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A detailed analysis is reported on a multiscale pharmacokinetic model, simulating the interaction of a drug with its target, the binding of the compounds and the outcome of their interaction. The analysis is based on the algorithmic computational singular perturbation (CSP) methodology. Among others, the analysis concludes that the partial equilibrium approximation and the quasi-steady-state approximation (PEA and QSSA) are valid in two distinct stages in the evolution of the process. Similar conclusions are reached from the algorithmic criteria for the validity of the QSSA and PEA. The reactions in the pharmacokinetic model that (i) generate the fast time scales, (ii) generate the constraints in which the system evolves and (iii) drive the system at various phases are identified, with the use of algorithmic CSP tools. These identifications are very important for the improvement of the model and for the identification of ways to control the evolution of the process. Regarding the qualitative understanding of the process, the present analysis systematises the findings in the literature and provides some new insights.

Lactate in the brain is considered an important fuel and signalling molecule for neuronal activity, especially during neuronal activation. Whether lactate is shuttled from astrocytes to neurons or from neurons to astrocytes leads to the contradictory Astrocyte to Neuron Lactate Shuttle (ANLS) or Neuron to Astrocyte Lactate Shuttle (NALS) hypotheses, both of which are supported by extensive, but indirect, experimental evidence. This work explores the conditions favouring development of ANLS or NALS phenomenon on the basis of a model that can simulate both by employing the two parameter sets proposed by Simpson et al.

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