Table 1.

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

Glu/Gln cycle model
d[GlngC4]/dt = (Vcycle +Veff)·GlugC4 − (Vcycle +Veff)·GlngC4
d[GlnnC4]/dt =Vcycle·GlngC4 −Vcycle·GlnnC4
d[GlunC4]/dt =Vcycle·GlnnC4 − (Vcycle +VTCAn)·GlunC4
d[GlugC3]/dt = (VTCAg +Veff)·OAAgC3 +Vcycle·GlunC3 − (Vcycle + Veff +VTCAg)·GlugC3
d[GlngC3]/dt = (Vcycle +Veff)·GlugC3 − (Vcycle +Veff)·GlngC3
d[OAAgC3]/dt = ½VTCAg·(GlugC3 + GlugC4) − (VTCAg +Veff)·OAAgC3
Internal exchange model
d[GlngC4]/dt =Veff·GlugC4 −Veff·GlngC4
Glu/αKG cycle model
d[GlngC4]/dt =Veff·GlugC4 −Veff·GlngC4
d[GlunC4]/dt =Vcycle·GlugC4 − (Vcycle +VTCAn)·GlunC4
  • Only the differential equations used to test the models and to derive metabolic fluxes are given. [Glxy 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.