Protein-protein interactions in neurodegenerative diseases: A conspiracy theory

Abstract

Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are associated with the prion-like propagation and aggregation of toxic proteins. A long standing hypothesis that amyloid-beta drives Alzheimer’s 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.

Network Diffusion Modeling Explains Longitudinal Tau PET Data

“…Motivated by the hypothesis that tau protein misfolds and spreads in a prion-like fashion (Jucker and Walker, 2011 ; Fornari et al, 2020 ), we use a Fisher-Kolmogorov model (Fisher, 1937 ; Kolmogorov et al, 1937 ) to characterize the accumulation of pathological tau in the brain (Fornari et al, 2019 ; Thompson et al, 2020 ). The model is governed by a single non-linear reaction-diffusion equation that predicts the spatio-temporal evolution of the unknown, the concentration of misfolded protein c ,…”

Braiding Braak and Braak: Staging patterns and model selection in network neurodegeneration

“…A family of Laplacians While the standard graph Laplacians is often used in many physical applications [12,13,14], various other forms have been studied in the literature [7,9,8]. For instance, in the early use of network diffusion to model proteopathy in neurodegenerative disease [7,9] the normalized form graph Laplacian is used.…”

“…In addition, we recall that W ii = 0 per assumption and that W ij = W ji as the network is undirected. The choice (25a) was used in diffusion models of proteopathy [7,9,8], whereas (25b) has been used in the context of more complex reaction and aggregation models [12,13] and (25c) appeared first in a model of Aβ-τ P interaction in Alzheimer's disease [14]. Since the dimensional Laplacian L = ρL has unit of 1/time, the constant ρ has either units of 1/time for the length-free scaling (25a), length over time, i.e.…”

“…These models range from complex, probabilistic [1,41] network models, fitted to substantial amounts of patient data, to deterministic, non-linear models of reaction-diffusion type. These reaction-diffusion models are defined continuously [5,42] and on structural brain connectomes [8,12,13,14]. They offer a differential-equations-based framework for a data-independent analysis of disease characteristics.…”

ResDock: Protein-Protein Docking Using Shape Complementarity of Surface Residues

“…They are classified, based on their function, as catalytic, regulatory, protective, storage, transport, toxic, structural, contractile, secretory, and exotic proteins. Since the interaction between proteins are specific, illformed interactions result in diseases like Alzhimer ' s disease [1], and Huntigton ' s disease. It is important to study the functions of proteins and the nature of interactions as no cure is found yet for the diseases mentioned above.…”