所有动物护理，程序和实验均根据NIH指南进行，并由加利福尼亚大学旧金山大学实验室动物护理行政小组批准，并遵循法国和欧洲动物实验指南，并符合巴黎大脑学院的机构动物福利指南。在温度控制的环境（22-24°C）中，小鼠（2-5个兄弟姐妹）组成（2-5个兄弟姐妹），并随意进入食物和水，并在正常的照明条件下（12小时的灯光漆循环）饲养，直到开始规则搬运实验。所有实验均使用PV-CRE，野生型C57/BL6和PV-CRE AI14系（Jackson Laboratory）进行。男性和雌性成年小鼠（实验时在8-10周和10-20周龄）分别用于切片电生理学和行为实验。

　　使用异氟烷（2.5％诱导，1.2–1.5％的维持，95％的氧气）将雄性和雌性小鼠麻醉，并放置在立体定位框架中（David Kopf仪器）。使用加热垫保持体温。进行了一个切口，以使用Bregma和Lambda作为垂直参考，以将头骨暴露为立体定位对准。从颅骨的背侧表面取出头皮和骨膜，并用手术刀进行评分以改善植入物粘附。通过35口径的斜角注射针（世界精密仪器）使用微刺泵（世界精密仪器，UMP3 Ultromicropump）注入100–150 NL min-1的病毒。输注后，将针在注射部位保持5-10分钟，然后慢慢撤回。手术后，允许小鼠恢复直到在加热垫上进行卧床，然后返回他们的家笼子。

　　For slice electrophysiology experiments using optogenetic opsins, mice were injected unilaterally in the mPFC, near the border between the prelimbic and infralimbic cortices (1.7 anterior-posterior (AP), + or −0.3 mediolateral (ML), and −2.75 dorsoventral (DV) mm relative to bregma) with 0.4 μl ofAAV5-EF1α-DIO-CHR2-EYFP（UNC矢量核）有选择地靶向表达CRE的神经元。为了允许病毒表达，注射后至少三周开始实验。为了逆行标记MPFC神经元，该标记是call染色与中等多形（MD）丘脑的投影，霍乱毒素亚基B（CTB）与Alexa Fluor 488（CTB-488，Invitrogen，Invitrogen，Invitrogen，Invitrogen，Invitrogen； 0.2％W/V，400 nl）Indio in a ips in opt ips Indref Ipt ips ips in in in in in in in in in in in ar a alexa fluor 488（ctb-488）。（1.7 AP，-0.4 mL和-2.5 DV MM相对于董事）和Alexa Fluor 594偶联的CTB（CTB-594，Invitrogen； Invitrogen; 0.2％W/V，400 NL）在MD thalamus中注入MD Thalamus（对比）（对比）（对比）（对比AAV-Dio-dio-dio-dio-dio-dio-dio-dio-dio-dio-dio-dio-dio-dio-dio 37）（ +/0.11）。相对于董事，-3.5 dv mm）。在NAC中注入NAC（0.2％w/v，400 nl）的MPFC神经元的逆行标记，CTB-488（0.2％w/v，400 nl）被注入NAC（与AAV-DIO-CHR2相对的对比）w/v，600 nL）被注入背侧纹状体（也与AAV-DIO-CHR2注射对侧）（+0.9 AP，+1.1.16 mL，-3.0 DV mm相对于胸膜）。为了让CTB的逆行运输时间，在注射CTB后一周开始了实验。

　　对于使用ENPHR和对照光遗传学的行为实验，将小鼠单方面注入MPFC，附近，近距离和额叶皮层之间的边界（1.7 AP， +或-0.3 mL，相对于Bregma相对于Bregma相对于1μlAav2-Fectore）1μ-EF2-EF1-FETER）（1.7 ap， +或-2.3 mL，-2.75 dV mm）。μL的AAV5-EF1α-DIO-EYFP（UNC矢量核心），AAV5-HSYNAPSIN-ENPHR3.0-EYFP（UNC矢量核心）或AAV5-HSYNAPSIN-TDTOMATO（UNC矢量核心），以选择性地靶向表达CRE的细胞或非主靶向靶向靶向前五角脑前神经元。注射病毒后，将200/240μM（核/外）直径为NA = 0.22，单纤维光插管（Doric镜头，MFC_200/240-0.22_2.3mm_flt）缓慢地插入MPFC中，直到纤维尖端延伸到dv深度为−2.25。使用metabond快速粘合剂（Parkell）将植入物固定在头骨上。为了允许病毒表达，行为实验至少在注射后五个星期开始。

　　对于使用NPHR和CHR2光遗传学的行为实验，将小鼠单方面注入MPFC，靠近前BIC和INIMBIC皮层之间的边界（1.7 AP，-0.3 mL，-2.75 dV mm相对于Bregma，相对于Bregma），添加了0.75μlAav8-n-n-fonf（Bregma）。0.75μL的AAV8-NEF-CON/FON-CHR2-MCHERRY（addgene）或0.75μlAAV8-EF1α-CON/FON-MCHERRY（addgene）和对侧PFC（1.7 AP，1.7 AP，+0.3 mL，+0.3 mL，+0.3 mL， +0.3 ml，-2.75 dVMM）与0.75 dVMM相对于0.7 dvrp.77 frp，在同侧PFC中有选择地靶向表达CRE的细胞，这些细胞将投影发送到对侧PFC。注射病毒后，将200/240μM（核/外）直径为NA = 0.22，单纤维光插管（Doric镜头，MFC_200/240-0.22_2.3mm_flt）缓慢地插入MPFC中，直到纤维尖端延伸到dv深度为−2.25。使用metabond快速粘合剂（Parkell）将植入物固定在头骨上。为了允许病毒表达，行为实验至少在注射后五个星期开始。

　　对于将双位点电压指示剂与光遗传学结合的行为实验，将小鼠在3个深度（DV：-2.5，-2.25和-2.0）以接下来的AP/mL进行双侧注射（DV：-2.5，-2.25和-2.0），用于MPFC：1.7 AP：1.7 AP，±0.3 ml，±0.3 ml，3×0.2×0.2×0.2μlAav1-ace-ace-ace-ace-ace-mneon（vira）2n-ace-mneon（还以1μlAAV2-EF1α-DIO-ENPHR3.0-BFP（ViroVek）或1μLAAV5-EF1α-DIO-MCHERRY（Unc-ef1α-Dio-Mcherry（Unc-Mcherry）（UNC VECTOR CORER）（UNC VECTOR CORER），与MPFC（1.7 ap，-0.3 mL和-2.75 dv mM相对于董事）也单方面注射。AAV2-HSYNAPSIN-ENPHR3.0-MCHERRY（UNC矢量核）或1μLAAV2-HSYNAPSIN-MCHERRY（UNC矢量核心）。注射病毒后，将两个400/430μm（核/外）直径，NA = 0.48，多模纤维植入物（Doric镜头，MFC_400/430-0.48_2.8_2.8mm_zf1.25_flt）缓慢地插入MPFC中，使用下一个coildites，MPFC缓慢地插入MPFC中。-2.14（DV）。为了允许病毒表达，行为实验至少在注射后五个星期开始。

　　对于将体内钙成像与光遗传学结合结合的行为实验，将小鼠在4个深度（DV：-2.75，-2.5，-2.25，-2.25，-2.0）下单侧注入以下AP/ML，用于MPFC：1.7 AP，+0.4 ml，+0.4 ml，+0.4 ml（+0.4 mL）AAV9-SYNAPSIN-JGCAMP7F-WPRE（addgene）。还将小鼠单方面地注入对侧MPFC（1.7 AP，-0.3 mL和-2.75 dV mM相对于Bregma），用1μLAAV2-EF1α-DIO-ENPHR3.0-MCHERRY（UNC VIRUS）（UNC VIRUS），1μLAV5-EF1α-DIO-MCHERRY（1μlAAV2-HSYNAPSIN-ENPHR3.0-MCHERRY（UNC病毒核心）或1μLAAV2-HSYNAPSIN-MCHERRY（UNC病毒核心）。注射病毒后，慢慢将0.5 mm×4.0 mm长的整合笑透镜（INSCOPIX）慢慢前进到MPFC中，直到将尖端置于1.7 AP，+0.4 ml，+0.4 ml，DV-2.25，并用metabond快速粘合剂（Parkell）固定在适当的位置。为了允许病毒表达，行为实验至少在注射后五个星期开始。

　　使用异氟烷麻醉成年小鼠并斩首，并迅速去除其大脑。使用振动型（VT1200S Leica微型系统）和冷冻切片溶液从成年小鼠的成年小鼠中切出冠状切片（250μm厚），其中Na+被蔗糖代替，然后在30-31°C的30-31°C下在30-31°C的室内孵育，然后在15分钟和室内进行录像，然后在30-31°C的室内进行孵育。ACSF包含（以毫米为单位）：126 NaHCO3，2.5 KCl，1.25 NaH2PO4，1 MGCL2，2 CaCl和10个葡萄糖。通过在两个半球之间的中线放置竖琴来确保切片。

　　在直立显微镜（BX51WI; olympus）上，在MPFC的ChR2阳性轴突纤维对侧的ChR2阳性轴突纤维（BX51WI; Olympus）的MPFC中获得了体细胞全细胞记录。使用多灯700A（分子设备）进行录音。贴片电极（尖端电阻= 2-6 MOHM）填充以下（以mm为单位）：130葡萄糖酸钾，10 kCl，10 hepes，10 egta，2 mgcl2，2 mgcl2，2 mgATP和0.3 NAGTP（用KOH调整为7.3 pH）。所有记录均为32.5±1°C。串联电阻通常为10–20MΩ，实验在30MΩ以上停止。

　　基于对250毫秒电流注射量从-200到450 PA的250毫秒电流注射的电流钳反应计算固有特性（每增加50 pa）。基于对当前脉冲的响应的响应，该脉冲比引起尖峰的最小水平高出100 pa。如果神经元在以下标准中遇到3个：动作电位（AP）半宽，则将神经元分类为快速峰值。 < 0.5 ms, firing frequency > 50 Hz，超极化后快速（FAHP）振幅> 14 mV和尖峰频率适应（SFA）指数 < 2.

　　Stimulation of channelrhodopsin (ChR2) in callosal PV terminals was performed using ~4–5 mW flashes of light generated by a Lambda DG-4 high-speed optical switch with a 300 W Xenon lamp (Sutter Instruments) or by an LED (Cairn Research OptoLED Lite), and an excitation filter set centred around 470 nm, delivered to the slice through a 40× objective (Olympus). Illumination was delivered across a full high-power (40×) field. To measure IPSPs, current-clamp recordings were performed while stimulating ChR2 using trains of light pulses (5 ms light pulses at 5 Hz, 20 Hz, and 40 Hz). In experiments in which glutamatergic and GABAA receptors were blocked, drugs were bath applied at the following concentrations (in μM): 10 CNQX (Tocris) or 20 DNQX (Tocris), 50 APV (Tocris), and 10 gabazine (Sigma). Drugs were prepared as concentrated stock solutions and were diluted in ACSF on the day of the experiment.

　　This cognitive flexibility task has been described previously6. In brief, mice are singly housed and habituated to a reverse light/dark cycle, and food intake is restricted until the mouse is 80–85% of the ad libitum feeding weight. After mice reached their target weight, they underwent one day of habituation. On this day, mice were given ten consecutive trials with the baited food bowl to ascertain that they could reliably dig and that only one bowl contained food reward. All mice were able to dig for the reward, and started the task the next day. At the start of each trial, the mouse was placed in its home cage to explore two bowls, each containing one odour and one digging medium, until it dug in one bowl, signifying a choice. As soon as a mouse began to dig in the incorrect bowl, the other bowl was removed, so there was no opportunity for ‘bowl switching’ (digging is defined as the sustained displacement of the medium within a bowl). The bait was a piece of a peanut butter chip (approximately 5–10 mg in weight) and the cues, either olfactory (odour) or somatosensory and visual (texture of the digging medium which hides the bait), were altered and counterbalanced. All cues were presented in small animal food bowls (All Living Things Nibble bowls, PetSmart) that were identical in colour and size. Digging media were mixed with the odour (0.01% by volume) and peanut butter chip powder (0.1% by volume). All odours were ground dried spices (McCormick or Alpi Nature garlic and McCormick or Albert Ménès coriander), and unscented digging medium (Mosser Lee White Sand Soil Cover or Scalare Sable de Rivière, Natural Integrity Clumping Clay or Monoprix cat litter).

　　After mice reached their target weight, they underwent one day of habituation. On this day, mice were given ten consecutive trials with the baited food bowl to ascertain that they could reliably dig and that only one bowl contained food reward. Specifically, the habituation trials are used to train the mouse on the mechanics of the task, there is no association made between food reward and cue. All mice were able to dig for the reward. Mice do not undergo any other specific training before being tested on the task. Then, on days 1 and 2 (and in some cases, on additional days as well), mice performed the task (this was the testing done for experiments). After the task was done for the day, the bowls were filled with different odour–medium combinations and food was evenly distributed among these bowls and given to the mouse so that no specific cue was rewarded greater than the other cues present. The same stimuli were used across days—only the cue that is associated with the food reward changed.

　　Mice were tested through a series of trials. The determination of which odour and medium to pair and which side (left or right) contained the baited bowl was randomized (subject to the requirement that the same combination of pairing and side did not repeat on more than three consecutive trials) using https://www.random.org. On each trial, while the particular odour–medium combination present in each of the two bowls may have changed, the particular stimulus (for example, a particular odour or medium) that signalled the presence of food reward remained constant over each portion of the task (initial association and rule shift). If the initial association paired a specific odour with food reward, then the digging medium would be considered the irrelevant dimension. The mouse is considered to have learned the initial association between stimulus and reward if it makes eight correct choices during ten consecutive trials. Each portion of the task ended when the mouse met this criterion. Following the initial association, the rule-shift portion of the task began, and the particular stimulus associated with reward underwent an extra-dimensional shift. For example, if an odour had been associated with reward during the initial association, then a digging medium was associated with reward during the rule-shift portion of the task. The mouse is considered to have learned this extra-dimensional rule shift if it makes 8 correct choices during ten consecutive trials. When a mouse makes a correct choice on a trial, it is allowed to consume the food reward before the next trial. Following correct trials, the mouse is transferred from the home cage to a holding cage for about 10 s while the new bowls were set up (ITI). After making an error on a trial, a mouse was transferred to the holding cage for about 2 min (ITI). For Extended Data Fig. 4p–z, the ITI following errors was 30 s in the holding cage. All animals performed the initial association in a similar number of trials (average: 10–15 trials). Experiments were performed blind to the virus injected. Videos were manually scored with a temporal resolution of 1 s.

　　For analyses (described below), the onset of digging was chosen as the time of a decision for two reasons. First, as noted above, once a mouse began to dig in the incorrect bowl, the other (correct) bowl was removed. Second, only upon the commencement of digging could a mouse determine whether reward was present in the chosen bowl and obtain feedback about whether or not it had made a correct choice. The time windows used for analysis excluded periods when the mouse moved from the home cage to the holding cage and vice versa.

　　This cognitive flexibility task was described previously6,8. Similarly to the mechanics of the rule-shift task described above, after the initial association, the rule-reversal portion of the task began, and the particular stimulus associated with reward underwent an intra-dimensional reversal. For example, if an odour had been associated with reward during the initial association, then the previously unrewarded odour became associated with reward during the rule-reversal portion of the task. The mouse was considered to have learned the intra-dimensional rule reversal when it made eight correct choices out of ten consecutive trials.

　　For behavioural experiments using optogenetic eNpHR stimulation: A 532 nm green laser (OEM Laser Systems) was coupled to the mono fibre-optic cannula (Doric Lenses) with a zirconia sleeve (Doric Lenses) through a 200-μm-diameter mono fibre-optic patch cord (Doric Lenses) and adjusted such that the final light power was 2.5 mW. For behavioural experiments using optogenetic ChR2 stimulation: A 473 nm blue laser (OEM Laser Systems) was coupled to the mono fibre-optic cannula (Doric Lenses) with a zirconia sleeve (Doric Lenses) through a 200 μm diameter mono fibre-optic patch cord (Doric Lenses, Inc.) and adjusted such that the final light power was 0.5 mW. A function generator (Agilent 33500B Series Waveform Generator) connected to the laser generated a 40-Hz train of 5-ms pulses.

　　Extended Data Fig. 2 shows experiments designed to control for potential behavioural effects of scattered light from one hemisphere activating eNpHR in PV neuron cell bodies in the contralateral hemisphere. These experiments used a final light power of 0.1 mW when connected to the 532 nm green laser (OEM Laser Systems) or 638 nm red laser (Doric Lenses). To determine the appropriate light power for these experiments, a mouse was implanted with a dual fibre-optic cannula (Doric Lenses; DFC_200/240-0.22_2.3mm_GS0.7_FLT) without virus injection in order to measure light scattering from one mPFC to the contralateral hemisphere. Using a dual fibre-optic patch cord (Doric Lenses; DFP_200/240/900-0.22_2m_GS0.7-2FC), light was delivered to the mPFC on one side, and the light coming through the other side was measured using a light meter (ThorLabs, PM100D). The final light power delivered to one mPFC was 2.5 mW, across wavelengths 532 nm, 594 nm, and 638 nm—similar to what was used in the optogenetic and optogenetic and dual-site voltage indicator experiments. Measurements of 40 nW, 20 nW, and 50 nW at the contralateral fibre were observed, respectively. Accounting for transmission loss of the patch cord (for example, only 80% of the light is transmitted from end to end), the scattered light power entering the fibre tip would be 50 nW, 25 nW and 62.5 nW respectively. This measurement likely overestimates the actual light entering via the fibre tip located in brain parenchyma since it will include both scattered light within the brain and contamination from ambient room light. Conversely, this measurement only includes light located in the vicinity of the fibre tip that is traveling at an appropriate angle to enter the fibre (which has numerical aperture 0.22 implying a 25.4° acceptance angle). Therefore, to be extremely conservative, experiments in Extended Data Fig. 2 utilized a final light power of 0.1 mW, which is >比测得的散射光功率强1,000倍。在此最终的光功率同侧，使用了532 nm和638 nm的病毒注射部位。

　　Experiments in Extended Data Fig. 2l–o were similar to other experiments using optogenetic eNpHR stimulation except in the following respects: mice were injected with 0.7 μl of AAV2-EF1α-DIO-eNpHR3.0-mCherry (UNC Vector Core) and 0.4 μl of AAV5-EF1α-DIO-ChR2-eYFP (UNC Vector Core), to selectively target Cre-expressing cells (although在这些实验中最终未使用CHR2刺激）。在ITIS期间（小鼠在固定笼中）在第2天（当时，在试验期间，在主机笼中关闭了光遗传学ENPHR刺激的光）。

　　对于所有光遗传实验，一旦小鼠在任务的初始关联部分达到80％的标准，就开始了光刺激。然后，在任务的规则转移部分开始之前，小鼠进行了三项针对光刺激的初始关联试验。在初始关联的这三个额外试验中，光刺激并没有改变小鼠的性能或行为。对注射病毒视而不见的实验。

　　使用双站点电压指示剂技术在每个记录位点测量高带宽，随时间变化的大量荧光信号8，如下所述进行了一些修改。

　　纤维式固执（400μm核心，Na = 0.48，低自动荧光纤维；多立克镜，MFC_400/430-0.48_2.8mm_zf1.25_flt），将其固定在每个靶标的大脑区域中。匹配的纤维光贴片线（Doric镜头，MFP_400/430/1100-0.48_2M_FC-ZF1.25）提供了动物和微型之间的轻路，永久性地对齐光学基础或“ Mini-Cube”（Mini-Cube”（Doric镜头，Doric镜头，，Dorcor镜头，，Doric镜头，，Doric镜头，，Doric镜头，，Doric镜头，，Doric Cuble，，，Dorcor镜头，，，Dorcior镜头，，Dorcior镜头，，，Dorcire corm，Doric Cube'FMC5_E1（460-490）_f1（500-540）_e2（555-570）_F2（580-600）_s _s）。在病毒注射1μlAAV2-EF1α-Dio-Enphr3.0-BFP（Virovek）或1μLAAV5-EF1α-Dio-MCherry（UNC vector Core）的同侧的同侧侧的一根纤维都用于从该记录的位点传递激发光和发出的荧光。病毒注射部位对侧的纤维与单独的迷你立方体连接（Doric镜头，FMC6_E1（460-490）_F1（500-540）_e2（555-570）_F2（555-570）_f2（580-600）_O（580-600）_O（580-600）_O（628-642）镜片），并用于从该记录位点传递激发光和光遗传学刺激，并收集发射的荧光。在每次记录之前，用异丙醇清洁贴片线和每个直径1.25毫米的氧化锆光植入物套圈，然后通过氧化锆套筒牢固地固定。

　　对于第一个迷你立方体SANS激光器端口，光学允许同时监视两个频谱分离的荧光团，并选择了用于匹配电压传感器的激发和发射光谱的DiChroic镜子和清理过滤器，并且使用了“ Mneon”使用（Mneon'电流传感器频道：激发460-460-460-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90-90 nm’;荧光团：激发555-570 nm，发射580–600 nm）。迷你立方体光学元件被密封并永久对齐，所有五个端口（样本到动物，两条激发线和两条发射线）均配备匹配的耦合光学元件和FC连接器，以允许模块化系统设计。

　　对于包含用于光遗传学刺激的端口的第二个迷你立方体，使用565 nm的LED和555-570 nm滤波器来激发TDTOMATO，使用580-600 nm滤波器用于TDTOMATO发射，并使用638 nm激光，用于628-642 nm filter fircite Enphr。用于激发ENPHR的光不会干扰基于遗传编码的基于同步的遗传编码的电压指示器，并且用于激发TDTomato的光无法激活ENPHR足以影响迁移性能。这是由于两个因素。首先，ENPHR和TDTOMATO激发光谱被抵消 - 例如，在605 nm处，ENPHR激活接近其峰值，而TDTOMATO的相对激发是 <1%. Second, the intensity used to excite tdTomato is just ~0.1 mW, which is ~50-fold less than what was used to activate eNpHR and disrupt rule-shift performance. The mini-cube optics are sealed and permanently aligned and all six ports (sample to animal, three excitation lines and two emission lines) are provided with matched coupling optics and FC connectors to allow for a modular system design.

　　To perform dual-site voltage indicator recordings, excitation light for each of the two colour channels was provided by a fibre-coupled LED (Center wavelengths 490 nm and 565 nm, Thorlabs M490F3 and M565F3) connected to the mini-cube by a patch cord (200 μm, NA = 0.39; Thorlabs M75L01). Using a smaller diameter for this patch cord than for the patch cord from the cube to the animal is critical to reduce the excitation spot size on the output fibre face and thus avoid cladding autofluorescence. LEDs were controlled by a 4-channel, 10-kHz-bandwidth current source (Thorlabs DC4104). LED current was adjusted to give a final light power at the animal (averaged during modulation, see below) of approximately 200 μW for the mNeon channel (460–490 nm excitation), and 100 μW for the Red channel (555–570 nm excitation).

　　Each of the two emission ports on the mini-cube was connected to an adjustable-gain photoreceiver (Femto, OE-200-Si-FC; Bandwidth set to 7 kHz, AC-coupled, ‘low’gain of ~5 × 107 V W−1) using a large-core high-NA fibre to maximize throughput (600 μm core, NA = 0.48 (Doric lenses, MFP_600/630/LWMJ-0.48_0.5m_FC-FC).

　　Note that, for dual-site voltage indicator recordings and optogenetics experiments, two completely independent optical setups were employed, with separate implants, patch cords, mini-cubes, LEDs, a separate laser, photoreceivers, and lock-in amplifiers.

　　At each recording site, each of the two LEDs was sinusoidally modulated at a distinct carrier frequency to reduce crosstalk due to overlap in fluorophore spectra. The corresponding photoreceiver outputs were then demodulated using lock-in amplification techniques. A single instrument (Stanford Research Systems, SR860) was used to generate the modulation waveform for each LED and to demodulate the photoreceiver output at the carrier frequency. To further reduce crosstalk between recording sites, distinct carrier frequencies (2, 2.5, 3.5 and 4 kHz) were used across sites. Low-pass filters on the lock-in amplifiers were selected to reject noise above the frequencies under study (cascade of 4 Gaussian FIR filters with 84 Hz equivalent noise bandwidth; final attenuation of signals are approximately −1dB (89% of original magnitude) at 20 Hz, −3dB (71% of original magnitude) at 40 Hz, and −6dB (50% of original magnitude) at 60 Hz).

　　Analogue signals were digitized by a multichannel real-time signal processor (Tucker-Davis Technologies; RX-8). The commercial software Synapse (Tucker-Davis Technologies) running on a PC was used to control the signal processor, write data streams to disk, and to record synchronized video from a generic infrared USB webcam (Ailipu Technology, ELP-USB100W05MT-DL36). Lock-in amplifier outputs were digitized at 3 kHz.

　　Analysis of voltage indicator data was described previously8 and was facilitated using the signal processing toolbox and MATLAB (Mathworks), using the following functions: fir1, filtfilt, and regress. All four signals during the entire time series of the experiment (left mNeon, left tdTomato, right mNeon, right tdTomato) were first filtered around a frequency of interest. To quantify zero-phase lag cross-hemispheric synchronization between left and right mNeon signals, a linear regression analysis was performed to predict the right mNeon signal using the following inputs: left mNeon signal, left tdTomato signal, and right tdTomato signal. The goodness of fit is compared to how well the regression works if the left mNeon signal is shuffled, i.e., if a randomly chosen segment of the original left mNeon signal is used, instead of the segment recorded at the same time as the right mNeon signal. R2 values are calculated as a function of time using one second segments and compared to the 99th percentile of the distribution of R2 values obtained from 100 fits to randomly shuffled data. The fraction of time points at which the R2 obtained from actual data exceeds the 99th percentile of the R2 values obtained from shuffled data was used to measure zero-phase lag synchronization between the left and right mNeon signals.

　　This analysis was performed at the time of the decision (for example, immediately following the beginning of digging in one bowl, until the end of digging), and smoothed measurements over a 5-min time window following the time point of interest. The first five trials of the rule shift were analysed. Experiments were performed, scored and analysed blind to virus injected.

　　For high temporal resolution quantification of synchrony between signals from dual-site voltage indicator recordings, we first bandpass-filtered Ace-mNeon and tdTomato signals as described above. Then, we ‘corrected’ the filtered Ace-mNeon signal (to minimize artefacts and noise) by fitting the ipsilateral filtered tdTomato signal via robust linear regression using the robustfit function in Matlab and a time windows of 250 ms. Then, we subtracted off this fit of the tdTomato signal from the filtered Ace-mNeon signal to obtain a corrected Ace-mNeon signal. We then calculated zero-lag cross-correlation between the corrected Ace-mNeon signals from the left and right mPFC across the whole session using 1-s windows.

　　Imaging data were collected using a miniaturized one-photon microscope (nVoke2; Inscopix). GCaMP7f signals (calcium activity) were detected using 435–460 nm excitation LED (0.1–0.2 mW), and optogenetic stimulation of eNpHR-expressing axons was performed using a second 590–650 nm excitation LED (1–2 mW light power). nVoke2 software (Inscopix) was used to control the microscope and collect imaging data. Images were acquired at 20 frames per second, spatially downsampled (4×), and were stored for offline data processing. An input TTL from a separate ANY-maze computer (Stoelting Europe) to the nVoke2 acquisition software were used to synchronize calcium imaging and mouse behaviour movies.

　　Calcium-imaging movies were preprocessed using Inscopix Data Processing Software (IDPS; Inscopix). The video frames were spatially filtered (bandpass) with cut-offs set to 0.008 pixel−1 (low) and 0.3 pixel−1 (high) followed by frame-by-frame motion correction for removing movement artefacts associated with respiration and head-unrestrained behaviour. The mean image over the imaging session was computed, and the dF/F was computed using this mean image. The resultant preprocessed movies were then exported into MATLAB, and cell segmentation was performed using an open-source calcium-imaging software (CIAPKG)30. Specifically, a principal component analysis/independent component analysis (PCA/ICA) approach was used to detect and extract regions of interest (presumed neurons) per field of view31. For each movie, the extracted output neurons were then manually sorted to remove overlapping neurons, neurons with low signal-to-noise ratio, and neurons with aberrant shapes. Accepted neurons and their calcium activity traces were exported to MATLAB for further analysis using custom scripts as previously described32. In brief, the s.d. (σ) of the calcium movie was calculated and this was used to perform threshold-based event detection on the traces by first detecting increases in dF/F exceeding 2 (over 1 s). Subsequently, events were detected that exceeded 10 for over 2 s and had a total area under the curve higher than 150σ. The peak of the event was estimated as the local maximum of the entire event. For an extracted output neuron, active frames were marked as the period from the beginning of an event until the calcium signal decreased 30% from the peak of the event (up to a maximum of 2 s).

　　We calculated the similarity of population activity vectors using the ‘cosine similarity’, which is equivalent to computing the normalized dot product between the two vectors, that is:

　　where xi and yi represent the average activity of the ith neuron in the two population activity vectors. Each vector was the average of activity during the 10 s immediately following a choice. We computed the similarity between each pair of vectors, then averaged this similarity across all the pairs from one mouse.

　　The first five trials of the rule shift were analysed. For Extended Data Fig. 10t–u, the last five initial association trials and the additional initial association trials during optogenetic inhibition were analysed.

　　All mice used for behavioural and imaging experiments were anaesthetized with Euthasol and transcardially perfused with 30 ml of ice-cold 0.01 M PBS followed by 30 ml of ice-cold 4% paraformaldehyde in PBS. Brains were extracted and stored in 4% paraformaldehyde for 24 h at 4 °C before being stored in PBS. Slices 70–100 μm thick were obtained on a Leica VT100S and mounted on slides. All imaging was performed on an Olympus MVX10, Nikon Eclipse 90i, Zeiss LSM510, Zeiss Axioskop2, Zeiss ApoTome.2, and Keyence BZ-X All-in-One Fluorescence Microscope. All mice were verified to have virus-driven expression and optical fibres located in the mPFC. For mice used in parvalbumin immunohistochemistry, 60-μm slices from PV-cre mice injected with AAV2-EF1α-DIO-ChR2-eYFP unilaterally in PFC were obtained on a Leica VT100S and were rinsed twice at room temperature (10 min each) in PBS and incubated overnight at 4 °C with 0.3% Triton X-1000, 0.1% normal donkey serum (NDS) and monoclonal anti-PV antibody (1:1,000; Sigma). Slices were then rinsed twice in PBS (10 min each) at room temperature and incubated with Alexa 688 goat anti-mouse antibody (1:500; Invitrogen) for 3 h at room temperature. Slices were then rinsed twice in PBS (10 min each) at room temperature and coverslipped in mounting medium. Immunofluorescence was then observed with Zeiss ApoTome.2 and images were acquired.

　　Statistical analyses were performed using Prism 8 (GraphPad) and detailed in the corresponding figure legends. Quantitative data are expressed as the mean and error bars represent the s.e.m. Group comparisons were made using two-way ANOVA followed by Bonferroni post hoc tests to control for multiple comparisons unless otherwise noted. Paired and unpaired two-tailed Student’s t-tests were used to make single-variable comparisons. Similarity of variance between groups was confirmed by the F test. Measurements were taken from distinct samples and from samples that were measured repeatedly. *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001. Comparisons with no asterisk or ‘NS’ had P > 0.05 and were considered not significant. No statistical methods were used to pre-determine sample sizes but our sample size choice was based on previous studies6,8 and are consistent with those generally employed in the field. Data distribution was assumed to be normal, but this was not formally tested.

　　For Fig. 3d,e,k,l, full statistics are: optogenetic inhibition of callosal mPFC PV terminals impairs rule shifts in DIO-eNpHR mice (n = 5) compared to DIO-mCherry controls (n = 4) on days 2 and 3 (two-way ANOVA (task day × virus); interaction: P = 0.0009). d, DIO-mCherry performance did not change (day 1 to 2: P = 0.28; day 1 to 3: P = 0.094; day 2 to 3: P >0.99）。d，e，k，l，双向方差分析（任务日×病毒）比较跨组的规则转移（RS）性能（相互作用：P< 0.0001), showed no group difference on day 1 but significant impairment on days 2 and 3 for DIO-eNpHR compared to DIO-mCherry and Syn-tdTomato. e, Optogenetic inhibition of mPFC callosal PV terminals impairs rule shifts in DIO-eNpHR mice compared to DIO-mCherry controls (day 1 to 2: P = 0.014; day 1 to 3: P = 0.012; day 2 to 3: P = 0.075). For Fig. 3f,g, full statistics are: 30–50 Hz synchronization is higher after RS errors than after RS correct decisions across task days in controls (n = 4 mice; two-way ANOVA; main effect of trial type: P = 0.0056; day 1: P = 0.004; day 2: P = 0.005; day 3: P = 0.022). g, Gamma synchrony is higher after RS errors than after RS correct decisions for DIO-eNpHR mice on day 1 (no light), but not days 2 and 3 (n = 5 mice; two-way ANOVA (trial type × task day); interaction: P = 0.0039; day 1: P = 0.0056; day 2: P = 0.16; day 3: P = 0.23). Differences in gamma synchrony between RS errors and correct trials are also significantly lower in DIO-eNpHR mice compared to controls on days 2 (two-way ANOVA (trial type × virus); interaction: P = 0.018) and 3 (two-way ANOVA (trial type × virus); interaction: P = 0.034). We then performed two-way ANOVA (task day × virus, type of error) comparing gamma synchrony across groups with appropriate post hoc tests corrected for multiple comparisons; gamma synchrony is lower for DIO-eNpHR mice compared to matched controls on error (interaction: P = 0.049), but not correct trials (interaction: P = 0.93) on both days 2 (P = 0.0089) and 3 (P = 0.016). For Fig. 3k–n, full statistics are: inhibiting callosal terminals does not affect rule shifts in Syn-eNpHR mice (n = 5) compared to controls (n = 4) across days (two-way ANOVA (task day × virus); P = 0.37). k, Performance of controls did not change across days (day 1 to 2: P = 0.48; day 1 to 3: P >0.99;第2至3天：P> 0.99）。l，综合体的性能不会在几天内发生变化（第1至2：p> 0.99;第1至3：p = 0.96;第2至3天：p = 0.85）。M，在RS误差后，半球间的30–50 Hz同步比对照组中的RS正确决策高（N = 4小鼠；双向方差分析；试验类型的主要效果：P = 0.020; P = 0.020;第1天：P = 0.015;第2天；第2天：P = 0.049; day 3：P = 0.025：P = 0.025）。n，在RS错误后伽马同步比在第1天（无光）的RS正确决策的RS更高。第2天用光废除，然后在第3天没有光线（n = 5小鼠；双向方差分析;（试用类型×任务日）；相互作用：P = 0.011;第1天：P = 0.037；第2天；第2天：P = 0.46：P = 0.46；第3天；第3：P = 0.021）。与误差（双向方差分析；相互作用：p = 0.045）相比，Syn-eNPHR小鼠的伽马同步较低，但在第2天（p = 0.043），但不是正确的试验（相互作用：P = 0.74），但在第3天（p = 0.58）（p = 0.58）。使用双向方差分析，然后使用Bonferroni事后比较。

　　For Fig. 4d–f, full statistics are: optogenetic inhibition of callosal PV terminals impairs rule shifts in DIO-eNpHR mice (n = 6) compared to controls (n = 6) and Syn-eNpHR mice (n = 6) on days 2 and 3 (two-way ANOVA (task day × virus); interaction: P< 0.0001). d, Performance of controls did not change (day 1 to 2: P = 0.057; day 1 to 3: P = 0.12; day 2 to 3: P = 0.67). e, Optogenetic inhibition of callosal PV terminals impairs rule shifts in DIO-eNpHR mice (day 1 to 2: P = 0.020; day 1 to 3: P = 0.010; day 2 to 3: P >0.99）。F，Syn-Enphr小鼠的性能没有改变（第1天至第2天：P = 0.58；第1至3：P = 0.82；第2至3天：P> 0.99）。对于图4H，J，完整的统计数据为：光遗传学抑制改变了专门在二型雌性小鼠中的活性向量的相似性（双向ANOVA，任务日的主要影响：P = 0.017;任务日×组相互作用：P = 0.32）。h，对于对照（n = 6只小鼠），在RS误差之后的活动向量与正确决策后的活动向量之间的相似性之间没有变化（第1至第2天P = 0.57;第1至1至3：P = 0.32：P = 0.32;第2至3：P = 3：P = 0.90）。i，在二胺（n = 6只小鼠）中，rs错误后的活动向量与第1天（原遗传抑制之前）到第2天到第2天（分别抑制期间和之后）（第1至1至2：p = 0.044; p = 0.044; 1至1至3：p = 0.00067; p = 0.0067; d day; d day; p y of第1天（分别抑制）之间的相似性有所增加。J，对于Syn-Enphr小鼠（n = 6只小鼠），在RS误差之后的活动向量与正确决策后的活动向量之间的相似性之间没有变化（第1至2天P = 0.99;第1至1至3天：P = 0.93：P = 0.93; Day 2至3：2至3：P = 0.98）。双向方差分析比较了二键型组中从第1天到第2天的活动矢量相似性的变化与由eNPHR阴性和突触素 - 增生小鼠组成的组，使用鼠标，DAY和DAY×组相互作用作为因素显示出显着的DAY×组相互作用（P = 0.040）。K -M，在首次关联期间（IA）和Rs期间进行错误试验的决定后向量之间的相似性。在二下小鼠中，几天的相似性增加（n = 6;双向方差分析（任务日×病毒）；相互作用：p = 0.025）。k，在对照组中，在IA误差和RS错误之后的种群活动矢量的相似性没有变化（n = 6;第1天至第2天：P = 0.99;第1至3：P = 0.52；第2至3天：P = 0.50）。l，在第2天和第3天的光遗传学抑制中 在IA与RS错误试验之后，人口活动媒介的相似性有所增加（第1至2天：P = 0.0038;第1至3天：P = 0.0045;第2至3天：P = 0.95）。M，在同步型小鼠中，在IA之后，人口活动向量与RS误差试验的相似性没有变化（n = 6;第1天至2：p = 0.41; p = 0.41;第1天至3：p = 0.90; p = 0.90;第2至3：p = 0：p = 0.24）。n, Controls have increases in average activity (fraction of frames in which a neuron is active, averaged across all neurons) during the 10 s following RS errors compared to the 10 s following RS correct decisions on all days (n = 6; two-way ANOVA, main effect of trial type: P = 0.010; day 1: Bonferroni P = 0.022; day 2: Bonferroni P = 0.015; day 3: Bonferronip = 0.016）。o，二二烷基小鼠的平均活性在误差后的平均活性增加（n = 6;双向方差分析（任务日×试验类型）；相互作用：p = 0.0003）。这种差异发生在第1天（Bonferroni P< 0.0001), but is abolished with light delivery on day 2 (Bonferroni P >0.99），即使在第3天没有进一步的光线输送（Bonferroni p> 0.99），并且仍在继续。P，在Syn-enphr小鼠中，错误试验后平均活动的总体增加（n = 6;双向方差分析，试验类型的主要效果：p = 0.0088）。这发生在第1天（Bonferroni P = 0.038）和3（Bonferroni P = 0.016），但第2天（Bonferroni P> 0.99）不进行光。除非另有说明，否则使用双向方差分析，然后进行Tukey事后比较。

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