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

  • Justin Torok
    Correspondence
    Reprint requests: Justin Torok and Ashish Raj, University of California San Francisco
    Affiliations
    Department of Radiology, University of California, San Francisco, San Francisco, California
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  • Chaitali Anand
    Affiliations
    Department of Radiology, University of California, San Francisco, San Francisco, California
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  • Parul Verma
    Affiliations
    Department of Radiology, University of California, San Francisco, San Francisco, California
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  • Ashish Raj
    Correspondence
    Reprint requests: Justin Torok and Ashish Raj, University of California San Francisco
    Affiliations
    Department of Radiology, University of California, San Francisco, San Francisco, California

    Department of Bioengineering, University of California, Berkeley and University of California, San Francisco, Berkeley, California

    Department of Radiology, Weill Cornell Medicine, New York, New York
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Open AccessPublished:August 28, 2022DOI:https://doi.org/10.1016/j.trsl.2022.08.008

      ABSTRACT

      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.

      Overview

      Alzheimer’s disease (AD) is an increasingly prevalent neurodegenerative disorder whose pathological hallmarks are abnormal deposits of amyloid-beta (Aβ) and microtubule-associated protein tau (τ). The buildup of aggregates of these proteins is progressive, irreversible, and associated with deficiencies in cognitive function and dementia. Both Aβ and τ exhibit characteristic spatiotemporal deposition patterns. The first Aβ plaques typically appear in temporobasal and frontomedial areas before spreading throughout the remaining neocortical areas and eventually the striatum.
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      Fig. 1
      Fig 1Survey of connectome-based spread models in AD. A: The NDM successfully recapitulated the spatiotemporal evolution of atrophy in AD in a patient cohort from ADNI.
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      the understanding the equilibria between oligomers and aggregates is of keen interest.
      Additionally, a necessary mathematical assumption endemic to connectome spread models is that all gray-matter regions have the same intrinsic properties, differing only in how they are connected to other regions. However, befitting their discrete biological functions, brain regions have distinct cytoarchitectures and neuronal compositions, some of which may be particularly susceptible to pathology.
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      and oligodendrocytes
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      Incorporating more features of AD biology at the level of the mathematical model while minimizing the risk of overfitting, particularly when regions are not treated identically, poses a significant challenge for enhancing current connectome-based spread approaches.
      Here, we will expand upon several important facets of AD pathogenesis requiring further exploration from a mathematical modeling perspective:
      • 1.
        Interactions between Aβ and τ
      • 2.
        Asymmetric flows on the brain connectome
      • 3.
        Neuroinflammation
      • 4.
        Selective cell-type vulnerability
      • 5.
        The relationship between neuronal activity and pathology
      For each, we will provide biological context that justifies the need for model augmentation, related recent advances in mathematical modeling, and suggestions for next steps for modeling at the whole-brain level. Our aim is to synthesize the wealth of knowledge gained in disparate subfields of research towards a unified mathematical framework of AD that deepens our insight of the disease process and provides accurate, subject-specific predictions that can be used clinically for diagnosis, prognosis, and the tailoring of treatment.

      The clinical utility of mathematical models

      A wide variety of tools have been applied to the problem of AD diagnosis. The primary method of diagnosing AD is through a battery of cognitive tests when the patient starts showing signs of dementia, such as the Mini Mental State Exam (MMSE)
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      or the Clinical Dementia Rating (CDR).
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      The Clinical Dementia Rating (CDR).
      Although these exams are widely used and easy to administer, misdiagnosis of patients showing mild cognitive impairment (MCI) is still common, because their symptoms may not indicate that they will convert to AD.
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      Accordingly, recent decades have seen significant developments in in vivo imaging techniques for detecting brain pathology directly. Aβ-sensitive positron emission tomography (PET) is currently in clinical use for the differential diagnosis of AD.
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      Disruptions in glucose metabolism, as measured by 2-[18F]fluoro-2-Deoxy-D-glucose PET (FDG-PET), can also facilitate the early detection of AD.
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      Although currently used only for research purposes, several PET radioligands for τ have also been developed, albeit with several off-target issues that remain to be solved.
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      Tau PET imaging in neurodegenerative tauopathies-still a challenge.
      Structural magnetic resonance imaging (sMRI) is a less-expensive and minimally invasive alternative for detecting pathological changes in the brain, using techniques such as voxel-based morphometry (VBM) to determine regional gray-matter loss.
      • Ashburner J.
      • Friston K.J.
      Voxel-based morphometry-the methods.
      Although the nonspecificity of brain atrophy as a biomarker has kept MRI-based atrophy detection from being the diagnostic tool of choice, several groups have been successful in using it to identify AD-related changes in structural brain features.
      • Dukart J.
      • Mueller K.
      • Horstmann A.
      • Barthel H.
      • Möller H.E.
      • Villringer A.
      • Sabri O.
      • Schroeter M.L.
      Combined evaluation of FDG-PET and MRI improves detection and differentiation of dementia.
      • Dukart J.
      • Kherif F.
      • Mueller K.
      • Adaszewski S.
      • Schroeter M.L.
      • Frackowiak R.S.J.
      • Draganski B.
      Generative FDG-PET and MRI Model of Aging and Disease Progression in Alzheimer’s Disease.
      To detect network-level changes in AD, diffusion tensor imaging (DTI), a special MRI sequence sensitive to the highly anisotropic diffusion of water within white-matter tracts, can map the structural connectome of the brain and identify disease-induced loss of white-matter integrity.
      • Rose S.E.
      • Janke PhD A.L.
      • Chalk J.B.
      Gray and white matter changes in Alzheimer’s disease: A diffusion tensor imaging study.
      Functional MRI (fMRI) is a complementary technique that can be used to detect AD-related changes in brain activity by the measuring the associated changes in blood oxygenation.
      • Amini M.
      • Pedram M.M.
      • Moradi A.
      • Ouchani M.
      Diagnosis of Alzheimer’s disease severity with fMRI images using robust multitask feature extraction method and convolutional neural network (CNN).
      Alternative technologies for investigating functional network dysfunction in AD include electroencephelography (EEG) and more recently magnetoencephelography (MEG), which detect brain activity with very high temporal resolution but lack the spatial resolution of fMRI. While these technologies are not in standard clinical use for AD diagnosis, they have been used to demonstrate abnormal oscillatory patterns in AD.
      • Nakamura A.
      • Cuesta P.
      • Fernández A.
      • Arahata Y.
      • Iwata K.
      • Kuratsubo I.
      • Bundo M.
      • Hattori H.
      • Sakurai T.
      • Fukuda K.
      • Washimi Y.
      • Endo H.
      • Takeda A.
      • Diers K.
      • Bajo R.
      • Maestú F.
      • Ito K.
      • Kato T.
      Electromagnetic signatures of the preclinical and prodromal stages of Alzheimer’s disease.
      • Pusil S.
      • López M.E.
      • Cuesta P.
      • Bruña R.
      • Pereda E.
      • Maestú F.
      Hypersynchronization in mild cognitive impairment: the ’X’ model.
      • Ranasinghe K.G.
      • Cha J.
      • Iaccarino L.
      • Hinkley L.B.
      • Beagle A.J.
      • Pham J.
      • Jagust W.J.
      • Miller B.L.
      • Rankin K.P.
      • Rabinovici G.D.
      • Vossel K.A.
      • Nagarajan S.S.
      Neurophysiological signatures in Alzheimer’s disease are distinctly associated with TAU, amyloid-β accumulation, and cognitive decline.
      • Ranasinghe K.G.
      • Petersen C.
      • Kudo K.
      • Mizuiri D.
      • Rankin K.P.
      • Rabinovici G.D.
      • Gorno-Tempini M.L.
      • Seeley W.W.
      • Spina S.
      • Miller B.L.
      • Vossel K.
      • Grinberg L.T.
      • Nagarajan S.S.
      Reduced synchrony in alpha oscillations during life predicts post mortem neurofibrillary tangle density in early-onset and atypical Alzheimer’s disease.
      • Smailovic U.
      • Koenig T.
      • Kåreholt I.
      • Andersson T.
      • Kramberger M.G.
      • Winblad B.
      • Jelic V.
      Quantitative EEG power and synchronization correlate with Alzheimer’s disease CSF biomarkers.
      Biophysical models can facilitate our understanding of these rich data in several key ways. Firstly, they can validate specific hypotheses about disease mechanisms that are difficult to observe directly in the clinic, often by linking disparate sources of data that are alone insufficient for explaining the disease process and cannot be combined in a purely statistical model. For instance, connectome spread models make concrete the mechanistic relationship between the brain connectome, determined by DTI, and brain-wide maps of imaging biomarkers measured by PET or sMRI.
      • Raj A.
      • Kuceyeski A.
      • Weiner M.
      A Network Diffusion Model of Disease Progression in Dementia.
      • Iturria-Medina Y.
      • Sotero R.C.
      • Toussaint P.J.
      • Evans A.C.
      Epidemic Spreading Model to Characterize Misfolded Proteins Propagation in Aging and Associated Neurodegenerative Disorders.
      • Weickenmeier J.
      • Kuhl E.
      • Goriely A.
      Multiphysics of Prionlike Diseases: Progression and Atrophy.
      They can also provide subject-specific predictions of future pathology not yet observed, which can guide diagnosis and prognosis.
      • Schäfer A.
      • Mormino E.C.
      • Kuhl E.
      Network Diffusion Modeling Explains Longitudinal Tau PET Data.
      • Raj A.
      • LoCastro E.
      • Kuceyeski A.
      • Tosun D.
      • Relkin N.
      • Weiner M.
      Network Diffusion Model of Progression Predicts Longitudinal Patterns of Atrophy and Metabolism in Alzheimer’s Disease.
      As mentioned above, one of the most important challenges in AD diagnosis is to find a test that discriminates between patients with MCI who will later go on to develop AD and those who will not. Given that AD-specific treatments are unlikely to be effective in MCI patients who are not on the AD disease trajectory, a biophysical model with sufficient predictive power may be able to identify those patients who will benefit from therapies currently in clinical trials, leading to higher success rates.
      • Yiannopoulou K.G.
      • Anastasiou A.I.
      • Zachariou V.
      • Pelidou S.-H.
      Reasons for failed trials of disease-modifying treatments for Alzheimer disease and their contribution in recent research.
      The identification of MCI-to-AD converters before the disease advances to the AD stage is also essential because the AD-associated loss of gray matter is effectively irreversible, so intervening prior to the loss of massive numbers of neurons is more likely to provide lasting, meaningful clinical benefits.
      • Guest F.L.
      • Rahmoune H.
      • Guest P.C.
      Early Diagnosis and Targeted Treatment Strategy for Improved Therapeutic Outcomes in Alzheimer’s Disease.
      The success of mathematical models of connectome-based spread allows exploration of another clinically relevant application: the possibility of “going back” in time to infer sites of pathology initiation that would best explain measured patterns of atrophy and pathology in a patient. For example, Torok et al. were able to “reverse” the NDM to infer the regional origins of pathology, called “seeds,” in individual patients on the AD spectrum.
      • Torok J.
      • Maia P.D.
      • Powell F.
      • Pandya S.
      • Raj A.
      A method for inferring regional origins of neurodegeneration.
      These patient-specific seeds, inferred by imposing a sparsity condition to constrain pathology to only a few regions, successfully reproduced known trends in AD and outperformed the best single-locus seed vector placed in the hippocampus. Subsequently, Maia et al. implemented a similar approach to infer seeds in PD, finding that PD patients could be grouped into two distinct clusters based on their seed patterns that exhibited markedly different ages of onset.
      • Maia P.D.
      • Pandya S.
      • Freeze B.
      • Torok J.
      • Gupta A.
      • Zeighami Y.
      • Raj A.
      Origins of atrophy in Parkinson linked to early onset and local transcription patterns.
      These approaches enforced a single seeding event; however, a related method allowing several seeding events up to the observation window also produced plausible prior states of pathology.
      • Hu C.
      • Hua X.
      • Ying J.
      • Thompson P.M.
      • Fakhri G.E.
      • Li Q.
      Localizing Sources of Brain Disease Progression with Network Diffusion Model.
      Therefore, biophysical models can give a glimpse into preclinical disease states that may be particularly useful for diagnosis.
      Lastly, the analysis of sufficiently rich biophysical models can reveal which processes control disease dynamics, thereby indicating key mechanisms that future treatments should be designed to disrupt. While further work with experimental models of AD and the continued development of methodological tools for studying AD in the clinic are also needed to fully realize all of these goals, we can still advance the state of AD mathematical modeling by incorporating more biological detail, as we expand upon in the following sections.

      Interactions between Aβ and τ define AD pathogenesis

      The prevailing view guiding the study of AD pathogenesis is the amyloid cascade hypothesis
      • Bloom G.S.
      Amyloid-β and Tau.
      • Ittner L.M.
      • Götz J.
      Amyloid-β and tau - a toxic pas de deux in Alzheimer’s disease.
      : From a complex interaction of genetic predispositions and environmental triggers, aberrant cleavage products of amyloid precursor protein (APP) aggregate to form Aβ plaques. At a later time, abnormal deposits of τ known as neurofibrillary tangles (NFTs) form, a process which is facilitated in part by Aβ. Once the ability of the brain to clear these pathological accumulations is exhausted, misfolded assemblies of τ spread throughout the brain along white-matter tracts, eventually leading to neuronal death and irreversible, progressive cognitive decline. However, several pieces of evidence complicate the picture above. Perhaps most importantly, cognitively normal individuals who are amyloid-positive (Aβ+) exhibit at most modest deficits compared to age-matched amyloid-negative (Aβ-) individuals.
      • Baker J.E.
      • Lim Y.Y.
      • Pietrzak R.H.
      • Hassenstab J.
      • Snyder P.J.
      • Masters C.L.
      • Maruff P.
      Cognitive impairment and decline in cognitively normal older adults with high amyloid-β: A meta-analysis.
      Conversely, a percentage of patients clinically diagnosed with AD exhibit τ but not Aβ pathology
      • Landau S.M.
      • Horng A.
      • Fero A.
      • Jagust W.J.
      Amyloid negativity in patients with clinically diagnosed Alzheimer disease and MCI.
      ; moreover, τ misfolding and propagation causes a wide array of neurodegenerative disorders, albeit with distinct deposition patterns and clinical features from AD.
      • Chung D.-e.C.
      • Roemer S.
      • Petrucelli L.
      • Dickson D.W.
      Cellular and pathological heterogeneity of primary tauopathies.
      Additionally, Aβ plaques and τ tangles poorly colocalize in the brains of AD patients at early stages of disease, making it challenging to understand how and when they interact to give rise to what is thought to be a canonical staging of neuropathology. There is evidence suggesting that Aβ and τ may interact at neuronal synapses and contribute to synaptic dysfunction.
      • Fein J.A.
      • Sokolow S.
      • Miller C.A.
      • Vinters H.V.
      • Yang F.
      • Cole G.M.
      • Gylys K.H.
      Co-Localization of Amyloid Beta and Tau pathology in Alzheimer’s Disease synaptosomes.
      • Spires-Jones T.L.
      • Hyman B.T.
      The Intersection of Amyloid Beta and Tau at Synapses in Alzheimer’s Disease.
      Further, Aβ may promote τ misfolding and aggregation through a cross-seeding mechanism.
      • Griner S.L.
      • Seidler P.
      • Bowler J.
      • Murray K.A.
      • Yang T.P.
      • Sahay S.
      • Sawaya M.R.
      • Cascio D.
      • Rodriguez J.A.
      • Philipp S.
      • Sosna J.
      • Glabe C.G.
      • Gonen T.
      • Eisenberg D.S.
      Structure-based inhibitors of amyloid beta core suggest a common interface with tau.
      • Guo J.-P.
      • Arai T.
      • Miklossy J.
      • McGeer P.L.
      Aβ and tau form soluble complexes that may promote self aggregation of both into the insoluble forms observed in Alzheimer’s disease.
      The interactions between Aβ and τ also need not be direct. For instance, the presence of amyloid particles in the extracellular space may trigger a cellular response that induces or facilitates the misfolding and aggregation of τ.
      • Rudenko L.K.
      • Wallrabe H.
      • Periasamy A.
      • Siller K.H.
      • Svindrych Z.
      • Seward M.E.
      • Best M.N.
      • Bloom G.S.
      Intraneuronal Tau Misfolding Induced by Extracellular Amyloid-β Oligomers.
      Nevertheless, studying either Aβ or τ in isolation gives an incomplete picture of AD pathogenesis, and a necessary extension going forward is to jointly model these two types of pathological aggregates.
      The foundational work in the biophysical modeling of AD pathology at the macroscopic level has focused on single-species models: for instance, τ in the case of the ND
      • Raj A.
      • LoCastro E.
      • Kuceyeski A.
      • Tosun D.
      • Relkin N.
      • Weiner M.
      Network Diffusion Model of Progression Predicts Longitudinal Patterns of Atrophy and Metabolism in Alzheimer’s Disease.
      • Torok J.
      • Maia P.D.
      • Powell F.
      • Pandya S.
      • Raj A.
      A method for inferring regional origins of neurodegeneration.
      and Fisher-Kolmogorov (FK) models,
      • Schäfer A.
      • Mormino E.C.
      • Kuhl E.
      Network Diffusion Modeling Explains Longitudinal Tau PET Data.
      • Weickenmeier J.
      • Kuhl E.
      • Goriely A.
      Multiphysics of Prionlike Diseases: Progression and Atrophy.
      • Weickenmeier J.
      • Jucker M.
      • Goriely A.
      • Kuhl E.
      A physics-based model explains the prion-like features of neurodegeneration in Alzheimer’s disease, Parkinson’s disease, and amyotrophic lateral sclerosis.
      • Kolgomorov A.
      • Petrovskii I.
      • Piscunov N.
      A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem.
      and Aβ in the case of the Epidemic Spread Model (ESM).
      • Iturria-Medina Y.
      • Sotero R.C.
      • Toussaint P.J.
      • Evans A.C.
      Epidemic Spreading Model to Characterize Misfolded Proteins Propagation in Aging and Associated Neurodegenerative Disorders.
      However, more recent work has turned towards combined Aβτ models at various spatial scales. Kuznetsov and Kuznetsov, following up on prior work solely modeling τ,
      • Kuznetsov I.
      • Kuznetsov A.
      Can numerical modeling help understand the fate of tau protein in the axon terminal?.
      modeled the effect of Aβ concentrations on the production and migration of τ in the axons of diseased neurons, where Aβ increased the autocatalysis of τ aggregation.
      • Kuznetsov I.A.
      • Kuznetsov A.V.
      Simulating the effect of formation of amyloid plaques on aggregation of tau protein.
      Their microscopic kinetic model was capable of fitting the distribution of axonal τ in an in vitro cell culture system.
      • Black M.M.
      • Slaughter T.
      • Moshiach S.
      • Obrocka M.
      • Fischer I.
      Tau Is Enriched on Dynamic Microtubules in the Distal Region of Growing Axons.
      Another valuable advance came from Bertsch et al., who simulated a multi-species model of Aβ and τ under conditions of purely isotropic diffusion.
      • Bertsch M.
      • Franchi B.
      • Meschini V.
      • Tesi M.C.
      • Tosin A.
      A sensitivity analysis of a mathematical model for the synergistic interplay of amyloid beta and tau on the dynamics of Alzheimer’s disease.
      In this system, they found that Aβ agglomeration rate controlled much of the dynamics of the system. Interestingly, only sufficiently small agglomeration rates were able to result in widespread brain malfunction, because the irreversible formation of nontoxic Aβ plaques in their model needed to be slow enough for the toxic oligomeric species to diffuse. Further, the addition of τ to the model resulted in more severe, widespread disease relative to its Aβ-only counterpart, reinforcing the notion that the true dynamics of brain malfunctioning only emerge when jointly modeling both Aβ and τ. These microscopic and mesoscopic models motivate the development of network-level interaction models that can be fit to clinical data.
      At the macroscopic level, too, there have been advances towards an integrated Aβτ mathematical model. Raj and Anand sought to model both protein species together by adding an Aβτ interaction term that induces τ expansion in brain regions where they co-localize, in addition to the connectome-based spread of both species.
      • Raj A.
      • Anand C.
      New applications of diffusion model based prediction of pathological brain alterations: Introducing amyloid-tau interactions.
      This minimalist approach reproduced the key features of the spread of both Aβ and τ in the brain as determined by PET imaging of MCI and AD patients. On the maximalist side, Bertsch et al., following up on their previous work discussed above,
      • Bertsch M.
      • Franchi B.
      • Raj A.
      • Tesi M.C.
      Macroscopic modelling of Alzheimer’s disease: difficulties and challenges.
      proposed a more general framework for exploring Aβ and τ dynamics at multiple spatiotemporal scales that includes mathematical treatments of: oligomer size dependence, the role of the lymphatic system, the secretion and reuptake of toxic species, neuronal dysfunction, and microglial activation in response to pathology (see Section Modeling interactions between pathology and the immune response below). We refer the reader to their work for the mathematical details of their highly detailed proposal.
      The approaches above illustrate the central tension in terms of biophysically modeling not only Aβτ interactions but all extensions to the network model: defining the simplest model that sufficiently captures the relevant features AD biology and does not compromise on its predictive capacity. On the one hand, the Raj and Anand model reduced the dynamics of Aβ and τ to a single term.
      • Raj A.
      • Anand C.
      New applications of diffusion model based prediction of pathological brain alterations: Introducing amyloid-tau interactions.
      While they demonstrated the predictive value of adding this term, questions remain about whether a more complex model incorporating more of the direct and indirect interactions of these two species could provide significantly more accurate predictions, which will be necessary for diagnosis and prognosis in the clinic. On the other, the model of Bertsch et al. requires significant exploration from a parameter sensitivity perspective to be useful as a predictive model.
      • Bertsch M.
      • Franchi B.
      • Raj A.
      • Tesi M.C.
      Macroscopic modelling of Alzheimer’s disease: difficulties and challenges.
      More specifically, to reduce the risk of overfitting, detailed analysis will be necessary to exclude features that are mathematically redundant or add little to the richness of the dynamics of the system. Nevertheless, these approaches represent an initial step towards a robust and clinically useful description of Aβ and τ interactions.

      Directionality of specific conformers parsimoniously explains diverging τ deposition patterns

      In addition to posing a challenge diagnostically for cases with mixed clinical presentations, how the misfolding of τ can give rise to such disorders as AD, FTLD, Pick’s disease, and corticobasal degeneration, among others, is an unresolved question. A parsimonious explanation is that each of these tauopathies has characteristic conformers of τ, and it is the differences in microscopic properties between these conformers that largely controls the rate of progression and the spatiotemporal patterns of τ deposition.
      • Chung D.-e.C.
      • Roemer S.
      • Petrucelli L.
      • Dickson D.W.
      Cellular and pathological heterogeneity of primary tauopathies.
      The evidence for this conformation-specific hypothesis of tauopathy comes from varied sources. Direct examination of the structure of τ aggregates using electron microscopy has revealed that τ aggregates from different sources adopt distinct conformations.
      • Falcon B.
      • Zhang W.
      • Murzin A.G.
      • Murshudov G.
      • Garringer H.J.
      • Vidal R.
      • Crowther R.A.
      • Ghetti B.
      • Scheres S.H.W.
      • Goedert M.
      Structures of filaments from Pick’s disease reveal a novel tau protein fold.
      • Karikari T.K.
      • Nagel D.A.
      • Grainger A.
      • Clarke-Bland C.
      • Crowe J.
      • Hill E.J.
      • Moffat K.G.
      Distinct Conformations, Aggregation and Cellular Internalization of Different Tau Strains.
      Synthetic τ fibrils coaxed to misfold and aggregate under various in vitro conditions exhibit different molecular properties,
      • Frost B.
      • Ollesch J.
      • Wille H.
      • Diamond M.I.
      Conformational Diversity of Wild-type Tau Fibrils Specified by Templated Conformation Change.
      and the injection of different fibrils into the brains of mice results in different patterns of τ deposition.
      • Kaufman S.K.
      • Thomas T.L.
      • Del Tredici K.
      • Braak H.
      • Diamond M.I.
      Characterization of tau prion seeding activity and strains from formaldehyde-fixed tissue.
      • Sanders D.W.
      • Kaufman S.K.
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      • Sharma A.M.
      • Mirbaha H.
      • Li A.
      • Barker S.J.
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      • Thorpe J.R.
      • Serpell L.C.
      • Miller T.M.
      • Grinberg L.T.
      • Seeley W.W.
      • Diamond M.I.
      Distinct Tau Prion Strains Propagate in Cells and Mice and Define Different Tauopathies.
      Clinically, the recent discovery of AD-specific phosphoepitopes of τ in the CSF and bloodstream that discriminate between patients with AD and patients with primary tauopathies with very high accuracy lends further credibility to the notion that τ-aggregate structure is a key factor in human disease.
      • Janelidze S.
      • Mattsson N.
      • Palmqvist S.
      • Smith R.
      • Beach T.G.
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      • Chai X.
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      • Eichenlaub U.
      • Zetterberg H.
      • Blennow K.
      • Reiman E.M.
      • Stomrud E.
      • Dage J.L.
      • Hansson O.
      Plasma P-tau181 in Alzheimer’s disease: relationship to other biomarkers, differential diagnosis, neuropathology and longitudinal progression to Alzheimer’s dementia.
      • Palmqvist S.
      • Janelidze S.
      • Quiroz Y.T.
      • Zetterberg H.
      • Lopera F.
      • Stomrud E.
      • Su Y.
      • Chen Y.
      • Serrano G.E.
      • Leuzy A.
      • Mattsson-Carlgren N.
      • Strandberg O.
      • Smith R.
      • Villegas A.
      • Sepulveda-Falla D.
      • Chai X.
      • Proctor N.K.
      • Beach T.G.
      • Blennow K.
      • Dage J.L.
      • Reiman E.M.
      • Hansson O.
      Discriminative Accuracy of Plasma Phospho-tau217 for Alzheimer Disease vs Other Neurodegenerative Disorders.
      • Thijssen E.H.
      • La Joie R.
      • Wolf A.
      • Strom A.
      • Wang P.
      • Iaccarino L.
      • Bourakova V.
      • Cobigo Y.
      • Heuer H.
      • Spina S.
      • VandeVrede L.
      • Chai X.
      • Proctor N.K.
      • Airey D.C.
      • Shcherbinin S.
      • Duggan Evans C.
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      • Karydas A.M.
      • Teunissen C.E.
      • Kramer J.H.
      • Grinberg L.T.
      • Seeley W.W.
      • Rosen H.
      • Boeve B.F.
      • Miller B.L.
      • Rabinovici G.D.
      • Dage J.L.
      • Rojas J.C.
      • Boxer A.L.
      Diagnostic value of plasma phosphorylated tau181 in Alzheimer’s disease and frontotemporal lobar degeneration.
      Microscopic properties of τ isolates from the brains of AD patients could also be tied to differences in their clinical presentations.
      • Dujardin S.
      • Commins C.
      • Lathuiliere A.
      • Beerepoot P.
      • Fernandes A.R.
      • Kamath T.V.
      • De Los Santos M.B.
      • Klickstein N.
      • Corjuc D.L.
      • Corjuc B.T.
      • Dooley P.M.
      • Viode A.
      • Oakley D.H.
      • Moore B.D.
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      • Jean-Gilles D.
      • Clark R.
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      • Moore R.
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      • Elwood F.
      • Steen J.A.
      • Kennedy M.E.
      • Hyman B.T.
      Tau molecular diversity contributes to clinical heterogeneity in Alzheimer’s disease.
      However, how distinct conformers of τ give rise to different clinical phenotypes is poorly understood.
      One of the mechanistic underpinnings of τ-conformer-specific deposition patterns may be that each species exhibits a different directional spread bias. In other words, τ may not migrate in a purely diffusive manner along concentration gradients, as is commonly assumed in connectome-based spread models, but instead spreads preferentially in the anterograde (ie, with axon polarity) or retrograde (ie, against axon polarity) directions. Biophysically, both healthy and pathological τ variants may freely diffuse or be transported by molecular motors attached to microtubules, giving rise to asymmetric τ distributions in the neuron.
      • Scholz T.
      • Mandelkow E.
      Transport and diffusion of Tau protein in neurons.
      The hyperphosphorylation of pathological τ disrupts its direct interactions with microtubules
      • Alonso A.C.
      • Zaidi T.
      • Grundke-Iqbal I.
      • Iqbal K.
      Role of abnormally phosphorylated tau in the breakdown of microtubules in Alzheimer disease.
      • Alonso A.d.C.
      • Grundke-Iqbal I.
      • Barra H.S.
      • Iqbal K.
      Abnormal phosphorylation of tau and the mechanism of Alzheimer neurofibrillary degeneration: Sequestration of microtubule-associated proteins 1 and 2 and the disassembly of microtubules by the abnormal tau.
      and the motor proteins themselves
      • Cuchillo-Ibanez I.
      • Seereeram A.
      • Byers H.L.
      • Leung K.
      • Ward M.A.
      • Anderton B.H.
      • Hanger D.P.
      Phosphorylation of tau regulates its axonal transport by controlling its binding to kinesin.
      • Rodríguez-Martín T.
      • Cuchillo-Ibáñez I.
      • Noble W.
      • Nyenya F.
      • Anderton B.H.
      • Hanger D.P.
      Tau phosphorylation affects its axonal transport and degradation.
      • Stern J.L.
      • Lessard D.V.
      • Hoeprich G.J.
      • Morfini G.A.
      • Berger C.L.
      Phosphoregulation of Tau modulates inhibition of kinesin-1 motility.
      ; together, these effects lead to aberrant axonal transport and the mis-sorting of τ into the neuronal somatodendritic compartment.
      • Ballatore C.
      • Lee V.M.
      • Trojanowski J.Q.
      Tau-mediated neurodegeneration in Alzheimer’s disease and related disorders.
      • Zempel H.
      • Dennissen F.J.
      • Kumar Y.
      • Luedtke J.
      • Biernat J.
      • Mandelkow E.-M.
      • Mandelkow E.
      Axodendritic sorting and pathological missorting of Tau are isoform-specific and determined by axon initial segment architecture.
      While axonal transport and diffusion occur on a much faster timescale than the detectable pathological changes during AD,
      • Scholz T.
      • Mandelkow E.
      Transport and diffusion of Tau protein in neurons.
      • Guedes-Dias P.
      • Holzbaur E.L.F.
      Axonal transport: Driving synaptic function.
      the establishment of persistent directional biases vastly influences how τ ultimately propagates along the brain connectome.
      To explore the phenomenon of τ axonal transport in the disease state at a microscopic level, Torok et al. developed a two-species, multicompartment model to explore the interactions between the pathological axonal transport of τ and the formation and breakdown of insoluble τ aggregates.
      • Torok J.
      • Maia P.D.
      • Verma P.
      • Mezias C.
      • Raj A.
      Emergence of directional bias in tau deposition from axonal transport dynamics.
      Leveraging insights from in vitro work demonstrating that the primary anterograde-directed motor protein, kinesin-1, has increased activity in the presence of monomeric hyperphosphorylated τ
      • Cuchillo-Ibanez I.
      • Seereeram A.
      • Byers H.L.
      • Leung K.
      • Ward M.A.
      • Anderton B.H.
      • Hanger D.P.
      Phosphorylation of tau regulates its axonal transport by controlling its binding to kinesin.
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      • Noble W.
      • Nyenya F.
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      Tau phosphorylation affects its axonal transport and degradation.
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      • Hoeprich G.J.
      • Morfini G.A.
      • Berger C.L.
      Phosphoregulation of Tau modulates inhibition of kinesin-1 motility.
      and is knocked down by τ aggregates,
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      • Lesne S.E.
      Soluble Conformers of A and Tau Alter Selective Proteins Governing Axonal Transport.
      the mathematical model poses a simple τ-concentration-dependent feedback mechanism on the anterograde velocity of τ transport. The authors interrogated the complex dynamics that emerge between the interplay of τ aggregation and axonal transport feedback, finding that higher aggregation rates generally led to stronger retrograde biases in τ deposition at steady-state. Although further experiments and more detailed modeling work are warranted, this work represents one of the first attempts to connect the microscopic properties of τ conformers to pathological changes that can be observed at macroscopic timescales.
      Directionally biased spread has also been explored at the whole-brain level. Mezias et al. explored the role of directionality using τ quantification in fifteen mouse models of tauopathy,
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      • Raj A.
      The role of directionality in determining spatiotemporal tau pathology differs between AD-like and non-AD-like mouse models.
      utilizing the Allen Mouse Brain Connectivity Atlas (AMBCA) from the Allen Institute for Brain Science (AIBS), which not only provides connection strengths between region-pairs but also the directionality of those connections.
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      • Cain N.
      • Mihalas S.
      • Wang Q.
      • Lau C.
      • Kuan L.
      • Henry A.M.
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      • Ouellette B.
      • Nguyen T.N.
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      • Slaughterbeck C.R.
      • Wakeman W.
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      • Ho A.
      • Nicholas E.
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      • Bohn P.
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      • Peng H.
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      • Phillips J.W.
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      • Wohnoutka P.
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      • Jones A.R.
      • Zeng H.
      A mesoscale connectome of the mouse brain.
      By introducing a bias parameter, they were able to demonstrate that τ fibrils formed in the presence of Aβ exhibit a more pronounced retrograde bias than Aβ-naive τ, an effect which may be attributed to higher τ aggregation rates in the Torok et al. framework discussed above.
      • Torok J.
      • Maia P.D.
      • Verma P.
      • Mezias C.
      • Raj A.
      Emergence of directional bias in tau deposition from axonal transport dynamics.
      Further, the temporal progression of directional bias as modeled by the axonal transport model could be parameterized to fit the network directional bias for a variety of mouse models (Fig 2). Given that significant in vitro evidence exists that Aβ indeed induces τ aggregation and the formation of unique τ conformations, the transport feedback mechanism parsimoniously explains divergence in τ deposition patterns in the context of connectome-based spread. Directional NDM models have also demonstrated that α-synuclein preferentially migrates in the retrograde direction in mouse models of PD,
      • Henderson M.X.
      • Cornblath E.J.
      • Darwich A.
      • Zhang B.
      • Brown H.
      • Gathagan R.J.
      • Sandler R.M.
      • Bassett D.S.
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      • Lee V.M.Y.
      Spread of α-synuclein pathology through the brain connectome is modulated by selective vulnerability and predicted by network analysis.
      • Mezias C.
      • Rey N.
      • Brundin P.
      • Raj A.
      Neural connectivity predicts spreading of alpha-synuclein pathology in fibril-injected mouse models: Involvement of retrograde and anterograde axonal propagation.
      suggesting that transport-mediated directional biases may be a common feature of prion-like neurodegenerative diseases.
      Fig. 2
      Fig 2Transport vs. network directional bias in mouse models of tauopathy. The network directional biases for a collection of tauopathy models, separated by whether the τ strains involved misfolded in the presence of Aβ or not,
      • Mezias C.
      • Raj A.
      The role of directionality in determining spatiotemporal tau pathology differs between AD-like and non-AD-like mouse models.
      were fit with using an axonal transport model including τ-kinesin interactions. The agreement between these two assessments of bias indicates that the interplay of axonal transport regulation and τ aggregation and fragmentation processes on a microscopic level can explain macroscopic directional biases. The mouse tauopathy data come from the following studies: “BoludaCBD”, “BoludaDSAD’
      • Boluda S.
      • Iba M.
      • Zhang B.
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      • Lee V.M.
      • Trojanowski J.Q.
      Differential induction and spread of tau pathology in young PS19 tau transgenic mice following intracerebral injections of pathological tau from Alzheimer’s disease or corticobasal degeneration brains.
      ; “Hurtado’
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      • Aboagye A.K.
      • Paul S.M.
      • Trojanowski J.Q.
      • Lee V.M.
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      ; “Clavaguera’
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      ; “KaufDS4”, “KaufDS6”, “KaufDS6110”, “KaufDS7”, “KaufDS9”, “KaufDS9110.”
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      • Thomas T.L.
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      • Braak H.
      • Diamond M.I.
      Characterization of tau prion seeding activity and strains from formaldehyde-fixed tissue.
      (Reproduced from
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      • Maia P.D.
      • Verma P.
      • Mezias C.
      • Raj A.
      Emergence of directional bias in tau deposition from axonal transport dynamics.
      ).
      Several challenges remain before we can fully integrate directional spread bias into connectome-based models of human disease. For one, rather than posing the network directional bias parameter phenomenologically, as has been done previously, it should be made a function of the axonal transport parameters and aggregation rate. In this way, the linkage between microscopic τ properties and macroscopic directional bias is made explicit. Axonal transport dysregulation may also be mediated by other interactions that have not yet been considered. For instance, a joint Aβτ model may be required to fully capture these dynamics, since there is evidence that Aβ impacts axonal transport in a τ-independent manner,
      • Ramser E.M.
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      Amyloid-β oligomers induce tau-independent disruption of BDNF axonal transport via calcineurin activation in cultured hippocampal neurons.
      dovetailing into the other considerations discussed in Section Interactions between Aβ and τ define AD pathogenesis. Another issue is that any mathematical description of directionally biased spread requires that the brain connectome be a directed, asymmetric graph that distinguishes afferents from efferents. However, DTI, the only technique capable of quantifying inter-regional connectivity in vivo, cannot resolve brain connectivity at this level and is definitionally undirected. One way to circumvent this issue is to infer the proportion of afferents to efferents in the human connectome by examining homologous brain structures in the AMBCA
      • Oh S.W.
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      A mesoscale connectome of the mouse brain.
      and the macaque connectivity atlas (CoCoMac),
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      The history of CoCoMac.
      which were obtained using viral tracing. While the assumption of homology will not hold across all connections, limiting the degree to which connection polarity can be completely determined, such a cross-species connectome should be sufficient for a preliminary exploration into fitting connectome-based spread models with directionality to clinical data. As a first demonstration, retrograde modes of transmission along a cross-species connectome were shown to produce the best-fitting connectome-based spread model for brain pathology in progressive supranuclear palsy (PSP) patients.
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      indicates that significant progress is underway in producing a fully directed, high-resolution human connectome, which will advance biophysical modeling in humans tremendously. Overall, the relaxation of the “diffusive spread” assumption in connectome-based models may represent an avenue to greatly increasing their accuracy without dramatically increasing their complexity.

      Modeling interactions between pathology and the immune response

      Discussion in the previous sections has been concerned with the mathematical modeling of Aβ and τ without any consideration of region-intrinsic properties. However, the presence of these pathological species effects a strong local response from the neuroimmune system, which is primarily mediated by microglia, the resident immune cells of the brain. Whether this response is protective or harmful appears to be context-dependent. Early in the disease process, microglia effectively clear Aβ pathology in mouse models,
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      Additionally, the neuroinflammatory response mounted by microglia in response to Aβ induces neurodegeneration; suppression of microglia in 5xFAD mice prevented hippocampal neuronal loss.
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      With regards to τ, too, the neuroimmune response is complex and multifaceted. Gliosis, the expansion of microglial populations as part of the immune response, was found to correlate with AD disease severity, both in terms of clinical symptoms and τ burden.
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      Activated microglia have also been shown to internalize τ aggregates, and were discovered in a postmortem examination of the brains of AD patients.
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      Although the above picture is incomplete, the microglial response is tightly coupled to both the emergence and progression of AD pathology.
      Of particular importance is the role of disease-associated microglia (DAM), a unique subtype of microglia identified from human AD brain samples and 5xFAD mouse models. These glia are characterized by a unique gene expression profile with elevated expression of certain AD-related genes and lower expression of homeostasis microglial genes.
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      Interestingly, a mouse tauopathy model expressing human TREM2R47H, a variant associated with increase AD risk, exhibited reduced τ pathology and neurodegeneration, suggesting that the DAM response is harmful with respect to τ.
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      Recently, a PET imaging study in cognitively normal, MCI, and AD subjects revealed that microglial activation, which was associated with TREM2 expression, followed Braak staging alongside τ pathology, and that microglial activation networks were more strongly associated with longitudinal τ progression.
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      Pascoal et al. also found that Aβ enhances microglia-activation-associated τ spreading, suggesting a role for activated microglia as mediators of the deleterious effects of Aβ on τ pathology.
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      Given the complex roles of the neuroimmune response in both remediating and potentiating AD-related pathological changes, the development of a mathematical model that can account for these different effects would yield greater insights into the disease process. Bertsch et al. recently proposed to model activated microglial populations as a function of Aβ and τ concentrations, with the latter depending in part upon activated-microglia-dependent clearance.
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      was able to demonstrate that a connectome-based model including of baseline TREM2 expression was significantly more predictive of τ pathology progression in mouse tauopathy models
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      than models including no gene expression information (Fig 3). Further, the values of the TREM2-associated accumulation and transmissibility parameters suggested that activated microglia are associated with a local reduction in τ accumulation rate, in agreement with observations of their ability to internalize and degrade τ,
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      Depletion of microglia and inhibition of exosome synthesis halt tau propagation.
      These results indicate that connectome-based spread models can be used to validate experimental observations at a whole-brain level.
      Fig. 3
      Fig 3Connectome-based model incorporating Trem2 provides a superior fit of mouse tauopathy. A: Glass-brain rendering of the τ pathology in DS9-injected mice
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      Characterization of tau prion seeding activity and strains from formaldehyde-fixed tissue.
      predominantly affects the entorhinal cortices (EC) and hippocampus (HIP) at early time points, then spreads throughout the neocortex, pallidal (PAL), and striatal (STR) areas. B: Glass-brain rendering of the τ pathology modeled using the Network Diffusion Model (NDM).
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      A Network Diffusion Model of Disease Progression in Dementia.
      C: Glass-brain rendering of the τ pathology modeled using the Nexopathy in silico model, which augments the NDM model with a term modeling the accumulation of τ pathology intra-regionally without incorporating effects from inflammation marker genes (NexIS:global). D: Glass-brain rendering of the τ pathology modeled using the NexIS model with Trem2-dependent modulation of τ accumulation and transmissibility (NexIS:Trem2). E: The per-time-point fits of the NDM are moderately strong, with R2 = 0.25 over all time points. F: The per-time-point fits of NexIS:global are similar to that of the NDM (E). However, because the addition of an accumulation term allows the model to account for the amplification of DS9 τ pathology over time (A) – note the difference in the scale of the y-axes between (E) & (F) – the overall fit across all time points is much stronger (R2 = 0.44). G: NexIS:Trem2 provides the best overall model for DS9 pathology, both in terms of per-time-point and overall fits (R2 = 0.52). (Reproduced from
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      ).
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      with an initial configuration given by baseline TREM2 expression. Particularly intriguing is the suggestion that there is a temporal staging of pathological events in AD with activated microglia as mediators of Aβ-induced τ pathology
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      ; here, connectome-based biophysical models of all three populations could uncover how they interact at a mechanistic level. Following the NexIS model comparison approach, models of varying complexity could be tested against each other to determine the key biophysical interactions that are necessary for achieving strong fits to imaging data. In this way, connectome-based biophysical models can be used to probe biological hypotheses about the roles of microglia in AD pathophysiology, which are still only partly understood.

      Reconciling cell-type vulnerability and connectome-based spread

      Another factor thought to contribute to the regional specificity of neurodegeneration in AD is selective neuronal vulnerability: the neuronal composition of strongly affected regions, such as the hippocampus and entorhinal cortex, confers to them a higher innate susceptibility to AD pathology.
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      With the advent of technologies such as single-cell RNA sequencing (scRNAseq) and single-nucleus RNA sequencing (snRNAseq), it has been established that the transcriptomic programming of the brain is altered in AD in a cell-type-specific manner.
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      indicates that selective vulnerability may indeed play an important role in the disease process. We note here that selective vulnerability is not in opposition to trans-neuronal spread as a disease mechanism and may not be entirely separable from it, because many of the vulnerable neuronal subtypes have long-range projections. Insofar as they are separable, however, it is likely that both cell-autonomous and trans-neuronal mechanisms contribute to the complex pathophysiology of AD.
      The isolation and transcriptomic characterization of neuronal subtypes that are particularly susceptible to AD pathology has been limited to brain subregions that are canonically affected early in the disease process, such as layer II of the entorhinal cortex.
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      From a biological perspective, there are several ways in which cell types may play a role in mediating the pathological spread of Aβ and τ, which directly inform how traditional models of connectome-based spread should be modified. A high density of neuronal cell types that are especially susceptible to proteinopathy in a given region may effectively increase the local accumulation rates of Aβ and τ; conversely, neuroprotective cell types, particularly certain support cells, may decrease these accumulation rates by enhancing clearance at a regional level. Another possibility is that the presence of certain cell types may modulate regional transmission rates. For instance Aβ is known to be cytotoxic to oligodendrocytes, the primary support cells responsible for the maintenance of the myelin sheath around long-range axons.
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      but since NexIS posits that local cell-type densities influence how pathology accumulates and spreads, neurodegeneration over time should also feed back into the evolution of Aβ and τ deposition. This suggests that NexIS be augmented to also describe atrophy, which should be straightforward from both mathematical-modeling and data-collection perspectives, since the T1-weighted MRI images used to assess regional volume loss (see Section The clinical utility of mathematical models) are often collected in tandem with PET imaging in large clinical datasets, such as the Alzheimer’s Disease Neuroimaging Initiative (ADNI).
      • Weiner M.W.
      • Veitch D.P.
      • Aisen P.S.
      • Beckett L.A.
      • Cairns N.J.
      • Green R.C.
      • Harvey D.
      • Jack C.R.
      • Jagust W.
      • Liu E.
      • Morris J.C.
      • Petersen R.C.
      • Saykin A.J.
      • Schmidt M.E.
      • Shaw L.
      • Siuciak J.A.
      • Soares H.
      • Toga A.W.
      • Trojanowski J.Q.
      The Alzheimer’s Disease Neuroimaging Initiative: A review of papers published since its inception.
      Overall, until recently it has not been possible to reconcile the impact of selective neuronal vulnerability in the context of connectome-based spread at a whole-brain level, and the MISS and NexIS platforms provide a promising avenue for exploring these two hypotheses together.

      Functional deficits in AD facilitate the disease process

      Evidence indicates that connectome-based spread of Aβ and τ pathology can be facilitated by abnormalities in structural or functional connectomes, but the contribution of each is the subject of ongoing research.
      • Raj A.
      • Kuceyeski A.
      • Weiner M.
      A Network Diffusion Model of Disease Progression in Dementia.
      • Brettschneider J.
      • Tredici K.D.
      • Lee V.M.-Y.
      • Trojanowski J.Q.
      Spreading of pathology in neurodegenerative diseases: a focus on human studies.
      • Jones D.T.
      • Knopman D.S.
      • Gunter J.L.
      • Graff-Radford J.
      • Vemuri P.
      • Boeve B.F.
      • Petersen R.C.
      • Weiner M.W.
      • Jack C.R.
      Cascading network failure across the Alzheimer’s disease spectrum.
      • Schmidt R.
      • de Reus M.A.
      • Scholtens L.H.
      • van den Berg L.H.
      • van den Heuvel M.P.
      Simulating disease propagation across white matter connectome reveals anatomical substrate for neuropathology staging in amyotrophic lateral sclerosis.
      • Seeley W.W.
      • Crawford R.K.
      • Zhou J.
      • Miller B.L.
      • Greicius M.D.
      Neurodegenerative Diseases Target Large-Scale Human Brain Networks.
      • Zhou J.
      • Gennatas E.D.
      • Kramer J.H.
      • Miller B.L.
      • Seeley W.W.
      Predicting regional neurodegeneration from the healthy brain functional connectome.
      Raj, 2021
      • Raj A.
      Graph Models of Pathology Spread in Alzheimer’s Disease: An Alternative to Conventional Graph Theoretic Analysis.
      argues that while it is possible that pathology spread follows functional network dysfunction
      • Jones D.T.
      • Knopman D.S.
      • Gunter J.L.
      • Graff-Radford J.
      • Vemuri P.
      • Boeve B.F.
      • Petersen R.C.
      • Weiner M.W.
      • Jack C.R.
      Cascading network failure across the Alzheimer’s disease spectrum.
      it is also possible that pathology is indeed driven by the structural connectome, and the association between pathology spread and functional network is a consequence of the strong coupling of functional and structural connectomes.
      • Greicius M.D.
      • Supekar K.
      • Menon V.
      • Dougherty R.F.
      Resting-State Functional Connectivity Reflects Structural Connectivity in the Default Mode Network.
      • Honey C.J.
      • Thivierge J.-P.
      • Sporns O.
      Can structure predict function in the human brain?.
      Even though the role of functional network deficits in pathology spread is unclear, cellular-level alterations in excitatory-inhibitory balance are also associated with Aβ and τ.
      • Chang C.-W.
      • Evans M.D.
      • Yu X.
      • Yu G.-Q.
      • Mucke L.
      Tau reduction affects excitatory and inhibitory neurons differently, reduces excitation/inhibition ratios, and counteracts network hypersynchrony.
      • Harris S.S.
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      • Maestú F.
      • de Haan W.
      • Busche M.A.
      • DeFelipe J.
      Neuronal excitation/inhibition imbalance: core element of a translational perspective on Alzheimer pathophysiology.
      • Palop J.J.
      • Mucke L.
      Network abnormalities and interneuron dysfunction in Alzheimer disease.
      • Pooler A.M.
      • Polydoro M.
      • Wegmann S.K.
      • Pitstick R.
      • Kay K.R.
      • Sanchez L.
      • Carlson G.A.
      • Gomez-Isla T.
      • Albers M.W.
      • Spires-Jones T.L.
      • Hyman B.T.
      Tau-amyloid interactions in the rTgTauEC model of early Alzheimer’s disease suggest amyloid-induced disruption of axonal projections and exacerbated axonal pathology.
      Particularly, basic science studies indicate that Aβ and τ are associated with neuronal hyper- and hypoactivity, respectively.
      • Harris S.S.
      • Wolf F.
      • De Strooper B.
      • Busche M.A.
      Tipping the Scales: Peptide-Dependent Dysregulation of Neural Circuit Dynamics in Alzheimer’s Disease.
      There is also evidence suggesting that neuronal action potentials stimulate the production of Aβ
      • Parihar M.S.
      • Brewer G.J.
      Amyloid-β as a Modulator of Synaptic Plasticity.
      and the release of endogenous τ,
      • Pooler A.M.
      • Phillips E.C.
      • Lau D.H.W.
      • Noble W.
      • Hanger D.P.
      Physiological release of endogenous tau is stimulated by neuronal activity.
      implicating a direct role for functional activity and the progression of protein-based pathologies. Together, the interactions between structural connectivity, functional connectivity, Aβ, and τ have significant roles in the evolution of AD-related brain dysfunction.
      Recently, these interactions were partly elucidated by a study combining MEG, PET, and biophysical modeling.
      • Ranasinghe K.G.
      • Verma P.
      • Cai C.
      • Xie X.
      • Kudo K.
      • Gao X.
      • Lerner H.
      • Mizuiri D.
      • Strom A.
      • Iaccarino L.
      • La Joie R.
      • Miller B.L.
      • Gorno-Tempini M.L.
      • Rankin K.P.
      • Jagust W.J.
      • Vossel K.
      • Rabinovici G.D.
      • Raj A.
      • Nagarajan S.S.
      Altered excitatory and inhibitory neuronal subpopulation parameters are distinctly associated with tau and amyloid in Alzheimer’s disease.
      In this work, the authors reported altered excitatory and inhibitory regional model parameters in AD. In particular, an excitatory model parameter was uniquely associated with τ deposition, partially mediating the altered oscillatory activity in the α frequency band. By contrast, the inhibitory model parameter was uniquely associated with Aβ deposition, partially mediating altered oscillatory activity in the δ-θ frequency band. This study opens up new directions of identifying cellular-level mechanisms in AD using biophysical modeling and multimodel imaging. More specifically, modeling the connectome-based spread of Aβ and τ and their interactions at a network level (see Section Interactions between Aβ and τ define AD pathogenesis), coupled with a mathematical description of how these species interact with the functional network in AD, could uncover novel mechanisms of clinical importance. Further, such a model could be augmented by incorporating region-intrinsic properties, such as densities of specific subpopulations of excitatory and inhibitory neurons (See Section Reconciling cell-type vulnerability and connectome-based spread). While previous modeling approaches have included a treatment of neuronal death as a function of Aβ and τ deposition,
      • Weickenmeier J.
      • Kuhl E.
      • Goriely A.
      Multiphysics of Prionlike Diseases: Progression and Atrophy.
      • Bertsch M.
      • Franchi B.
      • Raj A.
      • Tesi M.C.
      Macroscopic modelling of Alzheimer’s disease: difficulties and challenges.
      this coupling of protein pathology and functional abnormalities in AD is relatively unexplored and therefore presents a unique opportunity to interrogate their relationship at a whole-brain level.

      Concluding thoughts

      The directions for connectome-based biophysics models discussed above are by no means an exhaustive list, and as further insights are made into AD pathophysiology, mathematical models should be augmented to accommodate them. Pursuing each avenue of investigation on its own will likely yield at least incremental improvements in the network models’ predictive capacity, as has already been demonstrated in several cases.
      • Raj A.
      • Anand C.
      New applications of diffusion model based prediction of pathological brain alterations: Introducing amyloid-tau interactions.
      • Mezias C.
      • Raj A.
      The role of directionality in determining spatiotemporal tau pathology differs between AD-like and non-AD-like mouse models.
      • Anand C.
      • Maia P.
      • Torok J.
      • Mezias C.
      • Raj A.
      The effects of microglia on tauopathy progression can be quantified using nexopathy in Silico (Nexis) models.
      Further, the insights gained from more inclusive and robust models have the potential to identify key mechanistic interactions with translational impact. Moving forward, the field should move towards more complete biophysical descriptions of AD pathophysiology while maintaining parsimony where possible, given the risk of overfitting to pathology data that may be lacking in temporal resolution, spatial resolution, or both. We anticipate that as mathematical models continue to improve, the area of intersection between the diagnosis and prognosis AD in patients and biophysics-based modeling of the underlying pathology will only continue to grow.

      Acknowledgments

      We would like to thank Benjamin Sipes for his assistance in copy editing this manuscript and Christopher Mezias, PhD for his intellectual contributions regarding directed connectomes. The authors declare no conflicts of interest. This work is supported by the following grants: Alzheimer’s Association Grant #AARDFD-22-923931, NIH National Institute on Aging (NIH-NIA) Grant #RF1AG062196. Correspondence may be directed to [email protected] and [email protected]

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