Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online. © 2013 Copyright Taylor and Francis Group, LLC.

Regulation of DLK-1 kinase activity by calcium-mediated dissociation from an inhibitory isoform.

MAPKKK dual leucine zipper-bearing kinases (DLKs) are regulators of synaptic development and axon regeneration. The mechanisms underlying their activation are not fully understood. Here, we show that C. elegans DLK-1 is activated by a Ca(2+)-dependent switch from inactive heteromeric to active homomeric protein complexes. We identify a DLK-1 isoform, DLK-1S, that shares identical kinase and leucine zipper domains with the previously described long isoform DLK-1L but acts to inhibit DLK-1 function by binding to DLK-1L. The switch between homo- or heteromeric DLK-1 complexes is influenced by Ca(2+) concentration. A conserved hexapeptide in the DLK-1L C terminus is essential for DLK-1 activity and is required for Ca(2+) regulation. The mammalian DLK-1 homolog MAP3K13 contains an identical C-terminal hexapeptide and can functionally complement dlk-1 mutants, suggesting that the DLK activation mechanism is conserved. The DLK activation mechanism is ideally suited for rapid and spatially controlled signal transduction in response to axonal injury and synaptic activity.