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

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. (c) 2004 Elsevier Ltd. All rights reserved.