Table 1.

Differential equations describing ¹³C incorporation into gray matter according to three different models of neurotransmitter glutamate repletion

Glu/Gln cycle model
d[Gln_gC4]/dt = (V_cycle +V_eff)·Glu_gC4 − (V_cycle +V_eff)·Gln_gC4
d[Gln_nC4]/dt =V_cycle·Gln_gC4 −V_cycle·Gln_nC4
d[Glu_nC4]/dt =V_cycle·Gln_nC4 − (V_cycle +V_{TCA_n})·Glu_nC4
d[Glu_gC3]/dt = (V_{TCA_g} +V_eff)·OAA_gC3 +V_cycle·Glu_nC3 − (V_cycle + V_eff +V_{TCA_g})·Glu_gC3
d[Gln_gC3]/dt = (V_cycle +V_eff)·Glu_gC3 − (V_cycle +V_eff)·Gln_gC3
d[OAA_gC3]/dt = ½V_{TCA_g}·(Glu_gC3 + Glu_gC4) − (V_{TCA_g} +V_eff)·OAA_gC3
Internal exchange model

d[Gln_gC4]/dt =V_eff·Glu_gC4 −V_eff·Gln_gC4
Glu/αKG cycle model

d[Gln_gC4]/dt =V_eff·Glu_gC4 −V_eff·Gln_gC4
d[Glu_nC4]/dt =V′_cycle·Glu_gC4 − (V′_cycle +V_{TCA_n})·Glu_nC4

Only the differential equations used to test the models and to derive metabolic fluxes are given. [Glx_y Cz] is the concentration of metabolite Glx (Glu or Gln) labeled in the positionz in the compartment y (glial or neuronal cells) of gray matter.