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

Abstract

Alzheimer’s disease (AD) is a devastating illness affecting over 40 million people worldwide. Intraneuronal rise of amyloid beta in its oligomeric forms (iAβOs), has been linked to the pathogenesis of AD by disrupting cytosolic Ca2+ homeostasis. However, the specific mechanisms of action are still under debate and intense effort is ongoing to improve our understanding of the crucial steps involved in the mechanisms of AβOs toxicity. We report the development of a mathematical model describing a proposed mechanism by which stimulation of Phospholipase C (PLC) by iAβO, triggers production of IP3 with consequent abnormal release of Ca2+ from the endoplasmic reticulum (ER) through activation of IP3 receptor (IP3R) Ca2+ channels. After validating the model using experimental data, we quantify the effects of intracellular rise in iAβOs on model solutions. Our model validates a dose-dependent influence of iAβOs on IP3-mediated Ca2+ signaling. We investigate Ca2+ signaling patterns for small and large iAβOs doses and study the role of various parameters on Ca2+ signals. Uncertainty quantification and partial rank correlation coefficients are used to better understand how the model behaves under various parameter regimes. Our model predicts that iAβO alter IP3R sensitivity to IP3 for large doses. Our analysis also shows that the upstream production of IP3 can influence Aβ-driven solution patterns in a dose-dependent manner. Model results illustrate and confirm the detrimental impact of iAβOs on IP3 signaling.

Intracellular injection of brain extracts from Alzheimer’s disease patients trigger unregulated Ca2+ release from intracellular stores that hinders cellular bioenergetics

“…Using pharmacological and computational investigation, we proposed that one of the mechanisms by which synthetic Aβ42 oligomers affect cells functioning involve the overproduction IP 3 through stimulation of the G-protein complex triggering uncontrolled release of Ca 2+ though the IP 3 Rs [8, 10, 41]. Intriguingly, these experiments were carried out using synthetic Aβ42 oligomers with high immunoreactivity to OC antibody, implying that similar toxicity may be carry out by endogenous intracellular Aβ oligomer on neurons of AD affected brains.…”

“…Pharmacological and computational studies reveal that application of synthetic Aβ42 oligomers to different cells type, induce a G-protein-mediated stimulation of IP3 production, triggering intracellular Ca 2+ fluxes leading to a disruption of intracellular Ca 2+ homeostasis. [7, 8, 10, 11]…”

Upregulated Ca2+ release from the endoplasmic reticulum leads to impaired presynaptic function in Alzheimer’s disease

“…As a critical second messenger, the pathways for IP 3 metabolism are succinctly described in Eq. 5 [112, 114], with further details in Table 4 . Inhomogeneity of ligands persists throughout the bouton; however, we assume spatially homogenous compartments, and only track temporal evolution of ligands.…”

Computer-assisted proofs of Hopf bubbles and degenerate Hopf bifurcations

“…This non-local bifurcation structure, characterized by the connection of two Hopf bifurcations by a one-parameter branch of periodic orbits, has been given several names in different scientific fields. In intracellular calcium, it is frequently called a Hopf bubble [7,16,22,27]. In infectious-disease modelling, where the bifurcation typically occurs at an endemic equilibrium, the accepted term is endemic bubble [8,17,18,23,26].…”

“…For the function (s, u) → F s (u), denote by ∂ s the Fréchet derivative with respect to s, and D the derivative with respect to u. Given the interpolants ûs = (v s , ρs ) and Φs,j , let û and Φ j denote their Fréchet derivatives with respect to s. Also, denote ĉ s,j = ∂ s ĉs,j , for ĉs,j defined in (22). Note that these derivatives are constant, since the interpolants are linear in s. Then…”