Mathematical approaches to the evaluation of the flux of gamma-aminobutyrate in brain tissue in vitro.

In the preceding paper (Balázs, Machiyama, Hammond, Julian & Richter, 1970) the flux of gamma-aminobutyrate (GABA) was found, in guinea-pig brain-cortex slices incubated in glucose-saline medium, to represent about 10% of the total tricarboxylic acid cycle flux, as opposed to other estimates, which are as high as 40%. However, the latter value was deduced from experimental results by methods that made no allowance for the metabolic compartmentation of glutamate: a mathematical investigation was therefore undertaken to show that this omission necessarily leads to an overestimation of GABA flux. The magnitude of this over-estimation was shown by computer simulation methods to be of such an order as to bring the corrected value into agreement with the lower value. Computer simulation methods were also used to evaluate the GABA flux from the experimental results presented by Balázs et al. (1970) and a value of 0.0315mumol/min per g wet wt. was obtained. This value was also shown to be consistent, in the simulated system, with the experimentally observed time-courses for the radioactivity and quantity of aspartate. Since there is now evidence that GABA is itself a metabolically compartmented intermediate this possibility was considered mathematically, but it was found that in this case the assumption of compartmentation had little effect upon the value of GABA flux deduced on the basis of GABA homogeneity.