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Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Neurodegenerative disorders are an insidious group of diseases characterized by severe physical and cognitive effects that often have devastating consequences for the lives of affected individuals and their families. One feature common to a significant proportion of these diseases is that affected neurons commit to undergoing an active form of degeneration known as programmed cell death, or apoptosis. Although intense effort over the past several years has resulted is a remarkable increase in our understanding of the molecular events involved in neurodegeneration, our knowledge regarding the cellular and tissue properties that determine the temporal patterns of neuronal attrition is limited. We recently demonstrated that neurodegenerative kinetics in various diseases fit well to exponential decay functions, and proposed a universal one-hit switch mechanism in which mutant and injured neurons exist in a viable state characterized by an increased but constant risk of initiating apoptosis (Nature, 406, p. 195). Here we show that a heavy-tailed stretched exponential function is better able to account for neurodegenerative kinetic data. Moreover, normalization of all available data according to their corresponding best-fit stretched exponential parameters suggest that the generalized model is consistent with a universal mechanism of neuronal cell death that is greatly improved over the constant risk model. In contrast to the original model in which all cells exhibit an identical risk of initiating apoptosis, the stretched exponential model is consistent with each neuron experiencing a constant risk that is different from that experienced by other cells in the degenerating population, perhaps due to spatial differences in the cellular microenvironment. Intriguingly, the predicted distribution of risk across the cell population can be fit by a power-law function, further suggesting that scale-free properties of degenerating neuronal tissues might act as potent regulators of the kinetics of cell death in neural tissue. [Copyright &y& Elsevier]

Abstract: We recently demonstrated that cell loss kinetics in diverse forms of neurodegeneration (ND) suggests a universal death switch mechanism in which each cell is at a constant risk to initiate apoptosis. We proposed that mutant and injured neurons exist in a viable state typified by an increased risk of initiating death processes [Clarke, Collins, Leavitt, Andrews, Hayden, Lumsden, McInnes, A one-hit model of cell death in inherited neuronal degenerations, Nature 406 (2000) 195–199]. To date, however, measurements of cell death risk have been available only as averages across the affected cell population. Here we develop and apply a method of death kinetic analysis in which the risk factors vary across the neuronal population, as for example due to regional heterogeneities in the cellular microenvironment. We find that most cases of ND for which cell loss data has been obtained are better explained by death risks that vary from cell to cell, compared to death risk that is constant across the neuronal population. Strikingly, a common form of the frequency distribution defining the death risk heterogeneity is shared across most of these cases. This first characterization of the kinetic heterogeneity in one-hit neuronal death, therefore, suggests that the wide variety of ND now known may share mechanisms through which regional differences in the cellular microenvironment modulate the kinetics of cell loss. [Copyright &y& Elsevier]