Publisher Correction: Self-assembly of highly symmetrical, ultrasmall inorganic cages directed by surfactant micelles.

Change history: In Fig. 3b of this Letter, the labels for the outer (11.8 nm) and inner (7.4 nm) diameters of the structure were inadvertently omitted. Fig. 3 has been corrected online.

Self-assembly of highly symmetrical, ultrasmall inorganic cages directed by surfactant micelles.

Nanometre-sized objects with highly symmetrical, cage-like polyhedral shapes, often with icosahedral symmetry, have recently been assembled from DNA1-3, RNA 4 or proteins5,6 for applications in biology and medicine. These achievements relied on advances in the development of programmable self-assembling biological materials7-10, and on rapidly developing techniques for generating three-dimensional (3D) reconstructions from cryo-electron microscopy images of single particles, which provide high-resolution structural characterization of biological complexes11-13. Such single-particle 3D reconstruction approaches have not yet been successfully applied to the identification of synthetic inorganic nanomaterials with highly symmetrical cage-like shapes. Here, however, using a combination of cryo-electron microscopy and single-particle 3D reconstruction, we suggest the existence of isolated ultrasmall (less than 10 nm) silica cages ('silicages') with dodecahedral structure. We propose that such highly symmetrical, self-assembled cages form through the arrangement of primary silica clusters in aqueous solutions on the surface of oppositely charged surfactant micelles. This discovery paves the way for nanoscale cages made from silica and other inorganic materials to be used as building blocks for a wide range of advanced functional-materials applications.

Spatiotemporal functional interactivity among large-scale brain networks.

The macro-scale intrinsic functional network architecture of the human brain has been well characterized. Early studies revealed robust and enduring patterns of static connectivity, while more recent work has begun to explore the temporal dynamics of these large-scale brain networks. Little work to date has investigated directed connectivity within and between these networks, or the temporal patterns of afferent (input) and efferent (output) connections between network nodes. Leveraging a novel analytic approach, prediction correlation, we investigated the causal interactions within and between large-scale networks of the brain using resting state fMRI. This technique allows us to characterize information transfer between brain regions in both the spatial (direction) and temporal (duration) scales. Using data from the Human Connectome Project (N = 200) we applied prediction correlation techniques to four resting-state fMRI scans (each scan has TRs = 1200). Three central observations emerged. First, the strongest and longest duration connections were observed within the somatomotor, visual, and dorsal attention networks. Second, the short duration connections were observed for high-degree nodes in the visual and default networks, as well as in the hippocampus. Specifically, the connectivity profile of the highest-degree nodes was dominated by efferent connections to multiple cortical areas. Moderate high-degree nodes, particularly in hippocampal regions, showed an afferent connectivity profile. Finally, multimodal association nodes in lateral prefrontal brain regions demonstrated a short duration, bidirectional connectivity profile, consistent with this region's role in integrative and modulatory processing. These results provide novel insights into the spatiotemporal dynamics of human brain function.

Allosteric effects in bacteriophage HK97 procapsids revealed directly from covariance analysis of cryo EM data.

The information content of cryo EM data sets exceeds that of the electron scattering potential (cryo EM) density initially derived for structure determination. Previously we demonstrated the power of data variance analysis for characterizing regions of cryo EM density that displayed functionally important variance anomalies associated with maturation cleavage events in Nudaurelia Omega Capensis Virus and the presence or absence of a maturation protease in bacteriophage HK97 procapsids. Here we extend the analysis in two ways. First, instead of imposing icosahedral symmetry on every particle in the data set during the variance analysis, we only assume that the data set as a whole has icosahedral symmetry. This change removes artifacts of high variance along icosahedral symmetry axes, but retains all of the features previously reported in the HK97 data set. Second we present a covariance analysis that reveals correlations in structural dynamics (variance) between the interior of the HK97 procapsid with the protease and regions of the exterior (not seen in the absence of the protease). The latter analysis corresponds well with hydrogen deuterium exchange studies previously published that reveal the same correlation.

Effect of the viral protease on the dynamics of bacteriophage HK97 maturation intermediates characterized by variance analysis of cryo EM particle ensembles.

Cryo EM structures of maturation-intermediate Prohead I of bacteriophage HK97 with (PhI(Pro+)) and without (PhI(Pro-)) the viral protease packaged have been reported (Veesler et al., 2014). In spite of PhI(Pro+) containing an additional ∼ 100 × 24 kD of protein, the two structures appeared identical although the two particles have substantially different biochemical properties, e.g., PhI(Pro-) is less stable to disassembly conditions such as urea. Here the same cryo EM images are used to characterize the spatial heterogeneity of the particles at 17Å resolution by variance analysis and show that PhI(Pro-) has roughly twice the standard deviation of PhI(Pro+). Furthermore, the greatest differences in standard deviation are present in the region where the δ-domain, not seen in X-ray crystallographic structures or fully seen in cryo EM, is expected to be located. Thus presence of the protease appears to stabilize the δ-domain which the protease will eventually digest.

Dynamic and geometric analyses of Nudaurelia capensis ω virus maturation reveal the energy landscape of particle transitions.

Quasi-equivalent viruses that infect animals and bacteria require a maturation process in which particles transition from initially assembled procapsids to infectious virions. Nudaurelia capensis ω virus (NωV) is a T = 4, eukaryotic, single-stranded ribonucleic acid virus that has proved to be an excellent model system for studying the mechanisms of viral maturation. Structures of NωV procapsids (diameter = 480 Å), a maturation intermediate (410 Å), and the mature virion (410 Å) were determined by electron cryo-microscopy and three-dimensional image reconstruction (cryoEM). The cryoEM density for each particle type was analyzed with a recently developed maximum likelihood variance (MLV) method for characterizing microstates occupied in the ensemble of particles used for the reconstructions. The procapsid and the mature capsid had overall low variance (i.e., uniform particle populations) while the maturation intermediate (that had not undergone post-assembly autocatalytic cleavage) had roughly two to four times the variance of the first two particles. Without maturation cleavage, the particles assume a variety of microstates, as the frustrated subunits cannot reach a minimum energy configuration. Geometric analyses of subunit coordinates provided a quantitative description of the particle reorganization during maturation. Superposition of the four quasi-equivalent subunits in the procapsid had an average root mean square deviation (RMSD) of 3 Å while the mature particle had an RMSD of 11 Å, showing that the subunits differentiate from near equivalent environments in the procapsid to strikingly non-equivalent environments during maturation. Autocatalytic cleavage is clearly required for the reorganized mature particle to reach the minimum energy state required for stability and infectivity.

Dynamics in cryo EM reconstructions visualized with maximum-likelihood derived variance maps.

CryoEM data capture the dynamic character associated with biological macromolecular assemblies by preserving the various conformations of the individual specimens at the moment of flash freezing. Regions of high variation in the data set are apparent in the image reconstruction due to the poor density that results from the lack of superposition of these regions. These observations are qualitative and, to date, only preliminary efforts have been made to quantitate the heterogeneity in the ensemble of particles that are individually imaged. We developed and tested a quantitative method for simultaneously computing a reconstruction of the particle and a map of the space-varying heterogeneity of the particle based on an entire data set. The method uses a maximum likelihood algorithm that explicitly takes into account the continuous variability from one instance to another instance of the particle. The result describes the heterogeneity of the particle as a variance to be plotted at every voxel of the reconstructed density. The test, employing time resolved data sets of virus maturation, not only recapitulated local variations obtained with difference map analysis, but revealed a remarkable time dependent reduction in the overall particle dynamics that was unobservable with classical methods of analysis.

In vivo two-photon excited fluorescence microscopy reveals cardiac- and respiration-dependent pulsatile blood flow in cortical blood vessels in mice.

Subtle alterations in cerebral blood flow can impact the health and function of brain cells and are linked to cognitive decline and dementia. To understand hemodynamics in the three-dimensional vascular network of the cerebral cortex, we applied two-photon excited fluorescence microscopy to measure the motion of red blood cells (RBCs) in individual microvessels throughout the vascular hierarchy in anesthetized mice. To resolve heartbeat- and respiration-dependent flow dynamics, we simultaneously recorded the electrocardiogram and respiratory waveform. We found that centerline RBC speed decreased with decreasing vessel diameter in arterioles, slowed further through the capillary bed, and then increased with increasing vessel diameter in venules. RBC flow was pulsatile in nearly all cortical vessels, including capillaries and venules. Heartbeat-induced speed modulation decreased through the vascular network, while the delay between heartbeat and the time of maximum speed increased. Capillary tube hematocrit was 0.21 and did not vary with centerline RBC speed or topological position. Spatial RBC flow profiles in surface vessels were blunted compared with a parabola and could be measured at vascular junctions. Finally, we observed a transient decrease in RBC speed in surface vessels before inspiration. In conclusion, we developed an approach to study detailed characteristics of RBC flow in the three-dimensional cortical vasculature, including quantification of fluctuations in centerline RBC speed due to cardiac and respiratory rhythms and flow profile measurements. These methods and the quantitative data on basal cerebral hemodynamics open the door to studies of the normal and diseased-state cerebral microcirculation.

Alcohol exposure rate control through physiologically based pharmacokinetic modeling.

BACKGROUND: The instantaneous rate of change of alcohol exposure (slope) may contribute to changes in measures of brain function following administration of alcohol that are usually attributed to breath alcohol concentration (BrAC) acting alone. To test this proposition, a 2-session experiment was designed in which carefully prescribed, constant-slope trajectories of BrAC intersected at the same exposure level and time since the exposure began. This paper presents the methods and limitations of the experimental design. METHODS: Individualized intravenous infusion rate profiles of 6% ethanol (EtOH) that achieved the constant-slope trajectories for an individual were precomputed using a physiologically based pharmacokinetic model. Adjusting the parameters of the model allowed each infusion profile to account for the subject's EtOH distribution and elimination kinetics. Sessions were conducted in randomized order and made no use of feedback of BrAC measurements obtained during the session to modify the precalculated infusion profiles. In one session, an individual's time course of exposure, BrAC(t), was prescribed to rise at a constant rate of 6.0 mg% per minute until it reached 68 mg% and then descend at -1.0 mg% per minute; in the other, to rise at a rate of 3.0 mg% per minute. The 2 exposure trajectories were designed to intersect at a BrAC (t = 20 minutes) = 60 mg% at an experimental time of 20 minutes. RESULTS: Intersection points for 54 of 61 subjects were within prescribed deviations (range of ± 3 mg% and ± 4 minutes from the nominal intersection point). CONCLUSIONS: Results confirmed the feasibility of applying the novel methods for achieving the intended time courses of the BrAC, with technical problems limiting success to 90% of the individuals tested.

Three-dimensional reconstruction of the statistics of heterogeneous objects from a collection of one projection image of each object.

An estimation problem for statistical reconstruction of heterogeneous three-dimensional objects from two-dimensional tomographic data (single-particle cryoelectron microscope images) is posed as the problem of estimating class probabilities, means, and covariances for a Gaussian mixture where both the mean and covariance are stochastically structured. Both discrete (i.e., classes) and continuous heterogeneity is included. A maximum likelihood solution computed by a generalized expectation-maximization algorithm is presented and demonstrated on experimental images of Flock House Virus.

In vivo virus structures: simultaneous classification, resolution enhancement, and noise reduction in whole-cell electron tomography.

Sulfolobus Turreted Icosahedral Virus (STIV) experiences an extra-cellular environment of near boiling acid (80°C, pH 3) and particles purified under these conditions were previously analyzed by cryo electron microscopy and image reconstruction. Here we describe cryo-tomograms of Solfolobus cells infected with STIV and the maximum likelihood algorithm employed to compute reconstructions of virions within the cell. Virions in four different tomograms were independently reconstructed with an average of 91 particles per tomogram and their structures compared with each other and with the higher resolution single-particle reconstruction from purified virions. The algorithm described here automatically classified and oriented two different particle types within each cell and generated reconstructions of full and empty particles. Because the particles are randomly oriented within the cell, the reconstructions do not suffer from the missing wedge of data absent from the reciprocal-space tomogram. The fact that the particles have icosahedral symmetry is used to dramatically improve the signal to noise ratio in the reconstructions. The reconstructions have approximately 60Å resolution (based on Fourier Shell Correlation analysis among reconstructions computed by the algorithm described here from four different tomograms).

Ab initio maximum likelihood reconstruction from cryo electron microscopy images of an infectious virion of the tailed bacteriophage P22 and maximum likelihood versions of Fourier Shell Correlation appropriate for measuring resolution of spherical or cylindrical objects.

A maximum likelihood reconstruction method for an asymmetric reconstruction of the infectious P22 bacteriophage virion is described and demonstrated on a subset of the images used in [Lander, G.C., Tang, L., Casjens, S.R., Gilcrease, E.B., Prevelige, P., Poliakov, A., Potter, C.S., Carragher, B., Johnson, J.E., 2006. The structure of an infectious P22 virion shows the signal for headful DNA packaging. Science 312(5781), 1791-1795]. The method makes no assumptions at any stage regarding the structure of the phage tail or the relative rotational orientation of the phage tail and capsid but rather the structure and the rotation angle are determined as a part of the analysis. A statistical method for determining resolution consistent with maximum likelihood principles based on ideas for cylinders analogous to the ideas for spheres that are embedded in the Fourier Shell Correlation method is described and demonstrated on the P22 reconstruction. With a correlation threshold of .95, the resolution in the tail measured radially is greater than 0.0301A(-1) (33.3A) and measured axially is greater than 0.0142A(-1) (70.6A) both with probability p=0.02.

Reciprocal space representations of helical objects and their projection images for helices constructed from motifs without spherical symmetry.

Formulas for predicting the 3-D reciprocal space cube and 2-D reciprocal space images that are slices of the cube (corresponding to real space images that are projections of the real space cube) are derived for the case when the motif of a helical object is not spherically symmetric. These formulas generalize much-used formulas due to Cochran et al. [The structure of synthetic polypeptides. I. The transform of atoms on a helix, Acta Crystallogr. 5 (1952) 581-586], for the case of a spherically symmetric motif. The new formulas allow control of the spatial resolution of the motif ranging from low-resolution spherically symmetric motifs as in Cochran et al. through moderate-resolution nonsymmetrical motifs to atomic-resolution nonsymmetrical motifs which can also be treated by the methods of Cochran et al. as a superposition of spherically symmetric atomic motifs. The ability to control resolution may be useful in reconstruction algorithms analogous to phase extension algorithms in X-ray crystallography.

Reconstruction of Stochastic 3D Signals With Symmetric Statistics From 2D Projection Images Motivated by Cryo-Electron Microscopy.

Cryo-electron microscopy provides 2D projection images of the 3D electron scattering intensity of many instances of the particle under study (e.g., a virus). Both symmetry (rotational point groups) and heterogeneity are important aspects of biological particles and both aspects can be combined by describing the electron scattering intensity of the particle as a stochastic process with a symmetric probability law and, therefore, symmetric moments. A maximum likelihood estimator implemented by an expectation-maximization algorithm is described, which estimates the unknown statistics of the electron scattering intensity stochastic process from the images of instances of the particle. The algorithm is demonstrated on the bacteriophage HK97 and the virus [Formula: see text]. The results are contrasted with the existing algorithms, which assume that each instance of the particle has the symmetry rather than the less restrictive assumption that the probability law has the symmetry.

Experimentally constrained circuit model of cortical arteriole networks for understanding flow redistribution due to occlusion and neural activation.

Computations are described which estimate flows in all branches of the cortical surface arteriole network from two-photon excited fluorescence (2PEF) microscopy images which provide the network topology and, in selected branches red blood cell (RBC) speeds and lumen diameters. Validation is done by comparing the flow predicted by the model with experimentally measured flows and by comparing the predicted flow redistribution in the network due to single-vessel strokes with experimental observations. The model predicts that tissue is protected from RBC flow decreases caused by multiple occlusions of surface arterioles but not penetrating arterioles. The model can also be used to study flow rerouting due to vessel dilations and constrictions.

Exact reduced-complexity maximum likelihood reconstruction of multiple 3-D objects from unlabeled unoriented 2-D projections and electron microscopy of viruses.

In cryo-electron microscopy, the data is comprised of noisy 2-D projection images of the 3-D electron scattering intensity of the object where the orientation of the projections is unknown. Often, the images show randomly selected objects from a mixture of different types of objects. Objects of different type may be unrelated, e.g., different species of virus, or related, e.g., different conformations of the same species of virus. Due to the low SNR and the 2-D nature of the data, it is challenging to determine the type of the object shown in an individual image. A statistical model and maximum likelihood estimator that computes simultaneous 3-D reconstruction and labels using an expectation maximization algorithm exists but requires extensive computation due to the numerical evaluation of 3-D or 5-D integrations of a square matrix of dimension equal to the number of degrees of freedom in the 3-D reconstruction. By exploiting the geometry of rotations in 3-D, the estimation problem can be transformed so that the inner-most numerical integral has a scalar rather than a matrix integrand. This leads to a dramatic reduction in computation, especially as the number of degrees of freedom in the 3-D reconstruction increases. Numerical examples of the 3-D reconstructions are provided based on synthetic and experimental images where the objects are small spherical viruses.

Initial Validation for the Estimation of Resting-State fMRI Effective Connectivity by a Generalization of the Correlation Approach.

Resting-state functional MRI (rs-fMRI) is widely used to noninvasively study human brain networks. Network functional connectivity is often estimated by calculating the timeseries correlation between blood-oxygen-level dependent (BOLD) signal from different regions of interest (ROIs). However, standard correlation cannot characterize the direction of information flow between regions. In this paper, we introduce and test a new concept, prediction correlation, to estimate effective connectivity in functional brain networks from rs-fMRI. In this approach, the correlation between two BOLD signals is replaced by a correlation between one BOLD signal and a prediction of this signal via a causal system driven by another BOLD signal. Three validations are described: (1) Prediction correlation performed well on simulated data where the ground truth was known, and outperformed four other methods. (2) On simulated data designed to display the "common driver" problem, prediction correlation did not introduce false connections between non-interacting driven ROIs. (3) On experimental data, prediction correlation recovered the previously identified network organization of human brain. Prediction correlation scales well to work with hundreds of ROIs, enabling it to assess whole brain interregional connectivity at the single subject level. These results provide an initial validation that prediction correlation can capture the direction of information flow and estimate the duration of extended temporal delays in information flow between regions of interest ROIs based on BOLD signal. This approach not only maintains the high sensitivity to network connectivity provided by the correlation analysis, but also performs well in the estimation of causal information flow in the brain.

Statistical characterization of ensembles of symmetric virus particles: 3-D stochastic signal reconstruction from electron microscope images.

Stochastic models of nano-biomachines have been studied by 3-D reconstruction from cryo electron microscopy images in recent years. The image data is the projection of many heterogeneous instances of the object under study (e.g., a virus). Initial reconstruction algorithms require different instances of the object, while still heterogeneous, to have the same symmetry. This paper presents a maximum likelihood reconstruction approach which allows each object to lack symmetry while constraining the statistics of the ensemble of objects to have symmetry. This algorithm is demonstrated on bacteriophage HK97 and is contrasted with the former algorithm. Reconstruction results show that the proposed algorithm provides estimates that make more biological sense.

Virus particle dynamics derived from CryoEM studies.

The direct electron detector has revolutionized electron cryo-microscopy (CryoEM). Icosahedral virus structures are routinely produced at 4Å resolution or better and the approach has largely displaced virus crystallography, as it requires less material, less purity and often produces a structure more rapidly. Largely ignored in this new era of CryoEM is the dynamic information in the data sets that was not available in X-ray structures. Here we review an approach that captures the dynamic character of viruses displayed in the CryoEM ensemble of particles at the moment of freezing. We illustrate the approach with a simple model, briefly describe the details and provide a practical application to virus particle maturation.

A mathematical model relating cortical oxygenated and deoxygenated hemoglobin flows and volumes to neural activity.

OBJECTIVE: To describe a toolkit of components for mathematical models of the relationship between cortical neural activity and space-resolved and time-resolved flows and volumes of oxygenated and deoxygenated hemoglobin motivated by optical intrinsic signal imaging (OISI). APPROACH: Both blood flow and blood volume and both oxygenated and deoxygenated hemoglobin and their interconversion are accounted for. Flow and volume are described by including analogies to both resistive and capacitive electrical circuit elements. Oxygenated and deoxygenated hemoglobin and their interconversion are described by generalization of Kirchhoff's laws based on well-mixed compartments. MAIN RESULTS: Mathematical models built from this toolkit are able to reproduce experimental single-stimulus OISI results that are described in papers from other research groups and are able to describe the response to multiple-stimuli experiments as a sublinear superposition of responses to the individual stimuli. SIGNIFICANCE: The same assembly of tools from the toolkit but with different parameter values is able to describe effects that are considered distinctive, such as the presence or absence of an initial decrease in oxygenated hemoglobin concentration, indicating that the differences might be due to unique parameter values in a subject rather than different fundamental mechanisms.