Scale-free neurodegeneration: cellular heterogeneity and the stretched exponential kinetics of cell death

Exploring Patterns of Human Mortality and Aging: A Reliability Theory Viewpoint

The most important manifestation of aging is an increased risk of death with advancing age, a mortality pattern characterized by empirical regularities known as mortality laws. We highlight three significant ones: the Gompertz law, compensation effect of mortality (CEM), and late-life mortality deceleration and describe new developments in this area. It is predicted that CEM should result in declining relative variability of mortality at older ages. The quiescent phase hypothesis of negligible actuarial aging at younger adult ages is tested and refuted by analyzing mortality of the most recent birth cohorts. To comprehend the aging mechanisms, it is crucial to explain the observed empirical mortality patterns. As an illustrative example of data-directed modeling and the insights it provides, we briefly describe two different reliability models applied to human mortality patterns. The explanation of aging using a reliability theory approach aligns with evolutionary theories of aging, including idea of chronic phenoptosis. This alignment stems from their focus on elucidating the process of organismal deterioration itself, rather than addressing the reasons why organisms are not designed for perpetual existence. This article is a part of a special issue of the journal that commemorates the legacy of the eminent Russian scientist Vladimir Petrovich Skulachev (1935-2023) and his bold ideas about evolution of biological aging and phenoptosis.

Anomalous Self-Organization in Active Piles

Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity's strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak-Tang-Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.

The Complex Mechanisms by Which Neurons Die Following DNA Damage in Neurodegenerative Diseases

Human cells are exposed to numerous exogenous and endogenous insults every day. Unlike other molecules, DNA cannot be replaced by resynthesis, hence damage to DNA can have major consequences for the cell. The DNA damage response contains overlapping signalling networks that repair DNA and hence maintain genomic integrity, and aberrant DNA damage responses are increasingly described in neurodegenerative diseases. Furthermore, DNA repair declines during aging, which is the biggest risk factor for these conditions. If unrepaired, the accumulation of DNA damage results in death to eliminate cells with defective genomes. This is particularly important for postmitotic neurons because they have a limited capacity to proliferate, thus they must be maintained for life. Neuronal death is thus an important process in neurodegenerative disorders. In addition, the inability of neurons to divide renders them susceptible to senescence or re-entry to the cell cycle. The field of cell death has expanded significantly in recent years, and many new mechanisms have been described in various cell types, including neurons. Several of these mechanisms are linked to DNA damage. In this review, we provide an overview of the cell death pathways induced by DNA damage that are relevant to neurons and discuss the possible involvement of these mechanisms in neurodegenerative conditions.

Neuronal Cell Death

Neuronal cell death occurs extensively during development and pathology, where it is especially important because of the limited capacity of adult neurons to proliferate or be replaced. The concept of cell death used to be simple as there were just two or three types, so we just had to work out which type was involved in our particular pathology and then block it. However, we now know that there are at least a dozen ways for neurons to die, that blocking a particular mechanism of cell death may not prevent the cell from dying, and that non-neuronal cells also contribute to neuronal death. We review here the mechanisms of neuronal death by intrinsic and extrinsic apoptosis, oncosis, necroptosis, parthanatos, ferroptosis, sarmoptosis, autophagic cell death, autosis, autolysis, paraptosis, pyroptosis, phagoptosis, and mitochondrial permeability transition. We next explore the mechanisms of neuronal death during development, and those induced by axotomy, aberrant cell-cycle reentry, glutamate (excitoxicity and oxytosis), loss of connected neurons, aggregated proteins and the unfolded protein response, oxidants, inflammation, and microglia. We then reassess which forms of cell death occur in stroke and Alzheimer's disease, two of the most important pathologies involving neuronal cell death. We also discuss why it has been so difficult to pinpoint the type of neuronal death involved, if and why the mechanism of neuronal death matters, the molecular overlap and interplay between death subroutines, and the therapeutic implications of these multiple overlapping forms of neuronal death.

Mathematical and computational models of the retina in health, development and disease

The retina confers upon us the gift of vision, enabling us to perceive the world in a manner unparalleled by any other tissue. Experimental and clinical studies have provided great insight into the physiology and biochemistry of the retina; however, there are questions which cannot be answered using these methods alone. Mathematical and computational techniques can provide complementary insight into this inherently complex and nonlinear system. They allow us to characterise and predict the behaviour of the retina, as well as to test hypotheses which are experimentally intractable. In this review, we survey some of the key theoretical models of the retina in the healthy, developmental and diseased states. The main insights derived from each of these modelling studies are highlighted, as are model predictions which have yet to be tested, and data which need to be gathered to inform future modelling work. Possible directions for future research are also discussed. Whilst the present modelling studies have achieved great success in unravelling the workings of the retina, they have yet to achieve their full potential. For this to happen, greater involvement with the modelling community is required, and stronger collaborations forged between experimentalists, clinicians and theoreticians. It is hoped that, in addition to bringing the fruits of current modelling studies to the attention of the ophthalmological community, this review will encourage many such future collaborations.

The fluorescent pentameric oligothiophene pFTAA identifies filamentous tau in live neurons cultured from adult P301S tau mice

Identification of fluorescent dyes that label the filamentous protein aggregates characteristic of neurodegenerative disease, such as β-amyloid and tau in Alzheimer's disease, in a live cell culture system has previously been a major hurdle. Here we show that pentameric formyl thiophene acetic acid (pFTAA) fulfills this function in living neurons cultured from adult P301S tau transgenic mice. Injection of pFTAA into 5-month-old P301S tau mice detected cortical and DRG neurons immunoreactive for AT100, an antibody that identifies solely filamentous tau, or MC1, an antibody that identifies a conformational change in tau that is commensurate with neurofibrillary tangle formation in Alzheimer's disease brains. In fixed cultures of dorsal root ganglion (DRG) neurons, pFTAA binding, which also identified AT100 or MC1+ve neurons, followed a single, saturable binding curve with a half saturation constant of 0.14 μM, the first reported measurement of a binding affinity of a beta-sheet reactive dye to primary neurons harboring filamentous tau. Treatment with formic acid, which solubilizes filamentous tau, extracted pFTAA, and prevented the re-binding of pFTAA and MC1 without perturbing expression of soluble tau, detected using an anti-human tau (HT7) antibody. In live cultures, pFTAA only identified DRG neurons that, after fixation, were AT100/MC1+ve, confirming that these forms of tau pre-exist in live neurons. The utility of pFTAA to discriminate between living neurons containing filamentous tau from other neurons is demonstrated by showing that more pFTAA+ve neurons die than pFTAA-ve neurons over 25 days. Since pFTAA identifies fibrillar tau and other misfolded proteins in living neurons in culture and in animal models of several neurodegenerative diseases, as well as in human brains, it will have considerable application in sorting out disease mechanisms and in identifying disease-modifying drugs that will ultimately help establish the mechanisms of neurodegeneration in human neurodegenerative diseases.

Prognostic role of "prion-like propagation" in SOD1-linked familial ALS: an alternative view

“Prion-like propagation” has recently been proposed for disease spread in Cu/Zn superoxide dismutase 1 (SOD1)-linked familial amyotrophic lateral sclerosis (ALS). Pathological SOD1 conformers are presumed to propagate via cell-to-cell transmission. In this model, the risk-based kinetics of neuronal cell loss over time appears to be represented by a sigmoidal function that reflects the kinetics of intercellular transmission. Here, we describe an alternative view of prion-like propagation in SOD1-linked ALS – its relation to disease prognosis under the protective-aggregation hypothesis. Nucleation-dependent polymerization has been widely accepted as the molecular mechanism of prion propagation. If toxic species of misfolded SOD1, as soluble oligomers, are formed as on-pathway intermediates of nucleation-dependent polymerization, further fibril extension via sequential addition of monomeric mutant SOD1 would be protective against neurodegeneration. This is because the concentration of unfolded mutant SOD1 monomers, which serve as precursor of nucleation and toxic species of mutant SOD1, would decline in proportion to the extent of aggregation. The nucleation process requires that native conformers exist in an unfolded state that may result from escaping the cellular protein quality control machinery. However, prion-like propagation-SOD1 aggregated form self-propagates by imposing its altered conformation on normal SOD1-appears to antagonize the protective role of aggregate growth. The cross-seeding reaction with normal SOD1 would lead to a failure to reduce the concentration of unfolded mutant SOD1 monomers, resulting in continuous nucleation and subsequent generation of toxic species, and influence disease prognosis. In this alternative view, the kinetics of neuronal loss appears to be represented by an exponential function, with decreasing risk reflecting the protective role of aggregate and the potential for cross-seeding reactions between mutant SOD1 and normal SOD1.

Direct optic nerve sheath (DONS) application of Schwann cells prolongs retinal ganglion cell survival in vivo

Cell-based therapies are increasingly recognized as a potential strategy to treat retinal neurodegenerative disease. Their administration, however, is normally indirect and complex, often with an inability to assess in real time their effects on cell death and their migration/integration into the host retina. In the present study, using a partial optic nerve transection (pONT) rat model, we describe a new method of Schwann cell (SC) delivery (direct application to injured optic nerve sheath, SC/DONS), which was compared with intravitreal SC delivery (SC/IVT). Both SC/DONS and SC/IVT were able to be assessed in vivo using imaging to visualize retinal ganglion cell (RGC) apoptosis and SC retinal integration. RGC death in the pONT model was best fitted to the one-phase exponential decay model. Although both SC/DONS and SC/IVT altered the temporal course of RGC degeneration in pONT, SC/DONS resulted in delayed but long-lasting effects on RGC protection, compared with SC/IVT treatment. In addition, their effects on primary and secondary degeneration, and axonal regeneration, were also investigated, by histology, whole retinal counting, and modelling of RGC loss. SC/DONS was found to significantly reduce RGC apoptosis in vivo and significantly increase RGC survival by targeting secondary rather than primary degeneration. Both SC/DONS and SC/IVT were found to promote RGC axonal regrowth after optic nerve injury, with evidence of GAP-43 expression in RGC somas and axons. SC/DONS may have the potential in the treatment of optic neuropathies, such as glaucoma. We show that SC transplantation can be monitored in real time and that the protective effects of SCs are associated with targeting secondary degeneration, with implications for translating cell-based therapies to the clinic.

Modeling the polyglutamine aggregation pathway in Huntington's disease: from basic studies to clinical applications

Huntington's disease (HD) is among the polyglutamine (polyQ) disorders, which are caused by expansion of CAG-trinucleotide repeats. These disorders share common characteristics, and have thus long been thought to have a unifying pathogenic mechanism resulting from polyQ expansion. However, this scenario has recently become more complex, as studies have found multiple pathways for the assembly of disease-related polyQ protein aggregates that differ in both structure and toxicity. There are fascinating disease-specific aspects of the polyQ disorders, including the repeat-length dependence of both clinical features and the propensity of the expanded polyQ protein to aggregate. Such aggregation kinetics have proven useful in explaining the disease process. This chapter describes two risk-based stochastic kinetic models, the cumulative-damage and one-hit models, that describe genotype-phenotype correlations in patients with polyQ diseases and reflect alternative pathways of polyQ aggregation. Using repeat-length as an index, several models explore the quantitative connection between aggregation kinetics and clinical data from HD patients. The correlations between CAG repeat-length and age-of-onset are re-evaluated, and the rate of disease progression (as assessed by clinical measures and longitudinal imaging studies of brain structure) are surveyed. Finally, I present a mathematical model by which the time course of neurodegeneration in HD can be precisely predicted, and discuss the association of the models with the major controversies about HD pathogenesis.

Kinetics of neurodegeneration based on a risk-related biomarker in animal model of glaucoma

Background

Neurodegenerative diseases including Parkinson’s and Alzheimer’s diseases progress slowly and steadily over years or decades. They show significant between-subject variation in progress and clinical symptoms, which makes it difficult to predict the course of long-term disease progression with or without treatments. Recent technical advances in biomarkers have facilitated earlier, preclinical diagnoses of neurodegeneration by measuring or imaging molecules linked to pathogenesis. However, there is no established “biomarker model” by which one can quantitatively predict the progress of neurodegeneration. Here, we show predictability of a model with risk-based kinetics of neurodegeneration, whereby neurodegeneration proceeds as probabilistic events depending on the risk.

Results

We used five experimental glaucomatous animals, known for causality between the increased intraocular pressure (IOP) and neurodegeneration of visual pathways, and repeatedly measured IOP as well as white matter integrity by diffusion tensor imaging (DTI) as a biomarker of axonal degeneration. The IOP in the glaucomatous eye was significantly increased than in normal and was varied across time and animals; thus we tested whether this measurement is useful to predict kinetics of the integrity. Among four kinds of models of neurodegeneration, constant-rate, constant-risk, variable-risk and heterogeneity models, goodness of fit of the model and F-test for model selection showed that the time course of optic nerve integrity was best explained by the variable-risk model, wherein neurodegeneration kinetics is expressed in an exponential function across cumulative risk based on measured IOP. The heterogeneity model with stretched exponential decay function also fit well to the data, but without statistical superiority to the variable-risk model. The variable-risk model also predicted the number of viable axons in the optic nerve, as assessed by immunohistochemistry, which was also confirmed to be correlated with the pre-mortem integrity of the optic nerve. In addition, the variable-risk model identified the disintegrity in the higher-order visual pathways, known to underlie the transsynaptic degeneration in this disease.

Conclusions

These findings indicate that the variable-risk model, using a risk-related biomarker, could predict the spatiotemporal progression of neurodegeneration. This model, virtually equivalent to survival analysis, may allow us to estimate possible effect of neuroprotection in delaying progress of neurodegeneration.

Quantitative connection between polyglutamine aggregation kinetics and neurodegenerative process in patients with Huntington's disease

BACKGROUND

Despite enormous progress in elucidating the biophysics of aggregation, no cause-and-effect relationship between protein aggregation and neurodegenerative disease has been unequivocally established. Here, we derived several risk-based stochastic kinetic models that assess genotype/phenotype correlations in patients with Huntington's disease (HD) caused by the expansion of a CAG repeat. Fascinating disease-specific aspects of HD include the polyglutamine (polyQ)-length dependence of both age at symptoms onset and the propensity of the expanded polyQ protein to aggregate. In vitro, aggregation of polyQ peptides follows a simple nucleated growth polymerization pathway. Our models that reflect polyQ aggregation kinetics in a nucleated growth polymerization divided aggregate process into the length-dependent nucleation and the nucleation-dependent elongation. In contrast to the repeat-length dependent variability of age at onset, recent studies have shown that the extent of expansion has only a subtle effect on the rate of disease progression, suggesting possible differences in the mechanisms underlying the neurodegenerative process.

RESULTS

Using polyQ-length as an index, these procedures enabled us for the first time to establish a quantitative connection between aggregation kinetics and disease process, including onset and the rate of progression. Although the complexity of disease process in HD, the time course of striatal neurodegeneration can be precisely predicted by the mathematical model in which neurodegeneration occurs by different mechanisms for the initiation and progression of disease processes. Nucleation is sufficient to initiate neuronal loss as a series of random events in time. The stochastic appearance of nucleation in a cell population acts as the constant risk of neuronal cell damage over time, while elongation reduces the risk by nucleation in proportion to the increased extent of the aggregates during disease progression.

CONCLUSIONS

Our findings suggest that nucleation is a critical step in gaining toxic effects to the cell, and provide a new insight into the relationship between polyQ aggregation and neurodegenerative process in HD.

The genomic, biochemical, and cellular responses of the retina in inherited photoreceptor degenerations and prospects for the treatment of these disorders

The association of more than 140 genes with human photoreceptor degenerations, together with studies of animal models of these monogenic diseases, has provided great insight into their pathogenesis. Here we review the responses of the retina to photoreceptor mutations, including mechanisms of photoreceptor death. We discuss the roles of oxidative metabolism, mitochondrial reactive oxygen species, metabolic stress, protein misfolding, and defects in ciliary proteins, as well as the responses of Müller glia, microglia, and the retinal vasculature. Finally, we report on potential pharmacologic and biologic therapies, the critical role of histopathology as a prerequisite to treatment, and the exciting promise of gene therapy in animal models and in phase 1 trials in humans.

Quantitative relationships between huntingtin levels, polyglutamine length, inclusion body formation, and neuronal death provide novel insight into huntington's disease molecular pathogenesis

An expanded polyglutamine (polyQ) stretch in the protein huntingtin (htt) induces self-aggregation into inclusion bodies (IBs) and causes Huntington's disease (HD). Defining precise relationships between early observable variables and neuronal death at the molecular and cellular levels should improve our understanding of HD pathogenesis. Here, we used an automated microscope that tracks thousands of neurons individually over their entire lifetime to quantify interconnected relationships between early variables, such as htt levels, polyQ length, and IB formation, and neuronal death in a primary striatal model of HD. The resulting model revealed that mutant htt increases the risk of death by tonically interfering with homeostatic coping mechanisms rather than producing accumulated damage to the neuron, htt toxicity is saturable, the rate-limiting steps for inclusion body formation and death can be traced to different conformational changes in monomeric htt, and IB formation reduces the impact of the starting levels of htt of a neuron on its risk of death. Finally, the model that emerges from our quantitative measurements places critical limits on the potential mechanisms by which mutant htt might induce neurodegeneration, which should help direct future research.

One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death III: diffusion pulse death zones

This is the third of three papers in which we study a mathematical model of cytoskeleton-induced neuron death. In the first two papers of this suite [Lomasko, T., Clarke, G., Lumsden, C., 2007a. One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death I: cell fate arrival times. J. Theor. Biol. 249, 1-17, doi:10.1016/j.jtbi.2007.05.031; Lomasko, T., Clarke, G., Lumsden, C., 2007b. One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: transition state metastability. J. Theor. Biol. 249, 18-28, doi:10.1016/j.jtbi.2007.05.032], we established that the mean-field limit of our model relates the known patterns of neuron decline to specific scales of cytoskeleton reorganization and cell-cell interaction by diffusible death factors. In the mean-field limit, the spatially variable concentration of diffusing death factor is replaced by a constant average value. Recent empirical advances now permit the actual diffusion of such factors to be followed in intact neuropil. In this paper we therefore extend the model beyond the mean-field limit, to include the diffusion dynamics of death factor bursts released from dying neurons. A range of novel tissue degeneration patterns is observed, for which we confirm and extend the mean-field prediction that sigmoidal patterns of neuron population decay are a principal hallmark of cell death in the presence of death factor release.

One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: Transition state metastability

This is the second of two papers in which we study a mathematical model of cytoskeleton-induced neuron death. Recent evidence indicates that aggravated assembly or destruction of the cytoskeleton can trigger programmed death in neurons, by mechanisms as yet poorly understood. In our model, assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by a diffusible toxic factor released from dying neurons. In the companion report we established that the model relates the observed general patterns of neuron decline to specific scales of cytoskeleton reorganization and cell-cell interaction strength. In this paper we study the transit of neurons through states intermediate between initial viability and cell death in our model. We find that the stochastic flow of neuron fate, from viability to cell death, self-organizes into two distinct temporal phases. There is a rapid relaxation of the initial neuron population to a more disordered phase that is long-lived, or metastable, with respect to the time scales of change in single cells. Strikingly, cellular egress from this metastable phase follows the one-hit kinetic pattern of exponential decline now established as a principal hallmark of cell death in neurodegenerative disorders. Intermediate state metastability may therefore be an important element in the systems biology of one-hit neurodegeneration.

One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death I: Cell-fate arrival times

Much experimental evidence shows that the cytoskeleton is a downstream target and effector during cell death in numerous neurodegenerative diseases, including Parkinson's, Huntington's, and Alzheimer's diseases. However, recent evidence indicates that cytoskeletal dysfunction can also trigger neuronal death, by mechanisms as yet poorly understood. This is the first of two papers in which we study a mathematical model of cytoskeleton-induced neuron death. In our model, assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by the presence of cell interactions in the form of a diffusible toxic factor released by dying neurons. We find that, consistent with empirical observations, our model produces one-hit exponential and sigmoid patterns of cell dropout. In all cases, cell dropout is exponential-tailed and described accurately by a gamma distribution. The transition between exponential and sigmoidal is gradual, and determined by a synergetic interaction between the magnitude of fluctuations in cytoskeleton assembly control and by the degree of cell coupling. We conclude that a single mechanism involving neuron interactions and fluctuations in cytoskeleton assembly control is compatible with the experimentally observed range of neuronal attrition kinetics.