Structural insights into the mechanism of the sodium/iodide symporter.

The sodium/iodide symporter (NIS) is the essential plasma membrane protein that mediates active iodide (I-) transport into the thyroid gland, the first step in the biosynthesis of the thyroid hormones-the master regulators of intermediary metabolism. NIS couples the inward translocation of I- against its electrochemical gradient to the inward transport of Na+ down its electrochemical gradient1,2. For nearly 50 years before its molecular identification3, NIS was the molecule at the centre of the single most effective internal radiation cancer therapy: radioiodide (131I-) treatment for thyroid cancer2. Mutations in NIS cause congenital hypothyroidism, which must be treated immediately after birth to prevent stunted growth and cognitive deficiency2. Here we report three structures of rat NIS, determined by single-particle cryo-electron microscopy: one with no substrates bound; one with two Na+ and one I- bound; and one with one Na+ and the oxyanion perrhenate bound. Structural analyses, functional characterization and computational studies show the substrate-binding sites and key residues for transport activity. Our results yield insights into how NIS selects, couples and translocates anions-thereby establishing a framework for understanding NIS function-and how it transports different substrates with different stoichiometries and releases substrates from its substrate-binding cavity into the cytosol.

Quantifying the local resolution of cryo-EM density maps.

We propose a definition of local resolution for three-dimensional electron cryo-microscopy (cryo-EM) density maps that uses local sinusoidal features. Our algorithm has no free parameters and is applicable to other imaging modalities, including tomography. By evaluating the local resolution of single-particle reconstructions and subtomogram averages for four example data sets, we report variable resolution across a 4- to 40-Å range.

Statistical modeling and removal of lipid membrane projections for cryo-EM structure determination of reconstituted membrane proteins.

This paper describes steps in the single-particle cryo-EM 3D structure determination of membrane proteins in their membrane environment. Using images of the Kv1.2 potassium-channel complex reconstituted into lipid vesicles, we describe procedures for the merging of focal-pairs of exposures and the removal of the vesicle-membrane signal from the micrographs. These steps allow 3D reconstruction to be performed from the protein particle images. We construct a 2D statistical model of the vesicle structure based on higher-order singular value decomposition (HOSVD), by taking into account the structural symmetries of the vesicles in polar coordinates. Non-roundness in the vesicle structure is handled with a non-linear shape alignment to a reference, which ensures a compact model representation. The results show that the learned model is an accurate representation of the imaged vesicle structures. Precise removal of the strong membrane signals allows better alignment and classification of images of small membrane-protein particles, and allows higher-resolution 3D reconstruction.

State-dependent FRET reports calcium- and voltage-dependent gating-ring motions in BK channels.

Large-conductance voltage- and calcium-dependent potassium channels (BK, "Big K+") are important controllers of cell excitability. In the BK channel, a large C-terminal intracellular region containing a "gating-ring" structure has been proposed to transduce Ca(2+) binding into channel opening. Using patch-clamp fluorometry, we have investigated the calcium and voltage dependence of conformational changes of the gating-ring region of BK channels, while simultaneously monitoring channel conductance. Fluorescence resonance energy transfer (FRET) between fluorescent protein inserts indicates that Ca(2+) binding produces structural changes of the gating ring that are much larger than those predicted by current X-ray crystal structures of isolated gating rings.

SubspaceEM: A fast maximum-a-posteriori algorithm for cryo-EM single particle reconstruction.

Single particle reconstruction methods based on the maximum-likelihood principle and the expectation-maximization (E-M) algorithm are popular because of their ability to produce high resolution structures. However, these algorithms are computationally very expensive, requiring a network of computational servers. To overcome this computational bottleneck, we propose a new mathematical framework for accelerating maximum-likelihood reconstructions. The speedup is by orders of magnitude and the proposed algorithm produces similar quality reconstructions compared to the standard maximum-likelihood formulation. Our approach uses subspace approximations of the cryo-electron microscopy (cryo-EM) data and projection images, greatly reducing the number of image transformations and comparisons that are computed. Experiments using simulated and actual cryo-EM data show that speedup in overall execution time compared to traditional maximum-likelihood reconstruction reaches factors of over 300.

Directly reconstructing principal components of heterogeneous particles from cryo-EM images.

Structural heterogeneity of particles can be investigated by their three-dimensional principal components. This paper addresses the question of whether, and with what algorithm, the three-dimensional principal components can be directly recovered from cryo-EM images. The first part of the paper extends the Fourier slice theorem to covariance functions showing that the three-dimensional covariance, and hence the principal components, of a heterogeneous particle can indeed be recovered from two-dimensional cryo-EM images. The second part of the paper proposes a practical algorithm for reconstructing the principal components directly from cryo-EM images without the intermediate step of calculating covariances. This algorithm is based on maximizing the posterior likelihood using the Expectation-Maximization algorithm. The last part of the paper applies this algorithm to simulated data and to two real cryo-EM data sets: a data set of the 70S ribosome with and without Elongation Factor-G (EF-G), and a data set of the influenza virus RNA dependent RNA Polymerase (RdRP). The first principal component of the 70S ribosome data set reveals the expected conformational changes of the ribosome as the EF-G binds and unbinds. The first principal component of the RdRP data set reveals a conformational change in the two dimers of the RdRP.

Structure of the BK potassium channel in a lipid membrane from electron cryomicroscopy.

A long-sought goal in structural biology has been the imaging of membrane proteins in their membrane environments. This goal has been achieved with electron crystallography in those special cases where a protein forms highly ordered arrays in lipid bilayers. It has also been achieved by NMR methods in proteins up to 50 kilodaltons (kDa) in size, although milligram quantities of protein and isotopic labelling are required. For structural analysis of large soluble proteins in microgram quantities, an increasingly powerful method that does not require crystallization is single-particle reconstruction from electron microscopy of cryogenically cooled samples (electron cryomicroscopy (cryo-EM)). Here we report the first single-particle cryo-EM study of a membrane protein, the human large-conductance calcium- and voltage-activated potassium channel (BK), in a lipid environment. The new method is called random spherically constrained (RSC) single-particle reconstruction. BK channels, members of the six-transmembrane-segment (6TM) ion channel family, were reconstituted at low density into lipid vesicles (liposomes), and their function was verified by a potassium flux assay. Vesicles were also frozen in vitreous ice and imaged in an electron microscope. From images of 8,400 individual protein particles, a three-dimensional (3D) reconstruction of the BK channel and its membrane environment was obtained at a resolution of 1.7-2.0 nm. Not requiring the formation of crystals, the RSC approach promises to be useful in the structural study of many other membrane proteins as well.

Automatic cryo-EM particle selection for membrane proteins in spherical liposomes.

Random spherically constrained (RSC) single particle reconstruction is a method to obtain structures of membrane proteins embedded in lipid vesicles (liposomes). As in all single-particle cryo-EM methods, structure determination is greatly aided by reliable detection of protein "particles" in micrographs. After fitting and subtraction of the membrane density from a micrograph, normalized cross-correlation (NCC) and estimates of the particle signal amplitude are used to detect particles, using as references the projections of a 3D model. At each pixel position, the NCC is computed with only those references that are allowed by the geometric constraint of the particle's embedding in the spherical vesicle membrane. We describe an efficient algorithm for computing this position-dependent correlation, and demonstrate its application to selection of membrane-protein particles, GluA2 glutamate receptors, which present very different views from different projection directions.

Cryo-EM structures of Kv1.2 potassium channels, conducting and non-conducting.

We present near-atomic-resolution cryo-EM structures of the mammalian voltage-gated potassium channel Kv1.2 in open, C-type inactivated, toxin-blocked and sodium-bound states at 3.2 Å, 2.5 Å, 3.2 Å, and 2.9Å. These structures, all obtained at nominally zero membrane potential in detergent micelles, reveal distinct ion-occupancy patterns in the selectivity filter. The first two structures are very similar to those reported in the related Shaker channel and the much-studied Kv1.2-2.1 chimeric channel. On the other hand, two new structures show unexpected patterns of ion occupancy. First, the toxin α-Dendrotoxin, like Charybdotoxin, is seen to attach to the negatively-charged channel outer mouth, and a lysine residue penetrates into the selectivity filter, with the terminal amine coordinated by carbonyls, partially disrupting the outermost ion-binding site. In the remainder of the filter two densities of bound ions are observed, rather than three as observed with other toxin-blocked Kv channels. Second, a structure of Kv1.2 in Na+ solution does not show collapse or destabilization of the selectivity filter, but instead shows an intact selectivity filter with ion density in each binding site. We also attempted to image the C-type inactivated Kv1.2 W366F channel in Na+ solution, but the protein conformation was seen to be highly variable and only a low-resolution structure could be obtained. These findings present new insights into the stability of the selectivity filter and the mechanism of toxin block of this intensively studied, voltage-gated potassium channel.

REliable PIcking by Consensus (REPIC): a consensus methodology for harnessing multiple cryo-EM particle pickers.

Cryo-EM particle identification from micrographs ("picking") is challenging due to the low signal-to-noise ratio and lack of ground truth for particle locations. State-of-the-art computational algorithms ("pickers") identify different particle sets, complicating the selection of the best-suited picker for a protein of interest. Here, we present REliable PIcking by Consensus (REPIC), a computational approach to identifying particles common to the output of multiple pickers. We frame consensus particle picking as a graph problem, which REPIC solves using integer linear programming. REPIC picks high-quality particles even when the best picker is not known a priori or a protein is difficult-to-pick (e.g., NOMPC ion channel). Reconstructions using consensus particles without particle filtering achieve resolutions comparable to those from particles picked by experts. Our results show that REPIC requires minimal (often no) manual intervention, and considerably reduces the burden on cryo-EM users for picker selection and particle picking. Availability: https://github.com/ccameron/REPIC .

Methods for Cryo-EM Single Particle Reconstruction of Macromolecules Having Continuous Heterogeneity.

Macromolecules change their shape (conformation) in the process of carrying out their functions. The imaging by cryo-electron microscopy of rapidly-frozen, individual copies of macromolecules (single particles) is a powerful and general approach to understanding the motions and energy landscapes of macromolecules. Widely-used computational methods already allow the recovery of a few distinct conformations from heterogeneous single-particle samples, but the treatment of complex forms of heterogeneity such as the continuum of possible transitory states and flexible regions remains largely an open problem. In recent years there has been a surge of new approaches for treating the more general problem of continuous heterogeneity. This paper surveys the current state of the art in this area.

Hydration-layer models for cryo-EM image simulation.

To compare cryo-EM images and 3D reconstructions with atomic structures in a quantitative way it is essential to model the electron scattering by solvent (water or ice) that surrounds protein assemblies. The most rigorous method for determining the density of solvating water atoms for this purpose has been to perform molecular-dynamics (MD) simulations of the protein-water system. In this paper we adapt the ideas of bulk-water modeling that are used in the refinement of X-ray crystal structures to the cryo-EM solvent-modeling problem. We present a continuum model for solvent density which matches MD-based results to within sampling errors. However, we also find that the simple binary-mask model of Jiang and Brünger (1994) performs nearly as well as the new model. We conclude that several methods are now available for rapid and accurate modeling of cryo-EM images and maps of solvated proteins.

A Bayesian adaptive basis algorithm for single particle reconstruction.

Traditional single particle reconstruction methods use either the Fourier or the delta function basis to represent the particle density map. This paper proposes a more flexible algorithm that adaptively chooses the basis based on the data. Because the basis adapts to the data, the reconstruction resolution and signal-to-noise ratio (SNR) is improved compared to a reconstruction with a fixed basis. Moreover, the algorithm automatically masks the particle, thereby separating it from the background. This eliminates the need for ad hoc filtering or masking in the refinement loop. The algorithm is formulated in a Bayesian maximum-a-posteriori framework and uses an efficient optimization algorithm for the maximization. Evaluations using simulated and actual cryogenic electron microscopy data show resolution and SNR improvements as well as the effective masking of particle from background.

Expression, purification and functional reconstitution of slack sodium-activated potassium channels.

The slack (slo2.2) gene codes for a potassium-channel α-subunit of the 6TM voltage-gated channel family. Expression of slack results in Na(+)-activated potassium channel activity in various cell types. We describe the purification and reconstitution of Slack protein and show that the Slack α-subunit alone is sufficient for potassium channel activity activated by sodium ions as assayed in planar bilayer membranes and in membrane vesicles.

Structure and analysis of nanobody binding to the human ASIC1a ion channel.

ASIC1a is a proton-gated sodium channel involved in modulation of pain, fear, addiction, and ischemia-induced neuronal injury. We report isolation and characterization of alpaca-derived nanobodies (Nbs) that specifically target human ASIC1a. Cryo-electron microscopy of the human ASIC1a channel at pH 7.4 in complex with one of these, Nb.C1, yielded a structure at 2.9 Å resolution. It is revealed that Nb.C1 binds to a site overlapping with that of the Texas coral snake toxin (MitTx1) and the black mamba venom Mambalgin-1; however, the Nb.C1-binding site does not overlap with that of the inhibitory tarantula toxin psalmotoxin-1 (PcTx1). Fusion of Nb.C1 with PcTx1 in a single polypeptide markedly enhances the potency of PcTx1, whereas competition of Nb.C1 and MitTx1 for binding reduces channel activation by the toxin. Thus, Nb.C1 is a molecular tool for biochemical and structural studies of hASIC1a; a potential antidote to the pain-inducing component of coral snake bite; and a candidate to potentiate PcTx1-mediated inhibition of hASIC1a in vivo for therapeutic applications.

Improved hidden Markov models for molecular motors, part 1: basic theory.

Hidden Markov models (HMMs) provide an excellent analysis of recordings with very poor signal/noise ratio made from systems such as ion channels which switch among a few states. This method has also recently been used for modeling the kinetic rate constants of molecular motors, where the observable variable-the position-steadily accumulates as a result of the motor's reaction cycle. We present a new HMM implementation for obtaining the chemical-kinetic model of a molecular motor's reaction cycle called the variable-stepsize HMM in which the quantized position variable is represented by a large number of states of the Markov model. Unlike previous methods, the model allows for arbitrary distributions of step sizes, and allows these distributions to be estimated. The result is a robust algorithm that requires little or no user input for characterizing the stepping kinetics of molecular motors as recorded by optical techniques.

Improved hidden Markov models for molecular motors, part 2: extensions and application to experimental data.

Unbiased interpretation of noisy single molecular motor recordings remains a challenging task. To address this issue, we have developed robust algorithms based on hidden Markov models (HMMs) of motor proteins. The basic algorithm, called variable-stepsize HMM (VS-HMM), was introduced in the previous article. It improves on currently available Markov-model based techniques by allowing for arbitrary distributions of step sizes, and shows excellent convergence properties for the characterization of staircase motor timecourses in the presence of large measurement noise. In this article, we extend the VS-HMM framework for better performance with experimental data. The extended algorithm, variable-stepsize integrating-detector HMM (VSI-HMM) better models the data-acquisition process, and accounts for random baseline drifts. Further, as an extension, maximum a posteriori estimation is provided. When used as a blind step detector, the VSI-HMM outperforms conventional step detectors. The fidelity of the VSI-HMM is tested with simulations and is applied to in vitro myosin V data where a small 10 nm population of steps is identified. It is also applied to an in vivo recording of melanosome motion, where strong evidence is found for repeated, bidirectional steps smaller than 8 nm in size, implying that multiple motors simultaneously carry the cargo.

The N-terminal domain of Slack determines the formation and trafficking of Slick/Slack heteromeric sodium-activated potassium channels.

Potassium channels activated by intracellular Na(+) ions (K(Na)) play several distinct roles in regulating the firing patterns of neurons, and, at the single channel level, their properties are quite diverse. Two known genes, Slick and Slack, encode K(Na) channels. We have now found that Slick and Slack subunits coassemble to form heteromeric channels that differ from the homomers in their unitary conductance, kinetic behavior, subcellular localization, and response to activation of protein kinase C. Heteromer formation requires the N-terminal domain of Slack-B, one of the alternative splice variants of the Slack channel. This cytoplasmic N-terminal domain of Slack-B also facilitates the localization of heteromeric K(Na) channels to the plasma membrane. Immunocytochemical studies indicate that Slick and Slack-B subunits are coexpressed in many central neurons. Our findings provide a molecular explanation for some of the diversity in reported properties of neuronal K(Na) channels.

An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy.

Maximum-likelihood (ML) estimation has very desirable properties for reconstructing 3D volumes from noisy cryo-EM images of single macromolecular particles. Current implementations of ML estimation make use of the Expectation-Maximization (EM) algorithm or its variants. However, the EM algorithm is notoriously computation-intensive, as it involves integrals over all orientations and positions for each particle image. We present a strategy to speedup the EM algorithm using domain reduction. Domain reduction uses a coarse grid to evaluate regions in the integration domain that contribute most to the integral. The integral is evaluated with a fine grid in these regions. In the simulations reported in this paper, domain reduction gives speedups which exceed a factor of 10 in early iterations and which exceed a factor of 60 in terminal iterations.