The Smoothened receptor (SMO) belongs to the Class Frizzled of the G protein-coupled receptor (GPCR) superfamily, constituting a key component of the Hedgehog signalling pathway. Here we report the crystal structure of the multi-domain human SMO, bound and stabilized by a designed tool ligand TC114, using an X-ray free-electron laser source at 2.9 Å. The structure reveals a precise arrangement of three distinct domains: a seven-transmembrane helices domain (TMD), a hinge domain (HD) and an intact extracellular cysteine-rich domain (CRD). This architecture enables allosteric interactions between the domains that are important for ligand recognition and receptor activation. By combining the structural data, molecular dynamics simulation, and hydrogen-deuterium-exchange analysis, we demonstrate that transmembrane helix VI, extracellular loop 3 and the HD play a central role in transmitting the signal employing a unique GPCR activation mechanism, distinct from other multi-domain GPCRs.

Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomialtime constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity (or supermodularity) of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering. We then study the problem of attacking (i.e., removing) a set of installed sensors, under predefined attack budget constraints, to maximize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter. Again, we show that there is no polynomial-time constant-factor approximation algorithm for this problem, and show specifically that greedy algorithms can perform arbitrarily poorly.

Membrane mimics are indispensable tools in the structural and functional understanding of membrane proteins (MPs). Given stringent requirements of integral MP manipulations, amphiphile replacement is often required in sample preparation for various biophysical purposes. Current protocols generally rely on physical methodologies and rarely reach complete replacement. In comparison, we report herein a chemical alternative that facilitates the exhaustive exchange of membrane-mimicking systems for MP reconstitution. This method, named sacrifice-replacement strategy, was enabled by a class of chemically cleavable detergents (CCDs), derived from the disulfide incorporation in the traditional detergent n-dodecyl-β-d-maltopyranoside. The representative CCD behaved well in both solubilizing the diverse α-helical human G protein-coupled receptors and refolding of the β-barrel bacterial outer membrane protein X, and more importantly, it could also be readily degraded under mild conditions. By this means, the A2A adenosine receptor was successfully reconstituted into a series of commercial detergents for stabilization screening and nanodiscs for electron microscopy analysis. Featured by the simplicity and compatibility, this CCD-mediated strategy would later find more applications when being integrated in other biophysics studies.