Combined Model of Aggregation and Network Diffusion Recapitulates Alzheimer's Regional Tau-Positron Emission Tomography

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.

The role of A[Formula: see text] and Tau proteins in Alzheimer's disease: a mathematical model on graphs

In this Note we study a mathematical model for the progression of Alzheimer's Disease in the human brain. The novelty of our approach consists in the representation of the brain as two superposed graphs where toxic proteins diffuse, the connectivity graph which represents the neural network, and the proximity graph which takes into account the extracellular space. Toxic proteins such as [Formula: see text] amyloid and Tau play in fact a crucial role in the development of Alzheimer's disease and, separately, have been targets of medical treatments. Recent biomedical literature stresses the potential impact of the synergetic action of these proteins. We numerically test various modelling hypotheses which confirm the relevance of this synergy.

Endogenous pathology in tauopathy mice progresses via brain networks

Neurodegenerative tauopathies are hypothesized to propagate via brain networks. This is uncertain because we have lacked precise network resolution of pathology. We therefore developed whole-brain staining methods with anti-p-tau nanobodies and imaged in 3D PS19 tauopathy mice, which have pan-neuronal expression of full-length human tau containing the P301S mutation. We analyzed patterns of p-tau deposition across established brain networks at multiple ages, testing the relationship between structural connectivity and patterns of progressive pathology. We identified core regions with early tau deposition, and used network propagation modeling to determine the link between tau pathology and connectivity strength. We discovered a bias towards retrograde network-based propagation of tau. This novel approach establishes a fundamental role for brain networks in tau propagation, with implications for human disease.

Connectome-based biophysics models of Alzheimer's disease diagnosis and prognosis

With the increasing prevalence of Alzheimer's disease (AD) among aging populations and the limited therapeutic options available to slow or reverse its progression, the need has never been greater for improved diagnostic tools for identifying patients in the preclinical and prodomal phases of AD. Biophysics models of the connectome-based spread of amyloid-beta (Aβ) and microtubule-associated protein tau (τ) have enjoyed recent success as tools for predicting the time course of AD-related pathological changes. However, given the complex etiology of AD, which involves not only connectome-based spread of protein pathology but also the interactions of many molecular and cellular players over multiple spatiotemporal scales, more robust, complete biophysics models are needed to better understand AD pathophysiology and ultimately provide accurate patient-specific diagnoses and prognoses. Here we discuss several areas of active research in AD whose insights can be used to enhance the mathematical modeling of AD pathology as well as recent attempts at developing improved connectome-based biophysics models. These efforts toward a comprehensive yet parsimonious mathematical description of AD hold great promise for improving both the diagnosis of patients at risk for AD and our mechanistic understanding of how AD progresses.

Network Tau spreading is vulnerable to the expression gradients of APOE and glutamatergic-related genes

A key hallmark of Alzheimer's disease (AD) pathology is the intracellular accumulation of tau protein in the form of neurofibrillary tangles across large-scale networks of the human brain cortex. Currently, it is still unclear how tau accumulates within specific cortical systems and whether in situ genetic traits play a role in this circuit-based propagation progression. In this study, using two independent cohorts of cognitively normal older participants, we reveal the brain network foundation of tau spreading and its association with using high-resolution transcriptomic genetic data. We observed that specific connectomic and genetic gradients exist along the tau spreading network. In particular, we identified 577 genes whose expression is associated with the spatial spreading of tau. Within this set of genes, APOE and glutamatergic synaptic genes, such as SLC1A2, play a central role. Thus, our study characterizes neurogenetic topological vulnerabilities in distinctive brain circuits of tau spreading and suggests that drug development strategies targeting the gradient expression of this set of genes should be explored to help reduce or prevent pathological tau accumulation.

Coupled Neural–Glial Dynamics and the Role of Astrocytes in Alzheimer’s Disease

Neurodegenerative diseases such as Alzheimer’s (AD) are associated with the propagation and aggregation of toxic proteins. In the case of AD, it was Alzheimer himself who showed the importance of both amyloid beta (Aβ) plaques and tau protein neurofibrillary tangles (NFTs) in what he called the “disease of forgetfulness”. The amyloid beta forms extracellular aggregates and plaques, whereas tau proteins are intracellular proteins that stabilize axons by cross-linking microtubules that can form largely messy tangles. On the other hand, astrocytes and microglial cells constantly clear these plaques and NFTs from the brain. Astrocytes transport nutrients from the blood to neurons. Activated astrocytes produce monocyte chemoattractant protein-1 (MCP-1), which attracts anti-inflammatory macrophages and clears Aβ. At the same time, the microglia cells are poorly phagocytic for Aβ compared to proinflammatory and anti-inflammatory macrophages. In addition to such distinctive neuropathological features of AD as amyloid beta and tau proteins, neuroinflammation has to be brought into the picture as well. Taking advantage of a coupled mathematical modelling framework, we formulate a network model, accounting for the coupling between neurons and astroglia and integrating all three main neuropathological features with the brain connectome data. We provide details on the coupled dynamics involving cytokines, astrocytes, and microglia. Further, we apply the tumour necrosis factor alpha (TNF-α) inhibitor and anti-Aβ drug and analyze their influence on the brain cells, suggesting conditions under which the drug can prevent cell damage. The important role of astrocytes and TNF-α inhibitors in AD pathophysiology is emphasized, along with potentially promising pathways for developing new AD therapies.