Edinburgh Napier University

  The mammalian brain utilizes glucose as its main source of energy. However,it has been recently discovered that lactate can also be considered important as a fuel and a signaling molecule in neuronal activity, especially during neuronalactivation. The shuttling of lactate between the highly energy-demanding neurons and the astrocytes and during brain activation is of great importance. This lactate shuttling is currently described by two conflicting hypotheses, each one supported by experimental data: the Astrocyte to Neuron Lactate Shuttle (ANLS,according to which astrocytes provide lactate to neurons) and the Neuron to Astrocyte Lactate Shuttle (NALS, according to which neurons provide lactate to astrocytes). The mathematical models governing the brain metabolism processesare multi-scale in character, due to the wide range of time scales characterizing the various sub-processes. In such multi-scale models, it is often challenging toidentify the driving processes and time-scales characterizing the dynamics of the
system. Here, a modified version of the Simpson et al. (1) model that complies with both the ANLS and NALS hypotheses is analyzed using Computational Singular Perturbation (CSP) algorithm (2), in order to acquire the underlying physical understanding of the various features exhibited by this model (e.g, metabolicprofiles of astrocytes and neurons). CSP is an algorithmic method for asymptoticanalysis, which was introduced in the late 1980s and has been used extensively in systems of reactive flows and biological systems. Among others, CSP can lead tothe identification of (i) the processes generating the fast and slow time scales, (ii) the processes contributing to the establishing equilibrium states, (iii) the processes that control the evolution of the chemical species. The comparison of the two contradicting ANLS and NALS hypotheses is carried out via CSP, by identifying the physical features of the system that match the existing experimental results. Thegoal of this work is twofold: (i) a new algorithmic approach of asymptotic analysis on brain energy metabolism will be introduced, which is not hindered by the complexity of the mathematical model and (ii) the ability of CSP to manipulateneuronal activation will be demonstrated, by identifying the components of the model that influence the duration of the neuronal activation time and the desired levels of selected concentrations.