersion objectives). All data generated or analysed during this study are either included in this published article or are available from the corresponding authors on reasonable request.

News Article | April 27, 2016
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This study is based on data from 33 mice (both males and females, age >postnatal day (P) 60). Ten VGAT-ChR2-EYFP mice (Jackson Laboratory, JAX 014548) and nine PV-ires-cre44 crossed to Rosa26-LSL-ReaChR, red-shifted channelrhodopsin reporter mice (JAX 24846)45, were used for photoinhibition behaviour experiments. A subset of these mice (five VGAT-ChR2-EYFP mice, seven PV × ReaChR mice) was used for simultaneous electrophysiology and behaviour. Seven mice (six VGAT-ChR2-EYFP, one PV × ReaChR mice) were used for the callosotomy experiment. Two Tlx_PL56-cre (MMRRC 036547)46 crossed to Ai32 (Rosa26-ChR2 reporter mice, JAX 012569)47 mice were used for photoactivation experiment. Two untrained VGAT-ChR2-EYFP mice and two untrained PV × ReaChR mice were used to characterize the photoinhibition in ALM. One Tlx_PL56-cre mouse was used for anatomical characterization of the ALM axonal projection pattern. All procedures were in accordance with protocols approved by the Janelia Institutional Animal Care and Use Committee. Mice were housed in a 12 h:12 h reverse light:dark cycle and tested during the dark phase. On days not tested, mice received 1 ml of water. On other days, mice were tested in experimental sessions lasting 1–2 h, in which they received all their water (range, 0.5–2 ml). If mice did not maintain a stable body weight, they received supplementary water48. All surgical procedures were carried out aseptically under 1–2% isofluorane anaesthesia. Buprenorphine HCl (0.1 mg kg−1, intraperitoneal injection; Bedford Laboratories) was used for postoperative analgesia. Ketoprofen (5 mg kg−1, subcutaneous injection; Fort Dodge Animal Health) was used at the time of surgery and postoperatively to reduce inflammation. After the surgery, mice were allowed to recover for at least 3 days with free access to water before water restriction. The experiments were not randomized. The investigators were not blinded to allocation during experiments and outcome assessment. Mice were prepared for photoinhibition and electrophysiology with a clear-skull cap and a headpost3. The scalp and periosteum over the dorsal surface of the skull were removed. A layer of cyanoacrylate adhesive (Krazy glue, Elmer’s Products Inc.) was directly applied to the intact skull. A custom made headpost48 was placed on the skull with its anterior edge aligned with the suture lambda (approximately over cerebellum) and cemented in place with clear dental acrylic (Lang Dental Jet Repair Acrylic; 1223-clear). A thin layer of clear dental acrylic was applied over the cyanoacrylate adhesive covering the entire exposed skull, followed by a thin layer of clear nail polish (Electron Microscopy Sciences, 72180). The behavioural task and training have been described3, 48. The stimulus was a metal pin (0.9 mm in diameter), presented at one of two possible positions (Fig. 1a). The two pole positions were 4.29 mm apart along the anterior-posterior axis (approximately 40° of whisking angle) and were constant across sessions. The posterior pole position was 5 mm from the whisker pad. A two-spout lickport (4.5 mm between spouts) was used to record answer licks and deliver water rewards. At the beginning of each trial, the vertical pole moved into reach of the whiskers (0.2 s travel time), where it remained for 1 s, after which it was retracted (retraction time 0.2 s). The sample epoch is defined as the time between the pole movement onset to 0.1 s after the pole retraction onset (sample epoch, 1.3 s, Fig. 1a). Mice touched the object at both pole positions, typically with a different set of whiskers. The delay epoch (durations, 1.2–1.7 s) followed the sample epoch. An auditory ‘go’ cue indicated the end of the delay epoch (pure tone, 3.4 kHz, 0.1 s duration). Licking early during the trial was punished by a loud alarm sound (siren buzzer, 0.05 s duration), followed by a brief timeout (1–1.2 s). Licking the correct lickport after the go cue led to a liquid reward (3 μl). Licking the incorrect lickport triggered a timeout (2–5 s). Trials in which mice did not lick within a 1.5-s window after the go cue were rare and typically occurred at the end of a session. Light from a 473 nm laser (Laser Quantum, Gem 473) or a 594 nm laser (Cobolt Inc., Colbolt Mambo 100) was controlled by an acousto-optical modulator (AOM; Quanta Tech) and a shutter (Vincent Associates). Photoinhibition of ALM was performed through the clear-skull cap implant by directing the laser over the skull (beam diameter: 400 μm at 4σ). The light transmission through the intact skull is 50%3. Photoinhibition was deployed on 25% of the behavioural trials during behavioural testing. To prevent the mice from distinguishing photoinhibition trials from control trials using visual cues, a ‘masking flash’ (40 1-ms pulses at 10 Hz) was delivered using 470 nm or 591 nm LEDs (Luxeon Star) near the eyes of the mice. The masking flash began as the pole started to move and continued through the end of photoinhibition. For silencing we stimulated cortical GABAergic neurons in VGAT-ChR2-EYFP mice, or parvalbumin-positive interneurons in PV-ires-cre mice crossed to reporter mice expressing ReaChR45. The two methods resulted in similar photoinhibition (Extended Data Fig. 2). The photoinhibition silenced 90% of spikes (Extended Data Fig. 2b) in a cortical area of 1 mm radius (at half-max) through all cortical layers3 (Extended Data Fig. 2d). To minimize rebound excitation after photoinhibition offset, we linearly ramped down the laser power (100 or 200 ms). This photostimulus was empirically determined3 to produce robust photoinhibition with minimal rebound (Extended Data Fig. 2c). The duration of the delay epoch varied to accommodate different photoinhibition conditions. In the unilateral photoinhibition experiment (Fig. 1, Extended Data Fig. 2a), a fixed 1.3-s delay epoch was used. We used a 40-Hz photostimulus with a sinusoidal temporal profile (1.5 mW average power) and a 100-ms linear ramp. We photoinhibited for 0.5 s, including the 100 ms ramp, during different task epochs (Fig. 1a). Photostimuli ended 1.6 s (sample), 0.8 s (early delay), 0.3 s (late delay), or 0 s (before cue) before the go cue. We also tested unilateral photoinhibition of longer durations in separate experiments (1.3 s including a 100-ms ramp, Extended Data Fig. 3). To accommodate the longer photoinhibition, we randomly varied the duration of the delay epoch from 1.2 s to 1.7 s in 0.1-s increments. This resulted in photoinhibition that terminated at different times before the go cue. In the bilateral photoinhibition experiment (Fig. 2), a fixed 1.7-s delay epoch was used to allow more time for neuronal activity to recovery after photoinhibition. We photoinhibited for 0.8 s, including a 200-ms ramp during offset, either at the beginning of the sample epoch or at the beginning of the delay epoch. To photoinhibit single cortical locations (Fig. 2a, 1 laser spot), we used the 40-Hz sinusoidal photostimulus (1.5 mW average power). To photoinhibit multiple cortical locations (Fig. 2a, multiple laser spots), we used a constant photostimulus and a scanning galvo (GVSM002, Thorlabs), which stepped the laser beam sequentially through the photoinhibition sites at the rate of 1 step per 5 ms (step time: <0.2 ms; dwell time:>4.8 ms; measured using a photodiode). Peak power was adjusted depending on the number of cortical locations to achieve 1.5 mW average power per location. The photoinhibition during scanning was similar to the standard condition (Extended Data Fig. 2). To estimate the proportion of ALM silenced by photoinhibition, we estimated the boundaries of ALM using photoinhibition behavioural data from3. ALM was defined as the area where photoinhibition over the entire delay epoch produced significant behavioural effects. ALM boundaries (Fig. 1b, grey area) were derived by deconvolving the area producing significant behavioural effects with the point-spread function of the photoinhibition method3 (Extended Data Fig. 2d). At 80% activity reduction, photoinhibition with 1 laser spot covered 58% of ALM in one hemisphere (Fig. 1b). For photoactivation we stimulated layer 5 intratelencephalic neurons in Tlx_PL56-cre mice46 crossed to reporter mice expressing ChR2 (Ai32)30. The delay epoch was 1.3 s long. The photostimulus was a 20-Hz sinusoid (0.53 mW average power) applied during different task epochs (Extended Data Fig. 5b). Photoactivation was deployed on 40% of the behavioural trials during electrophysiology. A small craniotomy (diameter, 1 mm) was made over left ALM (centred on 2.5 mm anterior, 1.5 mm lateral) one day before the recording session3. Extracellular spikes were recorded using NeuroNexus silicon probes (A4x8-5 mm-100-200-177). The 32 channel voltage signals were multiplexed, digitized by a PCI6133 board at 312.5 kHz (National instrument) at 14 bit, demultiplexed (sampling at 19531.25 Hz) and stored for offline analysis. Three to seven recordings were made from each craniotomy. To minimize brain movement, a drop of silicone gel (3-4680, Dow Corning) was applied over the craniotomy after the electrode was in the tissue. The tissue was allowed to settle for several minutes before the recording started. During electrophysiology, photoinhibition was deployed on 40% of the trials to obtain a larger number of trials per condition. Three photoinhibition conditions were tested during each recording session. In the unilateral photoinhibition experiment (Fig. 1, Extended Data Fig. 2a), photoinhibition during sample, early delay, and late delay epoch were tested. In the bilateral photoinhibition experiment (Fig. 2, Extended Data Fig. 2a), photoinhibition of left ALM (ipsilateral, 1 laser spot), right ALM (contralateral, 1 laser spot), and both hemispheres (4 laser spot) were tested. In separate experiments (Extended Data Figs 2a and 7), ipsilateral photoinhibition with 4 laser spots, contralateral photoinhibition with 4 laser spots, and bilateral photoinhibition with 1 laser spot were tested. The placement of the corpus callosum cut was determined based on ALM axonal projection patterns. AAV2/1-CAG-EGFP (Addgene, plasmid 28014) was injected into one hemisphere of ALM (Extended Data Fig. 10c). The injection coordinate was 2.5 mm anterior to bregma and 1.5 mm lateral to the midline. The injection was made through the thinned skull using a custom volumetric injection system. Glass pipettes (Drummond) were pulled and bevelled to a sharp tip (outer diameter of 30 μm). Pipettes were back-filled with mineral oil and front-loaded with viral suspension immediately before injection. 50-nl volumes were injected 500 and 800 μm deep. Two weeks after injection, mice were perfused and their brains were sectioned (50 μm) and processed using standard fluorescent immunohistochemical techniques. Confocal images were acquired on a Zeiss microscope, a 10 × objective and a Hamamatsu Orca Flash 4 camera46. ALM axons extend caudally from the injection site. Corpus callosum axons separate from pyramidal tract and corticothalamic axons approximately 1.2 mm anterior to bregma. ALM corpus callosum axons were confined to the anterior regions of corpus callosum and were densest around 1 mm from bregma (Extended Data Fig. 10c). Corpus callosum axon bisection was made through an elongated craniotomy either over the left (3 mice) or right (4 mice) hemisphere. A 3.5-mm-deep cut was made using a micro knife (Fine Science Tools, 10318-14) mounted on a micromanipulator (Sutter Instrument). The cut was 0.5 mm from the midline and was at a slight angle to avoid the pyramidal tract and corticothalamic axons (Extended Data Fig. 10d). The cut extended from 1.5 mm anterior to bregma to 1 mm posterior. Care was taken to avoid damaging the superior sagittal sinus. In the same surgery, a second craniotomy was made over left ALM for electrophysiology. Approximately 17 h after the surgery mice were tested in behavioural experiments (Fig. 5, Extended Data Fig. 10). Mice were tested in daily recording sessions for 5–7 days after the callosotomy. Mice were perfused immediately after the last recording session and the brains were processed for histology (Extended Data Fig. 10d). In a subset of the mice, brain sections were stained for GFAP (mouse; Sigma G3893, 1:2,000 dilution) (Extended Data Fig. 10d). Performance was computed as the fraction of correct reports, excluding lick-early trials (Figs 1, 2, 3, 4, 5). Chance performance was 50%. We also separately computed the performance for lick-right and lick-left trials (Figs 3, 4 and Extended Data Figs 3, 6, 9). Behavioural effects of photoinhibition were quantified by comparing the performance under photoinhibition with control performance using two-tailed t-test (Figs 1, 2, 5 and Extended Data Fig. 3). The extracellular recording traces were band-pass filtered (300–6 kHz). Events that exceeded an amplitude threshold (4 s.d. of the background) were subjected to manual spike sorting to extract single units3. 1,012 single units were recorded during behaviour across 58 recording sessions (20 sessions of unilateral experiments, Fig. 1; 38 sessions of bilateral experiments, Fig. 2, Extended Data Fig. 7). Spike widths were computed as the trough-to-peak interval in the mean spike waveform. Units with spike width <0.35 ms were defined as fast-spiking neurons (72 out of 1,012) and units with spike widths >0.45 ms as putative pyramidal neurons (890 out of 1,012). Units with intermediate values (0.35–0.45 ms, 50 out of 1,012) were excluded. This classification was previously verified by optogenetic tagging of GABAergic neurons3. We concentrated our analyses on the putative pyramidal neurons. Neurons were tested for significant trial-type selectivity during the sample, delay, or response epochs, using the spike counts from the lick-left and lick-right trials (two-tailed t-test, P < 0.05). Neurons that significantly differentiated trial types during any one of the trial epochs were deemed ‘selective’ (634 out of 890). To compute selectivity (Figs 1, 2, 5 and Extended Data Fig. 1), we first determined each neuron’s preferred trial type using spike counts from a subset of the trials (10 trials), selectivity is calculated as the spike rate difference between the trial types on the remaining data. Standard errors of the mean were obtained by bootstrap across neurons. To quantify the effect of photoinhibition on individual ALM neuron spike rates (Figs 1, 2, 5 and Extended Data Figs 5, 7), we used a two-tailed t-test on spike counts binned in 400-ms windows (control versus photoinhibition). Spike counts from lick-right trials and lick-left trials were pooled. Spike rates were tested at different times during the task (in 50-ms time steps) and significance was reported for P < 0.01. Quantification of the effects of perturbations on movement selectivity was complicated by the fact that ALM selectivity is coupled to upcoming movements. Grouping trials by the final movement (for example, using only correct lick-right trials) to compute selectivity would miss the trials in which photoinhibition caused the mice to switch future movements, thus underestimating the effects of photoinhibition on selectivity. We therefore used all trials (correct and incorrect) to compute selectivity when quantifying selectivity changes caused by photoinhibition (Figs 1, 2, 5 and Extended Data Figs 5, 7). Selectivity change was the selectivity difference between control and photoinhibition trials. To quantify the recovery time course of selectivity after photoinhibition, we looked for the first time bin when selectivity on photoinhibition trials reached 80% of the control selectivity (Figs 1g, 2e, 5e and Extended Data Figs 5, 7, green lines). Standard errors of the mean were obtained by bootstrap across neurons. To analyse the relationship between ALM population activity and upcoming movements, we restricted analysis to the recording sessions from the bilateral photoinhibition experiments (Fig. 2) with >5 neurons recorded simultaneously for >5 trials per condition (16 out of 38 sessions, Figs 3, 4 and Extended Data Figs 6, 8, 9). For a population of n neurons, we found an n × 1 vector, in the n dimensional activity space that maximally separated the response vectors in lick-right trials and lick-left trials, we term this vector the coding direction (CD). Average spike counts were computed in a 400-ms window in 10-ms steps. For each movement direction (lick right and lick left, correct trials only) we computed the average spike counts and , n × 1 response vectors that described the population response at that time. During the sample and delay epochs the direction of the difference in the mean response vectors, , was stable (correlation of w values between late sample epoch versus late delay epoch, 0.61 ± 0.05; Extended Data Fig. 9b). We averaged the w values from the sample and delay epochs to obtain the coding direction (CD). Because our estimate of the covariance was noisy, the CD gave better discrimination than the linear discrimant vector (CD divided by the within-group covariance). The projection along the CD captured 65.6 ± 5.1% of the population selectivity for lick-left and lick-right trials over the sample and delay epochs (root mean square (r.m.s.), of the spike rate difference between lick-right trials and lick-left trials), and 36.4 ± 6.3% of the total variance in ALM task-related activity (Extended Data Fig. 8a). Activity variance was quantified as the r.m.s. of the baseline subtracted activity over the sample and delay epoch. To project the ALM population activity along the CD we used independent control and perturbation trials from the trials used to compute the CD. For each trial we computed the spike counts for each neuron, x (n × 1), at each time point. The projected trajectories in Figs 3, 5 and Extended Data Figs 6, 7, 8, 9 were obtained as CDTx. Both correct and incorrect trials were used to compute the projected trajectries, grouped by the instructed movements. To quantify the separation between trajectories on lick-right and lick-left trials, we computed ROC values using CDTx at the end of the delay epoch for each session. To average trajectories across multiple behavioural sessions (Figs 3, 5 and Extended Data Figs 7, 8, 9), we first offset the trajectories for a particularly session by subtracting the mean CDTx across all trials and time points in that session. This removed fluctuations in mean activity from session to session. The offsets were computed using the independent control trials that were used to calculate the CD. Standard errors of the mean were obtained by bootstrapping individual sessions. To predict upcoming movements using ALM responses projected onto the CD (Figs 3, 4 and Extended Data Figs 8b, 9), we used the response vector x from the last time bin before the go cue (last 400 ms of the delay epoch). For each session, we computed a decision boundary (DB) to best separate the projected responses, CDTx, from lick-right and lick-left trials: σ2 is the variance of the projected responses CDTx across multiple lick-right or lick-left trials. Both the CD and decision boundary were computed using independent control trials and separate control and photoinhibition trials were used to predict performance. Data from multiple sessions were pooled in Figs 3, 4 and Extended Data Fig. 9. We decomposed ALM activity into three forms of dynamics (Fig. 3 and Extended Data Fig. 8). The modes were computed using a subset of control trials (correct trials only) and ipsilateral perturbation trials. The projections in the figures are for independent control trials and perturbation trials. The projection along the CD (mode 1) captured the movement selectivity in activity. The persistent mode (mode 2) was the difference in the mean response vectors between ipsilateral perturbed and unperturbed lick-right trials at the go cue. Mode 3 was the mean response vectors between ipsilateral perturbed and unperturbed lick-left trials at the go cue, further rotated using Gram–Schmidt process to be orthogonal to mode 2. We did not orthogonalize the CD mode and persistent mode, so that any potential selectivity common to these modes was not removed. There was a small overlap between mode 1 and modes 2–3 (the activity variance and selectivity shared by modes 1–3 are quantified in Extended Data Fig. 8a). Modes 2 and 3 describe the vast majority of the persistent changes in activity after ipsilateral perturbations. Two additional modes (4 and 5) captured the remaining activity variance. We first found eigenvectors of the population activity matrix using singular value decomposition. The data for the singular value decomposition (SVD) was an n × t matrix, consisting of the baseline-subtracted PSTHs for n neurons, with the lick-right and lick-left trials concatenated together (t time bins). The first two eigenvectors (n × 1) were rotated using the Gram–Schmidt process to be orthogonal to modes 1–3, yielding modes 4 and 5. Modes 1–5 together explained 98.5 ± 0.5% of the total variance of task-related activity and 95.8 ± 1.2% of population selectivity over the sample and delay epochs. To predict upcoming movements using the projected responses on persistent mode and ramping mode (Fig. 3), we computed decision boundaries on the projected responses using the same procedures as for the CD mode. Model code can be found at https://github.com/kpdaie/LiDaie. We constructed neural networks that have the ability to produce slow ramps of preparatory activity (Fig. 6a) when receiving transient or constant input, similar to a subset of ALM neurons. Our models include a phenomenological attractor model (Fig. 6b), explicit integrators (Fig. 6c and Extended Data Fig. 1f, g), and recurrent neural networks (RNNs) trained to produce ramping output (Fig. 6d and Extended Data Fig. 2h, i). We compared the responses of the models and ALM to transient silencing. All networks were simulated for two seconds. Photoinhibition was simulated by holding the activity of half of the neurons in each network at zero for times 0.2 s < t < 1.0 s. Activity of the ith neuron r (t) was governed by the equation: The cellular time constant, τ, the connectivity matrix, W, and the synaptic nonlinearity, f(r), differed across the models. N is the number of neurons, is a tonic and non-selective input, and is Gaussian random noise. In all simulations networks received either transient (0.05 s < t < 0.1 s) or persistent (0.1 s < t < 1.9 s) sensory inputs I (t). The network was simulated with N = 100, τ = 100 ms, and linear synapses, . The connectivity matrix was constructed so that all eigenvalues except for one were equal to zero. The non-zero eigenvalue was set to 0.99, producing feedback so that the activity of the network decays with time constant (ref. 35). The input was either persistent (Extended Data Fig. 1f, left) or transient (Extended Data Fig. 1f, right), in which case the output from the integrator was cascaded into a second identical network to produce ramping activity. Silencing was simulated by holding the activity of a randomly-selected population of 50 neurons at zero for times 0.2 s < t < 1.0 s. Corrective feedback37 was incorporated into an integrator network to confer robustness against perturbations. The model consists of a pair of excitatory and inhibitory neurons. Corrective feedback was achieved by a mismatch in the time constants for excitatory and inhibitory connections, which generates negative derivative feedback. The network exhibits robustness against random perturbations that equally affect the excitatory and inhibitory neurons, but is not robust against asymmetric activation of inhibitory neurons (for example, photoinhibition). The function f(r) is linear f(r) = s where the auxiliary variable s is determined by the equation: The synaptic time constant determines how quickly the post-synaptic currents respond to changes in presynaptic activity. The synaptic time constants were: inhibitory synapses, 10 ms; excitatory to inhibitory neurons, 25 ms; excitatory to excitatory neurons, 100 ms. The network received a task-selective persistent input. Photoinhibition was simulated by injecting large currents into the inhibitory neuron and disallowing negative spike rates, which results in silencing of the excitatory neuron. We used FORCE22 training to minimize the difference between the network readout (z(t)) and a ramping waveform (Extended Data Fig. 1h). z(t) is a linear combination of the activity of each neuron with weights determined by the vector w (that is, ). Tuning of z(t) was accomplished by simulating the activity of an initially randomly connected recurrent neural network (RNN) for 2 seconds (time step, 1 ms) and adjusting W every 2 ms during the simulation. This process was repeated 30 times. The initial connectivity matrix was chosen to be sparse with a connection probability p = 0.1. Non-zero connections were chosen from a Gaussian random distribution. The variance in connection strength was . 1.5 is a gain factor which is sufficiently strong to produce chaotic activity49. In addition, we used τ = 200 ms, f(r) = tanh(r), N = 400 and transient input. Photoinhibition was simulated by transiently clamping the activity of a randomly-selected population of 200 (that is, N/2) neurons to zero. The network received either persistent (Extended Data Fig. 1h, left) or transient (Extended Data Fig. 1h, right) sensory input. For persistent input the network behaved similar to an integrator exhibiting a recovery of selectivity, albeit at an offset level upon removal of photoinhibition. RRNs were trained with FORCE as described above and further stabilized (tamed chaos)23. The algorithm was designed to stabilize selected trajectories in chaotic networks via a recursive retuning of recurrent connection strengths based on a recursive least-squares rule50. To minimize the number of synapses that required tuning, the FORCE network was made sparse by eliminating weak connections that were smaller than an arbitrary threshold and using linear regression to adjust the remaining weights to maintain the dynamics. Elimination of weak synapses reduced the time needed to train the network. Twenty iterations of the tamed chaos algorithm were then run with weights being adjusted every 10 ms. Perturbations were applied as described for the FORCE trained network above. This training resulted in a modest increase in the robustness of the network. Two identical two-neuron unilateral attractor modules were constructed so that each neuron excited itself with weight 0.5235 and inhibited the other neuron in the same module with −0.5235. Each neuron was reciprocally connected with one partner from the other module with strength 0.3. τ = 100 ms and , where . Transient input I (t) (amplitude, 0.1) was provided to either the right-preferring (blue, Fig. 6b) or left-preferring (red, Fig. 6b) neurons, depending on the trial type. All neurons received a tonic input T (t) with amplitude 0.5 and noise with variance 0.01. Two modules with inter-module connections were tuned to produce robustness against unilateral photoinhibition. Each module consisted of four neurons (numbers refer to neuronal indices, with reference to the connection matrix W): Right preferring integrator neurons (1, 5) and left preferring integrator neurons (2, 6). Integration was produced by positive feedback achieved through mutual inhibition between left and right preferring neurons with strength −1 (ref. 15); these integrating pairs are represented schematically by the circles labelled ∫ in Fig. 6c. The modules are connected through the recovery neurons (3, 7; ‘R’ in Fig. 6c) and gating inhibitory neurons (4, 8; ‘G’ in Fig. 6c). The input I (t) was persistent with amplitude 0.04 to the right-preferring neuron and −0.04 to the left-preferring neuron during lick-right trials. The signs of the inputs were flipped for lick-left trials. In addition, each integrator neuron received tonic input T (t) with amplitude 40.0 to produce baseline activity at 20.0. The recovery (Fig. 6c) and gating inhibitory (Fig. 6c) neurons together produce robustness. They receive positive input from the right-preferring neuron and negative input from the left-preferring neuron. After removal of photoinhibition, the recovery neuron restores the activity of the contralateral integrator neurons. This restorative connection has strength 0.5. To avoid excessive coupling between modules during normal function the recovery neuron is strongly inhibited by the gating neuron with strength −6.0. The full connectivity matrix is shown below. For example, element W is the connection from the recovery neuron in module 2 (neuron 7) onto the right preferring neuron of module 1 (neuron 1). The time constant of this network was τ = 10 ms. Synapses in this network were linear, but activity was restricted to be positive.  = 0 in this network. To generate a modular RNN we started, as above (see Trained RNN, FORCE learning), with a randomly connected RNN with N = 400. We then classified 200 neurons as module 1 and the other 200 as module 2. FORCE training was performed as described above, but we first tuned only the intra-modular connections so that each module could produce its own ramping output. Next, inter-modular connections were trained in the presence of transient photoinhibition (described above) of module 1, so that the output of module 1 would recover upon removal of photoinhibition and the output of module 2 would be minimally affected by the photoinhibition. This process was then repeated for photoinhibition of module 2. In this network T (t) = 0 and  = 0.

Experiments were performed in accordance with the regulations of the Institutional Animal Care and Use Committee of the University of California, San Diego. We used the following mouse lines: VGAT–ChR2–EYFP31 (Jackson Labs #014548), PV–Cre32 (Jackson Labs #008069), Gad2–Cre33 (Jackson Labs #010802) and Hoxd10–GFP34 (MMRRC #032065-UCD). Mice were bred by crossing homozygous VGAT–ChR2–EYFP, PV–Cre or Gad2–Cre males (all lines with a C57BL/6 background) with wild-type ICR females or homozygous Hoxd10–GFP females (ICR background) to C57BL/6 males. Mice were housed in a vivarium with a reversed light cycle (12 h day–12 h night). Mice of both genders were used for experiments at postnatal ages of 2–6 months. We used the following adeno-associated viruses (AAV) and canine adenovirus (CAV2): For the Cre recombinase (Cre)-dependent expression of Channelrhodopsin2 (ChR2)35, 36: AAV2/9.CAGGS.Flex.ChR2.tdTomato.SV40 (Addgene 18917; UPenn Vector Core). For the Cre-dependent expression of tdTomato: AAV2/1.CAG.Flex.tdTomato.WPRE.bGH (Allen Institute 864; UPenn Vector Core). For the expression of Cre: AAV2/9.hSyn.HI.eGFP-Cre.WPRE.SV40 (UPenn Vector Core). For Cre-dependent expression of the diphtheria toxin receptor (DTR)37: AAV2/1.Flex.DTR.GFP (Jessell laboratory; produced at UNC Vector Core). AAV2/9.CAGGS.Flex.ChR2.tdTomato.SV40 was bilaterally injected into the visual cortex of newborn PV–Cre or Gad2–Cre pups (postnatal day (P) 0–2). The virus was loaded into a bevelled glass micropipette (tip diameter 20–40 μm) mounted on a Nanoject II (Drummond) attached to a micromanipulator. Pups were anaesthetized by hypothermia and secured in a molded platform. In each hemisphere the virus was injected at two sites along the medial–lateral axis of the visual cortex. At each site we made three bolus injections of 28 nl. Each were at three different depths between 300 and 600 μm. Protein expression was verified by epi-fluorescent illumination through a dissection microscope (Leica MZ10F). Experiments were performed on animals with expression over the entire extent of visual cortex. AAV2/9.hSyn.HI.EGFP-Cre.WPRE.SV40 and AAV2/9.CAGGS.Flex.ChR2.tdTomato were mixed in 1:20 ratio. The mixture was injected into the visual cortex of newborn C57BL/6 pups (as described above). Protein expression was verified by epi-fluorescent illumination. Adult Hoxd10–GFP mice were anaesthetized with ~2% isoflurane (vol/vol) in O . The depth of anaesthesia was monitored with the toe-pinch response. The eyes were protected from drying by artificial tears. We cut open the scalp and thinned the skull to create a window of ~300–500 μm diameter. The remaining layer of bone in the window was thin enough to allow the penetration of the beveled glass pipette. A bolus of retrograde fluorescent microspheres (RetroBeads, Lumafluor Inc.) or CAV2.Cre virus (40 nl RetroBeads or 20 nl CAV2 virus) was injected into the NOT-DTN (coordinates (anteroposterior axis (AP) relative to bregma; mediolateral axis (ML) relative to the midline): AP: −1,260 μm; ML: 3,080 μm; depth: 1,960 μm; coordinates were adjusted based on the distance between bregma and lambda on mouse skull) using an UltraMicroPump (UMP3, WPI). The wound was sutured with a few stitches of 6-0 suture silk (Fisher Scientific NC9134710). Mice were perfused 3 days after the retrobead injection or 2 weeks after the CAV2 injection. AAV2/1.Flex.DTR.GFP was bilaterally injected into the visual cortex of VGAT–ChR2–EYFP pups between P0 and P2. CAV2.Cre virus was subsequently stereotactically injected into the NOT-DTN (same coordinates as above) bilaterally in mice of 2–6 months of age. Three to four weeks later we injected diphtheria toxin (DT 40 ng/g) intraperitoneally three times on alternate days. The OKR was assessed 11 or 12 days after the first diphtheria toxin injection. In control experiments, diphtheria toxin was replaced with PBS or diphtheria toxin was injected into mice that had not been infected with AAV2/1.Flex.DTR.GFP. Mice were implanted with a T-shaped head bar for head fixation. Mice were anaesthetized using ~2% isoflurane. The scalp and fascia were removed and a metal head bar was mounted over the midline using dental cement (Ortho-Jet powder; Lang Dental) mixed with black paint (iron oxide). We created a cranial window of ~3 × 3 mm (1.5–4.5 mm lateral to midline and 2.3–5.2 mm posterior to bregma) over the visual cortex on each hemisphere by gently thinning the skull until it appeared transparent when wetted by saline solution. The window was then covered with a thin layer of crazy glue. Following the surgery animals were injected subcutaneously with 0.1 mg/kg buprenorphine and allowed to recover in their home cage for at least 1 week. Several days before the test, mice were familiarized with head fixation in the recording setup. No visual stimulation was given. The horizontal OKR was elicited by a ‘virtual drum’ system39. Three computer LED monitors (Viewsonic VX2450wm-LED, 60-Hz refresh rate, gamma-corrected) were mounted orthogonally to each other to form a square enclosure that covered ~270° of visual field along the azimuth. The mouse head was immobilized at the centre of the enclosure with the nasal and temporal corners of the eye leveled. Visual stimuli were generated with Psychophysics Toolbox 3 running in Matlab (Mathworks). To ensure synchronized updating across multiple monitors we used AMD Eyefinity Technology (ATI FirePro V4800). The monitors displayed a vertical sinusoidal grating whose period (spacing between stripes) was adjusted throughout the azimuthal plane such that the projection of the grating on the eye had constant spatial frequency. In other words, the spatial frequency of the grating was perceived as constant throughout the visual field, as if the grating was drifting along the surface of a virtual drum. The dependence of pixel brightness on monitor coordinates was obtained by using this equation: B = L + L × C × sin(2π × x  × SF), where B is the brightness of pixels, L is the luminance in cd/m2, C is the contrast, SF is the spatial frequency and x is the azimuth of pixels in degrees, which is transformed from the Cartesian coordinates of the monitor into the cylindrical coordinates of the virtual drum by the following formula: x  = tan−1(x /D), where x is the horizontal pixel position in Cartesian coordinates and D is the distance from the centre of the monitors to the eye (Extended Data Fig. 1a). The grating drifted clockwise or counterclockwise in an oscillatory manner7, 11 (oscillation amplitude ± 5°; grating spatial frequency: 0.04–0.45 cpd; oscillation frequency 0.2–1 Hz, corresponding to a peak velocity of the stimulus of 6.28–31.4° s−1; contrast: 80%; mean luminance: 40 cd/m2). We chose the duration of the visual stimulus to allow the presentation of an integral number of oscillatory cycles (10 or 15 s for OKR test only; 7.5 s for simultaneous NOT-DTN electrophysiology and OKR test). Trials were spaced by an inter-stimulation interval of at least 8 s. The inter-stimulation interval following trials of cortical silencing was increased to 20 s. To measure the oscillation frequency tuning, spatial frequency was kept constant at 0.08 cpd; to measure the spatial frequency tuning oscillation, the frequency was kept at 0.4 Hz. To obtain the transfer function, we varied the spatial frequency of the visual stimulus rather than the oscillation frequency because OKR peak velocity is strongly modulated by spatial frequency and much less so by the oscillation frequency (consistent with previous observations7, 40; Extended Data Fig. 9a). The spatial frequency was varied from 0.04 to 0.45 cpd, and the oscillation frequency was kept constant at 0.4 Hz. To evaluate the directional preference of NOT-DTN neurons, one monitor was positioned 20 cm from the eye contralateral to the side of recording. Full-field sinusoidal drifting gratings (oscillation frequency: 1 Hz; spatial frequency: 0.08 cpd; mean luminance: 50 cd/m2; contrast: 100%) were used. Gratings were randomly presented at 12 equally spaced positions. The duration of the visual stimulus was 2 s and the inter-trial interval was 2.2 s. To visualize NOT-DTN with c-Fos immunostaining (c-Fos is an immediate early gene expressed in response to neuronal activity), OKR was elicited by drum stimulation of various spatial frequencies (0.04–0.45 cpd) with oscillation frequency 0.4 Hz, contrast 100% and luminance 50 cd/m2. Trials of oscillatory motion lasted for 15 s and were followed by an inter-trial interval of 8 s. The whole stimulation procedure took 60 min. The movement of the right eye was monitored through a high speed infrared (IR) camera (Imperx IPX-VGA 210; 100 Hz). The camera captured the reflection of the eye on an IR mirror (transparent to visible light, Edmund Optics #64-471) under the control of custom labview software and a frame grabber (National Instrument PCIe-1427). The pupil was identified online by thresholding pixel values or post hoc by combining thresholding and morphology operation and its profile was fitted with an ellipse to determine the centre. The eye position was measured by computing the distance between the pupil centre and the corneal reflection of a reference IR LED placed along the optical axis of the camera. To calibrate the measurement of the eye position, the camera and the reference IR LED were moved along a circumference centred on the image of the eye by ± 10° (Extended Data Fig. 1b). Three mouse lines (VGAT–ChR2–EYFP, PV–Cre and Gad2–Cre) were used in experiments involving optogenetic silencing of the visual cortex. They are equally efficient in silencing activity of visual cortex and interchangeable. VGAT–ChR2–EYFP mice were used in most of the silencing experiments, except in experiments illustrated in Extended Data Fig. 2a (PV–Cre line) and Extended Data Fig. 3b (all 3 lines). To photostimulate ChR2-expressing cortical inhibitory neurons in vivo, a 470-nm blue fibre-coupled LED (1 mm diameter, Doric Lenses) was placed ~5–10 mm above the cranial windows of each hemisphere. We restricted the illumination to the tissue under the cranial window by covering neighbouring areas with dental cement. An opaque shield of black clay prevented LED light from directly reaching the eyes. The total light power out of the LED fibre was 15–20 mW. Trials were alternated between visual stimulus alone and visual stimulus plus LED. The LED was turned on during the whole period of visual stimulation and turned off by ramping down the power over 0.5 s to limit rebound activation of the visual cortex. To photostimulate cortical input to the NOT-DTN in vivo, blue light illuminated only the visual cortex ipsilateral to the NOT-DTN where the probe was inserted. We dissected out the tissue overlying the horizontal semicircular canal in mice under ~2% isoflurane anaesthesia. A small hole was drilled in the canal with a miniature Busch Bur (0.25 mm, Gesswein) and the endolymph was partially drained. The horizontal semicircular canal was plugged with bone wax (FST 19009-00) to seal the opening and reduce the flow of the endolymph within the canal. The wound was sutured with a few stitches of 6/0 suture. Mice recovered for two days in their home cages before being tested for OKR. Sham lesions were done in the same way except that no hole was drilled and no wax was introduced in the semicircular canal. OKR gain (spatial frequency: 0.1 cpd; oscillation frequency: 0.4 Hz; contrast: 100%; mean luminance: 35 cd/m2) was assessed 1 day before and 1 h before OKR training. Two sessions (12 min) were used to minimize the effect of visual stimulation during OKR evaluation on OKR gain. During continuous OKR stimulation, a drum of the same visual parameters ran continuously for 38 min. OKR gain was then assessed again 12 min after OKR stimulation was finished. Mice were implanted with a T-shaped head bar for head fixation in the same way as described above for the OKR assessment, except that the procedure was done stereotactically with the help of an inclinometer (Digi-Key electronics 551-1002-1-ND). The inclinometer allowed us to calibrate the inclination of the two axis of the T bar relative to the anteroposterior (AP) and mediolateral (ML) axes of the skull before fixing it to the skull with dental cement. Three reference points with known coordinates were marked on the mouse skull because both bregma and lambda were inevitably masked by the dental cement holding the head bar. The head post on the recording rig was also calibrated with the same inclinometer to ensure that the recording probes were in register with the skull. Recordings from awake animals were performed using a method similar to that described previously43. One to two weeks before recording, mice were familiarized with head fixation within the recording setup over the course of two to four 50-min sessions. One day before recording, mice were anaesthetized with ~2% isoflurane. Whiskers and eyelashes contralateral to the recording side were trimmed to prevent interference with infrared video-oculography. To access the NOT-DTN we made an elongated, anteroposteriorly oriented craniotomy (~0.4 × 0.8 mm) around the coordinates of −3 mm (anteroposterior) and 1.3 mm (mediolateral). The coordinates were adjusted based on the distance between bregma and lambda on mouse skull. The craniotomy was then covered by Kwik-Cast Sealant (WPI). On the day of recording, after peeling off the Kwik-Cast cover, a drop of artificial cerebrospinal fluid (ACSF; in mM, 140 NaCl, 2.5 KCl, 2.5 CaCl , 1.3 MgSO , 1.0 NaH PO , 20 HEPES and 11 glucose, pH 7.4) was placed in the well of the craniotomy to keep the exposed brain moist. A 16-channel linear silicon probe (NeuroNexus a1x16-5mm-25-177) mounted on a manipulator (Luigs &Neumann) was slowly advanced into the brain to a depth of 2,000–2,200 μm. The occurrence of direction modulated activity upon visual stimulation was used to identify the NOT-DTN (see data analysis below). The probe was stained by lipophilic DiI to label the recording track for post hoc verification of successful targeting of the NOT-DTN. Recordings were not started until 20 min after insertion of the probe into the NOT-DTN. Signals were amplified 400-fold, band-pass filtered (0.3–5,000 Hz, with the presence of a notch filter) with an extracellular amplifier (A-M Systems 3600) and digitized at 32 kHz (National Instrument PCIe-6259) with custom-written software in Matlab. Raw data were stored on a computer hard drive for offline analysis. At the end of the recording session, brains were fixed by transcardial perfusion of 4% paraformaldehyde for histological analysis. Recordings from the superior colliculus or vLGN were done in the same way except that the coordinates of the craniotomy were 3.5 mm (anteroposterior) and 1 mm (mediolateral) for the superior colliculus and 2.5 mm (anteroposterior) and 2.3 mm (mediolateral) for the vLGN. For recordings from anaesthetized mice we used the same procedures as described above except that (1) the familiarization step was omitted and the craniotomy was performed immediately before recording; (2) animals were anaesthetized with urethane (1.2 g/kg, intraperitoneal) and given the sedative chlorprothixene (0.05 ml of 4 mg/ml, intramuscular), as previously described44; (3) body temperature was maintained at 37 °C using a feedback-controlled heating pad (FHC 40-90-8D); (4) a uniform layer of silicone oil was applied to the eyes to prevent drying; and (5) lactated Ringer’s solution was administrated at 3 ml/kg/h to prevent dehydration. Mice at postnatal days 15–30 were anaesthetized by intraperitoneal injection of ketamine and xylazine (100 mg/kg and 10 mg/kg, respectively), perfused transcardially with cold (0–4 °C) slice cutting solution ((in mM) 80 NaCl, 2.5 KCl, 1.3 NaH PO , 26 NaHCO , 20 d-glucose, 75 sucrose, 0.5 sodium ascorbate, 4 MgCl and 0.5 CaCl , 315 mOsm, pH 7.4, saturated with 95% O2/5% CO ) and decapitated. Brains were sectioned into coronal slices of 300–400 μm in cold cutting solution with a Super Microslicer Zero1 (D.S.K.). Slices containing the NOT-DTN were incubated in a submerged chamber at 34 °C for 30 min and then at room temperature (~21 °C) until used for recordings. During the whole procedure, the cutting solution was bubbled with 95% O /5% CO . Whole-cell recordings were done in ACSF (in mM: 119 NaCl, 2.5 KCl, 1.3 NaH PO , 26 NaHCO , 20 d-glucose, 0.5 sodium ascorbate, 4 MgCl , 2.5 CaCl , 300 mOsm, pH 7.4, saturated with 95% O /5% CO ). The ACSF was warmed to ~30 °C and perfused at 3 ml/min. NOT-DTN neurons were visualized with DIC infrared video-microscopy under a water immersion objective (40×, 0.8 NA) on an upright microscope (Olympus BX51WI) with an IR CCD camera (Till Photonics VX44). Whole-cell voltage-clamp recordings were performed with patch pipettes (borosilicate glass; Sutter Instruments) using a caesium-based internal solution ((in mM) 115 CsMeSO , 1.5 MgCl , 10 HEPES, 0.3 Na GTP, 4 MgATP, 10 Na -phosphocreatine, 1 EGTA, 2 QX-314-Cl, 10 BAPTA-tetracesium, 0.5% biocytin, 295 mOsm, pH 7.35). AMPA receptor-mediated EPSCs were recorded at the reversal potential for IPSCs (~−65 mV) and NMDA receptor-mediated EPSCs were recorded at +40 mV in the presence of the GABA receptor antagonist gabazine (5 μM, Tocris 1262) and the AMPA receptor antagonist NBQX (10 μM, Tocris 1044). To verify monosynaptic connectivity, we isolated NMDA receptor-mediated EPSCs in the presence of NBQX and high Mg2+ concentration (4 mM) or monosynaptic AMPA receptor-mediated EPSCs by a modified sCRACM approach45 in the presence of tetrodotoxin (TTX; 1 μM, Tocris 1069), 4-aminopyridine (4-AP; 1.5 mM, Abcam ab120122) and tetraethylammonium (TEA; 1.5 mM, ab120275). EPSCs were acquired and filtered at 4 kHz with a Multiclamp 700B amplifier, and digitized with a Digidata 1440A at 10 kHz under the control of Clampex 10.2 (Molecular Devices). Data were analysed offline with Clampfit 10.2 (Molecular Device). To photostimulate ChR2-expressing cortico-fugal axons, we delivered blue light using a collimated LED (470 nm) and a T-Cube LED Driver (Thorlabs) through the fluorescence illuminator port and the 40× objective. Light pulses of 10 ms and 5.5 mW/mm2 were given with a 20 s inter-stimulus interval. After recordings, slices were fixed by 4% paraformaldehyde for histology. After implanting the head bar, under anaesthesia (2% isoflurane), we dissected out part of the skull and removed, by aspiration, the area of the cortex and hippocampus overlaying the NOT-DTN. The identity of the NOT-DTN was assessed visually by its anatomy and stereotactic coordinates and verified electrophysiologically (see data analysis below). After the surgery, the mice were head-fixed and isoflurane was withdrawn. For at least the next 45 min, OKR performance and NOT-DTN activity were recorded. The GABA receptor agonist muscimol (0.2–1 mM in ACSF) was applied on top of the NOT-DTN. It took ~30 min for muscimol to silence the NOT-DTN, as assessed electrophysiologically. Pupillary dilation, as a side effect of silencing the olivary pretectal nucleus, was counteracted by topical application of 2% pilocarpine hydrochloride (agonist of muscarinic receptor, Tocris 0694) in saline to both eyes. Mice were perfused transcardially first with phosphate buffered saline (PBS, pH 7.4) and then with 4% paraformaldehyde in PBS (pH 7.4) under anaesthesia (ketamine 100 mg/kg and xylazine10 mg/kg; intraperitoneal injection). Brains were removed from the skull, post-fixed overnight in 4% paraformaldehyde and then immersed in 30% sucrose in PBS until they sank. Brains were subsequently coronally sectioned (40–60 μm sections) with a sliding microtome (Thermo Scientific HM450). Slices were incubated in blocking buffer (PBS, 5% goat serum (Life Technologies 16210-072), 1% Triton X-100) at room temperature for 2 h and then incubated with primary antibodies in blocking buffer at 4 °C overnight. The following primary antibodies were used: rabbit anti-GFP (1:1,000, Life Technologies A6455) and rabbit anti-c-Fos (1:1,000, Santa Cruz Biotechnology sc-52). The slices were washed three times with blocking buffer for 30 min each and then incubated with secondary antibodies conjugated with Alexa Fluor 488, 594 or 633 (1:800, Life Technologies A11008, A11012 or A21070, respectively) in blocking buffer for 2 h at room temperature. After being washed three times with blocking buffer for 10 min each, slices were mounted in Vectashield mounting medium containing DAPI (Vector Laboratories H1500). For c-Fos immunostaining, 90 min after the beginning of OKR stimulation (30 min after 60-min OKR simulation was finished), animals were perfused transcardially first with PBS and then with 4% paraformaldehyde in PBS. Brains were coronally sectioned into slices of 40 μm. To reveal the morphology of NOT-DTN neurons filled with biocytin, following fixation and blocking (see above), we incubated the slices with streptavidin conjugated with Alexa Fluor 647 (1:500, Life Technologies s32357) in blocking buffer overnight and then washed the slices three times. Images were acquired on a Leica SP5 confocal microscope, a Zeiss Axio Imager A1 epifluorescence microscope or an Olympus MVX10 stereoscope, and processed using ImageJ (National Institutes of Health). Analysis of eye tracking and in vivo electrophysiology was performed using custom-written codes in Matlab. Analysis of in vitro electrophysiology was done with Clampfit 10.2 (Molecular Devices). Saccade-like fast eye movements were removed from the recorded eye trajectory before computing OKR amplitude (Extended Data Fig. 1c). Saccades were detected as ‘spikes’ in the temporal derivative of the eye position (velocity) and replaced by linear interpolation. To derive the amplitude of the OKR we used the Fourier transform of the eye position as a function of time. The eye trajectories illustrated in this study are the averages of several cycles. The gain of the OKR was expressed as OKR gain = Amp /Amp , where Amp is the amplitude of eye movement and Amp the amplitude of drum movement. The OKR gain derived in the space domain is similar to that derived in the velocity domain (Extended Data Fig. 1f). In this study, we computed the gain in the space domain because deriving eye velocity from eye position introduces noise. Therefore, the OKR gain is 1 if the eye perfectly tracks the trajectory of the virtual drum and 0 if it does not track. The cortical contribution to the OKR gain is expressed as the percentage reduction in OKR gain caused by cortical silencing and calculated as ΔV (%) = (V − V )/V , where V and V are the values of the OKR gain measured under control conditions or during optogenetic cortical silencing, respectively. OKR potentiation is calculated as V / V , where V and V are the values of the OKR gain measured before and after vestibular lesion, respectively. The cortical contribution to OKR potentiation is expressed as PI = (ΔV − ΔV )/(ΔV − ΔV ), where ΔV and ΔV are the cortical contribution to the OKR gain before and after vestibular lesioning, respectively, and ΔV is the maximum possible cortical contribution to the OKR gain assuming that the entire amount of OKR potentiation depends on visual cortex. ΔV  = (V − V )/V . Hence PI is 1 if the entire amount of OKR potentiation depends on visual cortex and is 0 if the cortical contribution to OKR gain before vestibular lesion is the same as the cortical contribution to OKR gain after vestibular lesion (ΔV  = ΔV ) (Extended Data Fig. 3c, d). The cortical contribution to NOT-DTN activity is expressed as the cortical contribution to OKR gain but V and V are the firing rates of NOT-DTN neurons under control conditions or during optogenetic cortical silencing, respectively. Single units were isolated using spike-sorting Matlab codes, as described previously43. The raw extracellular signal was band-pass filtered between 0.5 and 10 kHz. Spiking events were detected with a threshold at 3.5 or 4 times the standard deviation of the filtered signal. Spike waveforms of four adjacent electrode sites were clustered using a k-means algorithm. After initial automated clustering, clusters were manually merged or split with a graphical user interface in Matlab. Unit isolation quality was assessed by considering refractory period violations and Fisher linear discriminant analysis. All units were assigned a depth according to the electrode sites at which their amplitudes were largest. Multi-unit spiking activity was defined as all spiking events exceeding the detection threshold after the removal of electrical noise or movement artefacts by the sorting algorithm. Individual spiking events were also assigned to one of the 16 recording sites according to where they showed the largest amplitude. For both single-unit activity and multi-unit activity, the visual response was computed as the mean firing rate during visual stimulation without baseline subtraction. Units recorded from visual cortex were assigned as regular-spiking neurons or fast-spiking putative inhibitory neurons based on the trough-to-peak times of spike waveforms43. A threshold of 0.4 ms was used to distinguish fast-spiking from regular-spiking units. The boundary of the NOT-DTN was determined by the appearance of a temporonasal directional bias in the multi-unit response to the visual stimulus. The preferred direction of an isolated NOT-DTN unit was determined by summing response vectors of 12 evenly spaced directions. The direction selectivity index (DSI) was calculated along the sampled orientation axis closest to the preferred direction according to the formula DSI = (R − R )/(R + R ), where R is the response at the preferred direction and R is the response at the opposite direction. The DSI of the response evoked by oscillatory drum movement was calculated as DSI = (R − R )/(R + R ), where R is the response during the temporonasal phase of drum movement and R is the response during the nasotemporal phase. The onset latency of optogenetically evoked activity of NOT-DTN neurons was determined as the time lag between the beginning of the LED illumination and the time point at which the firing rate reached three times the standard deviation of spontaneous activity. Similarly, the onset latency of optogenetically evoked EPSCs in NOT-DTN neurons was determined as the time lag between the beginning of the LED illumination and the time point at which the EPSC amplitude reached three times the standard deviation of baseline noise. Trial-by-trial jitter of optogenetically evoked EPSCs was calculated as the standard deviation of the onset latency. Analysis of c-Fos immunohistochemistry was performed with ImageJ (National Institutes of Health). c-Fos-positive cells were identified as continuous pixels after thresholding and counted automatically. To quantify the extent of overlap between arborization of GFP-expressing RGC axons and c-Fos expression in the NOT-DTN, their boundaries were manually drawn and the overlap coefficient r was calculated as where S1 is 1 if pixel i is within the domain of RGC axons, otherwise 0; and S2 is 1 if pixel i is within the domain of c-Fos immunohistochemistry, otherwise 0 (Extended Data Fig. 5c). For each animal, NOT-DTN multiunit activity was normalized to the average firing rate evoked by optimal spatial frequency. Data points of transfer functions from all animals were pooled, binned and averaged. The vectors (arrows in Extended Data Fig. 9g–i) start at the centre of mass of data points obtained at a given spatial frequency under control conditions (grey) and end at the centre of mass of data points obtained at the same spatial frequency during cortical silencing trials (blue). The x-axis value of the centre of mass is the NOT-DTN multiunit firing rate averaged over trials obtained at a given spatial frequency, normalized by the average firing rate evoked by the best spatial frequency. The y-axis value of the centre of mass is the average OKR gain obtained during the same trials. All samples or animals were included in the analysis except for the following exclusions: (1) in the analysis of OKR gain, trials in which video-oculography failed as a result of eye blinking or tears were excluded from analysis; (2) in Fig. 1g, h, one mouse was excluded from the analysis because its value of OKR potentiation was less than the threshold of 0.1; (3) in Fig. 3, two mice were excluded from the analysis because they were sick and lost a lot in body weight during experiments; (4) in Figs. 4, 5, one mouse was excluded because the identification of NOT-DTN failed; and (5) in statistics of the activities of superior colliculus and vLGN, recordings which were identified post hoc as missing the target structures were excluded from the analysis. These criteria were pre-established. Statistical analyses were done using statistics toolbox in Matlab. All data are presented as mean ± s.e.m. unless otherwise noted. Statistical significance was assessed using paired or unpaired t-tests and further confirmed with nonparametric Wilcoxon signed rank test or Wilcoxon rank sum test unless otherwise noted. Estimated sample sizes were retrospectively determined to achieve 80% power to detect expected effect sizes using Matlab. We did not intentionally select particular mice for treatment group or control group. No blinding was used. Owing to the limited sample size, the assumption of normal distribution was not tested. Nonparametric tests were used to confirm statistical significances reported by paired or unpaired t-tests. Thus, the conclusions of statistical tests were validated regardless of whether the data were normally distributed. The variance was not compared between groups. In t-tests, we assumed that samples were from distributions of unknown and unequal variances. The experiments were not randomized.

News Article | February 17, 2017
Site: www.prnewswire.co.uk

Research and Markets has announced the addition of the "Cell Analysis Global Market - Forecast to 2023" report to their offering. The cell analysis market is expected to grow at high single digit CAGR to reach $47,088 million by 2023. The major factor influencing the growth is enhanced precision of cell imaging and analysis systems which in turn reduce time and cost of drug discovery process. In addition, the factors like increasing incidence of cancer, increasing government investments, funds, and grants, availability of reagents and cell analysis instruments are driving the growth of the market. However, the major market restraints include high capital investments and a shortage of skilled labor for the high content screening procedure. The biggest opportunities for this market is the emerging APAC market, high content screening services provided by contract research organizations, automation in cancer research for its early diagnosis and reduction of cost in the cancer treatment. The cell analysis global market is a competitive and all the active players in this market are involved in innovating new and advanced products to maintain their market shares. The key players in the cell analysis global market include Agilent Technologies, Inc. (U.S.), Becton Dickinson and Company (U.S.), Bio-Rad Laboratories (U.S.), Danaher Corporation (U.S.), GE Healthcare (U.K.), Merck KGAA (Germany), Olympus Corporation (Japan), PerkinElmer, Inc. (U.S.), Promega Corporation (U.S.), Qiagen N.V. (Netherlands) and ThermoFisher Scientific, Inc. (U.S.). In order to offer the products with better software, most of the players in the cell analysis market are collaborating with companies and educational institutions. - 4titude (U.K.) - AB Sciex (U.S.) - Abbott Laboratories, Inc. (U.S.) - Abcam PLC (U.S.) - Abdos (India) - Abnova Corporation (Taiwan) - ACEA Bioscience, Inc (U.S.) - Active Motif (U.S.) - Adnagen (U.S.) - Advanced Cell Diagnostics (U.S.) - Agilent Technologies, Inc. (U.S.) - Alere (U.S.) - Analytik Jena AG (Germany) - Apocell (U.S.) - Applied Microarrays (U.S.) - Ausragen (U.S.) - Auxilab S.L (Spain) - Avantes BV (Netherlands) - Aven Inc (U.S.) - Aviva Bioscience (U.S.) - Becton Dickinson and Company (U.S.) - BGI (China) - Bibby Scientific Limited (U.K.) - Bio Care Medical LLC (U.S.) - BioDot Inc. (U.S.) - Biofluidica (U.S.) - Biologics (China) - BioMerieux SA (Germany) - Bio-Rad Laboratories (U.S.) - Bioron (France) - Biosearch Technologies (U.S.) - BioView (Israel) - BMS microscopes (Netherlands) - Bruker (U.S.) - Canopus Bioscience (U.S.) - Capp ApS (Denmark) - Carl Zeiss AG (Germany) - Cell Signaling Technology, Inc. (U.S.) - Cell-Vu (U.S.) - Cherry Biotech (France) - Cisbio Bioassays (France) - Clearbridge BioMedics (Singapore) - Corning Inc (U.S.) - Creatv Microtech inc (U.S.) - Cyflogic (Finland) - Cynvenio Biosystems (U.S.) - Cytognos S.L. (Spain) - DaAn Gene (China) - Danaher Corporation (U.S.) - Danish Micro Engineering (Denmark) - Diagenode (Netherlands) - DiscoveRx (U.S.) - Domel (Slovenia) - Dragon Laboratory Instruments Ltd (China) - eBioscience, Inc., (U.S.) - Eppendorf (Germany) - Etaluma, Inc (U.S.) - Eurofins Scientific (Luxembourg) - EXIQON (Denmark) - FEI Company (U.S.) - Fluidgm Corporation (U.S.) - Fluxion Biosciences (U.S.) - GE Healthcare (U.K.) - Genedata AG (Switzerland) - Genemed Biotechnologies Inc (U.S.) - General Biologicals (Taiwan) - Gyros AB (Sweden) - Handyem (Canada) - Hausser Scientific (U.S.) - Herolab GmbH (Germany) - Hettich lab technology (Germany) - Hoffmann-La Roche (Switzerland) - HORIBA, Ltd. (Japan) - Illumina (U.S.) - Immunodiagnostics systems (France) - Jasco (U.S.) - Jena Biosciences (Germany) - JEOL, Ltd. (Japan) - Jasco Analytical Instruments (U.S.) - Kapa Biosystems (U.S.) - Keyence Corporation (U.S.) - Kyratec (Australia) - Labcon (U.S.) - Labnet International, Inc (U.S.) - Lubio Science (Switzerland) - Luminex Corporation (U.S.) - LW Scientific (U.S.) - Macrogen Inc (South Korea) - Medical Econet (Austria) - Meijo techno (U.K.) - Merck KGaA (Germany) - Mettler-Toledo, Inc. (U.S.) - Micro-shot Technology Ltd (China) - Miltenyil Biotec (Germany) - Nanostring Technologies (U.S.) - New England Biolabs (U.S.) - Nikon Corporation (Japan) - Olympus Corporation (Japan) - Optika SRL., (Italy) - Ortho Clinical Diagnostics (U.S.) - Ortoalresa (Spain) - Oxford Nanopore Technologies, Ltd. (U.K.) - Pacific Biosciences (U.S.) - Panagene (South Korea) - Park Systems (Korea) - PerkinElmer Inc (U.S.) - Pheonix (U.S.) - PicoQuant GmbH (Germany) - Promega Corporation (U.S.) - Qiagen N.V. (Netherlands) - Quest Diagnostics (U.S.) - R&D Systems (U.S.) - Rain Dance Technologies (U.S.) - Rheonix (U.S.) - Rigaku Corporation (Japan) - RR Mechatronics (Netherlands) - Sacace Biotechnologies (Italy) - Sanyo (Japan) - Scienion (Germany) - Scientific Specialities Inc (U.S.) - Seegene (South Korea) - Seimens Healthcare (Germany) - Separation Technology, Inc (U.S.) - Shimadzu Scientific Instruments (Japan) - Sigma Laborzentrifugen GmbH (Germany) - Sohn GmbH (Germany) - Sony Biotechnology (U.S.) - Sprenson Bioscience (U.S.) - Stemcell Technologies (Canada) - Sysmex (Japan) - Tecan (Switzerland) - The Western Electric & Scientific Works (India) - ThermoFisher Scientific Inc (U.S.) - Thorlabs (U.S.) - Toyo Gosei Co., Ltd (Japan) - TrimGen Genetic Diagnostics (U.S.) - Vision Scientific Co Ltd (Korea) - Visitron Systems Gmbh (Germany) - Waters Corporation (U.S.) - Yokogawa Electric Corporation (Japan) - Zymo Research (U.S.) For more information about this report visit http://www.researchandmarkets.com/research/ngm5k6/cell_analysis About Research and Markets Research and Markets is the world's leading source for international market research reports and market data. 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News Article | December 15, 2016
Site: www.businesswire.com

WASHINGTON--(BUSINESS WIRE)--An industry-academic collaboration has achieved the first optical coherence tomography (OCT) images of cubic meter volumes. With OCT’s ability to provide difficult-to-obtain information on material composition, subsurface structure, coatings, surface roughness and other properties, this advance could open up many new uses for OCT in industry, manufacturing and medicine. The achievement also represents important progress toward developing a high-speed, low-cost OCT system on a single integrated circuit chip. “Our study demonstrates world-record results in cubic meter volume imaging, with at least an order of magnitude larger depth range and volume compared to previous demonstrations of three-dimensional OCT,” said James G. Fujimoto of the Massachusetts Institute of Technology (MIT), Massachusetts. “These results provide a proof-of-principle demonstration for using OCT in this new regime.” OCT, first invented by Fujimoto’s group and collaborators in the 1990s, is now the standard of care in ophthalmology and is increasingly used in cardiology and gastroenterology. Although OCT provides useful 3-D images with micron-scale resolution, it has been limited to imaging depths of just millimeters to a few centimeters. In The Optical Society's journal for high impact research, Optica, the researchers report high speed, 3-D OCT imaging with 15-micron resolution over a 1.5-meter area. They demonstrated the new OCT approach by imaging a mannequin, a bicycle and models of a human brain and skull. They also conducted measurements of objects ranging in scale from meters to microns. In addition to the advantages of high speeds and fine resolution, OCT enables imaging, profiling and distance measurement at multiple depths simultaneously while rejecting stray light. “Long-range OCT is a new range of operation that requires extremely high performance light sources, integrated optical receivers and signal processing,” Fujimoto said. Range in OCT refers to the depth range over which measurements can be simultaneously taken. It is possible to position the center of the OCT range very close to or far away from the imaging instrument. The new technique could be particularly useful for industrial and manufacturing settings, where it could potentially be used to monitor processes, take technical measurements and nondestructively evaluate materials. Macro-scale OCT could also enhance medical imaging, for example, by providing three-dimensional measurements in laparoscopy or mapping structures such as the upper airway. The light source that enables meter-range OCT is a tunable vertical cavity surface-emitting laser (VCSEL) developed by Thorlabs Inc. and Praevium Research. It uses a MEMS device to rapidly change, or sweep, the laser’s wavelength over time to perform what is called swept-source OCT. “Research by our group at MIT and our collaborators at Praevium Research and Thorlabs indicated that the coherence length of the VCSEL source was orders of magnitude longer than other swept laser technologies suitable for OCT, which suggested the possibility of long-range OCT imaging,” said Ben Potsaid of MIT and Thorlabs Inc., coauthor of the paper. Although the MIT researchers have experimented with the VCSEL light source for several years, light detection and data acquisition remained a challenge. These hurdles were overcome by advanced optical components designed for telecommunications applications. In the new work, the researchers used a new silicon photonics coherent optical receiver developed by Acacia Communications that replaced several bulky OCT components with integrated optics on a tiny, low-cost, single-chip photonic integrated circuit (PIC). Importantly, the PIC receiver supports the very high electrical frequencies and wide range of optical wavelengths required for swept-source OCT while also enabling what is known as quadrature detection, which doubles the OCT imaging range for a given data acquisition speed. “The development of OCT in the early 1990s greatly benefited from components and methods used in fiber optical communications,” said Fujimoto. “And still, 25 years later, advances in the optical communications industry continue to greatly benefit OCT.” In the paper, the researchers showed that meter-range OCT can obtain a strong signal from surfaces of varying geometry and materials. Their tests also indicated the technique’s performance has not reached the fundamental limits for the VCSEL laser source or PIC receiver. The researchers are working to develop and utilize even more low-cost, high-speed components with the goal of speeding up the data acquisition and processing steps. This could eventually allow real-time OCT imaging using customized integrated circuit chips. “As PIC technology continues to advance, one can realistically expect full OCT systems on a single chip within the next five years, dramatically lowering the size and cost,” said Chris Doerr of Acacia Communications, coauthor of the paper. “This would allow more people all over the world to benefit from OCT and open up new applications.” Optica is an open-access, online-only journal dedicated to the rapid dissemination of high-impact peer-reviewed research across the entire spectrum of optics and photonics. Published monthly by The Optical Society (OSA), Optica provides a forum for pioneering research to be swiftly accessed by the international community, whether that research is theoretical or experimental, fundamental or applied. Optica maintains a distinguished editorial board of more than 40 associate editors from around the world and is overseen by Editor-in-Chief Alex Gaeta, Columbia University, USA. For more information, visit Optica. Founded in 1916, The Optical Society (OSA) is the leading professional organization for scientists, engineers, students and business leaders who fuel discoveries, shape real-life applications and accelerate achievements in the science of light. Through world-renowned publications, meetings and membership initiatives, OSA provides quality research, inspired interactions and dedicated resources for its extensive global network of optics and photonics experts. For more information, visit osa.org/100.

News Article | November 21, 2016
Site: www.newsmaker.com.au

This report studies Scientific CMOS (sCMOS) Camera in Global market, especially in North America, Europe, China, Japan, Southeast Asia and India, focuses on top manufacturers in global market, with production, price, revenue and market share for each manufacturer, covering  Andor  Photometrics  QImaging  PCO AG  BAE Systems  LaVision  Photonics  Leica  Scientifica  Olympus  Thorlabs  Penlink AB  Veroptics Market Segment by Regions, this report splits Global into several key Regions, with production, consumption, revenue, market share and growth rate of Scientific CMOS (sCMOS) Camera in these regions, from 2011 to 2021 (forecast), like  North America  Europe  China  Japan  Southeast Asia  India Split by product type, with production, revenue, price, market share and growth rate of each type, can be divided into  Type I  Type II  Type III Split by application, this report focuses on consumption, market share and growth rate of Scientific CMOS (sCMOS) Camera in each application, can be divided into  Application 1  Application 2  Application 3 Global Scientific CMOS (sCMOS) Camera Market Research Report 2016  1 Scientific CMOS (sCMOS) Camera Market Overview  1.1 Product Overview and Scope of Scientific CMOS (sCMOS) Camera  1.2 Scientific CMOS (sCMOS) Camera Segment by Type  1.2.1 Global Production Market Share of Scientific CMOS (sCMOS) Camera by Type in 2015  1.2.2 Type I  1.2.3 Type II  1.2.4 Type III  1.3 Scientific CMOS (sCMOS) Camera Segment by Application  1.3.1 Scientific CMOS (sCMOS) Camera Consumption Market Share by Application in 2015  1.3.2 Application 1  1.3.3 Application 2  1.3.4 Application 3  1.4 Scientific CMOS (sCMOS) Camera Market by Region  1.4.1 North America Status and Prospect (2011-2021)  1.4.2 Europe Status and Prospect (2011-2021)  1.4.3 China Status and Prospect (2011-2021)  1.4.4 Japan Status and Prospect (2011-2021)  1.4.5 Southeast Asia Status and Prospect (2011-2021)  1.4.6 India Status and Prospect (2011-2021)  1.5 Global Market Size (Value) of Scientific CMOS (sCMOS) Camera (2011-2021) 7 Global Scientific CMOS (sCMOS) Camera Manufacturers Profiles/Analysis  7.1 Andor  7.1.1 Company Basic Information, Manufacturing Base and Its Competitors  7.1.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.1.3 Andor Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.1.4 Main Business/Business Overview  7.2 Photometrics  7.2.1 Company Basic Information, Manufacturing Base and Its Competitors  7.2.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.2.3 Photometrics Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.2.4 Main Business/Business Overview  7.3 QImaging  7.3.1 Company Basic Information, Manufacturing Base and Its Competitors  7.3.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.3.3 QImaging Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.3.4 Main Business/Business Overview  7.4 PCO AG  7.4.1 Company Basic Information, Manufacturing Base and Its Competitors  7.4.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.4.3 PCO AG Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.4.4 Main Business/Business Overview  7.5 BAE Systems  7.5.1 Company Basic Information, Manufacturing Base and Its Competitors  7.5.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.5.3 BAE Systems Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.5.4 Main Business/Business Overview  7.6 LaVision  7.6.1 Company Basic Information, Manufacturing Base and Its Competitors  7.6.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.6.3 LaVision Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.6.4 Main Business/Business Overview  7.7 Photonics  7.7.1 Company Basic Information, Manufacturing Base and Its Competitors  7.7.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.7.3 Photonics Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.7.4 Main Business/Business Overview  7.8 Leica  7.8.1 Company Basic Information, Manufacturing Base and Its Competitors  7.8.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.8.3 Leica Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.8.4 Main Business/Business Overview  7.9 Scientifica  7.9.1 Company Basic Information, Manufacturing Base and Its Competitors  7.9.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.9.3 Scientifica Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.9.4 Main Business/Business Overview  7.10 Olympus  7.10.1 Company Basic Information, Manufacturing Base and Its Competitors  7.10.2 Scientific CMOS (sCMOS) Camera Product Type, Application and Specification Type I Type II  7.10.3 Olympus Scientific CMOS (sCMOS) Camera Production, Revenue, Price and Gross Margin (2015 and 2016)  7.10.4 Main Business/Business Overview  7.11 Thorlabs  7.12 Penlink AB  7.13 Veroptics

University of Lübeck, Thorlabs Gmbh and Medizinisches Laserzentrum Lubeck Gmbh | Date: 2013-10-21

There is disclosed a method for detecting spatially structured sample volumes by means of coherent light and digital holography. There is also disclosed a method for analyzing the depth structure of samples in accordance with optical coherence tomography.

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