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

Abstract

The accumulation of Alzheimer’s disease (AD) associated Amyloid beta (Aβ) oligomers can trigger aberrant intracellular calcium (Ca2+) levels by disrupting the intrinsic Ca2+ 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 Ca2+ fluxes, the complexity of these interactions remains elusive. We have constructed a mathematical model that simulates Ca2+ 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 (IP3) 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 Ca2+ signals. The influence of a dynamic model for IP3 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 Ca2+ regulation in an AD environment.

Current understanding of metal ions in the pathogenesis of Alzheimer’s disease

“…Intracellular Ca 2+ dysregulation is an early manifestation of AD. Studies have shown that Ca 2+ concentrations near Aβ deposits are significantly increased, and the increase of Ca 2+ likely plays a key role in the cognitive deficits associated with AD [64,65]. Ca 2+ elevation can promote Aβ production and the cellular toxicity of Aβ, while the elevation of Aβ in turn contributes to the increased intracellular Ca 2+ .…”

Simulation of Ca2+oscillations in astrocytes mediated by amyloid beta in Alzheimer’s disease

“…Astrocytes are hypothesized as the primary target of Aneurotoxicity [2]. Recently, a computational model has been applied to investigate the effects of Aon Ca 2+ regulation in an AD environment [3]. So far, there has been no model addressing the unique features of astrocyte.…”

“…And the corresponding flux is: Referred to the previous work [3,4], the other Ca 2+ fluxes J CICR , J SERCA , J RyR , J LER , J in and J pm are written as:…”

Quantifying the dose-dependent impact of intracellular amyloid beta in a mathematical model of calcium regulation in xenopus oocyte

“…The flux terms in Eqs ( 1) and (2) can be modeled using various formulations, such as a saturating binding rate model for IP 3 R [34,35] and Markov models [36][37][38]. For our purposes, we assume that the flux from IP 3 Rs follows a formulation based on previous models found in [39][40][41].…”