Supplementary material
1. Equations used in two-compartment model
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Mass Balance:
dGluN/dt = Vcycle + VxN - (Vcycle + VxN)
dGluA/dt = Vcycle + VxAnet - (Vgln + VxA)
dGln/dt = Vgln - (Vcycle + Vgln_out)
dGluTotal/dt = 0
dLactate/dt = 2CMRgl - (Vpc + VpdhA + VpdhN)
dGlucose/dt = Vmax_Glc_in(Plasma_Glucose)/(Km_Glc_in + Plasma_Glucose) - (CMRgl +
(Vmax_Glc_out)(Glucose)/(Km_Glc_out + Glucose))
dOaaA/dt = Vpc + 0.5VtcaANet + 0.5VtcaANet + VxA - (VtcaANet2 + VxA)
dOaaN/dt = 0.5VtcaN + 0.5VtcaN + VxN - (VtcaN + VxN)
dαKGA/dt = VpdhA + VxA + CMRac + VkbA - (VtcaANet + VxAnet)
dαKGN/dt = VpdhN + VxN + VkbN - (VxN + VtcaN)
dAspN/dt = VxN - VxN
dAspA/dt = VxA - VxA
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Isotope Balance:
dGluN4/dt = Vcycle(Gln4/Gln) + VxN(αKGN4/αKGN) - (Vcycle + VxN)(GluN4/GluN)
dGluA4/dt = Vcycle(GluN4/GluN) + VxAnet(αKGA4/αKGA) - (Vgln + VxA)(GluA4/GluA)
dGln4/dt = Vgln(GluA4/GluA) - (Vcycle + Vgln_out)(Gln4/Gln)
dGluN3/dt = Vcycle(Gln3/Gln) + VxN(αKGN3/αKGN) - (Vcycle + VxN)(GluN3/GluN)
dGln3/dt = Vgln(GluA3/GluA) - (Vcycle + Vgln_out)(Gln3/Gln)
dGluA3/dt = Vcycle(GluN3/GluN) + VxAnet(αKGA3/αKGA) - (Vgln + VxA)(GluA3/GluA)
dLactateTotal3/dt = CMRgl(Glucose1/Glucose) - (Vpc + VpdhA + VpdhN)(LactateTotal3/LactateTotal)
dGlucose1/dt = Vmax_Glc_in(Plasma_Glucose1)/(Km_Glc_in + Plasma_Glucose) - (CMRgl +
(Vmax_Glc_out)(Glucose)/(Km_Glc_out + Glucose))(Glucose1/Glucose)
dLacA3/dt = Vpc(LactateTotal3/LactateTotal) + VpdhA(LactateTotal3/LactateTotal) - (VpdhA + Vpc ) (LacA3/LacA)
dLacN3/dt = VpdhN(LactateTotal3/LactateTotal) - VpdhN(LacN3/LacN)
dOaaA3/dt = Vpc(LacA3/LacA) + 0.5VtcaANet(αKGA4/αKGA) + 0.5VtcaANet(αKGA3/αKGA) + VxA(AspA3/AspA) -
(VtcaANet2 + VxA)(OaaA3/OaaA)
dOaaN3/dt = 0.5VtcaN(αKGN4/αKGN) + 0.5VtcaN(αKGN3/αKGN) + VxN(AspN3/AspN) - (VtcaN +
VxN)(OaaN3/OaaN)
dαKGA4/dt = VpdhA(LacA3/LacA) + VxA(GluA4/GluA) + CMRac(Acetate_in2/Acetate_in) +
VkbA(BHBplasma2,4/BHB_plasma) - (VtcaANet + VxAnet)( αKGA4/αKGA)
dαKGN4/dt = VpdhN(LacN3/LacN) + VxN(GluN4/GluN) + VkbN(BHBplasma2,4/BHBplasma) - (VxN + VtcaN) (
αKGN4/αKGN)
dαKGA3/dt = VxA(GluA3/GluA) + VtcaANet2(OaaA3/OaaA) - (VtcaANet + VxAnet)(αKGA3/αKGA)
dαKGN3/dt = VtcaN(OaaN3/OaaN) + VxN(GluN3/GluN) - (VxN + VtcaN)(αKGN3/αKGN)
dAspN3/dt = VxN(OaaN3/OaaN) - VxN(AspN3/AspN)
dAspA3/dt = VxA(OaaA3/OaaA) - VxA(AspA3/AspA)
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Combination Pools:
GluTotal4 = GluA + GluN
GluTotal3 = GluA + GluN
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Constraints and Correction factors:
In euglycemic animals where blood BHB levels were relatively low (and brain BHB oxidation
negligible), the value of ‘c’ was estimated according to:
c1 = Lac3(Ac)(Glu4N(Lac)/Lac3N(Lac)) (2)
where brain Lac3(Ac) is the steady-state percentage enrichment during the [2-13C]-acetate
infusion (and assumed to be equal to brain pyruvate-C3). The steady-state value for
Glu4N(Lac)/Lac3N(Lac) was assumed to equal ~1 based on a study of overnight fasted rats and
unpublished data from our laboratory for fed animals receiving infusions of [3-13C]-lactate.
In contrast to euglycemic animals, blood BHB levels were elevated in animals undergoing
hypoglycemic clamp and fasted overnight; for these animals, the value of ‘c’ was given by
c2 = Lac3(Ac)(1– (Glu4(BHB4)/BHB4(BHB4))) + BHB4(Ac)(Glu4(BHB4)/BHB4(BHB4)) (3)
where Glu4(BHB4)/BHB4(BHB4) was assumed to be ~0.12 (unpublished data, K. Behar and G.
Mason) measured in 24h fasted, halothane-anesthetized rats receiving an intravenous infusion
of [2,4-13C2]BHB.
In Eqn.3 the plasma BHB4(Ac) was used because brain BHB was below detection; thus, plasma
and brain BHB enrichments were assumed to be equal.
2. Comparison of standard deviations of group average (SD group) and
highest SD from Monte Carlo simulations (SD MC) for each flux in four
different study groups.
CMRac CMRgl Vcyc Vgln VpdhA VpdhN VtcaA VtcaN Vtca(tot)
Ctrl_eu 0.15 0.46 0.37 0.42 0.16 0.70 0.31 0.72 1.05
SD group 0.07 0.22 0.27 0.27 0.27 0.37 0.31 0.40 0.73
SD MC 0.01 0.07 0.07 0.06 0.05 0.14 0.06 0.12 0.14
Rh3D_eu 0.16 0.66 0.61 0.69 0.21 1.06 0.37 1.08 1.47
SD group 0.07 0.39 0.43 0.47 0.17 0.54 0.19 0.57 0.76
SD MC 0.01 0.07 0.09 0.07 0.06 0.15 0.07 0.15 0.15
Ctrl_hypo 0.15 0.54 0.52 0.54 0.06 0.96 0.21 1.01 1.26
SD group 0.04 0.23 0.15 0.23 0.14 0.32 0.15 0.31 0.49
SD MC 0.04 0.06 0.13 0.06 0.12 0.27 0.12 0.28 0.14
RH3D_hypo 0.14 0.40 0.48 0.47 0.03 0.73 0.19 0.76 0.99
SD group 0.07 0.23 0.24 0.28 0.06 0.35 0.20 0.42 0.68
SD MC 0.02 0.08 0.14 0.10 0.05 0.23 0.13 0.23 0.17