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

A nonlinear meccano for Alzheimer's emergence by amyloid β-mediated glutamatergic hyperactivity

The pathophysiological process of Alzheimer's disease (AD) is believed to begin many years before the formal diagnosis of AD dementia. This protracted preclinical phase offers a crucial window for potential therapeutic interventions, yet its comprehensive characterization remains elusive. Accumulating evidence suggests that amyloid-β (Aβ) may mediate neuronal hyperactivity in circuit dysfunction in the early stages of AD. At the same time, neural activity can also facilitate Aβ accumulation through intricate feed-forward interactions, complicating elucidating the conditions governing Aβ-dependent hyperactivity and its diagnostic utility. In this study, we use biophysical modeling to shed light on such conditions. Our analysis reveals that the inherently nonlinear nature of the underlying molecular interactions can give rise to the emergence of various modes of hyperactivity. This diversity in the mechanisms of hyperactivity may ultimately account for a spectrum of AD manifestations.

Data-driven Stochastic Model for Quantifying the Interplay Between Amyloid-beta and Calcium Levels in Alzheimer's Disease

The abnormal aggregation of extracellular amyloid-β ( A β ) in senile plaques resulting in calcium C a + 2 dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving A β deposition and C a + 2 dysregulation. Importantly, synaptic impairments, neuronal loss, and cognitive failure in AD patients are all related to the buildup of intraneuronal A β accumulation. Moreover, increasing evidence show a feed-forward loop between A β and C a + 2 levels, i.e. A β disrupts neuronal C a + 2 levels, which in turn affects the formation of A β . To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between A β and C a + 2 using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from 2-year visits for AD patients, we employ this method to investigate the interplay between A β and C a + 2 levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either A β metabolism or intracellular C a + 2 homeostasis causes the relative growth rate in both C a + 2 and A β , which corresponds to the development of AD. The imbalance of C a + 2 ions causes A β disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of C a + 2 ion transportation and deposition. This suggests that altering the C a + 2 balance or the balance between A β and C a + 2 by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy.

Monoclonal antibody therapy for Alzheimer's disease focusing on intracerebral targets

Alzheimer's disease (AD) is one of the most common neurodegenerative diseases. Due to the complexity of the disorder and the presence of the blood-brain barrier (BBB), its drug discovery and development are facing enormous challenges, especially after several failures of monoclonal antibody (mAb) trials. Nevertheless, the Food and Drug Administration's approval of the mAb aducanumab has ushered in a new day. As we better understand the disease's pathogenesis and identify novel intracerebral therapeutic targets, antibody-based therapies have advanced over the past few years. The mAb drugs targeting β-amyloid or hyperphosphorylated tau protein are the focus of the current research. Massive neuronal loss and glial cell-mediated inflammation are also the vital pathological hallmarks of AD, signaling a new direction for research on mAb drugs. We have elucidated the mechanisms by which AD-specific mAbs cross the BBB to bind to targets. In order to investigate therapeutic approaches to treat AD, this review focuses on the promising mAbs targeting intracerebral dysfunction and related strategies to cross the BBB.

How Can We Use Mathematical Modeling of Amyloid-β in Alzheimer's Disease Research and Clinical Practices?

The accumulation of amyloid-β (Aβ) plaques in the brain is considered a hallmark of Alzheimer's disease (AD). Mathematical modeling, capable of predicting the motion and accumulation of Aβ, has obtained increasing interest as a potential alternative to aid the diagnosis of AD and predict disease prognosis. These mathematical models have provided insights into the pathogenesis and progression of AD that are difficult to obtain through experimental studies alone. Mathematical modeling can also simulate the effects of therapeutics on brain Aβ levels, thereby holding potential for drug efficacy simulation and the optimization of personalized treatment approaches. In this review, we provide an overview of the mathematical models that have been used to simulate brain levels of Aβ (oligomers, protofibrils, and/or plaques). We classify the models into five categories: the general ordinary differential equation models, the general partial differential equation models, the network models, the linear optimal ordinary differential equation models, and the modified partial differential equation models (i.e., Smoluchowski equation models). The assumptions, advantages and limitations of these models are discussed. Given the popularity of using the Smoluchowski equation models to simulate brain levels of Aβ, our review summarizes the history and major advancements in these models (e.g., their application to predict the onset of AD and their combined use with network models). This review is intended to bring mathematical modeling to the attention of more scientists and clinical researchers working on AD to promote cross-disciplinary research.

Intracellular Injection of Brain Extracts from Alzheimer's Disease Patients Triggers Unregulated Ca2+ Release from Intracellular Stores That Hinders Cellular Bioenergetics

Strong evidence indicates that amyloid beta (Aβ) inflicts its toxicity in Alzheimer's disease (AD) by promoting uncontrolled elevation of cytosolic Ca²⁺ in neurons. We have previously shown that synthetic Aβ42 oligomers stimulate abnormal intracellular Ca²⁺ release from the endoplasmic reticulum stores, suggesting that a similar mechanism of Ca²⁺ toxicity may be common to the endogenous Aβs oligomers. Here, we use human postmortem brain extracts from AD-affected patients and test their ability to trigger Ca²⁺ fluxes when injected intracellularly into Xenopus oocytes. Immunological characterization of the samples revealed the elevated content of soluble Aβ oligomers only in samples from AD patients. Intracellular injection of brain extracts from control patients failed to trigger detectable changes in intracellular Ca²⁺. Conversely, brain extracts from AD patients triggered Ca²⁺ events consisting of local and global Ca²⁺ fluorescent transients. Pre-incubation with either the conformation-specific OC antiserum or caffeine completely suppressed the brain extract's ability to trigger cytosolic Ca²⁺ events. Computational modeling suggests that these Ca²⁺ fluxes may impair cells bioenergetic by affecting ATP and ROS production. These results support the hypothesis that Aβ oligomers contained in neurons of AD-affected brains may represent the toxic agents responsible for neuronal malfunctioning and death associated with the disruption of Ca²⁺ homeostasis.

Role of Microglia and Astrocytes in Alzheimer’s Disease: From Neuroinflammation to Ca2+ Homeostasis Dysregulation

Alzheimer’s disease (AD) is the most common form of dementia worldwide, with a complex, poorly understood pathogenesis. Cerebral atrophy, amyloid-β (Aβ) plaques, and neurofibrillary tangles represent the main pathological hallmarks of the AD brain. Recently, neuroinflammation has been recognized as a prominent feature of the AD brain and substantial evidence suggests that the inflammatory response modulates disease progression. Additionally, dysregulation of calcium (Ca2+) homeostasis represents another early factor involved in the AD pathogenesis, as intracellular Ca2+ concentration is essential to ensure proper cellular and neuronal functions. Although growing evidence supports the involvement of Ca2+ in the mechanisms of neurodegeneration-related inflammatory processes, scant data are available on its contribution in microglia and astrocytes functioning, both in health and throughout the AD continuum. Nevertheless, AD-related aberrant Ca2+ signalling in astrocytes and microglia is crucially involved in the mechanisms underpinning neuroinflammatory processes that, in turn, impact neuronal Ca2+ homeostasis and brain function. In this light, we attempted to provide an overview of the current understanding of the interactions between the glia cells-mediated inflammatory responses and the molecular mechanisms involved in Ca2+ homeostasis dysregulation in AD.

Impact of β-Amyloids Induced Disruption of Ca2+ Homeostasis in a Simple Model of Neuronal Activity

Alzheimer’s disease is characterized by a marked dysregulation of intracellular Ca²⁺ homeostasis. In particular, toxic β-amyloids (Aβ) perturb the activities of numerous Ca²⁺ transporters or channels. Because of the tight coupling between Ca²⁺ dynamics and the membrane electrical activity, such perturbations are also expected to affect neuronal excitability. We used mathematical modeling to systematically investigate the effects of changing the activities of the various targets of Aβ peptides reported in the literature on calcium dynamics and neuronal excitability. We found that the evolution of Ca²⁺ concentration just below the plasma membrane is regulated by the exchanges with the extracellular medium, and is practically independent from the Ca²⁺ exchanges with the endoplasmic reticulum. Thus, disruptions of Ca²⁺ homeostasis interfering with signaling do not affect the electrical properties of the neurons at the single cell level. In contrast, the model predicts that by affecting the activities of L-type Ca²⁺ channels or Ca²⁺-activated K⁺ channels, Aβ peptides promote neuronal hyperexcitability. On the contrary, they induce hypo-excitability when acting on the plasma membrane Ca²⁺ ATPases. Finally, the presence of pores of amyloids in the plasma membrane can induce hypo- or hyperexcitability, depending on the conditions. These modeling conclusions should help with analyzing experimental observations in which Aβ peptides interfere at several levels with Ca²⁺ signaling and neuronal activity.

Unraveling Aβ-Mediated Multi-Pathway Calcium Dynamics in Astrocytes: Implications for Alzheimer's Disease Treatment From Simulations

The accumulation of amyloid β peptide (Aβ) in the brain is hypothesized to be the major factor driving Alzheimer's disease (AD) pathogenesis. Mounting evidence suggests that astrocytes are the primary target of Aβ neurotoxicity. Aβ is known to interfere with multiple calcium fluxes, thus disrupting the calcium homeostasis regulation of astrocytes, which are likely to produce calcium oscillations. Ca²⁺ dyshomeostasis has been observed to precede the appearance of clinical symptoms of AD; however, it is experimentally very difficult to investigate the interactions of many mechanisms. Given that Ca²⁺ disruption is ubiquitously involved in AD progression, it is likely that focusing on Ca²⁺ dysregulation may serve as a potential therapeutic approach to preventing or treating AD, while current hypotheses concerning AD have so far failed to yield curable therapies. For this purpose, we derive and investigate a concise mathematical model for Aβ-mediated multi-pathway astrocytic intracellular Ca²⁺ dynamics. This model accounts for how Aβ affects various fluxes contributions through voltage-gated calcium channels, Aβ-formed channels and ryanodine receptors. Bifurcation analysis of Aβ level, which reflected the corresponding progression of the disease, revealed that Aβ significantly induced the increasing [Ca²⁺] _i and frequency of calcium oscillations. The influence of inositol 1,4,5-trisphosphate production (IP₃) is also investigated in the presence of Aβ as well as the impact of changes in resting membrane potential. In turn, the Ca²⁺ flux can be considerably changed by exerting specific interventions, such as ion channel blockers or receptor antagonists. By doing so, a "combination therapy" targeting multiple pathways simultaneously has finally been demonstrated to be more effective. This study helps to better understand the effect of Aβ, and our findings provide new insight into the treatment of AD.

A Neuron-Glial Model of Exosomal Release in the Onset and Progression of Alzheimer's Disease

Exosomes are nano-sized extracellular vesicles that perform a variety of biological functions linked to the pathogenesis of various neurodegenerative disorders. In Alzheimer's disease (AD), for examples, exosomes are responsible for the release of Aβ oligomers, and their extracellular accumulation, although the underpinning molecular machinery remains elusive. We propose a novel model for Alzheimer's Aβ accumulation based on Ca²⁺-dependent exosome release from astrocytes. Moreover, we exploit our model to assess how temperature dependence of exosome release could interact with Aβ neurotoxicity. We predict that voltage-gated Ca²⁺ channels (VGCCs) along with the transient-receptor potential M8 (TRPM8) channel are crucial molecular components in Alzheimer's progression.

Calcium Dyshomeostasis in Alzheimer's Disease Pathogenesis

Alzheimer’s disease (AD) is the most common age-related neurodegenerative disorder that is characterized by amyloid β-protein deposition in senile plaques, neurofibrillary tangles consisting of abnormally phosphorylated tau protein, and neuronal loss leading to cognitive decline and dementia. Despite extensive research, the exact mechanisms underlying AD remain unknown and effective treatment is not available. Many hypotheses have been proposed to explain AD pathophysiology; however, there is general consensus that the abnormal aggregation of the amyloid β peptide (Aβ) is the initial event triggering a pathogenic cascade of degenerating events in cholinergic neurons. The dysregulation of calcium homeostasis has been studied considerably to clarify the mechanisms of neurodegeneration induced by Aβ. Intracellular calcium acts as a second messenger and plays a key role in the regulation of neuronal functions, such as neural growth and differentiation, action potential, and synaptic plasticity. The calcium hypothesis of AD posits that activation of the amyloidogenic pathway affects neuronal Ca²⁺ homeostasis and the mechanisms responsible for learning and memory. Aβ can disrupt Ca²⁺ signaling through several mechanisms, by increasing the influx of Ca²⁺ from the extracellular space and by activating its release from intracellular stores. Here, we review the different molecular mechanisms and receptors involved in calcium dysregulation in AD and possible therapeutic strategies for improving the treatment.

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

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.

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

Background

The homeostasis of metal ions, such as iron, copper, zinc and calcium, in the brain is crucial for maintaining normal physiological functions. Studies have shown that imbalance of these metal ions in the brain is closely related to the onset and progression of Alzheimer's disease (AD), the most common neurodegenerative disorder in the elderly.

Main body

Erroneous deposition/distribution of the metal ions in different brain regions induces oxidative stress. The metal ions imbalance and oxidative stress together or independently promote amyloid-β (Aβ) overproduction by activating β- or γ-secretases and inhibiting α-secretase, it also causes tau hyperphosphorylation by activating protein kinases, such as glycogen synthase kinase-3β (GSK-3β), cyclin-dependent protein kinase-5 (CDK5), mitogen-activated protein kinases (MAPKs), etc., and inhibiting protein phosphatase 2A (PP2A). The metal ions imbalances can also directly or indirectly disrupt organelles, causing endoplasmic reticulum (ER) stress; mitochondrial and autophagic dysfunctions, which can cause or aggravate Aβ and tau aggregation/accumulation, and impair synaptic functions. Even worse, the metal ions imbalance-induced alterations can reversely exacerbate metal ions misdistribution and deposition. The vicious cycles between metal ions imbalances and Aβ/tau abnormalities will eventually lead to a chronic neurodegeneration and cognitive deficits, such as seen in AD patients.

Conclusion

The metal ions imbalance induces Aβ and tau pathologies by directly or indirectly affecting multiple cellular/subcellular pathways, and the disrupted homeostasis can reversely aggravate the abnormalities of metal ions transportation/deposition. Therefore, adjusting metal balance by supplementing or chelating the metal ions may be potential in ameliorating AD pathologies, which provides new research directions for AD treatment.

Amyloids: Regulators of Metal Homeostasis in the Synapse

Conformational changes in amyloidogenic proteins, such as β-amyloid protein, prion proteins, and α-synuclein, play a critical role in the pathogenesis of numerous neurodegenerative diseases, including Alzheimer’s disease, prion disease, and Lewy body disease. The disease-associated proteins possess several common characteristics, including the ability to form amyloid oligomers with β-pleated sheet structure, as well as cytotoxicity, although they differ in amino acid sequence. Interestingly, these amyloidogenic proteins all possess the ability to bind trace metals, can regulate metal homeostasis, and are co-localized at the synapse, where metals are abundantly present. In this review, we discuss the physiological roles of these amyloidogenic proteins in metal homeostasis, and we propose hypothetical models of their pathogenetic role in the neurodegenerative process as the loss of normal metal regulatory functions of amyloidogenic proteins. Notably, these amyloidogenic proteins have the capacity to form Ca²⁺-permeable pores in membranes, suggestive of a toxic gain of function. Therefore, we focus on their potential role in the disruption of Ca²⁺ homeostasis in amyloid-associated neurodegenerative diseases.