Analytical ultracentrifugation combined with X-ray and neutron scattering: Experiment and modelling

Analytical ultracentrifugation and solution scattering provide different multi-parameter structural and compositional information on proteins. The joint application of the two methods supplements high resolution structural studies by crystallography and NMR. We summarise the procedures required to obtain equivalent ultracentrifugation and X-ray and neutron scattering data. The constrained modelling of ultracentrifugation and scattering data is important to confirm the experimental data analysis and yields families of best-fit molecular models for comparison with crystallography and NMR structures. This modelling of ultracentrifugation and scattering data is described in terms of starting models, their conformational randomisation in trial-and-error fits, and the identification of the final best-fit models. Seven applications of these methods are described to illustrate the current state-of-the-art. These include the determination of antibody solution structures (the human IgG4 subclass, and oligomeric forms of human IgA and its secretory component), the solution structures of the complement proteins of innate immunity (Factor H and C3/C3u) and their interactions with macromolecular ligands (C-reactive protein), and anionic polysaccharides (heparin). Complementary features of joint ultracentrifugation and scattering experiments facilitate an improved understanding of crystal structures (illustrated for C3/C3u, C-reactive protein and heparin). If a large protein or its complex cannot be crystallised, the joint ultracentrifugation-scattering approach provides a means to obtain an overall macromolecular structure.     

Advances in sedimentation velocity analysis.

On February 20, 1996, a workshop titled "Advances in Sedimentation Velocity Analysis" was held at the Biophysical Society meeting in Baltimore, Maryland, in honor of Professor David Yphantis's 65th birthday. Although he is known more for his work with sedimentation equilibrium, David's work on instrumentation and data analysis is the foundation for many of the recent advances in both equilibrium and velocity sedimentation. Over the years he has trained numerous graduate students, most of whom have gone on to emphasize the use of analytical ultracentrifugation to answer biochemical questions involving macromolecular assembly. His laboratory was one of very few that continued to use and develop analytical ultracentrifugation during its nadir in the 1970s and early 1980s. The rebirth and resurgence of analytical ultracentrifugation owe a great deal to his persistence and enthusiasm. These efforts have borne fruit. In the last five years, through his work at the National Analytical Ultracentrifugation Facility, he has helped train nearly 100 individuals in the delicate art of nonlinear least-squares analysis of equilibrium sedimentation data. Furthermore, the number of researchers using the ultracentrifuge and the number of papers published has skyrocketed in the last few years. This workshop, then, was a way to thank David for his years of devotion to analytical ultracentrifugation.     

Using prior knowledge in the determination of macromolecular size-distributions by analytical ultracentrifugation

Analytical ultracentrifugation has reemerged as a widely used tool for the study of ensembles of biological macromolecules to understand, for example, their size-distribution and interactions in free solution. Such information can be obtained from the mathematical analysis of the concentration and signal gradients across the solution column and their evolution in time generated as a result of the gravitational force. In sedimentation velocity analytical ultracentrifugation, this analysis is frequently conducted using high resolution, diffusion-deconvoluted sedimentation coefficient distributions. They are based on Fredholm integral equations, which are ill-posed unless stabilized by regularization. In many fields, maximum entropy and Tikhonov-Phillips regularization are well-established and powerful approaches that calculate the most parsimonious distribution consistent with the data and prior knowledge, in accordance with Occam's razor. In the implementations available in analytical ultracentrifugation, to date, the basic assumption implied is that all sedimentation coefficients are equally likely and that the information retrieved should be condensed to the least amount possible. Frequently, however, more detailed distributions would be warranted by specific detailed prior knowledge on the macromolecular ensemble under study, such as the expectation of the sample to be monodisperse or paucidisperse or the expectation for the migration to establish a bimodal sedimentation pattern based on Gilbert-Jenkins' theory for the migration of chemically reacting systems. So far, such prior knowledge has remained largely unused in the calculation of the sedimentation coefficient or molecular weight distributions or was only applied as constraints. In the present paper, we examine how prior expectations can be built directly into the computational data analysis, conservatively in a way that honors the complete information of the experimental data, whether or not consistent with the prior expectation. Consistent with analogous results in other fields, we find that the use of available prior knowledge can have a dramatic effect on the resulting molecular weight, sedimentation coefficient, and size-and-shape distributions and can significantly increase both their sensitivity and their resolution. Further, the use of multiple alternative prior information allows us to probe the range of possible interpretations consistent with the data.     

Accounting for thermodynamic non-ideality in the Guinier region of small-angle scattering data of proteins

Hydrodynamic studies of the solution properties of proteins and other biological macromolecules are often hard to interpret when the sample is present at a reasonably concentrated solution. The reason for this is that solutions exhibit deviations from ideal behaviour which is manifested as thermodynamic non-ideality. The range of concentrations at which this behaviour typically is exhibited is as low as 1–2 mg/ml, well within the range of concentrations used for their analysis by techniques such as small-angle scattering. Here we discuss thermodynamic non-ideality used previously used in the context of light scattering and sedimentation equilibrium analytical ultracentrifugation and apply it to the Guinier region of small-angle scattering data. The results show that there is a complementarity between the radially averaged structure factor derived from small-angle X-ray scattering/small-angle neutron scattering studies and the second virial coefficient derived from sedimentation equilibrium analytical ultracentrifugation experiments.     

Characterization of heterologous protein-protein interactions using analytical ultracentrifugation.

Methods for quantitative characterization of heterologous protein-protein interactions by means of analytical ultracentrifugation (AUC) include sedimentation equilibrium, tracer sedimentation equilibrium, sedimentation velocity, and analytical band sedimentation. Fundamental principles governing the behavior of macromolecules in a centrifugal field are summarized, and the application of these principles to the interpretation of data obtained from each type of experiment is reviewed. Instrumentation and software for the acquisition and analysis of data obtained from different types of AUC experiments are described.     

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.     

Using Lamm-Equation modeling of sedimentation velocity data to determine the kinetic and thermodynamic properties of macromolecular interactions

The interaction of macromolecules with themselves and with other macromolecules is fundamental to the functioning of living systems. Recent advances in the analysis of sedimentation velocity (SV) data obtained by analytical ultracentrifugation allow the experimenter to determine important features of such interactions, including the equilibrium association constant and information about the kinetic off-rate of the interaction. The determination of these parameters is made possible by the ability of modern software to fit numerical solutions of the Lamm Equation with kinetic considerations directly to SV data. Herein, the SV analytical advances implemented in the software package SEDPHAT are summarized. Detailed analyses of SV data using these strategies are presented. Finally, a few highlights of recent literature reports that feature this type of SV data analysis are surveyed.     

Metabolism of apoB-100 in lipoproteins separated by density gradient ultracentrifugation in normal and Watanabe heritable hyperlipidemic rabbits

We have examined the capability of a previously developed compartmental model to explain the kinetics of radioiodinated apolipoprotein (apo) B-100 in very low density lipoproteins (VLDL), intermediate density lipoproteins (IDL), and low density lipoproteins (LDL) separated by density gradient ultracentrifugation after intravenous injection of radioiodinated VLDL into New Zealand white (NZW) and Watanabe heritable hyperlipidemic (WHHL) rabbits. Our model was developed primarily from kinetics in whole blood plasma of apoB-100 in particles with and without apoE after intravenous injection of large VLDL, total VLDL, IDL, and LDL. When the initial conditions for this model were assumed to be an intravenous injection of radiolabeled VLDL, the plasma VLDL and LDL simulations for NZW rabbits and the VLDL, IDL, and LDL simulations for WHHL rabbits were found to be inconsistent with the observed density gradient data. By adding a new pathway in the VLDL portion of the model for NZW rabbits and a new compartment in VLDL for WHHL rabbits, and by assuming some cross-contamination in the density gradient ultracentrifugal separations, it was possible to bring our model, which was based upon measurements of 125I-labeled apoB-100 in whole plasma, into conformity with the data obtained by density gradient ultracentrifugation. The relatively modest changes required in the model to fit the gradient ultracentrifugation data support the suitability of our approach to the kinetic analysis of the metabolism of apoB-100 in VLDL and its conversion to IDL and LDL based upon measurements of 125I-labeled apoB-100 in whole plasma after injection of radiolabeled VLDL, IDL, and LDL. Furthermore, the differences in kinetics observed by us between data from whole plasma and data from plasma submitted to ultracentrifugal separation from the same or similar animals highlight the fact that small variations that can occur in the separation of lipoprotein classes by buoyant density can lead to confusing results.     

Oligomeric state of membrane transport proteins analyzed with blue native electrophoresis and analytical ultracentrifugation

Blue native electrophoresis is used widely for the analysis of non-dissociated protein complexes with respect to composition, oligomeric state and molecular mass. However, the effects of detergent or dye binding on the mass and stability of the integral membrane proteins have not been studied. By comparison with analytical ultracentrifugation, we have evaluated whether the oligomeric state of membrane transport proteins is reflected reliably with blue native electrophoresis. For the analysis we have used two well-characterized transporters, that is, the major facilitator superfamily protein LacS and the phosphotransferase system EII(Mtl). For another member of the major facilitator superfamily, the xyloside transporter XylP from Lactobacillus pentosus, the complete analysis of the quaternary structure determined by analytical ultracentrifugation and freeze-fracture electron microscopy is presented.Our experiments show that during blue native electrophoresis the detergent bound to the proteins is replaced by the amphipathic Coomassie brilliant blue (CBB) dye. The mass of the bound CBB dye was quantified. Provided this additional mass of bound CBB dye is accounted for and care is taken in the choice and concentration of the detergent used, the mass of LacS, XylP and EII(Mtl) and four other membrane (transport) proteins could be deduced within 10 % error. Our data underscore the fact that the oligomeric state of many membrane transport proteins is dimeric.     

The Escherichia coli multidrug transporter EmrE is a dimer in the detergent-solubilised state

EmrE is a multidrug transporter that utilises the proton gradient across bacterial cell membranes to pump hydrophobic cationic toxins out of the cell. The structure of EmrE is very unusual, because it is an asymmetric homodimer containing eight alpha-helices, six of which form the substrate-binding chamber and translocation pathway. Despite this structural information, the precise oligomeric order of EmrE in both the detergent-solubilised state and in vivo is unclear, although it must contain an even number of subunits to satisfy substrate-binding data. We have studied the oligomeric state of EmrE, purified in a functional form in dodecylmaltoside, by high-resolution size-exclusion chromatography (hrSEC) and by analytical ultracentrifugation. The data from equilibrium analytical ultracentrifugation were analysed using a measured density increment for the EmrE-lipid-detergent complex, which showed that the purified EmrE was predominantly a dimer. This value was consistent with the apparent mass for the EmrE-lipid-detergent complex (137 kDa) determined by hrSEC. EmrE was purified under different conditions using minimal concentrations of dodecylmaltoside, which would have maintained the structure of any putative higher oligomeric states: this EmrE preparation had an apparent mass of 206 kDa by hrSEC and equilibrium analytical ultracentrifugation showed unequivocally that EmrE was a dimer, although it was associated with a much larger mass of phospholipid. In addition, the effect of the substrate tetraphenylphosphonium on the oligomeric state was also analysed for both preparations of EmrE; velocity analytical ultracentrifugation showed that the substrate had no effect on the oligomeric state. Therefore, in the detergent dodecylmaltoside and under conditions where the protein is fully competent for substrate binding, EmrE is dimeric and there is no evidence from our data to suggest higher oligomeric states. These observations are discussed in relation to the recently published structures of EmrE from two- and three-dimensional crystals.     

Anomalous sedimentation behaviour of the e-coli ribosomal system: 50S-30S ⇄ 50S + 30S

An experimental and theoretical study has been made into the effect of association-dissociation reactions on the sedimentation of the E. coli ribosomal system 50S-30S ⇄ 50S + 30S. It has been found that(a) the sedimentation pattern is strongly dependent on the rotor speed;(b) the ratio of components as measured using high-speed ultracentrifugation (30000–40000 r.p.m.) is independent of rotor speed; and(c) the speed of ultracentrifugation has a strong effect on the sedimentation coefficient of the ribosomal system as determined by the mean square second moment.The results of this paper demonstrate that ribosome sedimentation at low-speed ultracentrifugation is affected by some artefactual processes. A theoretical analysis of the experimental findings has shown that the observed effects cannot be attributed to the effect of the association-dissociation reaction not to the pressure dependence of the equilibrium constant of that reaction.On the other hand, at high-speed ultracentrifugation the ribosomal system sediments as a heterogeneous mixture of non-interacting components. Consequently, the shape of the boundary in this case will reflect the equilibrium composition of the ribosomal system.     

Study on heart mitochondrial creatine kinase using a cross-linking bifunctional reagent. I. The binding involves the octameric form of the enzyme

Bovine heart mitochondria suspended in 0.25 M sucrose were treated with 0.3% glutaraldehyde (GA). The membranes were disintegrated by ultrasonication in 0.25 M KCl and precipitated by centrifugation. The supernatant was assayed for creatine kinase (CKm) oligomeric forms by ultracentrifugation in a sucrose density gradient. A kinetic analysis of membrane-bound CKm was performed before and after ultrasonication. The data obtained suggest that the CKm octamer is the only form of CKm bound to mitochondrial membranes during GA treatment. This finding was confirmed by an analysis of extracts from untreated mitochondria using high resolution gel filtration.     

Turbidimetric ultracentrifugation. Application to the study of human serum very low density lipoprotein distributions.

In this communication it is shown that the sedimentation coefficient distribution may be accurately measured for very large particles using turbidimetric techniques and the ultraviolet-scanning analytical ultracentrifuge. A principal advantage is that turbidity is a function of the product of concentration and molecular weight; thus, large particles may be observed even when present in very small amounts. We propose to call this method of analysis "turbidimetric ultracentrifugation." We have used turbidimetric ultracentrifugation ot determine the sedimentation coefficient distribution for a sample of human serum very low density lipoproteins. This distribution is compared to that found with conventional schlieren techniques with good agreement.     

Ultracentrifugation micromethod for preparation of small experimental animal lipoproteins

Sequential flotation ultracentrifugation is commonly used in the preparation of plasma lipoproteins. However, protocols often require prolonged centrifugation time (48-72 h) and large plasma volumes (2-20 ml), which makes them unsuitable for studies on small laboratory animals. Although analytical techniques such as FPLC have often small sample requirements, further fraction analysis is often limited to the small fraction volume obtained. A sequential ultracentrifugation micromethod is described to obtain rat lipoprotein fractions from 400 microl of plasma in a cumulative centrifugation time of 7.5 h. Fraction volumes were determined and densities were adjusted to those of rat plasma lipoproteins. Polyacrylamide gel electrophoresis and enzymatic measurements of triglycerides, total cholesterol, and phospholipids were used to assess the purity of the lipoprotein fractions. The results were compared with those obtained from a classical sequential ultracentrifugation protocol. The micromethod presented here can be further adapted to other experimental animal species with little modifications.     

Absorption optics data processing with standard errors for sedimentation and diffusion coefficients from moving boundary ultracentrifugation

A data processing protocol is presented for moving boundary ultracentrifugation in which the boundary position and width are determined from absorption optics scanner traces. The best fitting Gaussian (normal probability) function is determined for each trace by weighted probit analysis. The boundary positions are used to determine the s-rate. The boundary spreading is used to determine the diffusion coefficient after correction for s-rate concentration dependence obtained elsewhere. Both linear and quadratic least-squares curve fittings are used. If the quadratic term is significant, it yields an estimate of concentration dependence from the boundary movement analysis and an estimate of the s-rate heterogeneity from the boundary spreading analysis.The carrying along of the internal standard errors at each step is emphasized. Suggestions for data processing and complete least-squares formulas are given.     

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.     

Comparative Analysis of the Effects of α-Crystallin and GroEL on the Kinetics of Thermal Aggregation of Rabbit Muscle Glyceraldehyde-3-Phosphate Dehydrogenase

Effects of α-crystallin and GroEL on the kinetics of thermal aggregation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase (GAPDH) have been studied using dynamic light scattering and analytical ultracentrifugation. The analysis of the initial parts of the dependences of the hydrodynamic radius of protein aggregates on time shows that in the presence of α-crystallin or GroEL the kinetic regime of GAPDH aggregation is changed from the regime of diffusion-limited cluster–cluster aggregation to the regime of reaction-limited cluster–cluster aggregation, wherein the sticking probability for the colliding particles becomes lower the unity. In contrast to α-crystallin, GroEL does not interfere with formation of the start aggregates which include denatured GAPDH molecules. On the basis of the analytical ultracentrifugation data the conclusion has been made that the products of dissociation of GAPDH and α-crystallin or GroEL play an important role in the interactions of GAPDH and chaperones at elevated temperatures.     

Self-association of diisopropylphosphoryl-alpha-chymotrypsin: the involvement of active site of the enzyme in its self-association behaviour

The self-association of diisopropylphosphoryl(DIP)-alpha-chymotrypsin is studied in order to find out whether the active site of the enzyme is involved in its self-association behaviour or not. Sedimentation coefficient as well as the weight-average (Archibald) molecular weight data are obtained as a function of concentration using an analytical ultracentrifugation technique. The analysis indicated that the experimental data fits the model of indefinite self-association. The comparison of the data with earlier data on alpha-chymotrypsin revealed that after the modification at the active site, the association constant for the self-association is reduced by about 47%, and the system deviated from ideality. Results showed further that Ser-195, at the active site, appears to be involved in the self-association behaviour of alpha-chymotrypsin; however, the participation of other groups at the active site is also implicated.     

Boundary analysis of sedimentation-velocity experiments with monodisperse and paucidisperse solutes

A method is presented which allows one to calculate a distribution of sedimentation coefficients from the boundries of sedimentation-velocity experiments with mono- or pauci-disperse solutes. With two solutes differences in S value as small as 20% can be resolved. In absence of heterogeneity and concentration-dependent effects, the analysis also provides values for the diffusion coefficient within an accuracy of ?10 to +5%. Tests with both simulated data and ultracentrifugation experiments on short DNA fragments show the value and the limitations of the method.     

Estimation of lipoprotein and apoprotein distribution in rat plasma by cumulative density ultracentrifugation and sodium dodecyl sulfate-polyacrylamide gel electrophoresis

Lipoprotein distribution in rat plasma determined after sequential ultracentrifugation (requiring 8 days of centrifugation to separate lipoproteins in five density classes), was compared to estimates based upon cumulative density ultracentrifugation (46 hr of ultracentrifugation). In general comparable values were obtained by the two methods with regard to protein, total cholesterol, cholesteryl ester, free cholesterol, and triacylglycerol distribution. However, the HDL3 protein concentration found by sequential ultracentrifugation was only about 50% of that found after the cumulative procedure. Apolipoproteins in lipoproteins isolated by the two methods were well separated by sodium dodecyl sulfate polyacrylamide gel electrophoresis. Color of the stained bands was extracted and read photometrically. A linear standard curve was obtained with albumin. Absorbance corresponding to 1 microgram/ml was 0.057. Below d = 1.100 g/ml (HDL2b) the two ultracentrifugation methods gave comparable results for all apoproteins. In contrast to this the level of apo A-I, apo E, and apo A-IV in the more dense types of HDL was higher when estimated by cumulative than by sequential ultracentrifugation. In HDL3 isolated by sequential ultracentrifugation the apo A-IV, apo E, and apo A-I concentrations were 51, 31, and 45% respectively, of values found after cumulative ultracentrifugation. The results indicate that cumulative density ultracentrifugation, followed by colorimetric determination of apoproteins separated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis, is a useful approach when studying lipoprotein distribution in rat plasma.