MATHEMATICAL MODEL FOR TIME TO NEURONAL APOPTOSIS DUE TO ACCRUAL OF DNA DOUBLE-STRAND BREAKS
Jennifer Rodriguez1, Chindu Mohanakumar2, Annabel Offer3, Carlos Castillo-Garsow4.
1California State University, Channel Islands, Camarillo, CA, 2University of Florida, Gainesville, FL, 3Texas Tech University, Lubbock, TX, 4Eastern Washington University, Cheney, WA.
We propose a mechanism to explain neuronal aging by tracking the number of non-transient DNA double-strand breaks (DSBs) and repairs over time that may lead to apoptosis. Neuronal apoptosis depends on the amount of space between DSBs as well as time. We derived 3 models to track the effects of neurodegeneration: a system of autonomous ordinary differential equations (ODEs), a probability model to track the spatial requirement, and a stochastic model that incorporates both the ODE temporal dynamics and a spatial probability model. Using these models, we estimated a distribution for the lifespan of a neuron and explored the effects of parameters on time to death. We identified 3 possible causes of premature neuron apoptosis: problems with coding critical repair proteins, issues with the neuron detecting DSBs, and issues with the neuron responding to DSBs.