Biological clues on neuronal degeneration based on theoretical fits of decay patterns: towards a mathematical neuropathology

The application of the best mathematical fit to quantitative data on cell death over time in models of nervous abiotrophies can yield useful clues as to the cellular properties of degenerative processes. We review data obtained in two neurogenetic models of movement disorders in the laboratory mouse, the ‘Purkinje cell degeneration’ (pcd) mutant, a model of cerebellar ataxia, and the ‘weaver’ (wv) mutant, a combined degeneration of multiple systems including the mesostriatal dopaminergic pathway. In the cerebellum of pcd mice, analyses of transsynaptic granule cell death subsequent to the genetically-determined degeneration of Purkinje cells show that granule neuron fallout follows a typical pattern of exponential decay. In the midbrain of weaver mice, regression fits show that dopaminergic neuron fallout combines two independent components, an initial exponential decay, superceded by a linear regression, with a threshold around 100 days. The biological connotations of such analyses are discussed in light of the empirical observations and the theoretical simulation models. The theoretical connotations may link neuron loss to specific cellular idiosyncracies in elucidating the pathogenesis of chronic neurodegenerative disorders, including Parkinson’s disease.