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The degrees of freedom of multi-compartment mathematical models for energymetabolism of a neuron-astrocyte complex may offer a key to understand thedifferent ways in which the energetic needs of the brain are met. In this paperwe address the problem within a steady state framework and we use thetechniques of linear algebra to identify the degrees of freedom first in alumped model, then in its extension to a spatially distributed case. Theinterpretation of the degrees of freedom in metabolic terms, more specificallyin terms of glucose and oxygen partitioning, is then leveraged to deriveconstraints on the free parameters needed to guarantee that the model isenergetically feasible. We also demonstrate how the model can be used toestimate the stoichiometric energy needs of the cells as well as the householdenergy based on observed oxidative cerebral metabolic rate (CMR) of glucose,and the glutamate cycling. Moreover, our analysis shows that in the lumpedmodel the direction of lactate dehydrogenase (LDH) in the cells can be deducedfrom the glucose partitioning between the compartments. The extension of thelumped model into a spatially distributed multi-compartment setting thatincludes diffusion fluxes from capillary to tissue increases the number ofdegrees of freedom, requiring the use of statistical sampling techniques. Theanalysis of distributed model reveals that some of the conclusions, e.g.,concerning the LDH activity and glucose partitioning, based on a spatiallylumped model may no longer hold.

Energy Demand and Metabolite Partitioning in Spatially Lumped and Distributed Models of Neuron-Astrocyte Complex