LEAPS-MPS: Mathematical Modeling of Brain Structure in Neurodegenerative Diseases Exhibiting Prion-Like Spreading

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Neurodegenerative diseases such as Alzheimer's Disease and Parkinson's Disease are associated with the spreading of neurotoxic proteins in the brain and the gradual loss of functional brain cells giving rise to symptoms according to where the damage takes place. Often the toxic proteins interact with and convert healthy proteins into toxic proteins. Both toxic and healthy proteins are transported between brain cells through complex pathways. Presently, an in-depth understanding of this spreading during disease progression is lacking in critical areas. With reference to clinical and experimental data for parameter inference, the investigator will develop mathematical models to describe the spread of toxic proteins qualitatively and quantitatively, with particular emphasis on brain structure. The results from this research will bring insights to new avenues of experimental and clinical exploration for treating disorders of the brain. The project will be conducted at a Hispanic Serving Institution and will provide research training and mentoring opportunities, including teaching computing and modeling skills relevant for the scientific workforce, at the undergraduate, graduate, and postdoctoral levels. The project is focused on the development of a model system of coupled, nonlinear differential equations for the biochemistry of proteins in different connectomes of the brain, with their associated pathways, and of a stochastic network model of protein transport to account for variations between brains. The system of differential equations can be studied from a dynamical systems perspective, with scientific computing, and asymptotic methods. The model results will enhance the understanding of potential disease trajectories, strategies for optimizing a particular outcome, and parameters that are of biological interest. The network model allows for considering distributions of parameters and other natural variations, quantifying uncertainty, and adding so-called logical conditions based in biology that are not well handled through differential equations. The project will address the question of existence of solutions to the model equations and establish properties of these solutions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.