Sedimentation Coefficient Research Articles

Sizes and conformations of hydrophilic and hydrophobic polyelectrolytes in solutions of various ionic strengths

The hydrodynamic characteristics of macromolecules of a random copolymer of N-methyl-N-vinylacetamide and N-methyl-N-vinylamine hydrochloride containing 43.6% charged units in the molecular-mass range of 27 × 103 to 355 × 103 are studied. For solutions in 0.2 M NaCl, sedimentation and translational-diffusion coefficients are determined. For salt-free solutions and for solutions in 0.2 and 5.0 M NaCl, the intrinsic viscosities of the fractions are found. The lengths of the statistical segments of the chains are estimated in terms of the Gray-Bloomfield-Hearst theory. The behavior of the polycation, whose uncharged counterpart is a hydrophilic polymer, is compared to the behavior of poly(sodium 4-styrenesulfonate), whose uncharged counterpart is a hydrophobic polymer. The comparison is based on normalized scaling relations. It is shown that the level of compaction of macromolecules of strong polyelectrolytes at a high ionic strength is determined by the degree of hydrophobicity of their polymer chains. Polyelectrolytes based on hydrophilic polymers cannot be compacted into a preglobular state; their chains preserve a swollen coil conformation up to maximally high values of ionic strength.

Electrokinetic and hydrodynamic properties of charged-particles systems

Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective diffusion coefficients, sedimentation coefficients, and electrophoretic mobilities and conductivities of ionic particle species in an external electric field. Advances by our group are also discussed, including a novel mode-coupling-theory method for conduction-diffusion and viscoelastic properties of strong electrolyte solutions. Furthermore, results are presented for dispersions of solvent-permeable particles, and particles with non-zero hydrodynamic surface slip. The concentration-dependent swelling of ionic microgels is discussed, as well as a far-reaching dynamic scaling behavior relating colloidal long- to short-time dynamics.

Settlement Calculation and Analysis of the Southwest Airport High Fills Settlement

This paper,according to the airport high fill measured data of Settlement, the filling height of not more than filling half the width of the settlement,is divided into central uniform settlement area and boundary affected zone; Central uniform settlement area can be regarded as one-dimensional compression state, layered summation method to calculate the theoretical final settlement value; then, according to the settlement data, using the hyperbolic method, exponential curve method to predict the final settlement, compared with the theoretical sedimentation value, thrust reversers experience in the specification formula coefficient, the ratio is the sedimentation coefficient of experience. The empirical coeffcient is 0.49~0.92.

Star-Brush-Shaped Macromolecules: Peculiar Properties in Dilute Solution

Star-brush-shaped poly(e-caprolactone)-block-poly(oligo(ethylene glycol) methacrylate (PCL-b-POEGMA) macromolecules were synthesized and studied by molecular hydrodynamic methods. The values of the intrinsic viscosity, the velocity sedimentation coefficient, the translational diffusion coefficient, and the frictional ratio were obtained in acetone. Molar masses (M) were determined by the Svedberg relation, and the correlations between the hydrodynamic values and the molar mass were obtained in the range of 19 < M × 10–3 g mol–1 < 124. Comparison of the scaling indexes of the intrinsic viscosity and sedimentation velocity coefficient versus molar mass corresponding to the conventional four-arm stars macromolecules with that of the star-brush-shaped copolymer macromolecules shows that the star-brush-shaped PCL-b-POEGMA macromolecules have the more dense organization in space which is connected with their different topology in contrast to the conventional stars macromolecules. The model of the PCL-b-POEGMA m...

Recent variation in reach‐scale bankfull discharge in the Lower Yellow River

ABSTRACTBankfull discharge is a key parameter in the context of river engineering and geomorphology, as an indicator of flood discharge capacity in alluvial rivers, and varying in response to the incoming flow and sediment regimes. Bankfull channel dimensions have significantly adjusted along the Lower Yellow River (LYR) due to recent channel degradation, caused by the operation of the Xiaolangdi Reservoir, which has led to longitudinal variability in cross‐sectional bankfull discharges. Therefore, it is more representative to describe the flood discharge capacity of the LYR, using the concept of reach‐averaged bankfull discharge. Previous simple mean methods to estimate reach‐scale bankfull discharge cannot meet the condition of flow continuity or account for the effect of different spacing between two sections. In this study, a general method to calculate cross‐sectional bankfull discharge using the simulated stage‐discharge relation is outlined briefly, and an integrated method is then proposed for estimating reach‐scale bankfull discharge. The proposed method integrates a geometric mean based on the log‐transformation with a weighted average based on the spacing between two consecutive sections, which avoids the shortcomings of previous methods. The post‐flood reach‐scale bankfull discharges in three different channel‐pattern reaches of the LYR were estimated annually during the period from 1999 to 2010 using the proposed method, based on surveyed post‐flood profiles at 91 sedimentation sections and the measured hydrological data at seven hydrometric sections. The calculated results indicate that: (i) the estimated reach‐scale bankfull discharges can effectively represent the flood discharge capacity of different reaches, with their ranges of variation being less than those of typical cross‐sectional bankfull discharges; and (ii) the magnitude of the reach‐scale bankfull discharge in each reach can respond well to the accumulative effect of incoming flow and sediment conditions. Finally, empirical relationships for different reaches in the LYR were developed between the reach‐scale bankfull discharge and the previous four‐year average discharge and incoming sediment coefficient during flood seasons, with relatively high correlation coefficients between them being obtained, and the reach‐scale bankfull discharges in different reaches predicted by the delayed response model were also presented for a comparison. These relations for the prediction of reach‐scale bankfull discharges were validated using the cross‐sectional profiles and hydrological data measured in 2011. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Ubiquitin Interacts with the Tollip C2 and CUE Domains and Inhibits Binding of Tollip to Phosphoinositides

A large number of cellular signaling processes are directed through internalization, via endocytosis, of polyubiquitinated cargo proteins. Tollip is an adaptor protein that facilitates endosomal cargo sorting for lysosomal degradation. Tollip preferentially binds phosphatidylinositol 3-phosphate (PtdIns(3)P) via its C2 domain, an association that may be required for endosomal membrane targeting. Here, we show that Tollip binds ubiquitin through its C2 and CUE domains and that its association with the C2 domain inhibits PtdIns(3)P binding. NMR analysis demonstrates that the C2 and CUE domains bind to overlapping sites on ubiquitin, suggesting that two ubiquitin molecules associate with Tollip simultaneously. Hydrodynamic studies reveal that ubiquitin forms heterodimers with the CUE domain, indicating that the association disrupts the dimeric state of the CUE domain. We propose that, in the absence of polyubiquitinated cargo, the dual binding of ubiquitin partitions Tollip into membrane-bound and membrane-free states, a function that contributes to the engagement of Tollip in both membrane trafficking and cytosolic pathways.

The Solution Structure of Heparan Sulfate Differs from That of Heparin: IMPLICATIONS FOR FUNCTION

The highly sulfated polysaccharides heparin and heparan sulfate (HS) play key roles in the regulation of physiological and pathophysiological processes. Despite its importance, no molecular structures of free HS have been reported up to now. By combining analytical ultracentrifugation, small angle x-ray scattering, and constrained scattering modeling recently used for heparin, we have analyzed the solution structures for eight purified HS fragments dp6-dp24 corresponding to the predominantly unsulfated GlcA-GlcNAc domains of heparan sulfate. Unlike heparin, the sedimentation coefficient s20,w of HS dp6-dp24 showed a small rotor speed dependence, where similar s20,w values of 0.82-1.26 S (absorbance optics) and 1.05-1.34 S (interference optics) were determined. The corresponding x-ray scattering measurements of HS dp6-dp24 gave radii of gyration RG values from 1.03 to 2.82 nm, cross-sectional radii of gyration RXS values from 0.31 to 0.65 nm, and maximum lengths L from 3.0 to 10.0 nm. These data showed that HS has a longer and more bent structure than heparin. Constrained scattering modeling starting from 5,000 to 12,000 conformationally randomized HS structures gave best fit dp6-dp24 molecular structures that were longer and more bent than their equivalents in heparin. Alternative fits were obtained for HS dp18 and dp24, indicating their higher bending and flexibility. We conclude that HS displays bent conformations that are significantly distinct from that for heparin. The difference is attributed to the different predominant monosaccharide sequence and reduced sulfation of HS, indicating that HS may interact differently with proteins compared with heparin.

Small-angle X-ray Solution Scattering Study of the Multi-aminoacyl-tRNA Synthetase Complex Reveals an Elongated and Multi-armed particle

In animal cells, nine aminoacyl-tRNA synthetases are associated with the three auxiliary proteins p18, p38, and p43 to form a stable and conserved large multi-aminoacyl-tRNA synthetase complex (MARS), whose molecular mass has been proposed to be between 1.0 and 1.5 MDa. The complex acts as a molecular hub for coordinating protein synthesis and diverse regulatory signal pathways. Electron microscopy studies defined its low resolution molecular envelope as an overall rather compact, asymmetric triangular shape. Here, we have analyzed the composition and homogeneity of the native mammalian MARS isolated from rabbit liver and characterized its overall internal structure, size, and shape at low resolution by hydrodynamic methods and small-angle x-ray scattering in solution. Our data reveal that the MARS exhibits a much more elongated and multi-armed shape than expected from previous reports. The hydrodynamic and structural features of the MARS are large compared with other supramolecular assemblies involved in translation, including ribosome. The large dimensions and non-compact structural organization of MARS favor a large protein surface accessibility for all its components. This may be essential to allow structural rearrangements between the catalytic and cis-acting tRNA binding domains of the synthetases required for binding the bulky tRNA substrates. This non-compact architecture may also contribute to the spatiotemporal controlled release of some of its components, which participate in non-canonical functions after dissociation from the complex.

Analysis of high-affinity assembly for AMPA receptor amino-terminal domains

Analytical ultracentrifugation (AUC) and steady-state fluorescence anisotropy were used to measure the equilibrium dissociation constant (Kd) for formation of dimers by the amino-terminal domains (ATDs) of the GluA2 and GluA3 subtypes of AMPA receptor. Previous reports on GluA2 dimerization differed in their estimate of the monomer-dimer Kd by a 2,400-fold range, with no consensus on whether the ATD forms tetramers in solution. We find by sedimentation velocity (SV) analysis performed using absorbance detection a narrow range of monomer-dimer Kd values for GluA2, from 5 to 11 nM for six independent experiments, with no detectable formation of tetramers and no effect of glycosylation or the polypeptide linker connecting the ATD and ligand-binding domains; for GluA3, the monomer-dimer Kd was 5.6 µM, again with no detectable tetramer formation. For sedimentation equilibrium (SE) experiments, a wide range of Kd values was obtained for GluA2, from 13 to 284 nM, whereas for GluA3, the Kd of 3.1 µM was less than twofold different from the SV value. Analysis of cell contents after the ∼1-week centrifuge run by silver-stained gels revealed low molecular weight GluA2 breakdown products. Simulated data for SE runs demonstrate that the apparent Kd for GluA2 varies with the extent of proteolysis, leading to artificially high Kd values. SV experiments with fluorescence detection for GluA2 labeled with 5,6-carboxyfluorescein, and fluorescence anisotropy measurements for GluA2 labeled with DyLight405, yielded Kd values of 5 and 11 nM, consistent with those from SV with absorbance detection. However, the sedimentation coefficients measured by AUC using absorbance and fluorescence systems were strikingly different, and for the latter are not consistent with hydrodynamic protein models. Thus, for unknown reasons, the concentration dependence of sedimentation coefficients obtained with fluorescence detection SV may be unreliable, limiting the usefulness of this technique for quantitative analysis.

Improving the thermal, radial, and temporal accuracy of the analytical ultracentrifuge through external references

Sedimentation velocity (SV) is a method based on first principles that provides a precise hydrodynamic characterization of macromolecules in solution. Due to recent improvements in data analysis, the accuracy of experimental SV data emerges as a limiting factor in its interpretation. Our goal was to unravel the sources of experimental error and develop improved calibration procedures. We implemented the use of a Thermochron iButton temperature logger to directly measure the temperature of a spinning rotor and detected deviations that can translate into an error of as much as 10% in the sedimentation coefficient. We further designed a precision mask with equidistant markers to correct for instrumental errors in the radial calibration that were observed to span a range of 8.6%. The need for an independent time calibration emerged with use of the current data acquisition software (Zhao et al., Anal. Biochem., 437 (2013) 104–108), and we now show that smaller but significant time errors of up to 2% also occur with earlier versions. After application of these calibration corrections, the sedimentation coefficients obtained from 11 instruments displayed a significantly reduced standard deviation of approximately 0.7%. This study demonstrates the need for external calibration procedures and regular control experiments with a sedimentation coefficient standard.

Multi-Signal Sedimentation Velocity Analysis with Mass Conservation for Determining the Stoichiometry of Protein Complexes

Multi-signal sedimentation velocity analytical ultracentrifugation (MSSV) is a powerful tool for the determination of the number, stoichiometry, and hydrodynamic shape of reversible protein complexes in two- and three-component systems. In this method, the evolution of sedimentation profiles of macromolecular mixtures is recorded simultaneously using multiple absorbance and refractive index signals and globally transformed into both spectrally and diffusion-deconvoluted component sedimentation coefficient distributions. For reactions with complex lifetimes comparable to the time-scale of sedimentation, MSSV reveals the number and stoichiometry of co-existing complexes. For systems with short complex lifetimes, MSSV reveals the composition of the reaction boundary of the coupled reaction/migration process, which we show here may be used to directly determine an association constant. A prerequisite for MSSV is that the interacting components are spectrally distinguishable, which may be a result, for example, of extrinsic chromophores or of different abundances of aromatic amino acids contributing to the UV absorbance. For interacting components that are spectrally poorly resolved, here we introduce a method for additional regularization of the spectral deconvolution by exploiting approximate knowledge of the total loading concentrations. While this novel mass conservation principle does not discriminate contributions to different species, it can be effectively combined with constraints in the sedimentation coefficient range of uncomplexed species. We show in theory, computer simulations, and experiment, how mass conservation MSSV as implemented in SEDPHAT can enhance or even substitute for the spectral discrimination of components. This should broaden the applicability of MSSV to the analysis of the composition of reversible macromolecular complexes.

Hydrodynamic characterization of recombinant human fibrinogen species

IntroductionFibrinogen is a key component of the blood coagulation system and plays important, diverse roles in several relevant pathologies such as thrombosis, hemorrhage, and cancer. It is a large glycoprotein whose three-dimensional molecular structure is not fully known. Furthermore, circulating fibrinogen is highly heterogeneous, mainly due to proteolytic degradation and alternative mRNA processing. Recombinant production of human fibrinogen allows investigating the impact on the three-dimensional structure of specific changes in the primary structure. MethodsWe performed analytical ultracentrifugation analyses of a full-length recombinant human fibrinogen, its counterpart purified from human plasma, and a recombinant human fibrinogen with both Aα chains truncated at amino acid 251, thus missing their last 359 amino acid residues. ResultsWe have accurately determined the translational diffusion and sedimentation coefficients (Dt(20,w)0, s(20,w)0) of all three species. This was confirmed by derived molecular weights within 1% for the full length species, and 5% for the truncated species, as assessed by comparison with SDS-PAGE/Western blot analyses and primary structure data. No significant differences in the values of Dt(20,w)0 and s(20,w)0 were found between the recombinant and purified full length human fibrinogens, while slightly lower and higher values, respectively, resulted for the recombinant truncated human fibrinogen compared to a previously characterized purified human fibrinogen fragment X obtained by plasmin digestion. ConclusionsFull-length recombinant fibrinogen is less polydisperse but hydrodynamically indistinguishable from its counterpart purified from human plasma. Recombinant Aα251-truncated human fibrinogen instead behaves differently from fragment X, suggesting a role for the Bβ residues 1–52 in inter-molecular interactions. Overall, these new hydrodynamic data will constitute a reliable benchmark against which models of fibrinogen species could be compared.

An analytical ultracentrifugation based study on the conformation of lambda carrageenan in aqueous solution

The conformation and heterogeneity of lambda-carrageenan, a sulphonated galactan from red seaweed, solubilised in aqueous solvent with the assistance of microwave irradiation, has been assessed by a combination of analytical ultracentrifugation, size-exclusion chromatography, light scattering and capillary viscometry. Preparations appeared generally unimodal on the basis of sedimentation coefficient distributions from sedimentation velocity although at the highest concentrations a shoulder appears with a sedimentation coefficient approximately 1.1 times greater than that of the main component. Even under conditions commensurate with charge suppression simple linear regression was insufficient to represent non-ideal concentration dependence and the extraction of the Grálen concentration dependence parameter ks. A more general fitting algorithm was therefore employed. Mark-Houwink-Kuhn-Sakurada analysis of the change in intrinsic viscosity [η] with molecular weight, together with the Wales-van Holde ratio (combination of ks with [η]) point to an extended flexible conformation for lambda-carrageenan in the (weight average) molecular weight range Mw=340,000-870,000g/mol. The origin of the larger sedimentation coefficient component appearing at the higher concentrations is considered.

Analysis of the River Flow and Sediment Concentration Change before and after Wenchuan Earthquake

Wenchuan earthquake triggered floods, landslide, collapse and secondary geological disaster,trigger a new soil and water loss, having the significant influence to the local river water quality.According to shaba and jiangyou station 2006 January to 2011 December flow and sediment concentration data for statistical analysis, this paper discusses the disaster area river water and sediment changes on the influence of river water quality before and after the earthquake. Results show that,the monthly average flow change trend does not take place obvious change before and after the earthquake,during the earthquake the monthly average sediment concentration is higher than any other in the same period of monthly average sediment concentration,jiangyou station and shaba station the average daily flow rate on May has no obvious change before and after earthquake, the earthquake for different regional influence is different , different regions of different section of the average sediment coefficient has certain space diversity,in jiangyou station the average sediment coefficient before the earthquake is more than the average sediment coefficient after the earthquake but the change of average sediment coefficient in shaba station was not significant before and after the earthquake.

Size and density measurement of core–shell Si nanoparticles by analytical ultracentrifugation

Si nanocrystals, terminated with cyclohexane and allylamine, were analyzed using analytical ultracentrifugation (AUC), dynamic light scattering (DLS) and transmission electron microscopy. We found that AUC yielded equivalent particle size distribution data to other nanoparticle characterization techniques, while also providing important information not probed by techniques such as DLS regarding the relative size of the particle core and shell components and the overall effective particle density. Estimates of particle core and shell dimensions are consistent with the particle’s optical properties within the quantum confinement representation and available theoretical Si nanocrystal models. Measurement of sedimentation velocity in several solvents with different densities presents a way to circumvent the ambiguity of simultaneous fitting of particle density and sedimentation coefficient and allows us to significantly reduce the uncertainty in the estimates of particle hydrodynamic diameter by finding the effective particle density value.

Analytical ultracentrifugation studies of oligomerization and DNA-binding of TtCarH, a Thermus thermophilus coenzyme B12-based photosensory regulator

Thermus thermophilus transcriptional factor TtCarH belongs to a newly discovered class of photoreceptors that use 5'-deoxyadenosylcobalamin (AdoB12) as the light-sensing chromophore. Photoregulation relies on the repressor activity of AdoB12-bound oligomers in the dark, which light counteracts by oligomer disruption due to AdoB12 photolysis. In this study, we investigated TtCarH self-association and binding to DNA in the dark and in the light using analytical ultracentrifugation (AUC) methods, both sedimentation velocity (SV) as well as equilibrium (SE). From a methodological point of view, this study shows that AUC can provide hydrodynamic insights in cases where light is a crucial determinant of solution properties. For the light-sensitive TtCarH, absorbance as well as interference AUC data yielded comparable results. Sedimentation coefficients and whole-body hydrodynamic analysis from SV experiments indicate that in solution apo-TtCarH and light-exposed AdoB12-TtCarH are predominantly aspherical, ellipsoidal monomers, in accord with SE data. By comparison, AdoB12-TtCarH exists as a more compact tetramer in the dark, with smaller forms such as dimers or monomers remaining undetected and low levels of larger oligomers appearing at higher protein concentrations. AUC analyses indicate that in the dark AdoB12-TtCarH associates as a tetramer with DNA but forms smaller complexes in the apo form or if exposed to light. The self-association and DNA-binding properties of TtCarH deduced from AUC are consistent with data from size-exclusion and DNA-binding gel-shift assays. AUC analyses together with hydrodynamic modeling provide insights into the AdoB12- and light-dependent self-association and DNA-binding of TtCarH.

Are fluorescence-detected sedimentation velocity data reliable?

Sedimentation velocity analytical ultracentrifugation is a classical biophysical technique that is commonly used to analyze the size, shape, and interactions of biological macromolecules in solution. Fluorescence detection provides enhanced sensitivity and selectivity relative to the standard absorption and refractrometric detectors, but data acquisition is more complex and can be subject to interference from several photophysical effects. Here, we describe methods to configure sedimentation velocity measurements using fluorescence detection and evaluate the performance of the fluorescence optical system. The fluorescence detector output is linear over a concentration range of at least 1 to 500nM fluorescein and Alexa Fluor 488. At high concentrations, deviations from linearity can be attributed to the inner filter effect. A duplex DNA labeled with Alexa Fluor 488 was used as a standard to compare sedimentation coefficients obtained using fluorescence and absorbance detectors. Within error, the sedimentation coefficients agree. Thus, the fluorescence detector is capable of providing precise and accurate sedimentation velocity results that are consistent with measurements performed using conventional absorption optics, provided the data are collected at appropriate sample concentrations and the optics are configured correctly.

Analytical ultracentrifugation as a tool for studying protein interactions

The last two decades have led to significant progress in the field of analytical ultracentrifugation driven by instrumental, theoretical, and computational methods. This review will highlight key developments in sedimentation equilibrium (SE) and sedimentation velocity (SV) analysis. For SE, this includes the analysis of tracer sedimentation equilibrium at high concentrations with strong thermodynamic non-ideality, and for ideally interacting systems the development of strategies for the analysis of heterogeneous interactions towards global multi-signal and multi-speed SE analysis with implicit mass conservation. For SV, this includes the development and applications of numerical solutions of the Lamm equation, noise decomposition techniques enabling direct boundary fitting, diffusion deconvoluted sedimentation coefficient distributions, and multi-signal sedimentation coefficient distributions. Recently, effective particle theory has uncovered simple physical rules for the co-migration of rapidly exchanging systems of interacting components in SV. This has opened new possibilities for the robust interpretation of the boundary patterns of heterogeneous interacting systems. Together, these SE and SV techniques have led to new approaches to study macromolecular interactions across the entire the spectrum of affinities, including both attractive and repulsive interactions, in both dilute and highly concentrated solutions, which can be applied to single-component solutions of self-associating proteins as well as the study of multi-protein complex formation in multi-component solutions.

Recorded scan times can limit the accuracy of sedimentation coefficients in analytical ultracentrifugation

We report systematic and large inaccuracies in the recorded elapsed time in data files from the analytical ultracentrifuge, leading to overestimates of the sedimentation coefficients of up to 10%. This far exceeds previously considered factors contributing to the uncertainty in this parameter and has significant ramifications for derived parameters such as hydrodynamic shape and molar mass estimates. The source of this error is currently unknown, but we found it to be quantitatively consistent across different instruments, increasing with rotor speed. Furthermore, its occurrence appears to correlate with the use of the latest data acquisition software from the manufacturer, in use in some of our laboratories for nearly 2years. Many of the recently published sedimentation coefficients may need to be reexamined. The problem can be easily recognized by comparing the file timestamps provided by the operating system with the elapsed scan times recorded within the data files. Therefore, we implemented a routine in SEDFIT that can automatically examine the data files, alert the user to significant discrepancies, and correct the scan times accordingly. This eliminates errors in the recorded scan times.

Prediction of Hydrodynamic and Other Solution Properties of Partially Disordered Proteins with a Simple, Coarse-Grained Model.

The possibility of validating structures of intrinsically disordered proteins against solution properties is a goal that would be most helpful in the understanding of their function. We have devised a scheme for the prediction of solution properties of partially disordered proteins that comprise one or more ordered domains, along with flexible tails or linkers. A very simple, coarse-grained, residue-level model, which is easily parametrized using available structural information, along with previously developed tools for the simulation of solution conformation and dynamics, allows the prediction of properties like sedimentation coefficients, relaxation times, and X-ray or neutron scattering. This is demonstrated for a variety of partially disordered proteins, for which well-characterized solution properties are very accurately evaluated, with predictions falling in most cases within experimental errors.