Protein-protein interactions in neurodegenerative diseases: a conspiracy theory.

Neurodegenerative diseases such as Alzheimers or Parkinsons are associated with the prion-like propagation and aggregation of toxic proteins. A long standing hypothesis that amyloid-beta drives Alzheimers disease has proven the subject of contemporary controversy; leading to new research in both the role of tau protein and its interaction with amyloid-beta. Conversely, recent work in mathematical modeling has demonstrated the relevance of nonlinear reaction-diffusion type equations to capture essential features of the disease. Such approaches have been further simplified, to network-based models, and offer researchers a powerful set of computationally tractable tools with which to investigate neurodegenerative disease dynamics. Here, we propose a novel, coupled network-based model for a two-protein system that includes an enzymatic interaction term alongside a simple model of aggregate transneuronal damage. We apply this theoretical model to test the possible interactions between tau proteins and amyloid-beta and study the resulting coupled behavior between toxic protein clearance and proteopathic phenomenology. Our analysis reveals ways in which amyloid-beta and tau proteins may conspire with each other to enhance the nucleation and propagation of different diseases, thus shedding new light on the importance of protein clearance and protein interaction mechanisms in prion-like models of neurodegenerative disease. Author SummaryIn 1906 Dr. Alois Alzheimer delivered a lecture to the Society of Southwest German Psychiatrists. Dr. Alzheimer presented the case of Ms. Auguste Deter; her symptoms would help to define Alzheimers disease (AD). Over a century later, with an aging world population, AD is at the fore of global neurodegenerative disease research. Previously, toxic amyloid-beta protein (A{beta}) was thought to be the primary driver of AD development. Recent research suggests that another protein, tau, plays a fundamental role. Toxic tau protein contributes to cognitive decline and appears to interact with toxic A{beta}; research suggests that toxic A{beta} may further increase the effects of toxic tau. Theoretical mathematical models are an important part of neurodegenerative disease research. Such models: enable extensible computational exploration; illuminate emergent behavior; and reduce research costs. We have developed a novel, theoretical mathematical model of two interacting species of proteins within the brain. We analyze the mathematical model and demonstrate a computational implementation in the context of A{beta}-tau interaction in the brain. Our model clearly suggests that: the removal rate of toxic protein plays a critical role in AD; and the A{beta}-tau conspiracy theory is a nuanced, and exciting path forward for Alzheimers disease research.