a–c, Plasma BCAAs (a), plasma BCKAs (b) and Ra (c) of BCAAs collected during [U-13C]-labelled BCAA steady-state infusion before (basal, fasted for 5 h) and during (clamp, fasted for 7 h) HIEC; n = 6 BckdkloxP/loxP and n = 6 BckdkloxP/loxP-HSA-CreER. d, Normalized labelling of quadricep TCA cycle intermediates by [U-13C]-labelled BCAAs; n = 6 BckdkloxP/loxP and n = 6 BckdkloxP/loxP-HSA-CreER. e, Blood glucose. f, GIR. g, Steady-state GIR during HIEC. h, Insulin before and during HIEC. i, Glucose Ra before and during HIEC; the black bar is the endogenous glucose measured using d-glucose-6,6-d2, while the grey bar is glucose infused during HIEC. e–i, n = 6 BckdkloxP/loxP and n = 6 BckdkloxP/loxP-HSA-CreER. a–i, Mice were male, 20–24-weeks old and fed Western diet for 12 weeks. j, Plasma BCAAs (n = 10 BckdkloxP/loxP and n = 8 BckdkloxP/loxP-HSA-CreER). k, Plasma BCKAs (n = 7 BckdkloxP/loxP and n = 7 BckdkloxP/loxP-HSA-CreER) in mice fasted for 5 h or refed for 2 h after overnight fasting. l, IP-GTT (1.5 g kg−1) in mice fasted for 5 h; n = 10 BckdkloxP/loxP and n = 8 BckdkloxP/loxP-HSA-CreER. m, AUC for GTT in l. n, Insulin at t = 0 (n = 8 BckdkloxP/loxP and n = 7 BckdkloxP/loxP-HSA-CreER) and t = 20 min (n = 10 BckdkloxP/loxP and n = 8 BckdkloxP/loxP-HSA-CreER) during the GTT from l. j–n, Mice were male, 14–24-weeks old and were fed HFD for 4 weeks. o, Western blotting of refed tissues (14-3-3 is the loading control); n = 6 BckdkloxP/loxP and n = 6 BckdkloxP/loxP-HSA-CreER. p, Labelling fraction of TCA cycle intermediates by [U-13C]-labelled BCAA gavage in the quadriceps of fed mice; n = 8 BckdkloxP/loxP and n = 8 BckdkloxP/loxP-HSA-CreER. o,p, Mice were male, 16–17-weeks old and were fed HFD for 4 weeks. q, Plasma BCAAs after 100 mg kg−1 vehicle or BT2 treatment the night before and the morning of GTT; n = 6 vehicle and n = 6 BT2. r, 1.5 g kg−1 IP-GTT in BckdkloxP/loxP-HSA-CreER mice fasted for 5 h after the same vehicle or BT2 regimen in q; n = 6 vehicle and n = 7 BT2. s, AUC from the GTT in r. t, Insulin at t = 0 and t = 20 during the GTT from r; n = 6 vehicle and n = 7 BT2. q–t, Mice were male, 12–20-weeks old and were fed HFD for 4 weeks; n = 6 BckdkloxP/loxP-HSA-CreER + Veh and n = 6–7 BckdkloxP/loxP-HSA-CreER + BT2. Data are presented as the mean ± s.e.m. When two groups were compared, a two-tailed Student’s t-test was used, with significance defined as *P < 0.05, **P < 0.01 and ***P < 0.001. In the experiments with multiple comparisons at different time points, a repeated measures, two-way ANOVA was used. a, Valine basal P = 0.001199, valine clamp P = 0.031378; leucine basal P = 0.000636, leucine clamp P = 0.020943; isoleucine basal P = 0.000046, isoleucine clamp P = 0.017202. b, KIC/KMV basal P = 0.002799, KIC/KMV clamp P = 0.001194; KIV basal P = 0.034170, KIV clamp P = 0.000816. d, Succinate P = 0.015469; malate P = 0.001603; glutamate P = 0.005976. j, Valine fasted P = 0.005766; leucine fasted P = 0.000365; isoleucine fasted P = 0.000065. k, KIC/KMV fasted P = 0.003234, KIC/KMV refed P = 0.008413; KIV fasted P = 0.001603, KIV-refed P = 0.001892. p, Succinate P = 0.000100; malate P = 0.000072; glutamate P = 0.000289. q, Valine P = 0.002310; leucine P = 0.001134; isoleucine P = 0.002717. s, P = 0.037021.