Limiting the sedimentation coefficient for sedimentation velocity data analysis: partial boundary modeling and g(s) approaches revisited

Brown and coworkers (Eur. Biophys. J. 38 (2009) 1079–1099) introduced partial boundary modeling (PBM) to simplify sedimentation velocity data analysis by excluding species outside the range of interest (e.g., aggregates, impurities) via restricting the sedimentation coefficient range being fitted. They strongly criticized the alternate approach of fitting g(s^∗) distributions using similar range limits, arguing that (i) it produces “nonoptimal fits in the original data space” and (ii) the g(s^∗) data transformations lead to gross underestimates of the parameter confidence intervals. It is shown here that neither of those criticisms is valid. These two approaches are not truly fitting the same data or in equivalent ways; thus, they should not actually give the same best-fit parameters. The confidence limits for g(s^∗) fits derived using F statistics, bootstrap, or a new Monte Carlo algorithm are in good agreement and show no evidence for significant statistical distortion. Here 15 g(s^∗) measurements on monoclonal antibody samples gave monomer mass estimates with experimental standard deviations of less than 1%, close to the confidence limit estimates. Tests on both real and simulated data help to clarify the strengths and drawbacks of both approaches. New algorithms for computing g(s^∗) and a scan-differencing approach for PBM are introduced.     

A histogram approach to the quality of fit in sedimentation velocity analyses

The quality of fit of sedimentation velocity data is critical to judge the veracity of the sedimentation model and accuracy of the derived macromolecular parameters. Absolute statistical measures are usually complicated by the presence of characteristic systematic errors and run-to-run variation in the stochastic noise of data acquisition. We present a new graphical approach to visualize systematic deviations between data and model in the form of a histogram of residuals. In comparison with the ideally expected Gaussian distribution, it can provide a robust measure of fit quality and be used to flag poor models.     

Precision of protein aggregation measurements by sedimentation velocity analytical ultracentrifugation in biopharmaceutical applications

Sedimentation velocity analytical ultracentrifugation (SV-AUC) is routinely applied in biopharmaceutical development to measure levels of protein aggregation in protein products. SV-AUC is free from many limitations intrinsic to size exclusion chromatography (SEC) such as mobile phase and column interaction effects on protein self-association. Despite these clear advantages, SV-AUC exhibits lower precision measurements than corresponding measurements by SEC. The precision of SV-AUC is influenced by numerous factors, including sample characteristics, cell alignment, centerpiece quality, and data analysis approaches. In this study, we evaluate the precision of SV-AUC in its current practice utilizing a multilaboratory, multiproduct intermediate precision study. We then explore experimental approaches to improve SV-AUC measurement precision, with emphasis on utilization of high quality centerpieces.     

Measuring low levels of protein aggregation by sedimentation velocity

The required performance of an analytical method depends on the purpose for which it will be used. As a methodology matures, it may find new application, and the performance demands placed on the method can increase. Sedimentation velocity analytical ultracentrifugation (SV-AUC) has a long and distinguished history with important contributions to molecular biology. Now the technique is transitioning into industrial settings, and among them, SV-AUC is now used to quantify the amount of protein aggregation in biopharmaceutical protein products, often at levels less than 1% of the total protein mass. In this paper, we review recent advances to SV methodology which have been shown to improve quantitation of protein aggregation. Then we discuss the performance of the SV method in its current state, with emphasis on the precision and quantitation limit of the method, in the context of existing industrial guidance on analytical method performance targets for quantitative methods.     

The use of analytical sedimentation velocity to extract thermodynamic linkage

For 25 years, the Gibbs Conference on Biothermodynamics has focused on the use of thermodynamics to extract information about the mechanism and regulation of biological processes. This includes the determination of equilibrium constants for macromolecular interactions by high precision physical measurements. These approaches further reveal thermodynamic linkages to ligand binding events. Analytical ultracentrifugation has been a fundamental technique in the determination of macromolecular reaction stoichiometry and energetics for 85 years. This approach is highly amenable to the extraction of thermodynamic couplings to small molecule binding in the overall reaction pathway. In the 1980s this approach was extended to the use of sedimentation velocity techniques, primarily by the analysis of tubulin-drug interactions by Na and Timasheff. This transport method necessarily incorporates the complexity of both hydrodynamic and thermodynamic nonideality. The advent of modern computational methods in the last 20 years has subsequently made the analysis of sedimentation velocity data for interacting systems more robust and rigorous. Here we review three examples where sedimentation velocity has been useful at extracting thermodynamic information about reaction stoichiometry and energetics. Approaches to extract linkage to small molecule binding and the influence of hydrodynamic nonideality are emphasized. These methods are shown to also apply to the collection of fluorescence data with the new Aviv FDS.     

Determination of protein complex stoichiometry through multisignal sedimentation velocity experiments

Determination of the stoichiometry of macromolecular assemblies is fundamental to an understanding of how they function. Many different biophysical methodologies may be used to determine stoichiometry. In the past, both sedimentation equilibrium and sedimentation velocity analytical ultracentrifugation have been employed to determine component stoichiometries. Recently, a method of globally analyzing multisignal sedimentation velocity data was introduced by Schuck and coworkers. This global analysis removes some of the experimental inconveniences and inaccuracies that could occur in the previously used strategies. This method uses spectral differences between the macromolecular components to decompose the well-known c(s) distribution into component distributions c_k(s); that is, each component k has its own c_k(s) distribution. Integration of these distributions allows the calculation of the populations of each component in cosedimenting complexes, yielding their stoichiometry. In our laboratories, we have used this method extensively to determine the component stoichiometries of several protein-protein complexes involved in cytoskeletal remodeling, sugar metabolism, and host-pathogen interactions. The overall method is described in detail in this work, as are experimental examples and caveats.     

MSTARA and MSTARI: interactive PC algorithms for simple, model independent evaluation of sedimentation equilibrium data

This paper describes a program available for PC's for the evaluation of molecular weights from sedimentation equilibrium. This program, in its two forms – MSTARA for absorption optical records and MSTARI for interference optical records – requires no prior assumption of the nature of the system (ideal, non-ideal, monodisperse, polydisperse, self-associating etc.) and takes into consideration the whole solute distribution (i.e. from solution meniscus to cell base) in the ultracentrifuge cell rather than just a selected data-set. MSTARA or MSTARI are therefore recommended as a first analysis programme of sedimentation equilibrium data coming off an absorption or interference based analytical ultracentrifuge. These programmes are therefore particularly well suited if heterogeneity (polydispersity or interaction phenomena) or non-ideality is suspected. Their use is demonstrated for a series of data-set types (ideal, non-ideal, polydisperse and self-associating). Although MSTARA and MSTARI are model independent, they provide the basis for more detailed analysis of interactions, polydisperse distributions or non-ideality via easy export of ASCII datafiles to model dependent routines. Received: 4 November 1996 / Accepted: 15 November 1996     

Evaluating the stoichiometry of macromolecular complexes using multisignal sedimentation velocity

Gleaning information regarding the molecular physiology of macromolecular complexes requires knowledge of their component stoichiometries. In this work, a relatively new means of analyzing sedimentation velocity (SV) data from the analytical ultracentrifuge is examined in detail. The method depends on collecting concentration profile data simultaneously using multiple signals, like Rayleigh interferometry and UV spectrophotometry. If the cosedimenting components of a complex are spectrally distinguishable, continuous sedimentation-coefficient distributions specific for each component can be calculated to reveal the molar ratio of the complex's components. When combined with the hydrodynamic information available from the SV data, a stoichiometry can be derived. Herein, the spectral properties of sedimenting species are systematically explored to arrive at a predictive test for whether a set of macromolecules can be spectrally resolved in a multisignal SV (MSSV) experiment. Also, a graphical means of experimental design and criteria to judge the success of the spectral discrimination in MSSV are introduced. A detailed example of the analysis of MSSV experiments is offered, and the possibility of deriving equilibrium association constants from MSSV analyses is explored. Finally, successful implementations of MSSV are reviewed.     

A case study and use of sedimentation equilibrium analytical ultracentrifugation as a tool for biopharmaceutical development

Analytical ultracentrifugation (AUC) has re-emerged as a powerful technique for protein characterisation. We report the pivotal role sedimentation equilibrium AUC has played in the development of macrophage inflammatory protein-1α (MIP-1α) as a protein therapeutic. MIP-1α has potential clinical applications in cancer but its clinical use is limited, since it associates to form large insoluble aggregates in physiological buffers. Using AUC as a screening technique, we have produced a biologically active variant of MIP-1α, BB-10010, which has a reduced tendency to aggregate in physiological buffers. The aggregation of protein based pharmaceuticals is routinely monitored by size exclusion chromatography (SEC). Comparison of the data acquired by SEC and AUC, demonstrates that owing to the complexity of BB-10010, AUC analysis is required in addition to SEC to provide a rigorous characterisation of molecular association. This work has been extended to include the use of AUC as an analytical tool to monitor the quality of BB-10010 during formulation and stability studies. Accepted: 6 October 1996     

Improved methods for fitting sedimentation coefficient distributions derived by time-derivative techniques

Time-derivative approaches to analyzing sedimentation velocity data have proven to be highly successful and have now been used routinely for more than a decade. For samples containing a small number of noninteracting species, the sedimentation coefficient distribution function, g(s *), traditionally has been fitted by Gaussian functions to derive the concentration, sedimentation coefficient, and diffusion coefficient of each species. However, the accuracy obtained by that approach is limited, even for noise-free data, and becomes even more compromised as more scans are included in the analysis to improve the signal/noise ratio (because the time span of the data becomes too large). Two new methods are described to correct for the effects of long time spans: one approach that uses a Taylor series expansion to correct the theoretical function and a second approach that creates theoretical g(s *) curves from Lamm equation models of the boundaries. With this second approach, the accuracy of the fitted parameters is approximately 0.1% and becomes essentially independent of the time span; therefore, it is possible to obtain much higher signal/noise when needed. This second approach is also compared with other current methods of analyzing sedimentation velocity data.     

Sedimentation velocity analysis of highly heterogeneous systems

This article discusses several improvements to the van Holde-Weischet (vHW) method [Biopolymers 17 (1978) 1387] that address its capability to deal with sedimentation coefficient distributions spanning a large range of s values. The method presented here allows the inclusion of scans early and late in the experiment that ordinarily would need to be excluded from the analysis due to ultracentrifuge cell end effects. Scans late in the experiment are compromised by the loss of a defined plateau region and by back-diffusion from the bottom of the cell. Early scans involve partial boundaries that have not fully cleared the meniscus. In addition, a major refinement of the algorithm for determining the boundary fractions is introduced, taking into account different degrees of radial dilution for different species in the system. The method retains its desirable model-independent properties (the analysis of sedimentation data does not require prior knowledge of a user-imposed model or range of sedimentation coefficients) and reports diffusion-corrected s value distributions, which can be presented either in a histogram format or the traditional integral distribution format. Data analyzed with the traditional vHW method are compared with those of the improved method to demonstrate the benefit from the added information in the analysis.     

Sedimentation velocity analytical ultracentrifugation and SEDFIT/c(s): limits of quantitation for a monoclonal antibody system

Sedimentation velocity analytical ultracentrifugation (SV-AUC) has emerged in the biopharmaceutical industry as a technique to detect small quantities of protein aggregates. However, the limits of detection and quantitation of these aggregates are not yet well understood. Although diverse factors (molecule, instrument, technique, and software dependent) preclude an all-encompassing measurement of these limits for the complete system, it is possible to use simulated data to determine the quantitation limits of the data analysis software aspect. The current study examines the performance of the SEDFIT/c(s) data analysis tool with simulated antibody monomer/dimer and monomer/aggregate systems. Under completely ideal conditions (zero noise, known meniscus, and shape factor homogeneity), the software limit of quantitation was 0.01% for the monomer/aggregate system and 0.03% for the less well-resolved monomer/dimer system. Under more realistic conditions (0.005 OD root mean square [RMS] noise, shape factor variability, and long solution column), the software limits of quantitation were 0.2 and 0.6% (0.002 and 0.006 OD) for the monomer/aggregate and monomer/dimer systems, respectively. Interestingly, diminished quantitation accuracy at very low levels of oligomer was not accompanied by deterioration of fit quality (as measured by root mean square deviation [RMSD] and residuals bitmap images).     

A statistical geometrical description of the human liver for probabilistic occupant models

Realistic numerical assessments of liver injury risk for the entire occupant population require incorporating inter-subject variations into numerical models. Statistical shape models of the abdominal organs have been shown to be useful tools for the investigation of the organ variations and could be applied to the development of statistical computational models. The main objective of this study was to establish a standard procedure to quantify the shape variations of a human liver in a seated posture, and construct three-dimensional (3D) statistical shape boundary models.     

Digitization of sedimentation equilibrium and velocity data for analysis by minicomputer

A procedure is described whereby phosphorylated seryl residues may be unequivocally identified during the sequential degradation of a polypeptide chain by the Edman technique. The phosphoseryl residue, Ser(P), was first converted by treatment with methylamine in dilute alkali to a β-methylaminoalanyl residue which was split from the polypeptide by the degradative procedure as the derived phenylthiohydantoin. This was identified by high-performance liquid chromatography. The procedure was highly effective when the Ser(P) occupied an isolated position in a polypeptide chain but was less so when grouped consecutively with other Ser(P).     

Biological evaluation of trace element data in human ovaries by statistical analysis

Analysis of variance, analysis of covariance, correlation coefficient, multiple correlation, and partial correlation coefficient statistical tests were applied to Cs, Cr, Co, Fe, Rb, Sc, Se, and Zn content in human ovaries in order to evaluate statistically the possible relationships between these trace elements at: the ovary as an organ, each ovarian phase separately, each morphological part independent of the ovarian phase, and between cortex and medulla within the ovarian phases. The element Cs seems to have a homogenous distribution between cortex and medulla within reproductive and menopausal phase. Zinc shows a trend to have an antagonistic relation with Cs, Cr, Co, and Fe during fetal and reproductive phases and not during menopausal phase. The relationship between Zn and Cs when Fe is kept constant could be used as a tool for the decontamination of the ovary from an abnormal Cs content or for the inhibition of the accumulation of the same element to the ovarian tissue.     

New statistical tools for analyzing the structure of animal groups

The statistical characterization of the spatial structure of large animal groups has been very limited so far, mainly due to a lack of empirical data, especially in three dimensions (3D). Here we focus on the case of large flocks of starlings (Sturnus vulgaris) in the field. We reconstruct the 3D positions of individual birds within flocks of up to few thousands of elements. In this respect our data constitute a unique set. We perform a statistical analysis of flocks' structure by using two quantities that are new to the field of collective animal behaviour, namely the conditional density and the pair correlation function. These tools were originally developed in the context of condensed matter theory. We explain what is the meaning of these two quantities, how to measure them in a reliable way, and why they are useful in assessing the density fluctuations and the statistical correlations across the group. We show that the border-to-centre density gradient displayed by starling flocks gives rise to an anomalous behaviour of the conditional density. We also find that the pair correlation function has a structure incompatible with a crystalline arrangement of birds. In fact, our results suggest that flocks are somewhat intermediate between the liquid and the gas phase of physical systems.