A third of marketed drugs act by binding to a G-protein-coupled receptor (GPCR) and either triggering or preventing receptor activation. Although recent crystal structures have provided snapshots of both active and inactive functional states of GPCRs, these structures do not reveal the mechanism by which GPCRs transition between these states. Here we… (More)
G protein-coupled receptors (GPCRs) relay diverse extracellular signals into cells by catalyzing nucleotide release from heterotrimeric G proteins, but the mechanism underlying this quintessential molecular signaling event has remained unclear. Here we use atomic-level simulations to elucidate the nucleotide-release mechanism. We find that the G protein α… (More)
Research on change-point detection, the classical problem of detecting abrupt changes in sequential data, has focused predominantly on datasets with a single observable. A growing number of time series datasets, however, involve many observables, often with the property that a given change typically affects only a few of the observables. We introduce a… (More)
This paper develops some basic theorems in elementary number theory, especially those appearing on mathematical Olympiads, from the perspective of groups, rings, and group actions.