The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative condition characterized by the progressive deterioration of motor neurons in the cortex and spinal cord. Using an automated robotic microscope platform that enables the longitudinal tracking of thousands of single neurons, we examine the effects a large library of compounds on modulating the survival of primary neurons expressing a mutation known to cause ALS. The goal of our analysis is to identify the few potentially beneficial compounds among the many assayed, the vast majority of which do not extend neuronal survival. This resembles the large-scale simultaneous inference scenario familiar from microarray analysis, but transferred to the survival analysis setting due to the novel experimental setup. We apply a three-component mixture model to censored survival times of thousands of individual neurons subjected to hundreds of different compounds. The shrinkage induced by our model significantly improves performance in simulations relative to performing treatment-wise survival analysis and subsequent multiple testing adjustment. Our analysis identified compounds that provide insight into potential novel therapeutic strategies for ALS.

In polyglutamine (polyQ) diseases, only certain neurons die, despite widespread expression of the offending protein. PolyQ expansion may induce neurodegeneration by impairing proteostasis, but protein aggregation and toxicity tend to confound conventional measurements of protein stability. Here, we used optical pulse labeling to measure effects of polyQ expansions on the mean lifetime of a fragment of huntingtin, the protein that causes Huntingtons disease, in living neurons. We show that polyQ expansion reduced the mean lifetime of mutant huntingtin within a given neuron and that the mean lifetime varied among neurons, indicating differences in their capacity to clear the polypeptide. We found that neuronal longevity is predicted by the mean lifetime of huntingtin, as cortical neurons cleared mutant huntingtin faster and lived longer than striatal neurons. Thus, cell type-specific differences in turnover capacity may contribute to cellular susceptibility to toxic proteins, and efforts to bolster proteostasis in Huntingtons disease, such as protein clearance, could be neuroprotective.

Mutations in leucine-rich repeat kinase 2 (LRRK2) and α-synuclein lead to Parkinson's disease (PD). Disruption of protein homeostasis is an emerging theme in PD pathogenesis, making mechanisms to reduce the accumulation of misfolded proteins an attractive therapeutic strategy. We determined if activating nuclear factor erythroid 2-related factor (Nrf2), a potential therapeutic target for neurodegeneration, could reduce PD-associated neuron toxicity by modulating the protein homeostasis network. Using a longitudinal imaging platform, we visualized the metabolism and location of mutant LRRK2 and α-synuclein in living neurons at the single-cell level. Nrf2 reduced PD-associated protein toxicity by a cell-autonomous mechanism that was time-dependent. Furthermore, Nrf2 activated distinct mechanisms to handle different misfolded proteins. Nrf2 decreased steady-state levels of α-synuclein in part by increasing α-synuclein degradation. In contrast, Nrf2 sequestered misfolded diffuse LRRK2 into more insoluble and homogeneous inclusion bodies. By identifying the stress response strategies activated by Nrf2, we also highlight endogenous coping responses that might be therapeutically bolstered to treat PD.

Polyglutamine (polyQ) stretches exceeding a threshold length confer a toxic function to proteins that contain them and cause at least nine neurological disorders. The basis for this toxicity threshold is unclear. Although polyQ expansions render proteins prone to aggregate into inclusion bodies, this may be a neuronal coping response to more toxic forms of polyQ. The exact structure of these more toxic forms is unknown. Here we show that the monoclonal antibody 3B5H10 recognizes a species of polyQ protein in situ that strongly predicts neuronal death. The epitope selectively appears among some of the many low-molecular-weight conformational states assumed by expanded polyQ and disappears in higher-molecular-weight aggregated forms, such as inclusion bodies. These results suggest that protein monomers and possibly small oligomers containing expanded polyQ stretches can adopt a conformation that is recognized by 3B5H10 and is toxic or closely related to a toxic species.