Thermodynamics for Reduced Models of Breakable Amyloid Filaments Based on Maximum Entropy Principle

Abstract

Amyloid filaments are associated with neurodegenerative diseases such as Alzheimer's and Parkinson's. Simplified models of amyloid aggregation are crucial because the original mass-action equations involve numerous variables, complicating analysis and understanding. While dynamical aspects of simplified models have been widely studied, their thermodynamic properties are less understood. In this study, we explore the Maximum Entropy Principle (MEP)-reduced models, initially developed for dynamical analysis, from a brand-new thermodynamic perspective. Analytical expressions along with numerical simulations demonstrate that the discrete MEP-reduced model strictly retains laws of thermodynamics, which holds true even when filament lengths transit from discrete values to continuous real numbers. Our findings not only clarify the thermodynamic consistency between the MEP-reduced models and the original models of amyloid filaments for the first time, but also suggest avenues for future research into the model-reduction thermodynamics.