CTF determination and correction for low dose tomographic tilt series

The resolution of cryo-electron tomography can be limited by the first zero of the microscope’s contrast transfer function (CTF). To achieve higher resolution, it is critical to determine the CTF and correct its phase inversions. However, the extremely low signal-to-noise ratio (SNR) and the defocus gradient in the projections of tilted specimens make this process challenging. Two programs, CTFPLOTTER and CTFPHASEFLIP, have been developed to address these issues. CTFPLOTTER obtains a 1D power spectrum by periodogram averaging and rotational averaging and it estimates the noise background with a novel approach, which uses images taken with no specimen. The background-subtracted 1D power spectra from image regions at different defocus values are then shifted to align their first zeros and averaged together. This averaging improves the SNR sufficiently that it becomes possible to determine the defocus for subsets of the tilt series rather than just the entire series. CTFPHASEFLIP corrects images line-by-line by inverting phases appropriately in thin strips of the image at nearly constant defocus. CTF correction by these methods is shown to improve the resolution of aligned, averaged particles extracted from tomograms. However, some restoration of Fourier amplitudes at high frequencies is important for seeing the benefits from CTF correction.     

A comparison of three noise reduction procedures applied to bird vocal signals

ABSTRACT.   Recordings of avian vocal signals in natural habitats include ambient noise. Often this background noise corrupts across all frequencies and is of substantial amplitude. Reducing this ambient noise to prepare vocal signals for playback stimuli or to remove habitat-specific noise signatures prior to analyzing a signal's acoustic characteristics can be useful. We conducted experimental evaluations of three noise reduction procedures to determine their effectiveness. We embedded two bird vocalizations ("clean" signals) in four kinds of natural noise, resulting in eight noise-signal combinations. We then applied three noise reduction procedures (Noise Profile, Band Pass, and Noise Estimate) to each of the embedded signals and compared the recovered signals to the original (clean) signals. Noise Profile filtering was effective in reducing noise and returning fairly high-quality signals from even severe levels of masking noise. The other two noise reduction procedures did not perform as well. For the two most corrupting maskers, however, Noise Profile filtering also altered the signal properties by reducing signal amplitude at those frequencies containing high levels of noise. Apart from this loss of amplitude, the quantitative features of the filtered signals were similar to those of the original model sounds. We conclude that Noise Profile filtering produces good results for cases where noise is approximately constant over the signal duration and the signal intensity exceeds noise intensity over the frequencies of interest.     

Accurate determination of local defocus and specimen tilt in electron microscopy

Accurate knowledge of defocus and tilt parameters is essential for the determination of three-dimensional protein structures at high resolution using electron microscopy. We present two computer programs, CTFFIND3 and CTFTILT, which determine defocus parameters from images of untilted specimens, as well as defocus and tilt parameters from images of tilted specimens, respectively. Both programs use a simple algorithm that fits the amplitude modulations visible in a power spectrum with a calculated contrast transfer function (CTF). The background present in the power spectrum is calculated using a low-pass filter. The background is then subtracted from the original power spectrum, allowing the fitting of only the oscillatory component of the CTF. CTFTILT determines specimen tilt parameters by measuring the defocus at a series of locations on the image while constraining them to a single plane. We tested the algorithm on images of two-dimensional crystals by comparing the results with those obtained using crystallographic methods. The images also contained contrast from carbon support film that added to the visibility of the CTF oscillations. The tests suggest that the fitting procedure is able to determine the image defocus with an error of about 10nm, whereas tilt axis and tilt angle are determined with an error of about 2 degrees and 1 degrees, respectively. Further tests were performed on images of single protein particles embedded in ice that were recorded from untilted or slightly tilted specimens. The visibility of the CTF oscillations from these images was reduced due to the lack of a carbon support film. Nevertheless, the test results suggest that the fitting procedure is able to determine image defocus and tilt angle with errors of about 100 nm and 6 degrees, respectively.     

Automatic CTF correction for single particles based upon multivariate statistical analysis of individual power spectra

Three-dimensional electron cryomicroscopy of randomly oriented single particles is a method that is suitable for the determination of three-dimensional structures of macromolecular complexes at molecular resolution. However, the electron-microscopical projection images are modulated by a contrast transfer function (CTF) that prevents the calculation of three-dimensional reconstructions of biological complexes at high resolution from uncorrected images. We describe here an automated method for the accurate determination and correction of the CTF parameters defocus, twofold astigmatism and amplitude-contrast proportion from single-particle images. At the same time, the method allows the frequency-dependent signal decrease (B factor) and the non-convoluted background signal to be estimated. The method involves the classification of the power spectra of single-particle images into groups with similar CTF parameters; this is done by multivariate statistical analysis (MSA) and hierarchically ascending classification (HAC). Averaging over several power spectra generates class averages with enhanced signal-to-noise ratios. The correct CTF parameters can be deduced from these class averages by applying an iterative correlation procedure with theoretical CTF functions; they are then used to correct the raw images. Furthermore, the method enables the tilt axis of the sample holder to be determined and allows the elimination of individual poor-quality images that show high drift or charging effects.     

Radial averages of astigmatic TEM images

The Contrast Transfer Function (CTF) of an image, which modulates images taken from a Transmission Electron Microscope (TEM), is usually determined from the radial average of the power spectrum of the image (Frank, J., Three-dimensional Electron Microscopy of Macromolecular Assemblies, Oxford University Press, Oxford, 2006). The CTF is primarily defined by the defocus. If the defocus estimate is accurate enough then it is possible to demodulate the image, which is popularly known as the CTF correction. However, it is known that the radial average is somewhat attenuated if the image is astigmatic (see Fernando, K.V., Fuller, S.D., 2007. Determination of astigmatism in TEM images. Journal of Structural Biology 157, 189-200) but this distortion due to astigmatism has not been fully studied or understood up to now. We have discovered the exact mathematical relationship between the radial averages of TEM images with and without astigmatism. This relationship is determined by a zeroth order Bessel function of the first kind and hence we can exactly quantify this distortion in the radial averages of signal and power spectra of astigmatic images. The argument to this Bessel function is similar to an aberration function (without the spherical aberration term) except that the defocus parameter is replaced by the differences of the defoci in the major and minor axes of astigmatism. The ill effects due this Bessel function are twofold. Since the zeroth order Bessel function is a decaying oscillatory function, it introduces additional zeros to the radial average and it also attenuates the CTF signal in the radial averages. Using our analysis, it is possible to simulate the effects of astigmatism in radial averages by imposing Bessel functions on idealized radial averages of images which are not astigmatic. We validate our theory using astigmatic TEM images.     

Thermodynamics of the control of metabolism

A theory is presented, describing the control analysis of metabolic systems in terms of Gibbs free energies, extending earlier work of Kacser and Burns (25), and Heinrich and Rapoport (29). It is shown that relationships exist between flux control coefficients (the degree to which enzymes control steady-state fluxes) and free-energy elasticity coefficients, defined as the fractional change in the rate of a reaction induced by a standard change in one free-energy difference, while all the other free-energy differences are kept constant. Application of this extended control analysis to some biochemical reactions, including proton translocation, demonstrates that

1. Problems arising in the control analysis because of conservation (sum concentration of substrate and product constant) can be circumvented.
2. Although free-energy elasticity coefficients are maximal when the reaction is close to equilibrium, they can also be significant when the reaction is not close to equilibrium.
3. Problems in the control analysis caused by compartmentation can be resolved by defining control parameters that refer to the organelle as a whole.
4. These latter control parameters obey the above-mentioned relationships.

     

goCTF: Geometrically optimized CTF determination for single-particle cryo-EM

Preferred particle orientation represents a recurring problem in single-particle cryogenic electron microcopy (cryo-EM). A specimen-independent approach through tilting has been attempted to increase particle orientation coverage, thus minimizing anisotropic three-dimensional (3D) reconstruction. However, focus gradient is a critical issue hindering tilt applications from being a general practice in single-particle cryo-EM. The present study describes a newly developed geometrically optimized approach, goCTF, to reliably determine the global focus gradient. A novel strategy of determining contrast transfer function (CTF) parameters from a sector of the signal preserved power spectrum is applied to increase reliability. Subsequently, per-particle based local focus refinement is conducted in an iterative manner to further improve the defocus accuracy. Novel diagnosis methods using a standard deviation defocus plot and goodness of fit heatmap have also been proposed to evaluate CTF fitting quality prior to 3D refinement. In a benchmark study, goCTF processed a published single-particle cryo-EM dataset for influenza hemagglutinin trimer collected at a 40-degree specimen tilt. The resulting 3D reconstruction map was improved from 4.1?Å to 3.7?Å resolution. The goCTF program is built on the open-source code of CTFFIND4, which adopts a consistent user interface for ease of use.     

Processing of Auditory Midbrain Interspike Intervals by Model Neurons

A question central to sensory processing is how signal information is encoded and processed by single neurons. Stimulus features can be represented through rate coding (via firing rate), temporal coding (via firing synchronization to temporal periodicities), or temporal encoding (via intricate patterns of spike trains). Of the three, examples of temporal encoding are the least documented. One region in which temporal encoding is currently being explored is the auditory midbrain. Midbrain neurons in the plainfin midshipman generate different interspike interval (ISI) distributions depending on the frequencies of the concurrent vocal signals. However, these distributions differ only along certain lengths of ISIs, so that any neurons trying to distinguish the distributions would have to respond selectively to specific ISI ranges. We used this empirical observation as a realistic challenge with which to explore the plausibility of ISI-tuned neurons that could validate this form of temporal encoding. The resulting modeled cells—point neurons optimized through multidimensional searching—were successfully tuned to discriminate patterns in specific ranges of ISIs. Achieving this task, particularly with simplified neurons, strengthens the credibility of ISI coding in the brain and lends credence to its role in auditory processing.     

Reanalysis of Models and an Improved Model of Biomass Size Spectra

Our reanalysis aimed at understanding the regularity in empirical biomass size spectra (BSS) suggests that the construction of BSS depends of the size interval and size scales used and different definitions of BSS in literature are therefore very different. Existing empirical models of BSS can be fitted perfectly to the observed data, but the biological basis of the fitted parameters is not explained and comparison and interpretation of the findings is therefore difficult. Parameters of mechanistic models of BSS have a biological background and are interpretable. Discrete mechanistic models based on Lindeman's trophic chain theory assume a constant ratio of size (or body mass) in two adjacent trophic levels. However, this biomass ratio is not comparable with that in two adjacent (logarithmic) size intervals in the measured biomass size spectra. The continuous model by Thiebaux and Dickie (1992) is based on the discrete model by Boudreau et al. (1991). We show how the validity of the transformation of a discrete form into a continous form depends on the size ranges of prey and predator population. The model by Platt and Denman (1977) does not represent a continuous formulation due to the use of normalized biomass defined in logarithmic size intervals. We suggest to eliminate the use of trophic levels and normalized biomass. On the basis of the reanalysis we formulate and improved continuous model based on the model by Silvert and Platt (1978). The model is based on Eulerian strategy which appears more adequate for the problem than the previously used Lagrangian strategy. The model appears to be able to demonstrate the regularity in observed BSS.     

Dispersal range analysis: quantifying individual variation in dispersal behaviour

A complete understanding of animal dispersal requires knowledge not only of its consequences at population and community levels, but also of the behavioural decisions made by dispersing individuals. Recent theoretical work has emphasised the importance of this dispersal process, particularly the phase in which individuals search the landscape for breeding opportunities. However, empirical advances are currently hampered by a lack of tools for quantifying these dispersal search tactics. Here, we review existing methods for quantifying movement that are appropriate for the dispersal search process, describe several new techniques that we developed for characterising movement and behaviour through an individuals dispersal range, and illustrate their use with data from Australasian treecreepers (Climacteridae). We also describe how the quantitative parameters we discuss are calculated in a freely available computer software package that we designed. Specifically, we present methods for calculating the area searched during dispersal, search rate, thoroughness, intensity, philopatry of search, timing of exploration, and surreptitiousness. When we applied this approach to the study of dispersal in treecreepers, we found that search area, philopatry and timing of exploration showed the greatest individual variation. Furthermore, search area, search rate, thoroughness and philopatry of search were all correlated, suggesting they may be useful parameters for further research on the causes and consequences of different dispersal search tactics. Finally, we make recommendations for modifying radiotracking protocols to facilitate more accurate assessment of individual variation in the dispersal process, and suggest future directions for this type of empirical work at the interface of population and behavioural ecology.     

Background noise from a natural chorus alters female discrimination of male calls in a Neotropical frog

Many animals communicate in environments with high levels of background noise. Although it is a fundamental prediction of signal detection theory that noise should reduce both detection and discrimination of signals, little is known about these effects in animal communication. Female treefrogs, Hyla ebraccata, in Costa Rica choose mates in large noisy multispecies choruses. We tested gravid females for preferences between computer-synthesized calls with carrier frequencies of 3240 and 2960 Hz (values near the mode and the fifth percentile of the population, respectively) in four levels of background noise from a natural chorus. In the absence of noise (signal/noise ratio >25 dB), females preferred the lower frequency. With moderate signal/noise ratios (6 and 9 dB), they did not discriminate between these frequencies. With low signal/noise ratios (3 dB), females preferred the frequency near the mode for the population. Similar experiments had previously demonstrated that females can detect the presence of a male's calls with signal/noise ratios of 3 dB or greater. Thus moderate levels of natural background sound reduced a female's ability to discriminate between males' calls even when she could detect them. In high levels of background sound, females abandoned discrimination for low-frequency calls and reverted to the task of detecting signals with modal properties for the population. These results justify recent theoretical analyses of the importance of receivers' errors in the evolution of communication.     

Variation in the sizes of eggs and oncospheres and the numbers and distributions of testes in the tapeworm, Hymenolepis diminuta

Four "strains" of Hymenolepis diminuta were examined for morphological variation. These included the ARME "strain" (currently maintained at the University of Keele, U.K.), the OSU "strain" (currently maintained at The Ohio State University) and the TOR (or UT) "strain" (currently maintained at the University of Toronto), all of which were derived from the parental RICE "strain," and the ANU "strain" (currently maintained at the Australian National University). Additionally, 2 separate "clonal" populations (populations derived from single cysticercoids) from both the OSU and ANU "strains" were examined. All "strains" and "clones" were maintained under identical conditions using Tenebrio molitor and male Sprague-Dawley rats as the intermediate and definitive hosts, respectively. The lengths and widths of eggs and larvae (oncospheres) passed in the hosts' feces, and the numbers and distributions of testes in proglottids were quantified and the data analyzed. Although analyses of the lengths and widths of eggs and larvae demonstrated significant differences among some "strains" and "clones," a discriminate analysis of the data indicated these parameters to be of questionable taxonomic significance. The eggs of all "strains" and "clones" consisted of 2 distinct populations differing in density and size but not infectivity; the relative proportions of eggs in the 2 populations were not determined. Considering all possible numbers and distributions of testes, 17 variations were seen in the strobilae of tapeworms. Analyses of the data demonstrated that the "strains" and "clones" could be differentiated clearly using only the frequencies of the 1p2a (1 poral and 2 aporal testes) or 1p3a distribution, or the frequencies of proglottids containing 3 or 4 testes; all other variations failed to clearly differentiate or group the various "strains" and "clones."(ABSTRACT TRUNCATED AT 250 WORDS)     

Chromatophore activity during natural pattern expression by the squid Sepioteuthis lessoniana: contributions of miniature oscillation

Squid can rapidly change the chromatic patterns on their body. The patterns are created by the expansion and retraction of chromatophores. The chromatophore consists of a central pigment-containing cell surrounded by radial muscles that are controlled by motor neurons located in the central nervous system (CNS). In this study we used semi-intact squid (Sepioteuthis lessoniana) displaying centrally controlled natural patterns to analyze spatial and temporal activities of chromatophores located on the dorsal mantle skin. We found that chromatophores oscillated with miniature expansions/retractions at various frequencies, even when the chromatic patterns appear macroscopically stable. The frequencies of this miniature oscillation differed between "feature" and "background" areas of chromatic patterns. Higher frequencies occurred in feature areas, whereas lower frequencies were detected in background areas. We also observed synchronization of the oscillation during chromatic pattern expression. The expansion size of chromatophores oscillating at high frequency correlated with the number of synchronized chromatophores but not the oscillation frequency. Miniature oscillations were not observed in denervated chromatophores. These results suggest that miniature oscillations of chromatophores are driven by motor neuronal activities in the CNS and that frequency and synchrony of this oscillation determine the chromatic pattern and the expansion size, respectively.     

DFT studies on the structural and vibrational properties of polyenes

Detailed density functional theory (DFT) calculations on the structure and harmonic frequencies of model all-trans and all-cis polyenes were undertaken. For the first time, we report on the convergence of selected B3LYP/6-311++G** and BLYP/6-311++G** calculated structural parameters resulting from a systematic increase in polyene size (chains containing 2 to 14 C?=?C units). The limiting values of the structural parameters for very long chains were estimated using simple three-parameter empirical formulae. BLYP/6-311++G** calculated ν(C?=?C) and ν(C–C) frequencies for all-trans and all-cis polyenes containing up to 14 carbon–carbon double bonds were used to estimate these values for very long chains. Correction of raw, unscaled vibrational data was performed by comparing theoretical and experimental wavenumbers for polyenes chains containing 3 to 12 conjugated C?=?C units with both ends substituted by tert-butyl groups. The corrected ν(C?=?C) and ν(C–C) wavenumbers for all-trans molecules were used to estimate the presence of 9 – 12 C?=?C units in all-trans polyene pigment in red coral.

Open image in new window

Graphical abstract Detailed density functional theory (DFT) calculations on the structure and harmonic frequencies of model all-trans and all-cis polyenes were undertaken. For the first time, we report on the convergence of selected B3LYP/6-311++G** and BLYP/6-311++G** calculated structural parameters resulting from a systematic increase in polyene size (chains containing 2 to 14 C=C units). The limiting values of the structural parameters for very long chains were estimated using simple three-parameter empirical formulae.

     

Minimization of lung pressure swings during high-frequency ventilation: a model

The goal of this theoretical study was to develop a simple computational model for determining the lung pressure excursions that accompany the maintenance of adequate gas transport through high-frequency airway oscillations applied via the trachea (HFAO) and by transthoracic means (HFTO). Respiratory mechanics and gas transport parameters estimated from the preceding companion study (J. Appl. Physiol. 67: 985-992, 1989) were used in the model for computing tracheal, alveolar, pleural, and transpulmonary pressure swings. Comparison of model predictions with corresponding data obtained in dogs showed close agreement. The specification of eucapnia as a constraint led to results that were significantly different from previous findings which had assumed constant airflow. We used the model to identify "quasi-optimal" strategies for HFAO and HFTO application in which all pressure excursions were kept below the corresponding levels produced by conventional mechanical ventilation operating at 15 breaths/min. The model suggests the application of both HFAO and HFTO at frequencies substantially lower than the settings commonly employed in high-frequency ventilation. Application of HFAO at frequencies ranging from 1 to 4 Hz is recommended, whereas for HFTO the quasi-optimal range lies between 1 and 1.7 Hz. In patients with chronic obstructive pulmonary disease, pressure costs during HFAO or HFTO are minimized in the vicinity of 1 Hz.     

Optimisation of Wavelength Modulated Raman Spectroscopy: Towards High Throughput Cell Screening

In the field of biomedicine, Raman spectroscopy is a powerful technique to discriminate between normal and cancerous cells. However the strong background signal from the sample and the instrumentation affects the efficiency of this discrimination technique. Wavelength Modulated Raman spectroscopy (WMRS) may suppress the background from the Raman spectra. In this study we demonstrate a systematic approach for optimizing the various parameters of WMRS to achieve a reduction in the acquisition time for potential applications such as higher throughput cell screening. The Signal to Noise Ratio (SNR) of the Raman bands depends on the modulation amplitude, time constant and total acquisition time. It was observed that the sampling rate does not influence the signal to noise ratio of the Raman bands if three or more wavelengths are sampled. With these optimised WMRS parameters, we increased the throughput in the binary classification of normal human urothelial cells and bladder cancer cells by reducing the total acquisition time to 6 s which is significantly lower in comparison to previous acquisition times required for the discrimination between similar cell types.     

Focus gradient correction applied to tilt series image data used in electron tomography

The resolution in 3D reconstructions from tilt series is limited to the information below the first zero of the contrast transfer function unless the signal is corrected computationally. The restoration is usually based on the assumption of a linear space-invariant system and a linear relationship between object mass density and observed image contrast. The space-invariant model is no longer valid when applied to tilted micrographs because the defocus varies in a direction perpendicular to the tilt axis and with it the shape of the associated point spread function. In this paper, a method is presented for determining the defocus gradient in thin specimens such as sections and 2D crystals, and for restoration of the images subsequently used for 3D reconstruction. The alignment procedure for 3D reconstruction includes area matching and tilt geometry refinement. A map with limited resolution computed from uncorrected micrographs is compared to a volume computed from corrected micrographs with extended resolution.     

Alignment error envelopes for single particle analysis

To determine the structure of a biological particle to high resolution by electron microscopy, image averaging is required to combine information from different views and to increase the signal-to-noise ratio. Starting from the number of noiseless views necessary to resolve features of a given size, four general factors are considered that increase the number of images actually needed: (1) the physics of electron scattering introduces shot noise, (2) thermal motion and particle inhomogeneity cause the scattered electrons to describe a mixture of structures, (3) the microscope system fails to usefully record all the information carried by the scattered electrons, and (4) image misalignment leads to information loss through incoherent averaging. The compound effect of factors 2-4 is approximated by the product of envelope functions. The problem of incoherent image averaging is developed in detail through derivation of five envelope functions that account for small errors in 11 "alignment" parameters describing particle location, orientation, defocus, magnification, and beam tilt. The analysis provides target error tolerances for single particle analysis to near-atomic (3.5 A) resolution, and this prospect is shown to depend critically on image quality, defocus determination, and microscope alignment.     

Designing lymphocyte functional structure for optimal signal detection: voilà, T cells

One basic task of immune systems is to detect signals from unknown "intruders" amidst a noisy background of harmless signals. To clarify the functional importance of many observed lymphocyte properties, I ask: What properties would a cell have if one designed it according to the theory of optimal detection, with minimal regard for biological constraints? Sparse and reasonable assumptions about the statistics of available signals prove sufficient for deriving many features of the optimal functional structure, in an incremental and modular design. The use of one common formalism guarantees that all parts of the design collaborate to solve the detection task. Detection performance is computed at several stages of the design. Comparison between design variants reveals e.g. the importance of controlling the signal integration time. This predicts that an appropriate control mechanism should exist. Comparing the design to reality, I find a striking similarity with many features of T cells. For example, the formalism dictates clonal specificity, serial receptor triggering, (grades of) anergy, negative and positive selection, co-stimulation, high-zone tolerance, and clonal production of cytokines. Serious mismatches should be found if T cells were hindered by mechanistic constraints or vestiges of their (co-)evolutionary history, but I have not found clear examples. By contrast, fundamental mismatches abound when comparing the design to immune systems of e.g. invertebrates. The wide-ranging differences seem to hinge on the (in)ability to generate a large diversity of receptors.     

Reduction of autofluorescence on DNA microarrays and slide surfaces by treatment with sodium borohydride

Microarray technology is currently being used extensively in functional genomics research and modern drug discovery and development. Henceforward, tremendous application potential for this technology exists in the fields of clinical diagnostics and prognostics, pathology, and toxicology for high-throughput analysis of "disease" gene expression. However, the major hurdle now in this technology is not the performance of the arrays but rather the efficient reproducibility of the hybridization signal intensity in a fluorescence-based analysis. The sensitivity of fluorescence detection on an array is to a large extent limited by the amount of background signal arising due to nonspecifically bound probes and fluorescence that is intrinsically associated with the chip substrate and/or the attached target DNA, the so-called autofluorescence. Here, we describe a simple and efficient method to reduce autofluorescence from undetermined sources on coated glass slides with and without DNA arrays. This sodium borohydride-mediated reduction process resulted in significantly lower and more even background fluorescence. This in turn extended the dynamic range of detection and reduced the average coefficient of variation of fluorescent signal ratios on DNA microarrays in addition to improving the detection of genes that are expressed at a low level.