A mathematical model for the effects of amyloid beta on intracellular calcium

The accumulation of Alzheimer’s disease (AD) associated Amyloid beta (Aβ) oligomers can trigger aberrant intracellular calcium (Ca(2+)) levels by disrupting the intrinsic Ca(2+) regulatory mechanism within cells. These disruptions can cause changes in homeostasis levels that can have detrimental effects on cell function and survival. Although studies have shown that Aβ can interfere with various Ca(2+) fluxes, the complexity of these interactions remains elusive. We have constructed a mathematical model that simulates Ca(2+) patterns under the influence of Aβ. Our simulations shows that Aβ can increase regions of mixed-mode oscillations leading to aberrant signals under various conditions. We investigate how Aβ affects individual flux contributions through inositol triphosphate (IP(3)) receptors, ryanodine receptors, and membrane pores. We demonstrate that controlling for the ryanodine receptor’s maximal kinetic reaction rate may provide a biophysical way of managing aberrant Ca(2+) signals. The influence of a dynamic model for IP(3) production is also investigated under various conditions as well as the impact of changes in membrane potential. Our model is one of the first to investigate the effects of Aβ on a variety of cellular mechanisms providing a base modeling scheme from which further studies can draw on to better understand Ca(2+) regulation in an AD environment.