Composite mathematical modeling of calcium signaling behind neuronal cell death in Alzheimer's disease

Mathematical models on Alzheimer's disease and its treatment: A review

Alzheimer's disease is a gradually advancing neurodegenerative disease. According to the report by "World Health Organization (WHO)", there are over 55 million individuals currently living with Alzheimer's disease and other dementia globally, and the number of sufferers is increasing every day. In absence of effective cures and preventive measures, this number is predicted to triple by 2050. The disease's origin is still unclear, and also no such treatment is available for eradicating the disease. Based on the crucial factors that are connected to the disease's progression, the authors developed several types of mathematical models. We review such mathematical models that are utilized to better understand the pathophysiology of Alzheimer's disease. Section-wise, we categorize the mathematical models in terms of different components that might be responsible for Alzheimer's disease. We explain the mathematical models with their descriptions and respective conclusions. In addition to mathematical models, we concentrate on biological aspects of the disease and possible therapeutic targets. We explore the disease's biological basis primarily to understand how proteins, glial cells, cytokines, genes, calcium signaling and oxidative stress contribute to the disease. We go through several treatment targets that might stop the progression of the disease or at least slow it down. We present a table that summarizes the mathematical models in terms of their formalisms, highlighting key components and important remarks.

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.

Hallmarks of neurodegenerative disease: A systems pharmacology perspective

Age-related central neurodegenerative diseases, such as Alzheimer's and Parkinson's disease, are a rising public health concern and have been plagued by repeated drug development failures. The complex nature and poor mechanistic understanding of the etiology of neurodegenerative diseases has hindered the discovery and development of effective disease-modifying therapeutics. Quantitative systems pharmacology models of neurodegeneration diseases may be useful tools to enhance the understanding of pharmacological intervention strategies and to reduce drug attrition rates. Due to the similarities in pathophysiological mechanisms across neurodegenerative diseases, especially at the cellular and molecular levels, we envision the possibility of structural components that are conserved across models of neurodegenerative diseases. Conserved structural submodels can be viewed as building blocks that are pieced together alongside unique disease components to construct quantitative systems pharmacology (QSP) models of neurodegenerative diseases. Model parameterization would likely be different between the different types of neurodegenerative diseases as well as individual patients. Formulating our mechanistic understanding of neurodegenerative pathophysiology as a mathematical model could aid in the identification and prioritization of drug targets and combinatorial treatment strategies, evaluate the role of patient characteristics on disease progression and therapeutic response, and serve as a central repository of knowledge. Here, we provide a background on neurodegenerative diseases, highlight hallmarks of neurodegeneration, and summarize previous QSP models of neurodegenerative diseases.

Computational analysis of cortical neuronal excitotoxicity in a large animal model of neonatal brain injury

BACKGROUND

Neonatal hypoxic brain injury is a major cause of intellectual and developmental disability. Hypoxia causes neuronal dysfunction and death in the developing cerebral cortex due to excitotoxic Ca²⁺-influx. In the translational piglet model of hypoxic encephalopathy, we have previously shown that hypoxia overactivates Ca²⁺/Calmodulin (CaM) signaling via Sarcoma (Src) kinase in cortical neurons, resulting in overexpression of proapoptotic genes. However, identifying the exact relationship between alterations in neuronal Ca²⁺-influx, molecular determinants of cell death, and the degree of hypoxia in a dynamic system represents a significant challenge.

METHODS

We used experimental and computational methods to identify molecular events critical to the onset of excitotoxicity-induced apoptosis in the cerebral cortex of newborn piglets. We used 2-3-day-old piglets (normoxic [Nx], hypoxic [Hx], and hypoxic + Src-inhibitor-treatment [Hx+PP2] groups) for biochemical analysis of ATP production, Ca²⁺-influx, and Ca²⁺/CaM-dependent protein kinase kinase 2 (CaMKK2) expression. We then used SimBiology to build a computational model of the Ca²⁺/CaM-Src-kinase signaling cascade, simulating Nx, Hx, and Hx+PP2 conditions. To evaluate our model, we used Sobol variance decomposition, multiparametric global sensitivity analysis, and parameter scanning.

RESULTS

Our model captures important molecular trends caused by hypoxia in the piglet brain. Incorporating the action of Src kinase inhibitor PP2 further validated our model and enabled predictive analysis of the effect of hypoxia on CaMKK2. We determined the impact of a feedback loop related to Src phosphorylation of NMDA receptors and activation kinetics of CaMKII. We also identified distinct modes of signaling wherein Ca²⁺ level alterations following Src kinase inhibition may not be a linear predictor of changes in Bax expression. Importantly, our model indicates that while pharmacological pre-treatment significantly reduces the onset of abnormal Ca²⁺-influx, there exists a window of intervention after hypoxia during which targeted modulation of Src-NMDAR interaction kinetics in combination with PP2 administration can reduce Ca²⁺-influx and Bax expression to similar levels as pre-treatment.

CONCLUSIONS

Our model identifies new dynamics of critical components in the Ca²⁺/CaM-Src signaling pathway leading to neuronal injury and provides a feasible framework for drug efficacy studies in translational models of neonatal brain injury for the prevention of intellectual and developmental disabilities.

Delineation of Neuroprotective Effects and Possible Benefits of AntioxidantsTherapy for the Treatment of Alzheimer's Diseases by Targeting Mitochondrial-Derived Reactive Oxygen Species: Bench to Bedside

Alzheimer's disease (AD) is considered the sixth leading cause of death in elderly patients and is characterized by progressive neuronal degeneration and impairment in memory, language, etc. AD is characterized by the deposition of senile plaque, accumulation of fibrils, and neurofibrillary tangles (NFTs) which are responsible for neuronal degeneration. Amyloid-β (Aβ) plays a key role in the process of neuronal degeneration in the case of AD. It has been reported that Aβ is responsible for the production of reactive oxygen species (ROS), depletion of endogenous antioxidants, increase in intracellular Ca²⁺ which further increases mitochondria dysfunctions, oxidative stress, release of pro-apoptotic factors, neuronal apoptosis, etc. Thus, oxidative stress plays a key role in the pathogenesis of AD. Antioxidants are compounds that have the ability to counteract the oxidative damage conferred by ROS. Therefore, the antioxidant therapy may provide benefits and halt the progress of AD to advance stages by counteracting neuronal degeneration. However, despite the beneficial effects imposed by the antioxidants, the findings from the clinical studies suggested inconsistent results which might be due to poor study design, selection of the wrong antioxidant, inability of the molecule to cross the blood-brain barrier (BBB), treatment in the advanced state of disease, etc. The present review insights into the neuroprotective effects and limitations of the antioxidant therapy for the treatment of AD by targeting mitochondrial-derived ROS. This particular article will certainly help the researchers to search new avenues for the treatment of AD by utilizing mitochondrial-derived ROS-targeted antioxidant therapies.

A multitude of signaling pathways associated with Alzheimer's disease and their roles in AD pathogenesis and therapy

The exact molecular mechanisms associated with Alzheimer's disease (AD) pathology continue to represent a mystery. In the past decades, comprehensive data were generated on the involvement of different signaling pathways in the AD pathogenesis. However, the utilization of signaling pathways as potential targets for the development of drugs against AD is rather limited due to the immense complexity of the brain and intricate molecular links between these pathways. Therefore, finding a correlation and cross-talk between these signaling pathways and establishing different therapeutic targets within and between those pathways are needed for better understanding of the biological events responsible for the AD-related neurodegeneration. For example, autophagy is a conservative cellular process that shows link with many other AD-related pathways and is crucial for maintenance of the correct cellular balance by degrading AD-associated pathogenic proteins. Considering the central role of autophagy in AD and its interplay with many other pathways, the finest therapeutic strategy to fight against AD is the use of autophagy as a target. As an essential step in this direction, this comprehensive review represents recent findings on the individual AD-related signaling pathways, describes key features of these pathways and their cross-talk with autophagy, represents current drug development, and introduces some of the multitarget beneficial approaches and strategies for the therapeutic intervention of AD.

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.

Tributyltin Alters Calcium Levels, Mitochondrial Dynamics, and Activates Calpains Within Dorsal Root Ganglion Neurons

Tributyltin (TBT) remains a global health concern. The primary route of human exposure to TBT is either through ingestion or skin absorption, but TBT's effects on the peripheral nervous system have still not been investigated. Therefore, we exposed in vitro sensory dorsal root ganglion (DRG) neurons to TBT at a concentration of 50-200 nM, which is similar to the observed concentrations of TBT in human blood samples. We observed that TBT causes extensive axon degeneration and neuronal death in the DRG neurons. Furthermore, we discovered that TBT causes an increase in both cytosolic and mitochondrial calcium levels, disrupts mitochondrial dynamics, decreases neuronal ATP levels, and leads to the activation of calpains. Additional experiments demonstrated that inhibition of calpain activation prevented TBT-induced fragmentation of neuronal cytoskeletal proteins and neuronal cell death. Thus, we conclude that calpain activation is the key executioner of TBT-induced peripheral neurodegeneration.

Power Failure of Mitochondria and Oxidative Stress in Neurodegeneration and Its Computational Models

The brain needs more energy than other organs in the body. Mitochondria are the generator of vital power in the living organism. Not only do mitochondria sense signals from the outside of a cell, but they also orchestrate the cascade of subcellular events by supplying adenosine-5'-triphosphate (ATP), the biochemical energy. It is known that impaired mitochondrial function and oxidative stress contribute or lead to neuronal damage and degeneration of the brain. This mini-review focuses on addressing how mitochondrial dysfunction and oxidative stress are associated with the pathogenesis of neurodegenerative disorders including Alzheimer's disease, amyotrophic lateral sclerosis, Huntington's disease, and Parkinson's disease. In addition, we discuss state-of-the-art computational models of mitochondrial functions in relation to oxidative stress and neurodegeneration. Together, a better understanding of brain disease-specific mitochondrial dysfunction and oxidative stress can pave the way to developing antioxidant therapeutic strategies to ameliorate neuronal activity and prevent neurodegeneration.

Susceptibility to cellular stress in PS1 mutant N2a cells is associated with mitochondrial defects and altered calcium homeostasis

Presenilin 1 (PS1) mutations are the most common cause of familial Alzheimer's disease (FAD). PS1 also plays a role in cellular processes such as calcium homeostasis and autophagy. We hypothesized that mutant presenilins increase cellular vulnerability to stress. We stably expressed human PS1, mutant PS1E280A and mutant PS1Δ9 in mouse neuroblastoma N2a cells. We examined early signs of stress in different conditions: endoplasmic reticulum (ER) stress, calcium overload, oxidative stress, and Aβ 1-42 oligomers toxicity. Additionally, we induced autophagy via serum starvation. PS1 mutations did not have an effect in ER stress but PS1E280A mutation affected autophagy. PS1 overexpression influenced calcium homeostasis and generated mitochondrial calcium overload modifying mitochondrial function. However, the opening of the mitochondrial permeability transition pore (MPTP) was affected in PS1 mutants, being accelerated in PS1E280A and inhibited in PS1Δ9 cells. Altered autophagy in PS1E280A cells was neither modified by inhibition of γ-secretase, nor by ER calcium retention. MPTP opening was directly regulated by γ-secretase inhibitors independent on organelle calcium modulation, suggesting a novel direct role for PS1 and γ-secretase in mitochondrial stress. We identified intrinsic cellular vulnerability to stress in PS1 mutants associated simultaneously with both, autophagic and mitochondrial function, independent of Aβ pathology.

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.