Figure 4.

(A) Synthetic glutamate C4 and glutamine C4 turnover curves (lines) generated by solving the four coupled differential equations describing the model in Figure 2 with [1-¹³C] or [1,6-¹³C₂] glucose infusion, the mean metabolic fluxes, and adding normally distributed noise (dots). The astroglial dilution is revealed in (A) by comparing the fractional enrichments of glutamate and glutamine C4. At the end point of glucose infusion, the concentration of glutamine and glutamate with ¹³C labels at C4 is 0.96 and 2.75 μmol/g, respectively. The end point fractional enrichment of glutamine C4 is 26% lower than that of glutamate C4 as observed experimentally (Shen et al., 1999). (B) An example of the probability density function for V_cyc with constraints ^aV_TCA ≤ 0.1, V_dil(Lac) = 0.05, and V_dil(Gln) = 0.14 μmol/g/min. (C) The corresponding probability density function of the “noise level” after fitting (σ_min). The mean χ² obtained is 60.8 with a standard deviation of 11.2. σ_min averaged over the 100 Monte Carlo data sets is 0.098 μmol/g with a standard deviation of 0.009 μmol/g. (This image is reproduced from Shen et al., 2009).