B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics.

Throughout an organism's life, a multitude of complex and interdependent biological systems transition through biophysical processes that serve as indicators of the underlying biological states. Inferring these latent, unobserved states is a goal of modern biology and neuroscience. However, in many experimental setups, we can at best obtain discrete snapshots of the system at different times and for different individuals. This challenge is particularly relevant in the study of Alzheimer's Disease (AD) progression, where we observe the aggregation of pathology in brain donors, but the underlying disease state is unknown. This paper proposes a biophysically motivated Bayesian framework (B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics), where the disease state is modeled and continuously inferred from observed quantifications of multiple AD pathological proteins. Inspired by biophysical models, we describe pathological burden as an exponential process. The progression of AD is modeled by assigning a latent score, termed pseudotime, to each pathological state, creating a pseudotemporal order of donors based on their pathological burden. We study the theoretical properties of the model using linearization to reveal convergence and identifiability properties. We provide Markov chain Monte Carlo estimation algorithms, illustrating the effectiveness of our approach with multiple simulation studies across various data conditions. Applying this methodology to data from the Seattle Alzheimer's Disease Brain Cell Atlas, we infer the pseudotime ordering of donors. Finally, we analyze the information within each pathological feature to refine the model, focusing on the most informative pathologies. This framework lays the groundwork for continuous pseudotime modeling in the analysis of neurodegenerative diseases.