A bayesian approach for quantifying trace amounts of antibody aggregates by sedimentation velocity analytical ultracentrifugation.

Sedimentation velocity analytical ultracentrifugation (SV-AUC) has become an important tool for the characterization of the purity of protein therapeutics. The work presented here addresses a need for methods orthogonal to size-exclusion chromatography for ensuring the reliable quantitation of immunogenic oligomers, for example, in antibody preparations. Currently the most commonly used approach for SV-AUC analysis is the diffusion-deconvoluted sedimentation coefficient distribution c(s) method, previously developed by us as a general purpose technique and implemented in the software SEDFIT. In both practical and theoretical studies, different groups have reported a sensitivity of c(s) for trace oligomeric fractions well below the 1% level. In the present work we present a variant of c(s) designed for the purpose of trace detection, with customized Bayesian regularization. The original c(s) method relies on maximum entropy regularization providing the most parsimonious distribution consistent with the data. In the present paper, we use computer simulations of an antibody system as example to demonstrate that the standard maximum entropy regularization, due to its design, leads to a theoretical lower limit for the detection of oligomeric traces and a consistent underestimate of the trace populations by approximately 0.1% (dependent on the level of regularization). This can be overcome with a recently developed Bayesian extension of c(s) (Brown et al., Biomacromolecules, 8:2011-2024, 2007), utilizing the known regions of sedimentation coefficients for the monomer and oligomers of interest as prior expectation for the peak positions in the distribution. We show that this leads to more clearly identifiable and consistent peaks and lower theoretical limits of quantization by approximately an order of magnitude for some experimental conditions. Implications for the experimental design of SV-AUC and practical detection limits are discussed.

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 method in the analytical ultracentrifuge for the study of protein-protein interactions.

Sedimentation analysis in the analytical ultracentrifuge can be employed to detect macromolecular interactions. Whenever two molecules interact the mass of the resulting complex is increased and this is reflected in the sedimentation behavior. In this chapter we discuss how this phenomenon can be utilized to determine quantitative parameters of an interaction. An example, interaction of single-stranded DNA binding protein with a subunit of DNA polymerase III holoenzyme is given together with a thorough treatment of the relating theory and a description of evaluation algorithms.

Spinning with Dave: David Yphantis's contributions to ultracentrifugation.

For nearly 50 years David Yphantis has helped advance analytical ultracentrifugation, promoted rigor in the thermodynamic analysis of biochemical data and encouraged students and colleagues to look for the deepest possible understanding of science. This article, written by five of Dave's students, presents some of the impressions he has made over the years.

Evidence for a monomeric structure of nonribosomal Peptide synthetases.

Nonribosomal peptide synthetases (NRPS) are multimodular biocatalysts that bacteria and fungi use to assemble many complex peptides with broad biological activities. The same modular enzymatic assembly line principles are found in fatty acid synthases (FAS), polyketide synthases (PKS), and most recently in hybrid NRPS/PKS multienzymes. FAS as well as PKS are known to function as homodimeric enzyme complexes, raising the question of whether NRPS may also act as homodimers. To test this hypothesis, biophysical methods (size exclusion chromatography, analytical equilibrium ultracentrifugation, and chemical crosslinking) and biochemical methods (two-affinity-tag-system and complementation studies with enzymes being inactivated in different catalytic domains) were applied to NRPS subunits from the gramicidin S (GrsA-ATE), tyrocidine (TycB(1)-CAT and TycB(2-3)-AT.CATE), and enterobactin (EntF-CATTe) biosynthetic systems. These methods had revealed the dimeric structure of FAS and PKS previously, but all three NRPS systems investigated are functionally active as monomers.

A new approximate whole boundary solution of the Lamm differential equation for the analysis of sedimentation velocity experiments.

Sedimentation velocity is one of the best-suited physical methods for determining the size and shape of macromolecular substances or their complexes in the range from 1 to several thousand kDa. The moving boundary in sedimentation velocity runs can be described by the Lamm differential equation. Fitting of suitable model functions or solutions of the Lamm equation to the moving boundary is used to obtain directly sedimentation and diffusion coefficients, thus allowing quick determination of size, shape and other parameters of macromolecules. Here we present a new approximate whole boundary solution of the Lamm equation that simultaneously allows the specification of sedimentation and diffusion coefficients with deviations smaller than 1% from the expected values.

Biophysical studies by ultracentrifugation.

Advances in data analysis are broadening the applicability of ultracentrifugation to the characterization of macromolecular behavior in complex solution. The direct fitting of sedimentation velocity data to the Lamm equation is emerging as a very powerful means to characterize size distributions, improve the precision of data analysis and increase experimental throughput. With improvements in data acquisition and analysis, ultracentrifugation is poised to make significant contributions to our understanding of how macromolecules behave in vivo.

Direct sedimentation analysis of interference optical data in analytical ultracentrifugation.

Sedimentation data acquired with the interference optical scanning system of the Optima XL-I analytical ultracentrifuge can exhibit time-invariant noise components, as well as small radial-invariant baseline offsets, both superimposed onto the radial fringe shift data resulting from the macromolecular solute distribution. A well-established method for the interpretation of such ultracentrifugation data is based on the analysis of time-differences of the measured fringe profiles, such as employed in the g(s*) method. We demonstrate how the technique of separation of linear and nonlinear parameters can be used in the modeling of interference data by unraveling the time-invariant and radial-invariant noise components. This allows the direct application of the recently developed approximate analytical and numerical solutions of the Lamm equation to the analysis of interference optical fringe profiles. The presented method is statistically advantageous since it does not require the differentiation of the data and the model functions. The method is demonstrated on experimental data and compared with the results of a g(s*) analysis. It is also demonstrated that the calculation of time-invariant noise components can be useful in the analysis of absorbance optical data. They can be extracted from data acquired during the approach to equilibrium, and can be used to increase the reliability of the results obtained from a sedimentation equilibrium analysis.

Direct determination of lipoprotein(a) cholesterol by ultracentrifugation and agarose gel electrophoresis with enzymatic staining for cholesterol.

Lipoprotein(a) [(Lp(a)], a low-density lipoprotein (LDL)-like particle, contains in addition to LDL a specific protein component, apolipoprotein(a) [apo(a)]. Conventionally, Lp(a) has been measured by immunological methods that distinguish between Lp(a) and LDL by dealing with apo(a) as an antigen. We describe a new method to determine Lp(a) on the basis of its cholesterol content. Very-low-density lipoproteins were removed from serum by preparative ultracentrifugation at a density of 1.006 kg/L. The infranate was subjected to agarose gel electrophoresis to separate Lp(a) and LDL. Lp(a) cholesterol was then determined by direct enzymatic staining for cholesterol. On electrophoresis of the > 1.006 kg/L (bottom) fraction, Lp(a) migrates to the pre-beta position, regardless of the genetic apo(a) isoform. The interassay CVs of Lp(a) cholesterol determinations ranged from 6.9% to 11.5%, and the results correlated well with the Lp(a) concentrations measured by immunonephelometry (r = 0.937). There was an inverse relation between the molecular mass of the genetically determined apo(a) isoforms and Lp(a) cholesterol concentrations. Patients with angiographically proven coronary artery disease (CAD) had significantly more Lp(a) cholesterol than healthy controls did. The ratio of Lp(a) cholesterol to immunologically determined Lp(a) tended to be lower in CAD patients, suggesting that Lp(a) particles contained less cholesterol than apo(a). In addition, the new method allows determination of LDL cholesterol without contamination by Lp(a).

Sequential ultracentrifugation micromethod for separation of serum lipoproteins and assays of lipids, apolipoproteins, and lipoprotein particles.

We describe a fast sequential separation of very-low-density, low-density, and high-density lipoproteins from 400 microL of serum, using the Beckman TL100 ultracentrifuge. The cumulative centrifugation time is 9.5 h. The purity of lipoprotein fractions was verified by a gel-filtration procedure. The major contaminant is the serum albumin, which can be eliminated by a second centrifugation at the same density. Enzymatic measurement of lipids shows good recovery (> 91%) and weak within-sample variation (< 7%). In comparison with a density-gradient procedure, the deleterious effects on the lipoprotein structure appear to be limited, as shown by the low concentrations of apolipoprotein (apo) E and apo A-I in the fraction > 1.21 kg/L. Furthermore, the micro-ultracentrifugation also gives a better recovery rate. Finally, we have studied the distribution of lipids, apolipoproteins, and lipoprotein particles (LpA-I:A-II, LpB:C-III, LpB:E) in each fraction separated from 10 serum samples from healthy subjects.