Cryo-electron tomography (CET) is the only available technique capable of characterizing the structure of biological macromolecules in conditions close to the native state. With the advent of subtomogram averaging, as a post-processing step to CET, resolutions in the (sub-) nanometer range have become within reach. In addition to advances in instrumentation and experiments, the reconstruction scheme has improved by inclusion of more accurate contrast transfer function (CTF) correction methods, better defocus estimation, and better alignments of the tilt-series and subtomograms. To quantify the importance of each contribution, we have split the full process from data collection to reconstruction into different steps. For the purpose of evaluation we have acquired tilt-series of ribosomes in such a way that we could precisely determine the defocus of each macromolecule. Then, we simulated tilt-series using the InSilicoTEM package and applied tomogram reconstruction and subtomogram averaging. Through large scale simulations under different conditions and parameter settings we find that tilt-series alignment is the resolution limiting factor for our experimental data. Using simulations, we find that when this alignment inaccuracy is alleviated, tilted CTF correction improves the final resolution, or equivalently, the same resolution can be achieved using less particles. Furthermore, we predict from which resolution onwards better CTF correction and defocus estimation methods are required. We obtain a final average using 3198 ribosomes with a resolution of 2.2nm on the experimental data. Our simulations suggest that with the same number of particles a resolution of 1.2nm could be achieved by improving the tilt-series alignment.
We propose a method for simultaneously measuring the position and emission color of single fluorescent emitters based on the use of a large pitch diffraction grating in the emission light path. The grating produces satellite spots adjacent to the main spot; the relative distance between the spots is a measure for the emission wavelength. We present proof-of-principle experiments on beads and mixtures of quantum dots using a spatial light modulator for making a programmable diffraction grating. A wavelength precision of around 10 nm can be achieved for 1000 signal photons and practical background levels, while maintaining a localization precision of around 10 nm.
A study of the uncertainty of localizing single-molecule emitters for super-resolution light microscopy is presented. Maximum likelihood estimation (MLE) is found to be superior to least-squares fitting for low background levels, but the performance difference between the two methods decreases to a few percent for practical background levels. It is shown that the performance limit of MLE, the Cramér-Rao lower bound, is well described by a concise analytical formula with only spot width and signal and background photon count as input parameters. These predictions for the lateral localization uncertainty are compared with the localization error obtained from repeated localizations of the same single-molecule emitter. Agreement within a few percent is found, thus verifying the validity of the fitting model and the concise analytical approximation. The analysis is extended by novel analytical results for the dependence of the axial localization uncertainty on background level for the astigmatic, bifocal, and double-helix methods.
Resolution in optical nanoscopy (or super-resolution microscopy) depends on the localization uncertainty and density of single fluorescent labels and on the samples spatial structure. Currently there is no integral, practical resolution measure that accounts for all factors. We introduce a measure based on Fourier ring correlation (FRC) that can be computed directly from an image. We demonstrate its validity and benefits on two-dimensional (2D) and 3D localization microscopy images of tubulin and actin filaments. Our FRC resolution method makes it possible to compare achieved resolutions in images taken with different nanoscopy methods, to optimize and rank different emitter localization and labeling strategies, to define a stopping criterion for data acquisition, to describe image anisotropy and heterogeneity, and even to estimate the average number of localizations per emitter. Our findings challenge the current focus on obtaining the best localization precision, showing instead how the best image resolution can be achieved as fast as possible.
The projection assumption (PA) and the weak-phase object approximation (WPOA) are commonly used to model image formation in cryo-electron microscopy. For simulating the next step in resolution improvement we show that it is important to revisit these two approximations as well as their limitations. Here we start off by inspecting both approximations separately to derive their respective conditions of applicability. The thick-phase grating approximation (TPGA) imposes less strict conditions on the interaction potential than PA or WPOA and gives comparable exit waves as a multislice calculation. We suggest the ranges of applicability for four models (PA, PA+WPOA, WPOA, and TPGA) given different interaction potentials using exit wave simulations. The conditions of applicability for the models are based on two measures, a worst-case (safest) and an average criterion. This allows us to present a practical guideline for when to use each image formation model depending on the spatial frequency, thickness and strength of the interaction potential of a macromolecular complex.
Accurate modeling of image formation in cryo-electron microscopy is an important requirement for quantitative image interpretation and optimization of the data acquisition strategy. Here we present a forward model that accounts for the specimens scattering properties, microscope optics, and detector response. The specimen interaction potential is calculated with the isolated atom superposition approximation (IASA) and extended with the influences of solvents dielectric and ionic properties as well as the molecular electrostatic distribution. We account for an effective charge redistribution via the Poisson-Boltzmann approach and find that the IASA-based potential forms the dominant part of the interaction potential, as the contribution of the redistribution is less than 10%. The electron wave is propagated through the specimen by a multislice approach and the influence of the optics is included via the contrast transfer function. We incorporate the detective quantum efficiency of the camera due to the difference between signal and noise transfer characteristics, instead of using only the modulation transfer function. The full model was validated against experimental images of 20S proteasome, hemoglobin, and GroEL. The simulations adequately predict the effects of phase contrast, changes due to the integrated electron flux, thickness, inelastic scattering, detective quantum efficiency and acceleration voltage. We suggest that beam-induced specimen movements are relevant in the experiments whereas the influence of the solvent amorphousness can be neglected. All simulation parameters are based on physical principles and, when necessary, experimentally determined.
Podosomes are cellular adhesion structures involved in matrix degradation and invasion that comprise an actin core and a ring of cytoskeletal adaptor proteins. They are most often identified by staining with phalloidin, which binds F-actin and therefore visualizes the core. However, not only podosomes, but also many other cytoskeletal structures contain actin, which makes podosome segmentation by automated image processing difficult. Here, we have developed a quantitative image analysis algorithm that is optimized to identify podosome cores within a typical sample stained with phalloidin. By sequential local and global thresholding, our analysis identifies up to 76% of podosome cores excluding other F-actin-based structures. Based on the overlap in podosome identifications and quantification of podosome numbers, our algorithm performs equally well compared to three experts. Using our algorithm we show effects of actin polymerization and myosin II inhibition on the actin intensity in both podosome core and associated actin network. Furthermore, by expanding the core segmentations, we reveal a previously unappreciated differential distribution of cytoskeletal adaptor proteins within the podosome ring. These applications illustrate that our algorithm is a valuable tool for rapid and accurate large-scale analysis of podosomes to increase our understanding of these characteristic adhesion structures.
Today, the resolution in phase-contrast cryo-electron tomography is for a significant part limited by the contrast transfer function (CTF) of the microscope. The CTF is a function of defocus and thus varies spatially as a result of the tilting of the specimen and the finite specimen thickness. Models that include spatial dependencies have not been adopted in daily practice because of their high computational complexity. Here we present an algorithm which reduces the processing time for computing the tilted CTF by more than a factor 100. Our implementation of the full 3D CTF has a processing time on the order of a Radon transform of a full tilt-series. We derive and validate an expression for the damping envelope function describing the loss of resolution due to specimen thickness. Using simulations we quantify the effects of specimen thickness on the accuracy of various forward models. We study the influence of spatially varying CTF correction and subsequent tomographic reconstruction by simulation and present a new approach for space-variant phase-flipping. We show that our CTF correction strategies are successful in increasing the resolution after tomographic reconstruction.
The gaussian function is simple and easy to implement as Point Spread Function (PSF) model for fitting the position of fluorescent emitters in localization microscopy. Despite its attractiveness the appropriateness of the gaussian is questionable as it is not based on the laws of optics. Here we study the effect of emission dipole orientation in conjunction with optical aberrations on the localization accuracy of position estimators based on a gaussian model PSF. Simulated image spots, calculated with all effects of high numerical aperture, interfaces between media, polarization, dipole orientation and aberrations taken into account, were fitted with a gaussian PSF based Maximum Likelihood Estimator. For freely rotating dipole emitters it is found that the gaussian works fine. The same, theoretically optimum, localization accuracy is found as if the true PSF were a gaussian, even for aberrations within the usual tolerance limit of high-end optical imaging systems such as microscopes (Marechals diffraction limit). For emitters with a fixed dipole orientation this is not the case. Localization errors are found that reach up to 40 nm for typical system parameters and aberration levels at the diffraction limit. These are systematic errors that are independent of the total photon count in the image. The gaussian function is therefore inappropriate, and more sophisticated PSF models are a practical necessity.
We describe an iterative algorithm that converges to the maximum likelihood estimate of the position and intensity of a single fluorophore. Our technique efficiently computes and achieves the Cramér-Rao lower bound, an essential tool for parameter estimation. An implementation of the algorithm on graphics processing unit hardware achieved more than 10(5) combined fits and Cramér-Rao lower bound calculations per second, enabling real-time data analysis for super-resolution imaging and other applications.
Upon activation, ERKs translocate from the cytoplasm to the nucleus. This process is required for the induction of many cellular responses, yet the molecular mechanisms that regulate ERK nuclear translocation are not fully understood. We have used a mouse embryo fibroblast ERK1-knock-out cell line expressing green fluorescent protein (GFP)-tagged ERK1 to probe the spatio-temporal regulation of ERK1. Real time fluorescence microscopy and fluorescence correlation spectroscopy revealed that ERK1 nuclear accumulation increased upon serum stimulation, but the mobility of the protein in the nucleus and cytoplasm remained unchanged. Dimerization of ERK has been proposed as a requirement for nuclear translocation. However, ERK1-Delta4, the mutant shown consistently to be dimerization-deficient in vitro, accumulated in the nucleus to the same level as wild type (WT), indicating that dimerization of ERK1 is not required for nuclear entry and retention. Consistent with this finding, energy migration Förster resonance energy transfer and fluorescence correlation spectroscopy measurements in living cells did not detect dimerization of GFP-ERK1-WT upon activation. In contrast, the kinetics of nuclear accumulation and phosphorylation of GFP-ERK1-Delta4 were slower than that of GFP-ERK1-WT. These results indicate that the differential shuttling behavior of the mutant is a consequence of delayed phosphorylation of ERK by MEK rather than dimerization. Our data demonstrate for the first time that a delay in cytoplasmic activation of ERK is directly translated into a delay in nuclear translocation.
The wormlike chain model describes the micromechanics of semiflexible polymers by introducing the persistence length. We propose a method of measuring the persistence length of DNA in a controllable near-native environment. Using a dark field microscope, the projected positions of a gold nanoparticle undergoing constrained Brownian motion are captured. The nanoparticle is tethered to a substrate using a single double stranded DNA (dsDNA) molecule and immersed in buffer. No force is exerted on the DNA. We carried out Monte Carlo simulations of the experiment, which give insight into the micromechanics of the DNA and can be used to interpret the motion of the nanoparticle. Our simulations and experiments demonstrate that, unlike other similar experiments, the use of nanometer instead of micrometer sized particles causes particle-substrate and particle-DNA interactions to be of negligible effect on the position distribution of the particle. We also show that the persistence length of the tethering DNA can be estimated with a statistical error of 2 nm, by comparing the statistics of the projected position distribution of the nanoparticle to the Monte Carlo simulations. The persistence lengths of 45 single molecules of four different lengths of dsDNA were measured under the same environmental conditions at high salt concentration. The persistence lengths we found had a mean value of 35 nm (standard error of 2.8 nm), which compares well to previously found values using similar salt concentrations. Our method can be used to directly study the effect of the environmental conditions (e.g., buffer and temperature) on the persistence length.
We have developed new methods for contrast transfer function (CTF) correction of tilted and/or thick specimens. In order to achieve higher resolutions in cryo-electron tomography (CryoET), it is necessary to account for the defocus gradient on a tilted specimen and possibly the defocus gradient within a thick specimen. CTF correction methods which account for these defocus differences have recently gained interest. However, there is no global CTF correction method available to this date (to process the entire field-of-view at once) which can use different inverse filters, e.g. phase-flipping or Wiener filter, and which can do so within a reasonable time for realistic image sizes. We show that the CTF correction methods presented in this paper correctly account for the spatially varying defocus, can employ different inverse filters and are significantly faster (>50×) than existing methods. We provide proof-of-principle implementations of all the presented CTF correction methods online.
We introduce a method for determining the position and orientation of fixed dipole emitters based on a combination of polarimetry and spot shape detection. A key element is an effective Point Spread Function model based on Hermite functions. The model offers a good description of the shape variations with dipole orientation and polarization detection channel, and provides computational advantages over the exact vectorial description of dipole image formation. The realized localization uncertainty is comparable to the free dipole case in which spots are rotationally symmetric and can be well modeled with a Gaussian. This result holds for all dipole orientations, for all practical signal levels, and for defocus values within the depth of focus, implying that the massive localization bias for defocused emitters with tilted dipole axis found with Gaussian spot fitting is eliminated.
One of the most complex molecular machines of cells is the nuclear pore complex (NPC), which controls all trafficking of molecules in and out of the nucleus. Because of their importance for cellular processes such as gene expression and cytoskeleton organization, the structure of NPCs has been studied extensively during the last few decades, mainly by electron microscopy. We have used super-resolution imaging by direct stochastic optical reconstruction microscopy (dSTORM) to investigate the structure of NPCs in isolated Xenopus laevis oocyte nuclear envelopes, with a lateral resolution of ~15 nm. By generating accumulated super-resolved images of hundreds of NPCs we determined the diameter of the central NPC channel to be 41 ± 7 nm and demonstrate that the integral membrane protein gp210 is distributed in an eightfold radial symmetry. Two-color dSTORM experiments emphasize the highly symmetric NPCs as ideal model structures to control the quality of corrections to chromatic aberration and to test the capability and reliability of super-resolution imaging methods.
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