Quantitative covariance NMR by regularization

The square root of a covariance spectrum, which offers high spectral resolution along both dimensions requiring only few t ₁ increments, yields in good approximation the idealized 2D FT spectrum provided that the amount of magnetization exchanged between spins is relatively small. When this condition is violated, 2D FT and covariance peak volumes may differ. A regularization method is presented that produces a modified covariance spectrum with cross-peak volumes that closely match their 2D FT analogues. The method is demonstrated for TOCSY spectra with variable mixing times.     

An improved ultrafast 2D NMR experiment: Towards atom-resolved real-time studies of protein kinetics at multi-Hz rates

Multidimensional NMR spectroscopy is a well-established technique for the characterization of structure and fast-time-scale dynamics of highly populated ground states of biological macromolecules. The investigation of short-lived excited states that are important for molecular folding, misfolding and function, however, remains a challenge for modern biomolecular NMR techniques. Off-equilibrium real-time kinetic NMR methods allow direct observation of conformational or chemical changes by following peak positions and intensities in a series of spectra recorded during a kinetic event. Because standard multidimensional NMR methods required to yield sufficient atom-resolution are intrinsically time-consuming, many interesting phenomena are excluded from real-time NMR analysis. Recently, spatially encoded ultrafast 2D NMR techniques have been proposed that allow one to acquire a 2D NMR experiment within a single transient. In addition, when combined with the SOFAST technique, such ultrafast experiments can be repeated at high rates. One of the problems detected for such ultrafast protein NMR experiments is related to the heteronuclear decoupling during detection with interferences between the pulses and the oscillatory magnetic field gradients arising in this scheme. Here we present a method for improved ultrafast data acquisition yielding higher signal to noise and sharper lines in single-scan 2D NMR spectra. In combination with a fast-mixing device, the recording of ¹H–¹⁵N correlation spectra with repetition rates of up to a few Hertz becomes feasible, enabling real-time studies of protein kinetics occurring on time scales down to a few seconds.     

Estimating the quality of reprogrammed cells using ES cell differentiation expression patterns

Somatic cells can be reprogrammed to a pluripotent state by over-expression of defined factors, and pluripotency has been confirmed by the tetraploid complementation assay. However, especially in human cells, estimating the quality of Induced Pluripotent Stem Cell(iPSC) is still difficult. Here, we present a novel supervised method for the assessment of the quality of iPSCs by estimating the gene expression profile using a 2-D "Differentiation-index coordinate", which consists of two "developing lines" that reflects the directions of ES cell differentiation and the changes of cell states during differentiation. By applying a novel liner model to describe the differentiation trajectory, we transformed the ES cell differentiation time-course expression profiles to linear "developing lines"; and use these lines to construct the 2-D "Differentiation-index coordinate" of mouse and human. We compared the published gene expression profiles of iPSCs, ESCs and fibroblasts in mouse and human "Differentiation-index coordinate". Moreover, we defined the Distance index to indicate the qualities of iPS cells, which based on the projection distance of iPSCs-ESCs and iPSCs-fibroblasts. The results indicated that the "Differentiation-index coordinate" can distinguish differentiation states of the different cells types. Furthermore, by applying this method to the analysis of expression profiles in the tetraploid complementation assay, we showed that the Distance index which reflected spatial distributions correlated the pluripotency of iPSCs. We also analyzed the significantly changed gene sets of "developing lines". The results suggest that the method presented here is not only suitable for the estimation of the quality of iPS cells based on expression profiles, but also is a new approach to analyze time-resolved experimental data.     

Potential bias in NMR relaxation data introduced by peak intensity analysis and curve fitting methods

We present an evaluation of the accuracy and precision of relaxation rates calculated using a variety of methods, applied to data sets obtained for several very different protein systems. We show that common methods of data evaluation, such as the determination of peak heights and peak volumes, may be subject to bias, giving incorrect values for quantities such as R₁ and R₂. For example, one common method of peak-height determination, using a search routine to obtain the peak-height maximum in successive spectra, may be a source of significant systematic error in the relaxation rate. The alternative use of peak volumes or of a fixed coordinate position for the peak height in successive spectra gives more accurate results, particularly in cases where the signal/noise is low, but these methods have inherent problems of their own. For example, volumes are difficult to quantitate for overlapped peaks. We show that with any method of sampling the peak intensity, the choice of a 2- or 3-parameter equation to fit the exponential relaxation decay curves can dramatically affect both the accuracy and precision of the calculated relaxation rates. In general, a 2-parameter fit of relaxation decay curves is preferable. However, for very low intensity peaks a 3 parameter fit may be more appropriate.     

Characterisation of structural tree root architecture using 3D digitising and AMAPmod software

A low-magnetic-field digitising device combined with AMAPmod, a software designed to analyse plant architecture, provided a very efficient method for measuring and studying the geometry and topology of the structural roots of trees. The digitising device measures co-ordinates in a 3D space. AMAPmod was used to assess several characteristics of the root architecture including spatial position, root lengths and volumes, branching order and branching pattern, and to reconstruct 3D images from the data to check for measurement errors. Structural root systems of three 20 to 28-year-old Quercus petraea and thirty 5-year-old Pinus pinaster were uprooted by using rapid mechanised techniques. Only roots with a diamter larger than 2 mm were measured. A fast and precise spatial localisation in combination with the topological characterisation of all root segments was carried out. Oak showed a stronger more oblique and vertical rooting, more branches, more forks and narrower branching angles than pine. Oak had only few small roots in the north west direction whereas half of pine root volume was located in the 10 cm upper soil volume. The contribution of this new method in the characterisation of structural root systems is discussed and other possible applications of this method in root studies are proposed. Since this method is precise and fairly rapid, it may be used for agronomic testing (i.e. comparing treatments) involving several dozen root systems. Almost all parameters needed for tree root system simulations can be estimated from such data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Maximum likelihood estimation of ancestral codon usage bias parameters in Drosophila

We present a likelihood method for estimating codon usage bias parameters along the lineages of a phylogeny. The method is an extension of the classical codon-based models used for estimating dN/dS ratios along the lineages of a phylogeny. However, we add one extra parameter for each lineage: the selection coefficient for optimal codon usage (S), allowing joint maximum likelihood estimation of S and the dN/dS ratio. We apply the method to previously published data from Drosophila melanogaster, Drosophila simulans, and Drosophila yakuba and show, in accordance with previous results, that the D. melanogaster lineage has experienced a reduction in the selection for optimal codon usage. However, the D. melanogaster lineage has also experienced a change in the biological mutation rates relative to D. simulans, in particular, a relative reduction in the mutation rate from A to G and an increase in the mutation rate from C to T. However, neither a reduction in the strength of selection nor a change in the mutational pattern can alone explain all of the data observed in the D. melanogaster lineage. For example, we also confirm previous results showing that the Notch locus has experienced positive selection for previously classified unpreferred mutations.     

Background suppression in frequency-domain fluorometry

Gated detection is often used in time-domain measurements of long-lived fluorophores for suppression of interfering short-lived autofluorescence. However, no direct method has been available for gated detection and background suppression when using frequency-domain fluorometry. We describe a direct method for real-time suppression of autofluorescence in frequency-domain fluorometry. The method uses a gated detector and the sample is excited by a pulsed train. The detector is gated on following each excitation pulse after a suitable time delay for decay of the prompt autofluorescence. Under the same experimental conditions a detectable reference signal is obtained by using a long lifetime standard with a known decay time. Because the sample and reference signals are measured under identical excitation, gating and instrumental conditions, the data can be analyzed as usual for frequency-domain data without further processing. We show by simulations that this method can be used to resolve single and multiexponential decays in the presence of short lifetime autofluorescence.     

HIFI-C: a robust and fast method for determining NMR couplings from adaptive 3D to 2D projections

We describe a novel method for the robust, rapid, and reliable determination of J couplings in multi-dimensional NMR coupling data, including small couplings from larger proteins. The method, “High-resolution Iterative Frequency Identification of Couplings” (HIFI-C) is an extension of the adaptive and intelligent data collection approach introduced earlier in HIFI-NMR. HIFI-C collects one or more optimally tilted two-dimensional (2D) planes of a 3D experiment, identifies peaks, and determines couplings with high resolution and precision. The HIFI-C approach, demonstrated here for the 3D quantitative J method, offers vital features that advance the goal of rapid and robust collection of NMR coupling data. (1) Tilted plane residual dipolar couplings (RDC) data are collected adaptively in order to offer an intelligent trade off between data collection time and accuracy. (2) Data from independent planes can provide a statistical measure of reliability for each measured coupling. (3) Fast data collection enables measurements in cases where sample stability is a limiting factor (for example in the presence of an orienting medium required for residual dipolar coupling measurements). (4) For samples that are stable, or in experiments involving relatively stronger couplings, robust data collection enables more reliable determinations of couplings in shorter time, particularly for larger biomolecules. As a proof of principle, we have applied the HIFI-C approach to the 3D quantitative J experiment to determine N-C′ RDC values for three proteins ranging from 56 to 159 residues (including a homodimer with 111 residues in each subunit). A number of factors influence the robustness and speed of data collection. These factors include the size of the protein, the experimental set up, and the coupling being measured, among others. To exhibit a lower bound on robustness and the potential for time saving, the measurement of dipolar couplings for the N-C′ vector represents a realistic “worst case analysis”. These couplings are among the smallest currently measured, and their determination in both isotropic and anisotropic media demands the highest measurement precision. The new approach yielded excellent quantitative agreement with values determined independently by the conventional 3D quantitative J NMR method (in cases where sample stability in oriented media permitted these measurements) but with a factor of 2–5 in time savings. The statistical measure of reliability, measuring the quality of each RDC value, offers valuable adjunct information even in cases where modest time savings may be realized. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Evaluation of a pictorial method to obtain subject‐specific inertial properties in equine limb segments

Data describing segmental masses and moments of inertia (MOI) of limb segments are required for inverse dynamic calculations. In horses, these values are usually calculated using regression equations that have been developed from a limited number of horses representing a small number of breeds. The objective of the present study was to evaluate the performance of a scaling method and a pictorial method for estimating of the values of segmental masses, lengths, and MOI in the equine limb segments by comparing their output with the standard technique involving direct measurements. Limbs of 30 horses of various breeds and sizes were disarticulated post mortem. Segmental masses, lengths, and MOI were determined using a standard method based on weighing the segments, measuring their length with calipers, and estimating the MOI from the rotational frequency of a trifilar pendulum. The scaling method used a jack‐knifing procedure to avoid the need for two data sets. The pictorial method was based on digitization of two orthogonal photographs to determine segmental volumes, which were combined with published values for average segment densities to determine the inertial parameters. Scaling method and pictorial method provided comparable estimation of segmental messes and lengths, but the scaling method performed better in estimating segmental MOI. The scaling method worked well enough in the majority of horses but there were a few horses in which it was less effective. The pictorial method sometimes showed a bias correctable by regression equations but it may not warrant the additional effort unless for specific cases.     

Estimation of the axis of a screw motion from noisy data--a new method based on Plücker lines

The problems of estimating the motion and orientation parameters of a body segment from two n point-set patterns are analyzed using the Plücker coordinates of a line (Plücker lines). The aim is to find algorithms less complex than those in conventional use, and thus facilitating more accurate computation of the unknown parameters. All conventional techniques use point transformation to calculate the screw axis. In this paper, we present a novel technique that directly estimates the axis of a screw motion as a Plücker line. The Plücker line can be transformed via the dual-number coordinate transformation matrix. This method is compared with Schwartz and Rozumalski [2005. A new method for estimating joint parameters from motion data. Journal of Biomechanics 38, 107-116] in simulations of random measurement errors and systematic skin movements. Simulation results indicate that the methods based on Plücker lines (Plücker line method) are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements. This investigation yielded practical results, which can be used to locate the axis of a screw motion in a noisy environment. Developing the dual transformation matrix (DTM) from noisy data and determining the screw axis from a given DTM is done in a manner analogous to that for handling simple rotations. A more robust approach to solve for the dual vector associated with DTM is also addressed by using the eigenvector and the singular value decomposition.     

Practical Model Fitting Approaches to the Direct Extraction of NMR Parameters Simultaneously from All Dimensions of Multidimensional NMR Spectra

A maximum likelihood (ML)-based approach has been established for the direct extraction of NMR parameters (e.g., frequency, amplitude, phase, and decay rate) simultaneously from all dimensions of a D-dimensional NMR spectrum. The approach, referred to here as HTFD-ML (hybrid time frequency domain maximum likelihood), constructs a time-domain model composed of a sum of exponentially-decaying sinusoidal signals. The apodized Fourier transform of this time-domain signal is a model spectrum that represents the best fit to the equivalent frequency-domain data spectrum. The desired amplitude and frequency parameters can be extracted directly from the signal model constructed by the HTFD-ML algorithm. The HTFD-ML approach presented here, as embodied in the software package CHIFIT, is designed to meet the challenges posed by model fitting of D-dimensional NMR data sets, where each consists of many data points (108 is not uncommon) encoding information about numerous signals (up to 105 for a protein of moderate size) that exhibit spectral overlap. The suitability of the approach is demonstrated by its application to the concerted analysis of a series of ten 2D 1H-15N HSQC experiments measuring 15N T1 relaxation. In addition to demonstrating the practicality of performing maximum likelihood analysis on large, multidimensional NMR spectra, the results demonstrate that this parametric model-fitting approach provides more accurate amplitude and frequency estimates than those obtained from conventional peak-based analysis of the FT spectrum. The improved performance of the model fitting approach derives from its ability to take into account the simultaneous contributions of all signals in a crowded spectral region (deconvolution) as well as to incorporate prior knowledge in constructing models to fit the data.     

Measuring egg size using digital photography: testing Hoyt's method using Florida Scrub-Jay eggs

ABSTRACT.   Egg volumes are most often estimated using a mathematical model that incorporates length and width measurements and a species-specific shape variable. Although adequate in many respects, this technique does not account for intraspecific variation in egg shape. We developed a computer-automated technique that uses calibrated digital photographs to render precise measurements of several egg-size parameters including length, width, volume, and surface area. The system extracts egg outlines from photographs, and divides each egg into latitudinal slices that are subsequently regarded as simple geometric shapes (cylinders or cone frustra) with volumes and surface areas that can be summed to generate size parameters for the entire egg. We tested this technique using 491 eggs from Florida Scrub-Jay ( Aphelocoma coerulescens ) nests and compared the resulting egg volumes with volumes calculated using the preeminent method of estimating volume from linear measurements. Our method was highly accurate, and differences between the volumes from our method and the alternative method were strongly associated with variation in egg shape. Advantages of our technique include decreased handling of eggs and increased accuracy. Software resources and additional information regarding the technique are available at http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm .     

The orthogonal tilt reconstruction method: an approach to generating single-class volumes with no missing cone for ab initio reconstruction of asymmetric particles

Generating reliable initial models is a critical step in the reconstruction of asymmetric single-particles by 3D electron microscopy. This is particularly difficult to do if heterogeneity is present in the sample. The Random Conical Tilt (RCT) method, arguably the most robust presently to accomplish this task, requires significant user intervention to solve the "missing cone" problem. We present here a novel approach, termed the orthogonal tilt reconstruction method, that eliminates the missing cone altogether, making it possible for single-class volumes to be used directly as initial references in refinement without further processing. The method involves collecting data at +45 degrees and -45 degrees tilts and only requires that particles adopt a relatively large number of orientations on the grid. One tilted data set is used for alignment and classification and the other set--which provides views orthogonal to those in the first--is used for reconstruction, resulting in the absence of a missing cone. We have tested this method with synthetic data and compared its performance to that of the RCT method. We also propose a way of increasing the level of homogeneity in individual 2D classes (and volumes) in a heterogeneous data set and identifying the most homogeneous volumes.     

Non-destructive stereological method for estimating the length of rigid root systems

A non-destructive method of total vertical projections for estimating the length of rigid root systems, not introduced yet in plant sciences, is described. It is demonstrated on measuring less and more dense root systems of seedlings of Zea mays grown at hypoxic or control conditions. Photographs of six vertical projections (30° apart) of each root system were taken and evaluated. The method being based on proved mathematical formula offers unbiased estimation of the length of a rigid root system, curved in three-dimensional space, by non-destructive means. Thus, it is applicable during ongoing experimentation on plants grown in a solution culture. It was shown that less than 120 intersections between the root projection and test lines in one photograph ensured sufficient precision of the method and that the observer subjectivity could be overcome by presented instructions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Measurement of subnanosecond anisotropy decays of protein fluorescence using frequency-domain fluorometry

We report the first anisotropy decays of protein fluorescence obtained using a frequency-domain fluorometer. The ultraviolet light source (300 nm) was a ring dye laser equipped with an intracavity frequency doubler, pumped by an argon ion laser. The data, measured at modulation frequencies from 2 to 200 MHz, reveal the presence of subnanosecond motions (0.1-0.2 ns) of the single tryptophan residues in melittin and monellin. For melittin the data also indicate the presence of slower motions near 1 ns, which may be the result of concerted motions of several peptide units. Smaller amplitude motions, on a similar timescale, were observed for the single tryptophan residue in staphylococcal nuclease. We demonstrate using N-acetyl-L-tryptophanamide in water that the method of frequency-domain fluorometry is capable of measuring correlation times as short as 50 ps. This method can provide data for the direct comparison of measured anisotropy decays with those predicted from molecular dynamics calculations.     

Calculation of volumes and systolic indices of heart ventricle from Halobatrachus didactylus: echocardiographic noninvasive method

The purpose of this work is to calculate end-systolic and end-diastolic volumes of Halobatrachus didactylus ventricles, from two-dimensional (2D) echocardiographic images, comparing four different linear methods, and to derive systolic indices of ventricular function-fractional shortening, ejection fraction, stroke volume, and cardiac output independent of the Fick principle. Echocardiography provided high resolution images of cardiac structures and allowed accurate linear measurements. The Simpson algorithm proved to be the best method of calculating ventricle volumes. As a corollary, ventricular mass can be derived from echocardiographic volume data. This noninvasive method promises wide utilization in experimental comparative cardiovascular biology.     

Spatially encoded strategies in the execution of biomolecular-oriented 3D NMR experiments

Three-dimensional nuclear magnetic resonance (3D NMR) provides one of the foremost analytical tools available for the elucidation of biomolecular structure, function and dynamics. Executing a 3D NMR experiment generally involves scanning a series of time-domain signals S(t ₃), as a function of two time variables (t ₁, t ₂) which need to undergo parametric incrementations throughout independent experiments. Recent years have witnessed extensive efforts towards the acceleration of this kind of experiments. Among the different approaches that have been proposed counts an “ultrafast” scheme, which distinguishes itself from other propositions by enabling—at least in principle—the acquisition of the complete multidimensional NMR data set within a single transient. 2D protein NMR implementations of this single-scan method have been demonstrated, yet its potential for 3D acquisitions has only been exemplified on model organic compounds. This publication discusses a number of strategies that could make these spatial encoding protocols compatible with 3D biomolecular NMR applications. These include a merging of 2D ultrafast NMR principles with temporal 2D encoding schemes, which can yield 3D HNCO spectra from peptides and proteins within ≈100 s timescales. New processing issues that facilitate the collection of 3D NMR spectra by relying fully on spatial encoding principles are also assessed, and shown capable of delivering HNCO spectra within 1 s timescales. Limitations and prospects of these various schemes are briefly addressed.     

An informative panel of somatic cell hybrids for physical mapping on human chromosome 19q.

A panel of 22 somatic cell hybrids divides the q arm of human chromosome 19 into 22 ordered subregions. The panel was characterized with respect to 41 genetic markers. In most cases, a single fragment of chromosome 19 was present in each hybrid. In two cell lines the presence of multiple fragments of the chromosome was demonstrated by segregation of these fragments in subclones. On the basis of the results of marker analysis in this panel, the most likely order of the markers tested is MANB-D19S7-PEPD-D19S9-GPI-C/EBP-TGFB1++ +-(CYP2A,BCKDHA,CGM2,NCA)-PSG1-(D19S8, XRCC1)-(ATP1A3,D19S19)-(D19S37,APOC2)-C KM-ERCC2-ERCC1-(D19S116,D19S117)- (D19S118,D19S119, D19S63,p36.1,D19S112,D19S62,D19S51,D19S54, D19S55)-pW39-D19S6-(D19S50,TNNT1)-D19S2 2-(HRC,CGB,FTL,PRKCG)-qter. This gene order is generally consistent with published physical and genetic mapping orders, although some discrepancies exist. By means of a mapping function that relates the frequency of cosegregation of markers to the distance between them, estimates were made of the sizes, in megabases, of the 19q subregions. The relative physical distances between reference markers were compared with published genetic distances for 19q. Excellent correlation was observed, suggesting that the physical distances calculated by this method are predictive of genetic distances in this region of the genome and, therefore, are just as useful in estimating relative positions of markers.     

High-resolution pyrimidine- and ribose-specific 4D HCCH-COSY spectra of RNA using the filter diagonalization method

The NMR spectra of nucleic acids suffer from severe peak overlap, which complicates resonance assignments. 4D NMR experiments can overcome much of the degeneracy in 2D and 3D spectra; however, the linear increase in acquisition time with each new dimension makes it impractical to acquire high-resolution 4D spectra using standard Fourier transform (FT) techniques. The filter diagonalization method (FDM) is a numerically efficient algorithm that fits the entire multi-dimensional time-domain data to a set of multi-dimensional oscillators. Selective 4D constant-time HCCH-COSY experiments that correlate the H5-C5-C6-H6 base spin systems of pyrimidines or the H1'-C1'-C2'-H2' spin systems of ribose sugars were acquired on the (13)C-labeled iron responsive element (IRE) RNA. FDM-processing of these 4D experiments recorded with only 8 complex points in the indirect dimensions showed superior spectral resolution than FT-processed spectra. Practical aspects of obtaining optimal FDM-processed spectra are discussed. The results here demonstrate that FDM-processing can be used to obtain high-resolution 4D spectra on a medium sized RNA in a fraction of the acquisition time normally required for high-resolution, high-dimensional spectra.     

NMR studies on the solution structure of a deletion mutant of the transcarboxylase biotin carrier subunit

A deletion mutant of the transcarboxylase biotin carrier protein was completely labeled with ¹³C and ¹⁵N. A multitude of 2D and 3D NMR spectra were recorded and assigned. An NMR solution structure was derived from the data and compared in detail with the recently published structure of the wild-type. It is shown that deletion of 30% of the amino acids does not alter the structure of the rigid protein core.