Nonequilibrium landscape of amyloid-beta and calcium ions in application to Alzheimer's disease.

Abstract

Amyloid-beta (Aβ) peptides and calcium ions (Ca^{2+}) serve critical roles in various physiological processes inside neurons, but their dysregulation is involved in the development of neurological disorders, including Alzheimer's disease. Particularly, Aβ_{42} peptides alter Ca^{2+} homeostasis, resulting in synaptic dysfunction and neuronal damage. On the other hand, Ca^{2+} ions can affect Aβ aggregation and clearance routes, either worsening or improving AD pathogenesis. We have considered a deterministic model for Aβ-Ca^{2+} interaction and studied its noise-induced dynamics. The stochastic sensitivity analysis helps to find the confidential ellipses for the stable attractors of the stochastic system. In addition, we have developed a network model based on the interaction between Aβ peptides and Ca^{2+} ions to comprehend their dynamics in the brain connectome better. The probabilistic evolution approach characterizes the dynamics of the stochastic network model and estimates the potentials required to escape from one attractor to another. The numerical simulations suggest that the more connected node requires more energy to switch its state, and the noise intensity plays a crucial role in such cases. Furthermore, this study reveals that external perturbations on Aβ-Ca^{2+} dynamics uncover novel targets for drug development and provide insights into the complex interplay between protein misfolding and synaptic dysfunction in Alzheimer's disease pathology.