Sedimentation equilibrium analysis of interference optical data by systematic noise decomposition.

An analytical method is described for removal of systematic signal offsets from interference optical data of sedimentation equilibrium gradients. It is demonstrated that the time-invariant signal contributions can be extracted from hydrodynamic modeling of interference profiles acquired during the approach to sedimentation equilibrium. This method is based on a technique for the explicit algebraic calculation of time-invariant noise components from sedimentation data, recently described for the direct modeling of sedimentation velocity experiments (P. Schuck and B. Demeler, Biophys. J. 76, 2288-2296, 1999). The calculated systematic signal offset is very well defined by the experimental data, stable over time, and its calculation is robust and to a large extent independent of the hydrodynamic model. The calculated time-invariant signal can be used to reduce the systematic errors in the measured sedimentation equilibrium profiles by more than an order of magnitude. It is shown that the resulting net equilibrium fringe profiles after subtraction of the time-invariant noise component allow equilibrium analyses consistent with those obtained from absorbance profiles. However, due to a higher dynamic range and the higher number of data points, the parameters derived from the net interference analysis can exhibit significantly improved precision. The presented study demonstrates the feasibility and potential of this analytical method for full exploitation of the remarkable precision of the interference optical data acquisition system, allowing sedimentation equilibrium experiments at loading concentrations below 0.05 mg/ml.     

Size-distribution analysis of proteins by analytical ultracentrifugation: strategies and application to model systems.

Strategies for the deconvolution of diffusion in the determination of size-distributions from sedimentation velocity experiments were examined and developed. On the basis of four different model systems, we studied the differential apparent sedimentation coefficient distributions by the time-derivative method, g(s*), and by least-squares direct boundary modeling, ls-g*(s), the integral sedimentation coefficient distribution by the van Holde-Weischet method, G(s), and the previously introduced differential distribution of Lamm equation solutions, c(s). It is shown that the least-squares approach ls-g*(s) can be extrapolated to infinite time by considering area divisions analogous to boundary divisions in the van Holde-Weischet method, thus allowing the transformation of interference optical data into an integral sedimentation coefficient distribution G(s). However, despite the model-free approach of G(s), for the systems considered, the direct boundary modeling with a distribution of Lamm equation solutions c(s) exhibited the highest resolution and sensitivity. The c(s) approach requires an estimate for the size-dependent diffusion coefficients D(s), which is usually incorporated in the form of a weight-average frictional ratio of all species, or in the form of prior knowledge of the molar mass of the main species. We studied the influence of the weight-average frictional ratio on the quality of the fit, and found that it is well-determined by the data. As a direct boundary model, the calculated c(s) distribution can be combined with a nonlinear regression to optimize distribution parameters, such as the exact meniscus position, and the weight-average frictional ratio. Although c(s) is computationally the most complex, it has the potential for the highest resolution and sensitivity of the methods described.     

Determination of the parameters of self-association by direct fitting of the omega function

Nonlinear regression is used to fit the omega function vs. protein concentration curves (first described by B.K. Milthorpe, P.D. Jeffrey and L.W. Nichol, Biophys. Chem. 3 (1975) 169) obtained from sedimentation equilibrium experiments on self-associating macromolecules. Nonlinear regression allows the direct fit of these curves with discrete or indefinite self-association reaction models in order to obtain values for the equilibrium constants and second virial coefficient. The method is independent of the choice of reference concentration and avoids the original method of extrapolating an omega function curve to zero concentration and then using the extrapolated value to construct a monomer activity curve used for analysis. This extrapolation can become very difficult for mild to strong self-associations where incorrectly extrapolated values lead to systematic error in the monomer activity curves. The method is applied to results from a mild, indefinite self-association, exemplified by the self-association of human spectrin, and to computer-simulated data of weak, mild and strong, indefinite self-associations.     

The stiffness of dsRNA: hydrodynamic studies on fluorescence-labelled RNA segments of bovine rotavirus.

The sedimentation coefficients of dsRNA segments of bovine rotavirus were determined in the analytical ultracentrifuge. The eleven segments were separated by preparative gel electrophoresis, and isolated by elution from gel pieces. The RNA was labelled by the intercalating fluorescent dye ethidium bromide at a ratio bound dye per base pair between 0.003 to 0.018. The analytical ultracentrifuge was equipped with a fluorescence recording optics. Sedimentation coefficients could be determined with amounts of RNA as little as 8 ng. All sedimentation coefficients were extrapolated to zero-concentration, zero-dye binding, and zero-impurities from the preparative gel electrophoresis. The hydrodynamic model of flexible cylinders was applied for the interpretation of the sedimentation coefficients. All dsRNA segments of rotavirus (663-3409 base pairs) and the dsRNA5 of cucumber mosaic virus (335 base pairs) fit the model of a "worm-like" or flexible cylinder with a persistence length of 1125 A and a hydrated diameter of 30 A. The results are compared with data from the literature on the persistence lengths of the B- and Z-forms of dsDNA and of viroids.     

Size-distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and lamm equation modeling

A new method for the size-distribution analysis of polymers by sedimentation velocity analytical ultracentrifugation is described. It exploits the ability of Lamm equation modeling to discriminate between the spreading of the sedimentation boundary arising from sample heterogeneity and from diffusion. Finite element solutions of the Lamm equation for a large number of discrete noninteracting species are combined with maximum entropy regularization to represent a continuous size-distribution. As in the program CONTIN, the parameter governing the regularization constraint is adjusted by variance analysis to a predefined confidence level. Estimates of the partial specific volume and the frictional ratio of the macromolecules are used to calculate the diffusion coefficients, resulting in relatively high-resolution sedimentation coefficient distributions c(s) or molar mass distributions c(M). It can be applied to interference optical data that exhibit systematic noise components, and it does not require solution or solvent plateaus to be established. More details on the size-distribution can be obtained than from van Holde-Weischet analysis. The sensitivity to the values of the regularization parameter and to the shape parameters is explored with the help of simulated sedimentation data of discrete and continuous model size distributions, and by applications to experimental data of continuous and discrete protein mixtures.     

Unbiased estimates of the number of nucleotide substitutions when substitution rate varies among different sites

When the number of nucleotides examined is relatively small, the estimators of nucleotide substitutions between DNA sequences often introduce systematic error even if the data used fit the mathematical model underlying the estimation formula. The systematic error of this kind is especially large for models that allow variation in substitution rate among different sites. In the present paper we present a number of formulas that produce virtually bias-free estimates of evolutionary distances for these models. Correspondence to: M. Nei     

Spatial conservation priorities are highly sensitive to choice of biodiversity surrogates and species distribution model type

Pressure to conserve biodiversity with limited resources has led to increasing use of species distribution models (SDMs) for spatial conservation prioritization. Published spatial prioritization exercises often focus on well‐studied groups, with data compiled from on‐line databases of ad‐hoc collections. Conservation plans generally aim to protect all components of biodiversity, and it is implied that the species used in prioritization act as surrogates. Here, we assess the sensitivity of spatial priorities to model and surrogate choice using a case study from a fragmented agricultural area of south eastern Australia that is poorly represented in the national reserve system. We model the distributions of 30 species of bird, microbat and bee using two types of SDM; generalised linear models based on systematic surveys that yield presence and absence observations, and MaxEnt models based on biodiversity database records. Eight prioritization scenarios were tested using Zonation software, and were based on either the presence–background or presence–absence SDMs and combinations of surrogacy among the three taxa. We found low correlations between SDMs generated for the same species using different modelling frameworks (μ = 0.18, n = 26). Area under the receiver operating characteristic curve (AUC) estimates generated by MaxEnt were optimistic; on average 1.36 times higher than when tested against the systematic survey data. Conservation priorities were sensitive to the choice of surrogate and type of data used to fit SDMs, and though bats and birds formed moderately good surrogates for each other, there was less compelling evidence of surrogacy for bees. Because valid surrogacy is unlikely with most existing data sets, investment in high quality data for less‐surveyed groups prior to planning should still be a priority. If this is not possible, then it is advisable to analyse the sensitivity of conservation plans to the assumed surrogacy and quality of data available.     

Analysis of time-resolved fluorescence anisotropy decays.

We discuss the analysis of time-correlated single photon counting measurements of fluorescence anisotropy. Particular attention was paid to the statistical properties of the data. The methods used previously to analyze these experiments were examined and a new method was proposed in which parallel- and perpendicular-polarized fluorescence curves were fit simultaneously. The new method takes full advantage of the statistical properties of the measured curves; and, in some cases, it is shown to be more sensitive than other methods to systematic errors present in the data. Examples were presented using experimental and simulated data. The influence of fitting range on extracted parameters and statistical criteria for evaluating the quality of fits are also discussed.     

Forage quality and the costs of lactation for female gelada baboons

Field studies of two species of baboons suggest that Altmann's model of maternal time budgets (1980, Baboon Mothers and Infants, Cambridge, Massachusetts: Harvard University Press) provides a good qualitative but a poor quantitative fit to observed changes in the time that mothers spend feeding across infant age. We suggest that the poor quantitative fit might be explained by the fact that food quality varies across time, so that females are forced to feed for longer to gain the same nutrient intake when quality is poor. The hypothesis was tested with data from both gelada baboons,Theropithecus gelada , and Altmann's own baboons, Papio cynocephalus, with rainfall and ambient temperature as indices of vegetation nutritional quality. The results confirm that a three-factor model incorporating infant age, rainfall in the 2 preceding months and current ambient temperature provides a significantly improved fit to the observed data. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

Development and field validation of a regional,management‐scale habitat model: A koala Phascolarctos cinereus case study

Species distribution models have great potential to efficiently guide management for threatened species, especially for those that are rare or cryptic. We used MaxEnt to develop a regional‐scale model for the koala Phascolarctos cinereus at a resolution (250 m) that could be used to guide management. To ensure the model was fit for purpose, we placed emphasis on validating the model using independently‐collected field data. We reduced substantial spatial clustering of records in coastal urban areas using a 2‐km spatial filter and by modeling separately two subregions separated by the 500‐m elevational contour. A bias file was prepared that accounted for variable survey effort. Frequency of wildfire, soil type, floristics and elevation had the highest relative contribution to the model, while a number of other variables made minor contributions. The model was effective in discriminating different habitat suitability classes when compared with koala records not used in modeling. We validated the MaxEnt model at 65 ground‐truth sites using independent data on koala occupancy (acoustic sampling) and habitat quality (browse tree availability). Koala bellows (n = 276) were analyzed in an occupancy modeling framework, while site habitat quality was indexed based on browse trees. Field validation demonstrated a linear increase in koala occupancy with higher modeled habitat suitability at ground‐truth sites. Similarly, a site habitat quality index at ground‐truth sites was correlated positively with modeled habitat suitability. The MaxEnt model provided a better fit to estimated koala occupancy than the site‐based habitat quality index, probably because many variables were considered simultaneously by the model rather than just browse species. The positive relationship of the model with both site occupancy and habitat quality indicates that the model is fit for application at relevant management scales. Field‐validated models of similar resolution would assist in guiding management of conservation‐dependent species.     

Analyses of sedimentation equilibrium data

A numerical procedure is presented which can quite adequately compute the molecular weight averages as a function of solute concentration from sedimentation equilibrium data for homogeneous systems and for monomer-dimer associating systems with a possible extension to heterogeneous systems where monotonic variation in the weight average molecular weight is observed such as in weakly associating or dissociating systems. The procedure utilizes the method of orthogonal polynomials for curve fitting which allows for a rapid determination of best fit with minimal round off error. The procedure is particularly applicable in cases where the concentration of solute at the meniscus can be considered to be neither appreciable and reasonably well determined as in low speed sedimentation equilibrium experiments, nor essentially zero as in high speed sedimentation equilibrium experiments where the calculations become somewhat more simplified. The use of moderate speed sedimentation equilibrium has the advantage of providing a more broad concentration distribution in the centrifuge cell which yields more extensive information concerning dissociating systems yet still provides results at low solute concentrations where most solutes can be considered to be behaving ideally.     

Application of calculated sedimentation ratios in the specification of models for protein dimers, trimers, tetramers and pentamers

In the preceding paper a systematic method for delineating quaternary structures compatible with the sedimentation behaviour of oligomeric assemblies was developed. In this companion paper the approach is illustrated by its application to a number of oligomeric proteins, namely beta-lactoglobulin, aminoacyl transferase, succinic semialdehyde dehydrogenase, arginine decarboxylase, and the arthropod hemocyanins. Structures of these proteins based on comparisons of calculated and experimental sedimentation coefficients are presented and, wherever possible, compared with those obtained by other techniques. The usefulness and limitations of the method are assessed. It is concluded that the sedimentation analysis will usually yield a reasonably good representation of the mode of assembly of protein molecules in oligomeric structures if accurate experimental data are available. A high degree of resolution of structural detail is not expected and since, in addition, the sedimentation ratio method is seldom definitive to one structure, it is most valuable when used in a conformatory or eliminative way with results from techniques more specifically designed for structure determination.     

Analysis of lambing distribution in the Ripollesa sheep breed. I. Development and comparison of circular von Mises models

Circular data originates in a wide range of scientific fields and can be analyzed on the basis of directional statistics and special distributions wrapped around the circumference. However, both propensity to transform non-linear to linear data and complexity of directional statistics limited the generalization of the circular paradigm in the animal breeding framework, among others. Here, we generalized a circular mixed (CM) model within the context of Bayesian inference. Three different parametrizations with different hierarchical structures were developed on basis of the von Mises distribution; moreover, both goodness of fit and predictive ability from each parametrization were compared through the analyses of 110 116 lambing distribution records collected from Ripollesa sheep herds between 1976 and 2017. The naive circular (NC) model only accounted for population mean and homogeneous circular variance, and reached the lowest goodness-of-fit and predictive ability. The CM model assumed a hierarchical structure for the population mean by accounting for systematic (ewe age and lambing interval) and permanent environmental sources of variation (flock-year-season and ewe). This improved goodness of fit by reducing both the deviance information criterion (DIC; −2520 units) and the mean square error (MSE; −12.4%) between simulated and predicted lambing data when compared against the NC model. Finally, the last parametrization expanded CM model by also assuming a hierarchical structure with systematic and permanent environmental factors for the variance parameter of the von Mises distribution (i.e. circular canalization (CC) model). This last model reached the best goodness of fit to lambing distribution data with a DIC estimate 5425 units lower than the one for NC model (MSE reduced 13.2%). The same pattern revealed when models were compared in terms of predictive ability. The superiority revealed by CC model emphasized the relevance of heteroskedasticity for the analysis of lambing distribution in the Ripollesa breed, and suggested potential applications for the sheep industry, even genetic selection for canalization. The development of CM models on the basis of the von Mises distribution has allowed to integrate flexible hierarchical structures accounting for different sources of variation and affecting both mean and dispersion terms. This must be viewed as a useful statistical tool with multiple applications in a wide range of research fields, as well as the livestock industry. The next mandatory step should be the inclusion of genetic terms in the hierarchical structure of the models in order to evaluate their potential contribution to current selection programs.     

The association behaviour of beta-lactamases. Sedimentation equilibrium studies in ammonium sulphate solutions.

The beta-lactamases (EC 3.5.2.6) from TEM plasmid RP4, Bacillus licheniformis 749/C and Enterobacter cloacae P99 were studied in solution over a wide concentration range by equilibrium sedimentation. Though crystal symmetries indicate that all three enzymes are potentially dimeric in their crystal forms, in 50 mM-sodium cacodylate at pH 6.5 the enzymes show only a small tendency to associate, indicated by a weight-average Mr (Mw) at 3% (w/v) concentration about 9% greater than that of the monomer. Although the mode of association could not be determined, this extent of association corresponded to a dimerization constant of about 2 X 10(2) M-1. In 2.1 M-(NH4)2SO4 the B. licheniformis enzyme shows some association at concentrations over 1%, displaying an Mw value at 7% concentration about 60% more than the monomer. Under the same conditions Mw for the Entero. P99 enzyme is about 60% greater than the monomer near the solubility limit of about 2%. However, the Mw for the TEM enzyme is over twice that of the monomer at its solubility limit (3%) in 1.7 M-(NH4)2SO4. Fitting the sedimentation data of the TEM enzyme in 1.7 M-(NH4)2SO4 with a dimerization model and an indefinite-isodesmic-association model yielded equilibrium constants of 1.5 X 10(4) and 3.3 X 10(2) M-1 respectively, with the indefinite-isodesmic model giving the better fit. Fitting the data for the other two enzymes yielded values of 1.4 X 10(3) and 1.7 X 10(2) M-1 respectively for the Entero. P99 enzyme and 4.5 X 10(2) and 45 M-1 respectively for the B. licheniformis enzyme. It could not be determined which model was the better fit for these two enzymes. Since none of the beta-lactamases studied here showed strong evidence of the terminal aggregate being a dimer, we conclude that crystalline dimers, if they exist, will not be tightly associated or physiologically significant.     

An approach to the isolation of biological particles using sedimentation analysis

A systematic, general approach for the design of an initial purification procedure for any biological particle is described in this communication. A series of centrifugations in fixed angle rotors has been used to obtain information on the sedimentation behavior of particles of interest (Anderson, N.G. (1967) Anal. Biochem. 23, 72-83). Refinements of this technique have facilitated the determination of sedimentation profiles of subcellular organelle markers in suspensions of murine spleen and brain. The degree of homogeneity of several particles with respect to size can be ascertained from the sedimentation profiles. Alterations in these profiles after mechanical disruption and treatment with detergents are readily measurable and have been found to be useful in both the characterization and isolation of subcellular particles. Because fixed angle rotors are used in these studies, the data obtained can be directly applied to the development of a preparatory scheme for purification of a desired particle. These methods for sedimentation analysis are readily applicable to subcellular organelles, macromolecular complexes, viruses, viral-like agents, and a variety of macromolecules.     

A data-integration approach to correct sampling bias in species distribution models using multiple datasets of breeding birds in the Swiss Alps

It is essential to accurately model species distributions and biodiversity in response to many ecological and conservation challenges. The primary means of reliable decision-making on conservation priority are the data on the distributions and abundance of species. However, finding data that is accurate and reliable for predicting species distribution could be challenging. Data could come from different sources, with different designs, coverage, and potential sampling biases. In this study, we examined the emerging methods of modelling species distribution that integrate data from multiple sources such as systematic or standardized and casual or occasional surveys. We applied two modelling approaches, “data-pooling” and “ model-based data integration” that each involves combining various datasets to measure environmental interactions and clarify the distribution of species. Our paper demonstrates a reliable data integration workflow that includes gathering information on model-based data integration, creating a sub-model of each dataset independently, and finally, combining it into a single final model. We have shown that this is a more reliable way of developing a model than a data pooling strategy that combines multiple data sources to fit a single model. Moreover, data integration approaches could improve the poor predictive performance of systematic small datasets, through model-based data integration techniques that enhance the predictive accuracy of Species Distribution Models. We also identified, consistent with previous research, that machine learning algorithms are the most accurate techniques to predict bird species distribution in our heterogeneous study area in the western Swiss Alps. In particular, tree-dependent ensembles of Random Forest (RF) contribute to a better understanding of the interactions between species and the environment.     

Reversible self-association of recombinant bovine factor B

The recombinant bovine factor B, obtained by a newly developed bacterial expression system, was found to exhibit features characteristic of a reversible self-associating system. Using size-sieving chromatography, distribution of the factor B species ranged from a monomer to a trimer, but not oligomers of higher molecular weights. At high protein concentrations, factor B migrated as a single band in a native gel. Cross-linking with the amino-reactive cross-linking reagent bis (sulfosuccinimidyl) suberate (BS), at a low cross-linker to protein ratio yielded cross-linked products identified as factor B dimer and trimer. The cross-linking pattern was shown to be a function of the protein and cross-linker concentrations. The range of sedimentation coefficients in a sedimentation velocity experiment suggested that the largest particle present in the distribution was more than twice as large as the smallest. The data obtained under multiple conditions in the sedimentation equilibrium experiments are best fit to a model describing a reversible self-association of a monomer-trimer of factor B species, with a dissociation constant Kd(1,3)=2.48x10(-10) M(2).     

Vincristine-induced self-association of calf brain tubulin

The vincristine-induced self-association of tubulin has been examined in a sedimentation velocity study as a function of free drug concentration in PG buffer (0.01 M NaPi and 10(-4) M GTP, pH 7.0) at 20 degrees C. Analysis of the weight-average sedimentation coefficient (S20,w) as a function of protein concentration showed a good fit with the model of an indefinite, isodesmic self-association mechanism. Analysis of the apparent association constants in terms of the Wyman linkage relations showed a good fit to mediation of the self-association by the binding of one ligand molecule. The intrinsic association constant for dimerization of the vincristine-liganded tubulin was found to be 3.8 X 10(5) M-1, and the intrinsic equilibrium constant for the binding of the self-association-linked vincristine molecule had a value of 3.5 X 10(4) M-1, consistent with that measured by fluorescence in our laboratory [Prakash, V., & Timasheff, S. N. (1983) J. Biol. Chem. 258, 1689-1697]. Both reactions are stronger in the presence of vincristine than of vinblastine, reflecting the oxidation of a -CH3 group to -CHO when going from the latter drug to the former one.     

Statistical estimation of gene expression using multiple laser scans of microarrays

We propose a statistical model for estimating gene expression using data from multiple laser scans at different settings of hybridized microarrays. A functional regression model is used, based on a non-linear relationship with both additive and multiplicative error terms. The function is derived as the expected value of a pixel, given that values are censored at 65 535, the maximum detectable intensity for double precision scanning software. Maximum likelihood estimation based on a Cauchy distribution is used to fit the model, which is able to estimate gene expressions taking account of outliers and the systematic bias caused by signal censoring of highly expressed genes. We have applied the method to experimental data. Simulation studies suggest that the model can estimate the true gene expression with negligible bias. AVAILABILITY: FORTRAN 90 code for implementing the method can be obtained from the authors.