How the formation of amyloid plaques and neurofibrillary tangles may be related: a mathematical modelling study

Effect of diffusivity of amyloid beta monomers on the formation of senile plaques

Alzheimer's disease (AD) presents a perplexing question: why does its development span decades, even though individual amyloid beta (Aβ) deposits (senile plaques) can form rapidly in as little as 24 hours, as recent publications suggest? This study investigated whether the formation of senile plaques can be limited by factors other than polymerization kinetics alone. Instead, their formation may be limited by the diffusion-driven supply of Aβ monomers, along with the rate at which the monomers are produced from amyloid precursor protein and the rate at which Aβ monomers undergo degradation. A mathematical model incorporating the nucleation and autocatalytic process (via the Finke-Watzky model), as well as Aβ monomer diffusion, was proposed. The obtained system of partial differential equations was solved numerically, and a simplified version was investigated analytically. The computational results predicted that it takes approximately 7 years for Aβ aggregates to reach a neurotoxic concentration of 50 μM. Additionally, a sensitivity analysis was performed to examine how the diffusivity of Aβ monomers and their production rate impact the concentration of Aβ aggregates.

Pedunculoside alleviates cognitive deficits and neuronal cell apoptosis by activating the AMPK signaling cascade

BACKGROUND

Mitochondrial dysfunction emerges as an early pathological hallmark of Alzheimer's disease (AD). The reduction in mitochondrial membrane potential and the elevation of reactive oxygen species (ROS) production are pivotal in the initiation of neuronal cell apoptosis. Pedunculoside(Ped), a novel triterpene saponin derived from the dried barks of Ilex rotunda Thunb, exhibits a potent anti-inflammatory effect. In the course of drug screening, we discovered that Ped offers significant protection against apoptosis induced by Aβ1-42. Nevertheless, the role and mechanism of Ped in AD are yet to be elucidated.

METHODS

Oxidative stress was evaluated by measuring mitochondrial membrane potential and intracellular ROS production. The expression of proteins associated with apoptosis was determined using western blot analysis and flow cytometry. In vivo, the pathological characteristics of AD were investigated through Western blot and tissue immunofluorescence techniques. Cognitive function was assessed using the Morris Water Maze and Novel Object Recognition tests.

RESULTS

We demonstrated that Ped decreased apoptosis in PC12 cells, reduced the generation of intracellular ROS, and restored mitochondrial membrane potential. Mechanistically, we found that the protective effect of Ped against Aβ-induced neurotoxicity was associated with activation of the AMPK/GSK-3β/Nrf2 signaling pathway. In vivo, Ped alleviated memory deficits and inhibited neuronal apoptosis, inflammation, and oxidative stress in the hippocampus of 3 × Tg AD mice, along with the activation of the AMPK signaling pathway.

CONCLUSION

The findings indicate that Ped exerts its neuroprotective effects against oxidative stress and apoptosis through the AMPK signaling cascade. The results demonstrate that Ped is a potential candidate for the treatment of AD.

The growth rate of senile plaques is determined by the competition between the rate of deposition of free Aβ aggregates into plaques and the autocatalytic production of free Aβ aggregates

The formation of amyloid beta (Aβ) deposits (senile plaques) is one of the hallmarks of Alzheimer's disease (AD). This study investigates what processes are primarily responsible for their formation. A model is developed to simulate the diffusion of amyloid beta (Aβ) monomers, the production of free Aβ aggregates through nucleation and autocatalytic processes, and the deposition of these aggregates into senile plaques. The model suggests that efficient degradation of Aβ monomers alone may suffice to prevent the growth of senile plaques, even without degrading Aβ aggregates and existing plaques. This is because the degradation of Aβ monomers interrupts the supply of reactants needed for plaque formation. The impact of Aβ monomer diffusivity is demonstrated to be small, enabling the application of the lumped capacitance approximation and the derivation of approximate analytical solutions for limiting cases with both small and large rates of Aβ aggregate deposition into plaques. It is found that the rate of plaque growth is governed by two competing processes. One is the deposition rate of free Aβ aggregates into senile plaques. If this rate is small, the plaque grows slowly. However, if the rate of deposition of Aβ aggregates into senile plaques is very large, the free Aβ aggregates are removed from the intracellular fluid by deposition into the plaques, leaving insufficient free Aβ aggregates to catalyze the production of new aggregates. This suggests that under certain conditions, Aβ plaques may offer neuroprotection and impede their own growth. Additionally, it indicates that there exists an optimal rate of deposition of free Aβ aggregates into the plaques, at which the plaques attain their maximum size.

Pivotal role of AGE-RAGE axis in brain aging with current interventions

Brain aging is characterized by several structural, biochemical and molecular changes which can vary among different individuals and can be influenced by genetic, environmental and lifestyle factors. Accumulation of protein aggregates, altered neurotransmitter composition, low-grade chronic inflammation and prolonged oxidative stress have been shown to contribute to brain tissue damage. Among key metabolic byproducts, advanced glycation end products (AGEs), formed endogenously through non-enzymatic reactions or acquired directly from the diet or other exogenous sources, have been detected to accumulate in brain tissue, exerting detrimental effects on cellular structure and function, contributing to neurodegeneration and cognitive decline. Upon binding to signal transduction receptor RAGE, AGEs can initiate pro-inflammatory pathways, exacerbate oxidative stress and neuroinflammation, thus impairing neuronal function and cognition. AGE-RAGE signaling induces programmed cell death, disrupts the blood-brain barrier and promotes protein aggregation, further compromising brain health. In this review, we investigate the intricate relationship between the AGE-RAGE pathway and brain aging in order to detect affected molecules and potential targets for intervention. Reduction of AGE deposition in brain tissue either through novel pharmacological therapeutics, dietary modifications, and lifestyle changes, shows a great promise in mitigating cognitive decline associated with brain aging.

Numerical and Analytical Simulation of the Growth of Amyloid-β Plaques

Numerical and analytical solutions were employed to calculate the radius of an amyloid-β (Aβ) plaque over time. To the author's knowledge, this study presents the first model simulating the growth of Aβ plaques. Findings indicate that the plaque can attain a diameter of 50 μm after 20 years of growth, provided the Aβ monomer degradation machinery is malfunctioning. A mathematical model incorporates nucleation and autocatalytic growth processes using the Finke-Watzky model. The resulting system of ordinary differential equations was solved numerically, and for the simplified case of infinitely long Aβ monomer half-life, an analytical solution was found. Assuming that Aβ aggregates stick together and using the distance between the plaques as an input parameter of the model, it was possible to calculate the plaque radius from the concentration of Aβ aggregates. This led to the "cube root hypothesis," positing that Aβ plaque size increases proportionally to the cube root of time. This hypothesis helps explain why larger plaques grow more slowly. Furthermore, the obtained results suggest that the plaque size is independent of the kinetic constants governing Aβ plaque agglomeration, indicating that the kinetics of Aβ plaque agglomeration is not a limiting factor for plaque growth. Instead, the plaque growth rate is limited by the rates of Aβ monomer production and degradation.

Personalized Computational Causal Modeling of the Alzheimer Disease Biomarker Cascade

BACKGROUND

Mathematical models of complex diseases, such as Alzheimer's disease, have the potential to play a significant role in personalized medicine. Specifically, models can be personalized by fitting parameters with individual data for the purpose of discovering primary underlying disease drivers, predicting natural history, and assessing the effects of theoretical interventions. Previous work in causal/mechanistic modeling of Alzheimer's Disease progression has modeled the disease at the cellular level and on a short time scale, such as minutes to hours. No previous studies have addressed mechanistic modeling on a personalized level using clinically validated biomarkers in individual subjects.

OBJECTIVES

This study aimed to investigate the feasibility of personalizing a causal model of Alzheimer's Disease progression using longitudinal biomarker data.

DESIGN/SETTING/PARTICIPANTS/MEASUREMENTS

We chose the Alzheimer Disease Biomarker Cascade model, a widely-referenced hypothetical model of Alzheimer's Disease based on the amyloid cascade hypothesis, which we had previously implemented mathematically as a mechanistic model. We used available longitudinal demographic and serial biomarker data in over 800 subjects across the cognitive spectrum from the Alzheimer's Disease Neuroimaging Initiative. The data included participants that were cognitively normal, had mild cognitive impairment, or were diagnosed with dementia (probable Alzheimer's Disease). The model consisted of a sparse system of differential equations involving four measurable biomarkers based on cerebrospinal fluid proteins, imaging, and cognitive testing data.

RESULTS

Personalization of the Alzheimer Disease Biomarker Cascade model with individual serial biomarker data yielded fourteen personalized parameters in each subject reflecting physiologically meaningful characteristics. These included growth rates, latency values, and carrying capacities of the various biomarkers, most of which demonstrated significant differences across clinical diagnostic groups. The model fits to training data across the entire cohort had a root mean squared error (RMSE) of 0.09 (SD 0.081) on a variable scale between zero and one, and were robust, with over 90% of subjects showing an RMSE of < 0.2. Similarly, in a subset of subjects with data on all four biomarkers in at least one test set, performance was high on the test sets, with a mean RMSE of 0.15 (SD 0.117), with 80% of subjects demonstrating an RMSE < 0.2 in the estimation of future biomarker points. Cluster analysis of parameters revealed two distinct endophenotypic groups, with distinct biomarker profiles and disease trajectories.

CONCLUSION

Results support the feasibility of personalizing mechanistic models based on individual biomarker trajectories and suggest that this approach may be useful for reclassifying subjects on the Alzheimer's clinical spectrum. This computational modeling approach is not limited to the Alzheimer Disease Biomarker Cascade hypothesis, and can be applied to any mechanistic hypothesis of disease progression in the Alzheimer's field that can be monitored with biomarkers. Thus, it offers a computational platform to compare and validate various disease hypotheses, personalize individual biomarker trajectories and predict individual response to theoretical prevention and therapeutic intervention strategies.

Diagnosing Alzheimer's disease: Which dementia screening test to use in elderly Puerto Ricans with mild cognitive impairment and early Alzheimer's disease?

Typically, Alzheimer's disease (AD) diagnosis is not made at its earliest period, for instance, at mild cognitive impairment (MCI) and early AD (E-AD). Our study aims to demonstrate a correlation between the screening tools, including the Mini-Mental State Examination (MMSE), Montreal Cognitive Assessment (MoCA), and Clinical Dementia Rating (CDR), and the biological biomarkers in the cerebrospinal fluid (CSF) amyloid beta 1-42 (Aβ42), phosphorylated tau (p-tau) proteins and total tau (t-tau)/Aβ42 ratio in Puerto Ricans > 55 years old with MCI and E-AD. We evaluated 30 participants, including demographics, memory scales, and CSF biomarkers. Twenty-eight CSF biomarkers (Aβ42, p-tau protein, and t-tau/Aβ42 ratio) were analyzed using the Meso Scale Discovery Platform (MSD). Associations between memory scales (MoCA, MMSE, CDR) and CSF markers were performed using Spearman rho correlation. Our study revealed a statistical association favoring a direct relationship between MMSE and MoCA with t-tau/Aβ42 ratio in CSF (P = 0.022, P = 0.035, respectively). We found a trend toward significance with an inverse relationship with MMSE and Aβ42 (P = 0.069) and a direct relationship with MMSE and p-tau (P = 0.098). MMSE and MoCA screening tests were identified with a statistically significant association with the CSF biomarkers, specifically t-tau/Aβ42 ratio, in elderly Puerto Ricans with MCI and E-AD. Puerto Ricans > 55 years old with MCI and E-AD could be screened confidently with MMSE and MoCA for a higher likelihood of earlier detection and, thus, initiation of disease-modifying treatment and prompt non-pharmacological interventions.

Stability and bifurcation analysis of Alzheimer's disease model with diffusion and three delays

A reaction-diffusion Alzheimer's disease model with three delays, which describes the interaction of β-amyloid deposition, pathologic tau, and neurodegeneration biomarkers, is investigated. The existence of delays promotes the model to display rich dynamics. Specifically, the conditions for stability of equilibrium and periodic oscillation behaviors generated by Hopf bifurcations can be deduced when delay σ (σ=σ1+σ2) or σ3 is selected as a bifurcation parameter. In addition, when delay σ and σ3 are selected as bifurcation parameters, the stability switching curves and the stable region are obtained by using an algebraic method, and the conditions for the existence of Hopf bifurcations can also be derived. The effects of time delays, diffusion, and treatment on biomarkers are discussed via numerical simulations. Furthermore, sensitivity analysis at multiple time points is drawn, indicating that different targeted therapies should be taken at different stages of development, which has certain guiding significance for the treatment of Alzheimer's disease.

Targeting microglial autophagic degradation of the NLRP3 inflammasome for identification of thonningianin A in Alzheimer’s disease

Background

NLRP3 inflammasome-mediated neuroinflammation plays a critical role in the pathogenesis and development of Alzheimer’s disease (AD). Microglial autophagic degradation not only decreases the deposits of extracellular Aβ fibrils but also inhibits the activation of NRLP3 inflammasome. Here, we aimed to identify the potent autophagy enhancers from Penthorum chinense Pursh (PCP) that alleviate the pathology of AD via inhibiting the NLRP3 inflammasome.

Methods

At first, autophagic activity-guided isolation was performed to identify the autophagy enhancers in PCP. Secondly, the autophagy effect was monitored by detecting LC3 protein expression using Western blotting and the average number of GFP-LC3 puncta per microglial cell using confocal microscopy. Then, the activation of NLRP3 inflammasome was measured by detecting the protein expression and transfected fluorescence intensity of NLRP3, ASC, and caspase-1, as well as the secretion of proinflammatory cytokines. Finally, the behavioral performance was evaluated by measuring the paralysis in C. elegans, and the cognitive function was tested by Morris water maze (MWM) in APP/PS1 mice.

Results

Four ellagitannin flavonoids, including pinocembrin-7-O-[4″,6″-hexahydroxydiphenoyl]-glucoside (PHG), pinocembrin-7-O-[3″-O-galloyl-4″,6″-hexahydroxydiphenoyl]-glucoside (PGHG), thonningianin A (TA), and thonningianin B (TB), were identified to be autophagy enhancers in PCP. Among these, TA exhibited the strongest autophagy induction effect, and the mechanistic study demonstrated that TA activated autophagy via the AMPK/ULK1 and Raf/MEK/ERK signaling pathways. In addition, TA effectively promoted the autophagic degradation of NLRP3 inflammasome in Aβ(1–42)-induced microglial cells and ameliorated neuronal damage via autophagy induction. In vivo, TA activated autophagy and improved behavioral symptoms in C. elegans. Furthermore, TA might penetrate the blood-brain barrier and could improve cognitive function and ameliorate the Aβ pathology and the NLRP3 inflammasome-mediated neuroinflammation via the AMPK/ULK1 and Raf/MEK/ERK signaling pathways in APP/PS1 mice.

Conclusion

We identified TA as a potent microglial autophagy enhancer in PCP that promotes the autophagic degradation of the NLRP3 inflammasome to alleviate the pathology of AD via the AMPK/ULK1 and Raf/MEK/ERK signaling pathways, which provides novel insights for TA in the treatment of AD.

Supplementary Information

The online version contains supplementary material available at 10.1186/s41232-022-00209-7.

Prediction of Medical Conditions Using Machine Learning Approaches: Alzheimer’s Case Study

Alzheimer’s Disease (AD) is a highly prevalent condition and most of the people suffering from it receive the diagnosis late in the process. The diagnosis is currently established following an evaluation of the protein biomarkers in cerebrospinal fluid (CSF), brain imaging, cognitive tests, and the medical history of the individuals. While diagnostic tools based on CSF collections are invasive, the tools used for acquiring brain scans are expensive. Taking these into account, an early predictive system, based on Artificial Intelligence (AI) approaches, targeting the diagnosis of this condition, as well as the identification of lead biomarkers becomes an important research direction. In this survey, we review the state-of-the-art research on machine learning (ML) techniques used for the detection of AD and Mild Cognitive Impairment (MCI). We attempt to identify the most accurate and efficient diagnostic approaches, which employ ML techniques and therefore, the ones most suitable to be used in practice. Research is still ongoing to determine the best biomarkers for the task of AD classification. At the beginning of this survey, after an introductory part, we enumerate several available resources, which can be used to build ML models targeting the diagnosis and classification of AD, as well as their main characteristics. After that, we discuss the candidate markers which were used to build AI models with the best results in terms of diagnostic accuracy, as well as their limitations.

Nonlocal models in the analysis of brain neurodegenerative protein dynamics with application to Alzheimer's disease

It is well known that today nearly one in six of the world’s population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of such disorders, some fundamentals of the progression of associated diseases are in urgent need of further clarification. In this paper, we focus on Alzheimer’s disease, where it is believed that the concentration changes in amyloid-beta and tau proteins play a central role in its onset and development. A multiscale model is proposed to analyze the propagation of these concentrations in the brain connectome. In particular, we consider a modified heterodimer model for the protein–protein interactions. Higher toxic concentrations of amyloid-beta and tau proteins destroy the brain cell. We have studied these propagations for the primary and secondary and their mixed tauopathies. We model the damage of a brain cell by the nonlocal contributions of these toxic loads present in the brain cells. With the help of rigorous analysis, we check the stability behaviour of the stationary points corresponding to the homogeneous system. After integrating the brain connectome data into the developed model, we see that the spreading patterns of the toxic concentrations for the whole brain are the same, but their concentrations are different in different regions. Also, the time to propagate the damage in each region of the brain connectome is different.

Homocysteine metabolism as the target for predictive medical approach, disease prevention, prognosis, and treatments tailored to the person

Homocysteine (Hcy) metabolism is crucial for regulating methionine availability, protein homeostasis, and DNA-methylation presenting, therefore, key pathways in post-genomic and epigenetic regulation mechanisms. Consequently, impaired Hcy metabolism leading to elevated concentrations of Hcy in the blood plasma (hyperhomocysteinemia) is linked to the overproduction of free radicals, induced oxidative stress, mitochondrial impairments, systemic inflammation and increased risks of eye disorders, coronary artery diseases, atherosclerosis, myocardial infarction, ischemic stroke, thrombotic events, cancer development and progression, osteoporosis, neurodegenerative disorders, pregnancy complications, delayed healing processes, and poor COVID-19 outcomes, among others. This review focuses on the homocysteine metabolism impairments relevant for various pathological conditions. Innovative strategies in the framework of 3P medicine consider Hcy metabolic pathways as the specific target for in vitro diagnostics, predictive medical approaches, cost-effective preventive measures, and optimized treatments tailored to the individualized patient profiles in primary, secondary, and tertiary care.

Integration of Machine Learning Methods to Dissect Genetically Imputed Transcriptomic Profiles in Alzheimer's Disease

The genetic component of many common traits is associated with the gene expression and several variants act as expression quantitative loci, regulating the gene expression in a tissue specific manner. In this work, we applied tissue-specific cis-eQTL gene expression prediction models on the genotype of 808 samples including controls, subjects with mild cognitive impairment, and patients with Alzheimer's Disease. We then dissected the imputed transcriptomic profiles by means of different unsupervised and supervised machine learning approaches to identify potential biological associations. Our analysis suggests that unsupervised and supervised methods can provide complementary information, which can be integrated for a better characterization of the underlying biological system. In particular, a variational autoencoder representation of the transcriptomic profiles, followed by a support vector machine classification, has been used for tissue-specific gene prioritizations. Interestingly, the achieved gene prioritizations can be efficiently integrated as a feature selection step for improving the accuracy of deep learning classifier networks. The identified gene-tissue information suggests a potential role for inflammatory and regulatory processes in gut-brain axis related tissues. In line with the expected low heritability that can be apportioned to eQTL variants, we were able to achieve only relatively low prediction capability with deep learning classification models. However, our analysis revealed that the classification power strongly depends on the network structure, with recurrent neural networks being the best performing network class. Interestingly, cross-tissue analysis suggests a potentially greater role of models trained in brain tissues also by considering dementia-related endophenotypes. Overall, the present analysis suggests that the combination of supervised and unsupervised machine learning techniques can be used for the evaluation of high dimensional omics data.

Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

Evaluating the sensitivity of biological models to various model parameters is a critical step towards advancing our understanding of biological systems. In this paper, we investigated sensitivity coefficients for a model simulating transport of tau protein along the axon. This is an important problem due to the relevance of tau transport and agglomeration to Alzheimer's disease and other tauopathies, such as some forms of parkinsonism. The sensitivity coefficients that we obtained characterize how strongly three observables (the tau concentration, average tau velocity, and the percentage of tau bound to microtubules) depend on model parameters. The fact that the observables strongly depend on a parameter characterizing tau transition from the retrograde to the anterograde kinetic states suggests the importance of motor-driven transport of tau. The observables are sensitive to kinetic constants characterizing tau concentration in the free (cytosolic) state only at small distances from the soma. Cytosolic tau can only be transported by diffusion, suggesting that diffusion-driven transport of tau only plays a role in the proximal axon. Our analysis also shows the location in the axon in which an observable has the greatest sensitivity to a certain parameter. For most parameters, this location is in the proximal axon. This could be useful for designing an experiment aimed at determining the value of this parameter. We also analyzed sensitivity of the average tau velocity, the total tau concentration, and the percentage of microtubule-bound tau to cytosolic diffusivity of tau and diffusivity of bound tau along the MT lattice. The model predicts that at small distances from the soma the effect of these two diffusion processes is comparable.

Simulating the effect of formation of amyloid plaques on aggregation of tau protein

In this paper, we develop a mathematical model that enables the investigation of the production and intracellular transport of amyloid precursor protein (APP) and tau protein in a neuron. We also investigate the aggregation of APP fragments into amyloid-β (Aβ) as well as tau aggregation into tau oligomers and neurofibrillary tangles. Using the developed model, we investigate how Aβ aggregation can influence tau transport and aggregation in both the soma and the axon. We couple the Aβ and tau agglomeration processes by assuming that the value of the kinetic constant that describes the autocatalytic growth (self-replication) reaction step of tau aggregation is proportional to the Aβ concentration. The model predicts that APP and tau are distributed differently in the axon. While APP has a uniform distribution along the axon, tau's concentration first decreases and then increases towards the synapse. Aβ is uniformly produced along the axon while misfolded tau protein is mostly produced in the proximal axon. The number of Aβ and tau polymers originating from the axon is much smaller than the number of Aβ and tau polymers originating from the soma. The rate of production of misfolded tau polymers depends on how strongly their production is facilitated by Aβ.

A numerical study of sensitivity coefficients for a model of amyloid precursor protein and tau protein transport and agglomeration in neurons at the onset of Alzheimer's disease

Modeling of intracellular processes occurring during the development of Alzheimer's disease (AD) can be instrumental in understanding the disease and can potentially contribute to finding treatments for the disease. The model of intracellular processes in AD, which we previously developed, contains a large number of parameters. To distinguish between more important and less important parameters we performed a local sensitivity analysis of this model around the values of parameters that give the best fit with published experimental results. We show that the effect of model parameters on the total concentration of amyloid precursor protein (APP) and tau protein in the axon, respectively, is reciprocal to the effect of the same parameters on the average velocities of the same proteins during their transport in the axon. The results of our analysis also suggest that in the beginning of AD the aggregation of amyloid-ß and misfolded tau protein have little effect on transport of APP and tau in the axon, which suggests that early effects of AD may be reversible.