Challenges for the modern analytical ultracentrifuge analysis of polysaccharides

This article reviews some of the recent advances in analytical ultracentrifugation and how these advances have impacted--and can impact--on our understanding of the size, shape through conformation modelling, interactions and charge properties of polysaccharides in solution, particularly when used in combination with other solution techniques and also imaging techniques. Specifically we look at (1) polysaccharide polydispersity and simple shape analysis by sedimentation velocity, and in particular using new approaches such as SEDFIT analysis; (2) polysaccharide molecular-weight analysis by sedimentation equilibrium and MSTAR analysis and how this complements analysis of size exclusion chromatography coupled to multi-angle laser light scattering; (3) polysaccharide conformation analysis using traditional procedures such as the Wales-van Holde ratio, power law or 'scaling' relations, more specialised treatments for rigid cylindrical structures, semi-flexible chains and worm-like coils and complications through draining effects; (4) Analysis of polysaccharide interactions and in particular complex formation phenomena, focusing on interesting applications in the areas of mucoadhesion and sedimentation fingerprinting; and (5) the possibilities for macromolecular charge and charge screening measurement.     

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 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.     

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.     

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.     

Characterization of macromolecular heterogeneity by equilibrium sedimentation techniques

New graphical procedures have been developed to investigate the heterogeneity of protein preparations using sedimentation equilibrium. The heterogeneous systems that can be studied include self-associating systems contaminated by incompetent monomer, self-associating systems contaminated by non-dissociating oligomer and simple non-interacting monomer-oligmer disperse systems. The new procedures are based on the concentration dependence of the apparent association constants estimated by a non-linear least square fitting program (NONLIN), on the assumption of conservation of mass during sedimentation and on the applications of several standard techniques for statistical inferences of NONLIN estimations. The procedures outlined here can detect various types of heterogeneity, discriminate amongst different types of heterogeneity, estimate the amount of contaminant causing heterogeneity and determine the true equilibrium constant of the self-associating components. The procedures appear to be sensitive, accurate and easily applicable when tested using both protein samples and computer simulated data.     

Convection-free boundary sedimentation of dilute protein solutions

Use of the density gradient sedimentation velocity technique appears to be essential for the accurate determination of the mean sedimentation coefficients of dilute protein solutions. When performed on an analytical ultracentrifuge equipped with a photoelectric-scanning-absorption optical system, the density gradient sedimentation velocity technique has been shown to be particularly useful in studying the subunit association-dissociation equilibria of multisubunit enzyme systems. The time factor has been shown to be a major advantage of the density gradient sedimentation velocity technique, as opposed to the sedimentation equilibrium technique, in studying the subunit association-dissociation equilibria of multisubunit enzymes such as rabbit muscle apo-glyceraldehyde-3-phosphate dehydrogenase, which is very unstable in dilute solution.     

Caldesmon. Molecular weight and subunit composition by analytical ultracentrifugation

A wide range of values has been reported for the subunit and molecular weights of smooth muscle caldesmon. There have also been conflicting reports concerning whether caldesmon is a monomer or dimer. We attempted to resolve these uncertainties by determining the molecular weight of chicken gizzard smooth muscle caldesmon using the technique of sedimentation equilibrium in the analytical ultracentrifuge. Unlike previous methods that have been used to estimate the molecular weight of caldesmon, the molecular weight determined by equilibrium sedimentation does not depend upon assumptions about the shape of the molecule. We concluded that caldesmon in solution is monomeric with a molecular mass of 93 +/- 4 kDa, a value that is much less than those previously reported in the literature. This new value, in conjunction with sedimentation velocity experiments, led to the conclusion that caldesmon is a highly asymmetric molecule with an apparent length of 740 A in solution. The mass of a cyanogen bromide fragment, with an apparent mass of 37 kDa from sodium dodecyl sulfate-polyacrylamide gel electrophoresis, was determined to be 25.1 +/- 0.6 kDa using sedimentation equilibrium. These results imply that the reported molecular weights of other fragment(s) of caldesmon have also been overestimated. We have determined an optical extinction coefficient for caldesmon (E1%(280 nm) = 3.3) by determining its concentration from its refractive index which was measured in the analytical ultracentrifuge. From the above values of the molecular weight and the extinction coefficient, we redetermined that the caldesmon molecule has two cysteines and recalculated the stoichiometric molar ratio of actin/tropomyosin/caldesmon in the smooth muscle thin filament to be 28:4:1.     

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.     

Sedimentation velocity analysis of heterogeneous protein-protein interactions: sedimentation coefficient distributions c(s) and asymptotic boundary profiles from Gilbert-Jenkins theory

Interacting proteins in rapid association equilibrium exhibit coupled migration under the influence of an external force. In sedimentation, two-component systems can exhibit bimodal boundaries, consisting of the undisturbed sedimentation of a fraction of the population of one component, and the coupled sedimentation of a mixture of both free and complex species in the reaction boundary. For the theoretical limit of diffusion-free sedimentation after infinite time, the shapes of the reaction boundaries and the sedimentation velocity gradients have been predicted by Gilbert and Jenkins. We compare these asymptotic gradients with sedimentation coefficient distributions, c(s), extracted from experimental sedimentation profiles by direct modeling with superpositions of Lamm equation solutions. The overall shapes are qualitatively consistent and the amplitudes and weight-average s-values of the different boundary components are quantitatively in good agreement. We propose that the concentration dependence of the area and weight-average s-value of the c(s) peaks can be modeled by isotherms based on Gilbert-Jenkins theory, providing a robust approach to exploit the bimodal structure of the reaction boundary for the analysis of experimental data. This can significantly improve the estimates for the determination of binding constants and hydrodynamic parameters of the complexes.     

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.     

Thermodynamic analysis of the dissociation of the aldolase tetramer substituted at one or both of the subunit interfaces

The fructose-1,6-bis(phosphate) aldolase isologous tetramer tightly associates through two different subunit interfaces defined by its 222 symmetry. Both single- and double-interfacial mutant aldolases have a destabilized quaternary structure, but there is little effect on the catalytic activity. These enzymes are however thermolabile. This study demonstrates the temperature-dependent dissociation of the mutant enzymes and determines the dissociation free energies of both mutant and native aldolase. Subunit dissociation is measured by sedimentation equilibrium in the analytical ultracentrifuge. At 25 degrees C the tetramer-dimer dissociation constants for each single-mutant enzyme are similar, about 10(-6) M. For the double-mutant enzyme, sedimentation velocity experiments on sucrose density gradients support a tetramer-monomer equilibrium. Furthermore, sedimentation equilibrium experiments determined a dissociation constant of 10(-15) M3 for the double-mutant enzyme. By the same methods the upper limit for the dissociation constant of wild-type aldolase A is approximately 10(-28) M3, which indicates an extremely stable tetramer. The thermodynamic values describing monomer-tetramer and dimer-tetramer equilibria are analyzed with regard to possible cooperative interaction between the two subunit interfaces.     

X-ray crystallographic and analytical ultracentrifugation analyses of truncated and full-length yeast copper chaperones for SOD (LYS7): a dimer-dimer model of LYS7-SOD association and copper delivery

Copper-zinc superoxide dismutase (CuZnSOD) acquires its catalytic copper ion through interaction with another polypeptide termed the copper chaperone for SOD. Here, we combine X-ray crystallographic and analytical ultracentrifugation methods to characterize rigorously both truncated and full-length forms of apo-LYS7, the yeast copper chaperone for SOD. The 1.55 A crystal structure of LYS7 domain 2 alone (L7D2) was determined by multiple-isomorphous replacement (MIR) methods. The monomeric structure reveals an eight-stranded Greek key beta-barrel similar to that found in yeast CuZnSOD, but it is substantially elongated at one end where the loop regions of the beta-barrel come together to bind a calcium ion. In agreement with the crystal structure, sedimentation velocity experiments indicate that L7D2 is monomeric in solution under all conditions and concentrations that were tested. In contrast, sedimentation velocity and sedimentation equilibrium experiments show that full-length apo-LYS7 exists in a monomer-dimer equilibrium under nonreducing conditions. This equilibrium is shifted toward the dimer by approximately 1 order of magnitude in the presence of phosphate anion. Although the basis for the specificity of the LYS7-SOD interaction as well as the exact mechanism of copper insertion into SOD is unknown, it has been suggested that a monomer of LYS7 and a monomer of SOD may associate to form a heterodimer via L7D2. The data presented here, however, taken together with previously published crystallographic and analytical gel filtration data on full-length LYS7, suggest an alternative model wherein a dimer of LYS7 interacts with a dimer of yeast CuZnSOD. The advantages of the dimer-dimer model over the heterodimer model are enumerated.     

Analysis of heterologous interacting systems by sedimentation velocity: curve fitting algorithms for estimation of sedimentation coefficients, equilibrium and kinetic constants

Analytical ultracentrifugation (AUC) has played and will continue to play an important role in the investigation of protein-protein, protein-DNA and protein-ligand interactions. A major advantage of AUC over other methods is that it allows the analysis of systems free in solution in nearly any buffer without worry about spurious interactions with a supporting matrix. Large amounts of high-quality data can be acquired in relatively short times. Advances in software for the treatment of AUC data over the last decade have eliminated many of the tedious aspects of AUC data analysis, allowing relatively rapid analysis of complicated systems that were previously unapproachable. A software package called sedanal is described that can perform global fits to AUC sedimentation velocity data obtained for both interacting and non-interacting, macromolecular multi-species, multi-component systems, by combining data from multiple runs over a range of sample concentrations and component ratios. Interaction parameters include both forward and reverse rate constants, or equilibrium constants, for each reaction, as well as concentration dependence of both sedimentation and diffusion coefficients. sedanal fits to time-difference data to eliminate time-independent systematic errors inherent in AUC data. The sedanal software package is based on the use of finite-element numerical solutions of the Lamm equation.     

An externally adjustable motor-driven Rayleigh slit assembly for the analytical ultracentrifuge

Precise alignment of the Rayleigh optical system of the Beckman Instruments Model E analytical ultracentrifuge is prerequisite to the performance of difference sedimentation velocity, difference sedimentation equilibrium, and high-speed equilibrium ultracentrifugation. One of the components required for precise alignment is an adjustable Rayleigh slit assembly. An externally adjustable assembly has been developed which offers some advantages over previous designs. The rotational movement is motor driven, allowing external adjustment by a single operator, who can monitor visually changes in the fringe pattern while the rotor is spinning. Installation of the slit assembly is simple and requires no permanent modifications of the armor plate, since the slit assembly is attached directly to the collimating lens holder. The slit assembly can be removed and replaced easily whenever the collimating lens is cleaned. The alignment procedure, involving rotation of both slit assembly and cylinder lens, can be carried out in less than 3 hr.     

A parameterized overspeeding method for the rapid attainment of low-speed sedimentation equilibrium

The approach of a solution of dilute, monodisperse, globular macromolecules to low-speed sedimentation equilibrium in an ultracentrifuge is simulated by numerical integration of the Lamm equation. Various combinations of overspeed time and angular velocity are used to assess the conditions needed to minimize the time it takes the solution to attain sedimentation equilibrium. The optimal overspeeding time and angular velocity are determined over a wide range of values of the molecular weight (relative molar mass) of the solute and the radial distance between the meniscus and base of the solution. The results may be expressed as simple functions which allow facile calculation of (a) the optimal overspeeding time and velocity, and (b) the time required to reach sedimentation equilibrium. The results are in reasonable agreement with previous analytical solutions which were based on several simplifying assumptions. The parameterized overspeeding procedure is shown to be robust over a wide range of conditions, and typically leads to a greater than 5-fold reduction in centrifugation time.     

Tools for the Quantitative Analysis of Sedimentation Boundaries Detected by Fluorescence Optical Analytical Ultracentrifugation

Fluorescence optical detection in sedimentation velocity analytical ultracentrifugation allows the study of macromolecules at nanomolar concentrations and below. This has significant promise, for example, for the study of systems of high-affinity protein interactions. Here we describe adaptations of the direct boundary modeling analysis approach implemented in the software SEDFIT that were developed to accommodate unique characteristics of the confocal fluorescence detection system. These include spatial gradients of signal intensity due to scanner movements out of the plane of rotation, temporal intensity drifts due to instability of the laser and fluorophores, and masking of the finite excitation and detection cone by the sample holder. In an extensive series of experiments with enhanced green fluorescent protein ranging from low nanomolar to low micromolar concentrations, we show that the experimental data provide sufficient information to determine the parameters required for first-order approximation of the impact of these effects on the recorded data. Systematic deviations of fluorescence optical sedimentation velocity data analyzed using conventional sedimentation models developed for absorbance and interference optics are largely removed after these adaptations, resulting in excellent fits that highlight the high precision of fluorescence sedimentation velocity data, thus allowing a more detailed quantitative interpretation of the signal boundaries that is otherwise not possible for this system.     

Effect of large refractive index gradients on the performance of absorption optics in the Beckman XL-A/I analytical ultracentrifuge: an experimental study

An analytical centrifuge cell was modified to detect refraction of light transmitted through the cell caused by refractive index gradients formed by sedimenting solute during centrifugation. Sedimentation velocity and sedimentation equilibrium experiments were carried out in this cell on solutions containing high concentrations of protein and polysaccharide in a Beckman-Coulter XLA analytical ultracentrifuge. Analysis of the results indicates that in the absence of an optical artifact easily recognized as a "black band," the dependence of apparent absorbance upon radial position reported by the instrument may be considered a reliable measure of the solute concentration gradient.     

Density contrast sedimentation velocity for the determination of protein partial-specific volumes

The partial-specific volume of proteins is an important thermodynamic parameter required for the interpretation of data in several biophysical disciplines. Building on recent advances in the use of density variation sedimentation velocity analytical ultracentrifugation for the determination of macromolecular partial-specific volumes, we have explored a direct global modeling approach describing the sedimentation boundaries in different solvents with a joint differential sedimentation coefficient distribution. This takes full advantage of the influence of different macromolecular buoyancy on both the spread and the velocity of the sedimentation boundary. It should lend itself well to the study of interacting macromolecules and/or heterogeneous samples in microgram quantities. Model applications to three protein samples studied in either H(2)O, or isotopically enriched H(2) (18)O mixtures, indicate that partial-specific volumes can be determined with a statistical precision of better than 0.5%, provided signal/noise ratios of 50-100 can be achieved in the measurement of the macromolecular sedimentation velocity profiles. The approach is implemented in the global modeling software SEDPHAT.     

Quaternary solution structures of galectins-1, -3, and -7

Galectins are a growing family of animal lectins with functions in growth regulation and cell adhesion that bind beta-Gal residues in oligosaccharides. Evidence indicates that some of the biological properties of galectins are due to their cross-linking activities with multivalent glycoconjugate receptors. Therefore determination of the quaternary solution structures of these proteins is important in understanding their structure-function properties. The present study reports analytical sedimentation velocity and equilibrium data for galectins-1, -3, and -7 in the absence and presence of bound LacNAc, the natural ligand epitope. Galectin-1 from bovine heart and recombinant human galectin-7 were found to be stable dimers by both methods. In contrast, recombinant murine galectin-3, as well as its proteolytical derived C-terminal domain, are predominantly monomeric. The presence of LacNAc at concentrations sufficient to fully saturate the proteins had no significant effect on either the weight average molecular weight determined by sedimentation equilibrium or the hydrodynamic properties determined from sedimentation velocity experiments. These results show that binding of a monovalent ligand does not affect oligomerization of these galectins.