0.9999), Day 2 (post hoc t(28) = 0.6978, P > 0.9999), nor Day 3 (post hoc t(28) = 0.4652, P > 0.9999). o, Inhibition disrupts rule shift performance in DIO-eNpHR-expressing mice compared to controls when light is delivered continuously throughout the RS on Day 4 (post hoc t(28) = 9.886, P < 0.0001). Two-way ANOVA followed by Bonferroni post hoc comparisons was used. ****P < 0.0001./p> 0.9999; same and incorrect post hoc t(26) = 0.1486, P > 0.9999; different location two-way ANOVA (trial type × virus); interaction: F(1,13) = 13.87, P = 0.0026; different and correct post hoc t(26) = 3.724, P = 0.0019; different and incorrect post hoc t(26) = 3.724, P = 0.0019). i, Same as h but for the next 5 RS trials (n = 7 DIO-mCherry control mice; same location two-way ANOVA (trial type × virus); interaction: F(1,13) = 3.214, P = 0.0963; same and correct post hoc t(26) = 1.793, P = 0.1693; same and incorrect post hoc t(26) = 1.793, P = 0.1693; different location two-way ANOVA (trial type × virus); interaction: F(1,13) = 8.948, P = 0.0104; different and correct post hoc t(26) = 2.991, P = 0.0120; different and incorrect post hoc t(26) = 2.991, P = 0.0120). j–k, The overall speed (meters per second) of mice during the first 5 IA and RS trials across days in the cohort of mice used for microendoscopic Ca2+ imaging (n = 6 eNpHR-negative controls; n = 6 DIO-eNpHR mice; two-way ANOVA (IA vs. RS × task day) for control mice: interaction: F(1,10) = 0.00271, P = 0.9595; two way-ANOVA (IA vs. RS × task day) for DIO-eNpHR mice: interaction: F(1,10) = 1.378, P = 0.2677). l–m, There is no difference in the amount of time (seconds) mice spent exploring bowls before making a decision during the first 5 IA and RS trials across days in the microendoscope experimental dataset (n = 6 eNpHR-negative controls; n = 6 DIO-eNpHR mice; two-way ANOVA (IA vs. RS × task day) for control mice: interaction: F(1,10) = 0.5053, P = 0.4934; two way-ANOVA (IA vs. RS × task day) for DIO-eNpHR mice: interaction: F(1,10) = 0.1147, P = 0.7419). n–o, The first move of the mouse toward the correct bowl (percent) during the first 5 IA and RS trials across days in the Ca2+ imaging experimental dataset (n = 6 eNpHR-negative controls; n = 6 DIO-eNpHR mice; two-way ANOVA (IA vs. RS × task day) for control mice: interaction: F(1,10) = 3.347, P = 0.0973; two way-ANOVA (IA vs. RS × task day) for DIO-eNpHR mice: interaction: F(1,10) = 0.1316, P = 0.7244). p–z, Effects of inhibiting callosal PV+ projections during a version of the RS task using a shorter (30 second) intertrial interval (ITI). p, Experimental design: Day 1, no light delivery; Day 2, continuous light during the RS for optogenetic inhibition of callosal PV terminals ; Day 3, no light was delivered. q, Representative image showing DIO-eYFP expression in one mPFC and a fiber-optic cannula implanted in the contralateral mPFC in a PV-Cre mouse. r, Representative image showing DIO-eNpHR-mCherry (DIO-eNpHR) expression in one mPFC and a fiber-optic cannula implanted in the contralateral mPFC in a PV-Cre mouse. s,w, IA performance with a 30 s ITI in eNpHR-negative mice (n = 6) and eNpHR-expressing mice (n = 8; two-way ANOVA (task day × virus); interaction: F(2,24) = 0.1585, P = 0.8543). t,x, Optogenetic inhibition of mPFC callosal PV terminals with a 30 s ITI impairs rule shift performance in DIO-eNpHR mice (n = 8) compared to controls (n = 6; two-way ANOVA (task day × virus); interaction: F(2,24) = 50.79, P < 0.0001). t, Performance of DIO-eYFP controls did not change from Day 1 to Day 2 (Tukey's post hoc q(5) = 1.606, P = 0.5356), Day 1 to Day 3 (Tukey's post hoc q(5) = 1.035, P = 0.7567), nor Day 2 to Day 3 (Tukey's post hoc q(5) = 0.4344, P = 0.9498). x, Inhibition disrupts rule shift performance in DIO-eNpHR mice from Day 1 to Day 2 (Tukey's post hoc q(7) = 15.34, P < 0.0001), Day 1 to Day 3 (Tukey's post hoc q(7) = 21.75, P < 0.0001), but not Day 2 to Day 3 (Tukey's post hoc q(7) = 2.679, P = 0.2101). u, y, Optogenetic inhibition of callosal PV terminals increases perseverative errors in DIO-eNpHR mice (n = 8 mice) compared to DIO-eYFP controls (n = 6 mice; two-way ANOVA (task day × virus) interaction: F(2,24) = 19.79, P < 0.0001). v, z, Optogenetic inhibition of callosal PV terminals has no effect on random errors in DIO-eNpHR mice (n = 8) compared to DIO-eYFP controls (n = 6; two-way ANOVA (task day × virus); interaction: F(2,24) = 1.079, P = 0.3559). u, v, Light delivery does not affect the number of perseverative (post hoc t(5) = 0.000 – 1.000, P > 0.9999) or random (post hoc t(5) = 0.4152 – 0.7906, P > 0.9999) errors in DIO-eYFP controls across days. y, z, Optogenetic inhibition of callosal PV terminals on Day 2 increased the number of perseverative (post hoc t(7) = 6.008, P = 0.0016 from Day 1 to Day 2; post hoc t(7) = 5.844, P = 0.0019 from Day 1 to Day 3; but not from Day 2 to Day 3: post hoc t(7) = 1.111, P = 0.9093) but not random (post hoc t(7) = 0.000 – 2.198, P = 0.1918 – > 0.9999) errors compared to no stimulation. Two-way ANOVA followed by Bonferroni post hoc comparisons was used unless otherwise noted. Data were expressed as mean ± s.e.m. **P < 0.01, ****P < 0.0001; scale bar, 100 μm./p> 0.9999) errors in DIO-eYFP controls. g, h, Optogenetic inhibition of callosal PV terminals on Day 2 increased the number of perseverative (post hoc t(13) = 10.75, P < 0.0001) and random (post hoc t(13) = 3.145, P = 0.0155) errors compared to no stimulation on Day 1. k, l, o, p, Optogenetic inhibition of all callosal projections has no effect on perseverative errors in Syn-eNpHR mice (n = 6) compared to controls (n = 4; two-way ANOVA (task day × virus); interaction: F(1,8) = 0.0, P > 0.9999) nor on random errors (two-way ANOVA (task day × virus); interaction: F(1,8) = 0.07805, P = 0.787). Two-way ANOVA followed by Bonferroni post hoc comparisons was used. *P < 0.05, ****P < 0.0001; scale bars, 250 μm and 100 μm, respectively./p> 0.9999). By contrast, rule shift performance in mice expressing both NpHR and ChR2 (h; n = 8) is significantly different across days than that of mice which express NpHR-only (two-way ANOVA (task day × virus); interaction: F(3,27) = 6.747, P = 0.0015). Optogenetic inhibition of mPFC callosal PV terminals causes NpHR+ChR2-expressing mice (n = 8) to take a large number of trials to learn rule shifts on Day 1 and this does not change on Day 2 (no light) (post hoc t(7) = 1.446, P > 0.9999). However, RS learning is rescued by 40 Hz optogenetic stimulation on Day 3 (post hoc t(7) = 10.91, P < 0.0001) and this improvement does not change on ‘Day 4’ of testing which occurs one week later (post hoc t(7) = 0.6394, P > 0.9999). f, i: Optogenetic inhibition followed by stimulation of callosal PV terminals changes the number of perseverative errors in mice expressing both NpHR and ChR2 (n = 8 mice) compared to controls expressing only NpHR (n = 3 mice; two-way ANOVA; main effect of task day: F(2.015,18.13) = 7.167, P = 0.0050; main effect of virus: F(1,9) = 14.31, P = 0.0043; interaction: F(3,27) = 5.324, P = 0.0052). By contrast, there is no difference in numbers of random errors (two-way ANOVA; main effect of task day: F(1.491,13.42) = 1.706, P = 0.2189; main effect of virus: F(1,9) = 1.523, P = 0.2483; interaction: F(3,27) = 0.2901, P = 0.8322). f, Once mice expressing NpHR only receive optogenetic inhibition on Day 1, the number of perseverative errors is stable across days (n = 3 mice; Day 1 to Day 2: post hoc t(2) = 1.222, P > 0.9999; Day 1 to Day 3: post hoc t(2) = 1.299, P > 0.9999; Day 1 to Day 4: post hoc t(2) = 0.3111, P > 0.9999; Day 2 to Day 3: post hoc t(2) = 0.3780, P > 0.9999; Day 2 to Day 4: post hoc t(2) = 1.606, P > 0.9999; Day 3 to Day 4: post hoc t(2) = 2.000, P > 0.9999). g, In mice that express NpHR only (n = 3 mice), numbers of random errors are also stable across days (Day 1 to Day 2: post hoc t(2) = 1.387, P > 0.9999; Day 1 to Day 3: post hoc t(2) = 1.732, P > 0.9999; Day 1 to Day 4: post hoc t(2) = 1.000, P > 0.9999; Day 2 to Day 3: post hoc t(2) = 1.000, P > 0.9999; Day 2 to Day 4: post hoc t(2) = 1.000, P > 0.9999; Day 3 to Day 4: post hoc t(2) = 0.3780, P > 0.9999). i, 40 Hz stimulation of callosal PV terminals on Day 3 reduces the number of perseverative errors in mice expressing both NpHR and ChR2 (n = 8; Day 1 to Day 2: post hoc t(7) = 0.6494, P > 0.9999; Day 1 to Day 3: post hoc t(7) = 5.218, P = 0.0074; Day 1 to Day 4: post hoc t(7) = 6.416, P = 0.0022; Day 2 to Day 3: post hoc t(7) = 4.822, P = 0.0115; Day 2 to Day 4: post hoc t(7) = 12.33, P < 0.0001; Day 3 to Day 4: post hoc t(7) = 0.4971, P > 0.9999). j, 40 Hz stimulation on Day 3 does not affect the number of random errors in mice expressing both NpHR and ChR2 (n = 8 mice; Day 1 to Day 2: post hoc t(7) = 0.7061, P > 0.9999; Day 1 to Day 3: post hoc t(7) = 0.6417, P > 0.9999; Day 1 to Day 4: post hoc t(7) = 1.210, P > 0.9999; Day 2 to Day 3: post hoc t(7) = 0.3140, P > 0.9999; Day 2 to Day 4: post hoc t(7) = 0.4237, P > 0.9999; Day 3 to Day 4: post hoc t(7) = 0.7977, P > 0.9999). Two-way ANOVA followed by Bonferroni post hoc comparisons was used. *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001; scale bars, 100 μm and 50 μm, respectively./p> 0.9999) or random (Day 1 to Day 2: post hoc t(14) = 0.284, P > 0.9999; Day 1 to Day 3: post hoc t(14) = 0.284, P > 0.9999; Day 2 to Day 3: post hoc t(14) = 0.0, P > 0.9999) errors in controls across days. g, h, Optogenetic inhibition of callosal PV terminals induces perseveration on Day 2 and Day 3 compared to no stimulation on Day 1 (Day 1 to Day 2: post hoc t(14) = 4.092, P = 0.0033; Day 1 to Day 3: post hoc t(14) = 6.405, P < 0.0001; Day 2 to Day 3: post hoc t(14) = 2.313, P = 0.1094), but has no effect on random errors (Day 1 to Day 2: post hoc t(14) = 1.524, P = 0.4493; Day 1 to Day 3: post hoc t(14) = 0.254, P > 0.9999; Day 2 to Day 3: post hoc t(14) = 1.27, P = 0.6744). i, PV-Cre Ai14 mice had bilateral AAV-DIO-Ace2N-4AA-mNeon (Ace-mNeon) injections, an ipsilateral AAV-Synapsin-eNpHR-BFP (Syn-eNpHR) or AAV-Synapsin-mCherry (Syn-mCherry) injection and multimode fiber-optic implants in both prefrontal cortices. j, Representative images from mice injected with a control virus (Syn-mCherry), showing mCherry, Ace-mNeon, and tdTomato expression in the mPFC ipsi to the virus injection, and Ace-mNeon and tdTomato in the contra hemisphere. k, n, Experimental design: Day 1, no light delivery; Day 2, continuous light for inhibition during the R; Day 3, no light delivery. l, m, o, p, Optogenetic inhibition of callosal terminals does not change the number of perseverative errors in Syn-eNpHR mice (n = 5 mice, l-m) compared to Syn-mCherry controls (n = 4 mice, l-m; two-way ANOVA (task day × virus); interaction: F(2,14) = 1.933, P = 0.1814), and has no effect on random errors (two-way ANOVA (task day × virus); interaction: F(2,14) = 0.3789, P = 0.6914). l, m, Light delivery does not affect the number of perseverative (Day 1 to Day 2: post hoc t(3) = 1.464, P = 0.7183; Day 1 to Day 3: post hoc t(3) = 0.8783, P > 0.9999; Day 2 to Day 3: post hoc t(3) = 0.4804, P > 0.9999) or random (Day 1 to Day 2: post hoc t(3) = 1.732, P = 0.5451; Day 2 to Day 3: post hoc t(3) = 1.732, P = 0.5451) errors in controls across days. o, p, Nonspecific optogenetic inhibition of all callosal projections does not affect the number of perseverative (n = 5 mice; Day 1 to Day 2: post hoc t(4) = 0.6882, P > 0.9999; Day 1 to Day 3: post hoc t(4) = 2.108, P = 0.3081; Day 2 to Day 3: post hoc t(4) = 1.121, P = 0.9752) or random (Day 1 to Day 2: post hoc t(4) = 0.4082, P > 0.9999; Day 1 to Day 3: post hoc t(4) = 1.000, P > 0.9999; Day 2 to Day 3: post hoc t(4) = 0.000, P > 0.9999) errors in Syn-eNpHR mice across days. Two-way ANOVA followed by Bonferroni post hoc comparisons was used. **P < 0.01, ****P < 0.0001; scale bars, 50 μm./p> 0.9999; Day 3: post hoc t(24) = 1.763, P = 0.2717). g–i, We also re-analyzed the TEMPO data collected from PV-Cre Ai14 mice injected in one mPFC with DIO-eNpHR to identify specific times when optogenetic inhibition of callosal PV+ projections disrupts gamma synchrony. We measured the change in gamma synchrony (calculated in 1 s windows for various time points relative to behavioral events) between Day 1 (control) and Day 2 (optogenetic inhibition) for both errors (filled circles) and correct choices (open circles) during the first 5 RS trials in PV-Cre mice expressing DIO-eNpHR. g, This change in gamma synchrony (change = Day 2 – Day 1) is not significantly different for error vs. correct trials around the time of trial start (n = 5 mice; two-way ANOVA (time point × error vs. correct); interaction: F(15,64) = 1.642, P = 0.0874). h, This change in gamma synchrony is more negative for error vs. correct trials around the start of digging (n = 5 mice; two-way ANOVA (time point × error vs. correct); interaction: F(15,64) = 1.931, P = 0.0360). i, This change in gamma synchrony is more negative for error vs. correct trials around the end of digging (n = 5 mice; two-way ANOVA (time point × error vs. correct); interaction: F(10,44) = 2.096, P = 0.0454). j, Example traces of left (L) and right (R) Ace2n-4AA-mNeon (Ace-mNeon) traces (green and red, respectively), from 0–10 s after dig start on RS correct and error trials in a DIO-eNpHR-expressing mouse and k, zoomed in on the period 6–7 s after dig start. l, The time course of gamma synchrony (correlation values calculated from filtered and cleaned Ace-mNeon signals) from 0–10 s after dig start for these two example trials. Two-way ANOVA followed by Bonferroni post hoc comparisons was used. Data were expressed as mean ± s.e.m. *P < 0.05, **P < 0.01./p>