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Updated: Jun 30, 2026

A Simple Neuronal Mechanical Injury Methodology to Study Drosophila Motor Neuron Degeneration
Published on: July 19, 2017
One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death III: diffusion pulse death
Tatiana Lomasko1, Charles J Lumsden
1Department of Medicine, Institute of Medical Science, University of Toronto, Toronto, Ontario, Canada. tatiana.lomasko@utoronto.ca
Abstract:
This is the third of three papers in which we study a mathematical model of cytoskeleton-induced neuron death. In the first two papers of this suite [Lomasko, T., Clarke, G., Lumsden, C., 2007a. One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death I: cell fate arrival times. J. Theor. Biol. 249, 1-17, doi:10.1016/j.jtbi.2007.05.031; Lomasko, T., Clarke, G., Lumsden, C., 2007b. One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: transition state metastability. J. Theor. Biol. 249, 18-28, doi:10.1016/j.jtbi.2007.05.032], we established that the mean-field limit of our model relates the known patterns of neuron decline to specific scales of cytoskeleton reorganization and cell-cell interaction by diffusible death factors. In the mean-field limit, the spatially variable concentration of diffusing death factor is replaced by a constant average value. Recent empirical advances now permit the actual diffusion of such factors to be followed in intact neuropil. In this paper we therefore extend the model beyond the mean-field limit, to include the diffusion dynamics of death factor bursts released from dying neurons. A range of novel tissue degeneration patterns is observed, for which we confirm and extend the mean-field prediction that sigmoidal patterns of neuron population decay are a principal hallmark of cell death in the presence of death factor release.
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