HIV-1 Env trimers asymmetrically engage CD4 receptors in membranes.

Human immunodeficiency virus 1 (HIV-1) infection is initiated by binding of the viral envelope glycoprotein (Env) to the cell-surface receptor CD41-4. Although high-resolution structures of Env in a complex with the soluble domains of CD4 have been determined, the binding process is less understood in native membranes5-13. Here we used cryo-electron tomography to monitor Env-CD4 interactions at the membrane-membrane interfaces formed between HIV-1 and CD4-presenting virus-like particles. Env-CD4 complexes organized into clusters and rings, bringing the opposing membranes closer together. Env-CD4 clustering was dependent on capsid maturation. Subtomogram averaging and classification revealed that Env bound to one, two and finally three CD4 molecules, after which Env adopted an open state. Our data indicate that asymmetric HIV-1 Env trimers bound to one and two CD4 molecules are detectable intermediates during virus binding to host cell membranes, which probably has consequences for antibody-mediated immune responses and vaccine immunogen design.

New measures of anisotropy of cryo-EM maps.

We propose two new measures of resolution anisotropy for cryogenic electron microscopy maps: Fourier shell occupancy (FSO), and the Bingham test (BT). FSO varies from 1 to 0, with 1 representing perfect isotropy, and lower values indicating increasing anisotropy. The threshold FSO = 0.5 occurs at Fourier shell correlation resolution. BT is a hypothesis test that complements the FSO to ensure the existence of anisotropy. FSO and BT allow visualization of resolution anisotropy. We illustrate their use with different experimental cryogenic electron microscopy maps.

Efficient standardization of clinical T2-weighted images: Phase-conjugacy e-CAMP with projected gradient descent.

PURPOSE: To standardize T 2 $$ {}_2 $$ -weighted images from clinical Turbo Spin Echo (TSE) scans by generating corresponding T 2 $$ {}_2 $$ maps with the goal of removing scanner- and/or protocol-specific heterogeneity. METHODS: The T 2 $$ {}_2 $$ map is estimated by minimizing an objective function containing a data fidelity term in a Virtual Conjugate Coils (VCC) framework, where the signal evolution model is expressed as a linear constraint. The objective function is minimized by Projected Gradient Descent (PGD). RESULTS: The algorithm achieves accuracy comparable to methods with customized sampling schemes for accelerated T 2 $$ {}_2 $$ mapping. The results are insensitive to the tunable parameters, and the relaxed background phase prior produces better T 2 $$ {}_2 $$ maps compared to the strict real-value enforcement. It is worth noting that the algorithm works well with challenging T 2 $$ {}_2 $$ w-TSE data using typical clinical parameters. The observed normalized root mean square error ranges from 6.8% to 12.3% over grey and white matter, a clinically common level of quantitative map error. CONCLUSION: The novel methodological development creates an efficient algorithm that allows for T 2 $$ {}_2 $$ map generated from TSE data with typical clinical parameters, such as high resolution, long echo train length, and low echo spacing. Reconstruction of T 2 $$ {}_2 $$ maps from TSE data with typical clinical parameters has not been previously reported.

Voxel-based logistic analysis of PPMI control and Parkinson's disease DaTscans.

A comprehensive analysis of the Parkinson's Progression Markers Initiative (PPMI) Dopamine Transporter Single Photon Emission Computed Tomography (DaTscan) images is carried out using a voxel-based logistic lasso model. The model reveals that sub-regional voxels in the caudate, the putamen, as well as in the globus pallidus are informative for classifying images into control and PD classes. Further, a new technique called logistic component analysis is developed. This technique reveals that intra-population differences in dopamine transporter concentration and imperfect normalization are significant factors influencing logistic analysis. The interactions with handedness, sex, and age are also evaluated.

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.

Broadband multimode fiber spectrometer.

A general-purpose all-fiber spectrometer is demonstrated to overcome the trade-off between spectral resolution and bandwidth. By integrating a wavelength division multiplexer with five multimode optical fibers, we have achieved 100 nm bandwidth with 0.03 nm resolution at wavelength 1500 nm. An efficient algorithm is developed to reconstruct the spectrum from the speckle pattern produced by interference of guided modes in the multimode fibers. Such an algorithm enables a rapid, accurate reconstruction of both sparse and dense spectra in the presence of noise.

Sex differences in the brain's dopamine signature of cigarette smoking.

Cigarette smoking is a major public health danger. Women and men smoke for different reasons and cessation treatments, such as the nicotine patch, are preferentially beneficial to men. The biological substrates of these sex differences are unknown. Earlier PET studies reported conflicting findings but were each hampered by experimental and/or analytical limitations. Our new image analysis technique, lp-ntPET (Normandin et al., 2012; Morris et al., 2013; Kim et al., 2014), has been optimized for capturing brief (lasting only minutes) and highly localized dopaminergic events in dynamic PET data. We coupled our analysis technique with high-resolution brain scanning and high-frequency motion correction to create the optimal experiment for capturing and characterizing the effects of smoking on the mesolimbic dopamine system in humans. Our main finding is that male smokers smoking in the PET scanner activate dopamine in the right ventral striatum during smoking but female smokers do not. This finding-men activating more ventrally than women-is consistent with the established notion that men smoke for the reinforcing drug effect of cigarettes whereas women smoke for other reasons, such as mood regulation and cue reactivity. lp-ntPET analysis produces a novel multidimensional endpoint: voxel-level temporal patterns of neurotransmitter release ("DA movies") in individual subjects. By examining these endpoints quantitatively, we demonstrate that the timing of dopaminergic responses to cigarette smoking differs between men and women. Men respond consistently and rapidly in the ventral striatum whereas women respond faster in a discrete subregion of the dorsal putamen.

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.

A Physics-Based Algorithm to Universally Standardize Routinely Obtained Clinical T2-Weighted Images.

RATIONALE AND OBJECTIVES: MR images can be challenging for machine learning and other large-scale analyses because most clinical images, for example, T2-weighted (T2w) images, reflect not only the biologically relevant T2 of tissue but also hardware and acquisition parameters that vary from site to site. Quantitative T2 mapping avoids these confounds because it quantitatively isolates the biological parameter of interest, thus representing a universal standardization across sites. However, efforts to incorporate quantitative mapping sequences into routine clinical practice have seen slow adoption. Here we show, for the first time, that the routine T2w complex raw dataset can be successfully regarded as a quantitative mapping sequence that can be reconstructed with classical optimization methods and physics-based constraints. MATERIALS AND METHODS: While previous constrained reconstruction methods are unable to reconstruct a T2 map based on this data, the expanding-constrained alternating minimization for parameter mapping (e-CAMP), which employs stepwise initialization, a linearized version of the exponential model and a phase conjugacy constraint, is demonstrated to provide useful quantitative maps directly from a vendor T2w single image data. RESULTS: This paper introduces the method and demonstrates its performance using simulations, retrospectively undersampled brain images, and prospectively acquired T2w images taken on both phantom and brain. CONCLUSION: Because T2w scans are included in nearly every protocol, this approach could open the door to creating large, standardized datasets without requiring widespread changes in clinical protocols.

Constrained alternating minimization for parameter mapping (CAMP).

OBJECTIVE: To improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images. APPROACH: In multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps. In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12. MAIN RESULTS: CAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias. SIGNIFICANCE: For a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

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.

Hierarchical Denoising of Ordinal Time Series of Clinical Scores.

Clinical scores (disease rating scales) are ordinal in nature. Longitudinal studies which use clinical scores produce ordinal time series. These time series tend to be noisy and often have a short-duration. This paper proposes a denoising method for such time series. The method uses a hierarchical approach to draw statistical power from the entire population of a study's patients to give reliable, subject-specific results. The denoising method is applied to MDS-UPDRS motor scores for Parkinson's disease.

Steerable Near-Quadrature Filter Pairs in Three Dimensions.

Steerable filter pairs that are near quadrature have many image processing applications. This paper proposes a new methodology for designing such filters. The key idea is to design steerable filters by minimizing a departure-from-quadrature function. These minimizing filter pairs are almost exactly in quadrature. The polar part of the filters is nonnegative, monotonic, and highly focused around an axis, and asymptotically the filters achieve exact quadrature. These results are established by exploiting a relation between the filters and generalized Hilbert matrices. These near-quadrature filters closely approximate three dimensional Gabor filters. We experimentally verify the asymptotic mathematical results and further demonstrate the use of these filter pairs by efficient calculation of local Fourier shell correlation of cryogenic electron microscopy.

Cryo-EM structure of the plant 26S proteasome.

Targeted proteolysis is a hallmark of life. It is especially important in long-lived cells that can be found in higher eukaryotes, like plants. This task is mainly fulfilled by the ubiquitin-proteasome system. Thus, proteolysis by the 26S proteasome is vital to development, immunity, and cell division. Although the yeast and animal proteasomes are well characterized, there is only limited information on the plant proteasome. We determined the first plant 26S proteasome structure from Spinacia oleracea by single-particle electron cryogenic microscopy at an overall resolution of 3.3 Å. We found an almost identical overall architecture of the spinach proteasome compared with the known structures from mammals and yeast. Nevertheless, we noticed a structural difference in the proteolytic active ß1 subunit. Furthermore, we uncovered an unseen compression state by characterizing the proteasome's conformational landscape. We suspect that this new conformation of the 20S core protease, in correlation with a partial opening of the unoccupied gate, may contribute to peptide release after proteolysis. Our data provide a structural basis for the plant proteasome, which is crucial for further studies.

Self-normalized Classification of Parkinson's Disease DaTscan Images.

Classifying SPECT images requires a preprocessing step which normalizes the images using a normalization region. The choice of the normalization region is not standard, and using different normalization regions introduces normalization region-dependent variability. This paper mathematically analyzes the effect of the normalization region to show that normalized-classification is exactly equivalent to a subspace separation of the half rays of the images under multiplicative equivalence. Using this geometry, a new self-normalized classification strategy is proposed. This strategy eliminates the normalizing region altogether. The theory is used to classify DaTscan images of 365 Parkinson's disease (PD) subjects and 208 healthy control (HC) subjects from the Parkinson's Progression Marker Initiative (PPMI). The theory is also used to understand PD progression from baseline to year 4.

Hierarchical MAP Denoising of Longitudinal Hamilton Depression Rating Scores.

The Hamilton Depression Rating Scale provides ordinal ratings for evaluating different aspects of depression. These ratings are usually quite noisy, and longitudinal patterns in the ratings can be difficult to discern. This paper proposes a hierarchical maximum-a-posteriori (MAP) method for denoising the ordinal time series of such ratings. Real-world data from a clinical trial are analyzed using the model. Denoising reveals subject-specific longitudinal patterns, predicts future ratings, and reveals progression patterns via principal component analysis.

Robust Bayesian Analysis of Early-Stage Parkinson's Disease Progression Using DaTscan Images.

This paper proposes a mixture of linear dynamical systems model for quantifying the heterogeneous progress of Parkinson's disease from DaTscan Images. The model is fitted to longitudinal DaTscans from the Parkinson's Progression Marker Initiative. Fitting is accomplished using robust Bayesian inference with collapsed Gibbs sampling. Bayesian inference reveals three image-based progression subtypes which differ in progression speeds as well as progression trajectories. The model reveals characteristic spatial progression patterns in the brain, each pattern associated with a time constant. These patterns can serve as disease progression markers. The subtypes also have different progression rates of clinical symptoms measured by MDS-UPDRS Part III scores.

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.

Measuring local-directional resolution and local anisotropy in cryo-EM maps.

The introduction of local resolution has enormously helped the understanding of cryo-EM maps. Still, for any given pixel it is a global, aggregated value, that makes impossible the individual analysis of the contribution of the different projection directions. We introduce MonoDir, a fully automatic, parameter-free method that, starting only from the final cryo-EM map, decomposes local resolution into the different projection directions, providing a detailed level of analysis of the final map. Many applications of directional local resolution are possible, and we concentrate here on map quality and validation.