Mathematical models of amyloid-beta production, aggregation, and treatment in Alzheimer's disease

Abstract

Amyloid-beta peptides have long been associated with the pathology of Alzheimer's disease. A two-pronged approach to investigating amyloid-beta in the context of Alzheimer's disease is presented with an amyloid aggregation reaction model and a macrolevel model of a potentially disease-modifying treatment for Alzheimer's disease.

Amyloid-beta oligomers are believed to be one of the principle neurotoxic species in Alzheimer's disease. A kinetic model was constructed to elucidate the aggregation of these toxic oligomers and the fibrils that they eventually form. The effects of osmolytes and polymers on amyloids are explored to better relate results to in vivo conditions. The kinetics of Alzheimer's-relevant amyloid-beta mutants are also modeled.

Amyloid-beta removal through apolipoprotein E binding has been shown to be up-regulated by bexarotene, a drug approved by the U.S. Food and Drug Administration for treating a class of non-Hodgkin's lymphoma. A mathematical model was constructed to simulate amyloid-beta production throughout the lifespan of diseased mice and demonstrate the efficacy of bexarotene treatments in reducing amyloid-beta load. Both aspects of the model are based on and consistent with previous experimental results. Low dosages of bexarotene were unable to stem cell death, but dosages at and above a critical concentration were found to recover healthy brain cells. Early treatment was shown to have significantly improved efficacy. Relevance with respect to bexarotene-based amyloid-beta-clearance mechanism and direct treatment for Alzheimer's disease is emphasized.