Analytical Ultracentrifugation

Techniques and Methods

By David J. Scott, Stephen E. Harding, Arthur J. Rowe

The Royal Society of Chemistry

Copyright © 2005 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85404-547-1

Contents

Chapter 1 A Brief Introduction to the Analytical Ultracentrifugation of Proteins for Beginners D.J. Scott and P. Schuck, 1,
Chapter 2 Diffusion-Deconvoluted Sedimentation Coefficient Distributions for the Analysis of Interacting and Non-Interacting Protein Mixtures P. Schuck, 26,
Chapter 3 Models for Direct Boundary Fitting of Indefinite Ligand-Linked Self-Association J.J. Correia, C.A. Sontag, W.F. Stafford and P.J. Sherwood, 51,
Chapter 4 Allowance for Thermodynamic Nonideality in Sedimentation Equilibrium P. R. Wills and D.J. Winzor, 64,
Chapter 5 Using Analytical Ultracentrifugation of DNA in CsCl Gradients to Explore Large-Scale Properties of Genomes O. Clay, N. Carels, C.J. Douady and G. Bernardi, 104,
Chapter 6 Lammnum: A Program to Study Self-Associating Macromolecules in Sedimentation Velocity Experiments J. Behlke and O. Ristau, 122,
Chapter 7 Correcting for the Buoyancy of Macromolecules: Density Increments and Apparent Partial Specific Volumes with Particular Reference to the Study of Membrane Proteins P.J.G. Butler and C.G. Tate, 133,
Chapter 8 Application of Weighted Robust Regression to Equilibrium Ultracentrifugation M.S. Lewis and M.M. Reily, 152,
Chapter 9 The Synthetic Boundary Technique of Analytical Ultracentrifugation: A Valuable Tool to Study Structure Formation Processes Online C. Wandrey and L. Bourdillon, 162,
Chapter 10 Protein–DNA Interactions Studied at Sedimentation Equilibrium M.A. Daugherty and M.G. Fried, 195,
Chapter 11 UltraScan – A Comprehensive Data Analysis Software Package for Analytical Ultracentrifugation Experiments B. Demeler, 210,
Chapter 12 Analysis of Polysaccharide Size, Shape and Interactions S.E. Harding, 231,
Chapter 13 Analytical Ultracentrifugation as a Key Complementary Technique in Structural Biology R.J.C. Gilbert, 253,
Chapter 14 Introduction to Differential Sedimentation I. Laidlaw and M. Steinmetz, 270,
Chapter 15 Relating Small Angle Scattering and Analytical Ultracentrifugation in Multidomain Proteins S.J. Perkins, Hannah E. Gilbert, Y.C. Lee, Z.S. and P.B. Furtado, 291,
Chapter 16 Modelling of Biopolymers P. Zipper, H. Durchschlag and A. Krebs, 320,
Chapter 17 Fitting of Thermodynamic Data from Equilibrium Ultracentrifugation by Robust Least-Squares with Reduced Parameter Cross-Correlation Coefficients M.S. Lewis, M.M. Reily and L.A. Holladay, 372,
Chapter 18 Calculation of Volume, Surface, and Hydration Properties of Biopolymers H. Durchschlag and P. Zipper, 389,
Chapter 19 Analysis of Membrane Proteins Using Analytical Ultracentrifugation K.G. Fleming, 432,
Chapter 20 Solution Properties of Flexible Macromolecules: Theoretical and Computational Approaches J. Garcia De La Torre, A. Ortega and H.E. Perez Sanchez, 449,
Chapter 21 The ELLIPS Suite of Whole-Body Protein Conformation Algorithms for Microsoft WINDOWS S.E. Harding, H. Cölfen and Z. Aziz, 468,
Chapter 22 Weak Interactions: Optimal Algorithms for Their Study in the AUC A.J. Rowe, 484,
Chapter 23 Analytical Ultracentrifugation of Colloids H. Cölfen, 501,
Subject Index, 584,

CHAPTER 1

A Brief Introduction to the Analytical Ultracentrifugation of Proteins for Beginners

DAVID J. SCOTT AND PETER SCHUCK

1 Introduction

Analytical ultracentrifugation (AUC) is one of the classical methods for the characterization of purified proteins in dilute solutions, and as such there is a large body of theoretical and practical studies in the literature going back eight decades, covering aspects including the technical implementation of AUC, the theoretical foundation of ultracentrifugation in thermodynamics and physical chemistry of macromolecules, and the mathematical analysis of ultracentrifugation experiments. Developed in the 1920s by The Svedberg, and redesigned into a commercial instrument by Edward Pickels, it became a central technique in the development of biochemistry and molecular biology. While the technique was in decline in the 1970s and 1980s, new instrumentation and numerical analysis in the 1990s stimulated renewed interest in AUC, in particular for the study of protein interactions.

For the novice, however, the highly developed technical aspects in conjunction with the multitude of analytical approaches can be daunting. Therefore, this introduction to the book is unashamedly aimed at the novice who has come into contact with the methodology of the analytical ultracentrifuge and wishes to use the instrument for the characterization of globular protein samples in solution. Such a novice can be a molecular biologist, a protein crystallographer or NMR spectroscopist, or working as part of a high-through-put proteomics project, with interest in the characterization of the aggregation state, heterogeneity and thermodynamic characterization of reversible interactions of proteins. The aim of the present introduction is to provide help in where to start, or how to design and analyse a successful AUC experiment. Necessarily, this requires a very selective presentation, and for more in-depth information and descriptions of selected sedimentation velocity (SV) and sedimentation equilibrium (SE) methods, the reader is referred to recent reviews, monographs, practical protocols, and websites, and, of course, subsequent chapters in this book. Fortunately, with regard to the data interpretation, the mathematical details of advanced analysis methods are largely encapsulated in software. However, in addition to general knowledge in modelling of data and non-linear regression, their use requires understanding of the basic concepts behind them.

2 What Can I Do with My Protein Sample?

At its most basic level, AUC simply consists of the application of a centrifugal force with the simultaneous real-time observation of the resulting redistribution of the macromolecule. Analysis can be performed from first principles, given quantitative and rigorous data on a particular sample. This requires no label or other chemical modification of the proteins; such as would occur in cross-linking or many fluorescence experiments; and no interaction with any matrix or surface, as would be required for gel filtration or surface plasmon resonance. As proteins are studied in solution, the experimentalist has direct access to their solution properties: a key strength of the technique. A central feature of sedimentation experiments for the study of protein interactions is that faster sedimenting complexes are transported through a solution of the slower sedimenting components. Consequently, reversibly formed complexes that dissociate can readily re-associate during the experiment, thus permitting the hydrodynamic and thermodynamic characterization of even weak and transient interactions.

Analytical ultracentrifugation of non-interacting proteins can reveal the molar mass, gross shape, and the heterogeneity of the sample. The latter includes the detection of even trace quantities of oligomers and aggregates, which can be of interest in biotechnology applications or aid in the interpretation of biosensor experiments. For interacting systems, protein complexes can be characterized with regard to their stoichiometry and the thermodynamic and kinetic constants of complex formation. Importantly, sedimentation techniques can distinguish between multiple coexisting complexes of different stoichiometries and also provide information on self-association properties, on mixed self- and hetero-association. The latter can be a crucial information for the biophysical study of protein interactions with other techniques, such as isothermal titration calorimetry. Hydrodynamic separation also yields information on the low-resolution structure of protein complexes and can enable the detection of conformational changes.

Although a large number of specialized centrifugation techniques have been developed for a variety of studies, such as analytical zone sedimentation, difference sedimentation, synthetic boundary measurements, density gradient or fractionating and short-column techniques, the vast majority of ultracentrifugation experiments for the characterization of proteins are conducted by either conventional loading SV or long-column SE, which will be described in the following sections.

Ideally, both SV and SE techniques should be carried out on your sample, starting with SV to characterize the purity of the material. It is possible to characterise effectively a sample with SV using the latest analysis methods, however, both methods are highly complementary. The essential piece of information needed to plan an AUC experiment is to make sure at least three different concentrations of the sample are analysed, covering as wide a concentration range as possible. This is because concentration-dependent behaviour of the sample provides an information-rich data set that is highly effective in characterizing the solution properties of proteins, in particular, their interactions. This applies equally for SV and for SE. For equilibrium experiments there is the additional requirement that data should be obtained, where possible, in a sequence of experiments at three different rotor speeds.

The quantity of material required is typically of the order of a few hundred micrograms. Owing to the concentration gradients established during centrifugation, a 10- to 1000-fold concentration range is typically observed in a single cell, and a size range of three decades in molar mass can be covered in a single experiment. Interacting components under study may have sizes ranging from peptides to very large multiprotein complexes. In general, affinities in the range of 104–108 M-1 can be determined, and kinetic dissociation rate constants of the order of ~10-5–10-2 s-1 can be distinguished.

3 General Principles

Conceptually, the analytical ultracentrifuge can be thought of as a conventional preparative centrifuge that is equipped with an optical system for the observation of the protein distribution in real time during the centrifugation. The acquired data report on the spatial gradients that result from the application of the centrifugal field, and their evolution with time. Analytical rotors accept specialized assemblies for containing, typically, 100–400 µL of sample between windows that are optically transparent and perpendicular to the plane of rotation. The optical detection system is synchronized with the rotor revolution, such that data are acquired only while the sample assembly is in the light path (Figure 1).

The most commonly used optical detection systems are a dual-beam UV/VIS spectrophotometer equipped with monochromator (ABS) and a highly sensitive laser interferometer which records the refractive index gradients (IF). The ABS system requires typical loading concentrations between 0.1 and 1.5 OD, dependent on the type of experiment, and has the advantage of being able to selectively detect the protein, for example at 280 nm (for the aromatic amino acids), 230 nm (peptide backbone), or for characteristic chromophores in the VIS, if present. The IF system is not selective, but completely linear in concentration and offers high signal-to-noise ratios and rapid data acquisition (which can be particularly valuable for observing the time course of sedimentation). Drawbacks of the IF system are the experimental requirement to have a precise match of the composition of the reference buffer, and systematic time-invariant signal offsets to be accounted for in the data analysis (see below). More practical information with regard to the selection of the optical system can be found in refs. 14, 16 and 33.

Two basic types of experiments are possible: (a) the application of a high centrifugal force and the analysis of the time course of the sedimentation process, termed sedimentation velocity (SV); and (b) the application of a low centrifugal force that permits the diffusion to balance the sedimentation such that a time-invariant equilibrium gradient can be observed, termed sedimentation equilibrium (SE). Both SV and SE approaches are uniquely suited for the study of protein interactions. First, as a basis for the analysis of protein interactions, it is necessary to become familiar with the principle of sedimentation for non-interacting proteins.

The sedimentation process is governed by three factors – the gravitational force, the buoyancy and the hydrodynamic friction. The gravitational force is Fsed = mω2r (with m the protein mass, ω2 the rotor angular velocity, and r the distance from the centre of rotation). Since it is proportional to the square of the rotor speed, adjusting the rotor speed permits the study of a wide range of particle sizes, ranging from small peptides to very large protein complexes (<1 kDa to >1 GDa). The buoyancy force Fb =-m]vρω2 (with v the effective protein partial-specific volume and ρ the solvent density) opposes the sedimentation (following Archimedes principle) and is governed by the mass of the displaced solvent. Thus, protein partial-specific volumes are important, and the density effects of protein glycosylation, bound detergent and preferential hydration may be relevant considerations. Finally, the frictional force is governed by the hydrodynamic translational frictional coefficient as well as the migration velocity, and can be expressed as Ff = s(kT/D)ω2 (with k the Boltzmann constant, T the absolute temperature, and D the diffusion constant), where the sedimentation coefficient s = v/ω2 is a molecular constant (with v the absolute migration velocity). This permits the measurement of the low-resolution shape of the proteins and their complexes in terms of Stokes radii. A key parameter is the sedimentation coefficient s (measured in units of Svedberg, with 1 S = 10-13 s). From the balance of these three forces, one can derive the Svedberg equation

s/D = M(1 – [bar.v]ρ/RT (1)

(with M denoting the protein molar mass, and R denoting the gas constant), which provides a fundamental relationship between the three directly measurable quantities for a single protein component: the sedimentation coefficient (obtained from the migration of the sedimentation boundary with time in SV), the diffusion coefficient (obtained from the spread of the sedimentation boundary with time in SV) and the molar mass (obtained from the exponential gradient in SE).

4 Sedimentation Velocity

The principle behind SV is quite straightforward: at a high rotor speed, typically 40 000 rpm or above, the vast majority of proteins will sediment to the bottom of the cell. This deceptively simple process is highly information rich, as the sedimentation depends both on the size and shape of the protein. Hence a 50-kDa protein may sediment slower than a 40-kDa protein due to the heavier protein being highly elongated. If a protein self-associates with concentration then its apparent rate of sedimentation will change when either raising or lowering the loading concentration. SV will also give information on solution heterogeneity.

4.1 Setting Up a Simple Sedimentation Velocity Experiment

When first characterizing a sample by AUC, a typical amount of protein required would be 1 mL at 1 OD280, assuming the use of the ABS detection system, or at 0.5–1 mg mL-1, assuming the IF detection system. This will be enough for SV with three cells at three-fold dilutions, and have some sample left to perform an SE run. The three velocity cells should be loaded with 400 µL of sample: this will be a sample volume that fills ca. 85% of the length of the cell. Typically, concentrations can be at 1:1, 1:3 and 1:10 of the stock concentration. Generally, the concentration range should be as wide as possible, with the constraint not to exceed 1 mg mL-1 (to prevent non-ideal sedimentation), and to remain well within the detection limits (e.g., 0.05 mg mL-1<c for the IF system, and 0.05 OD <c<1.5 OD for the ABS system). The reason for the concentration series is simple: for a self-associating system, lowering the concentration sufficiently will cause oligomers to dissociate into smaller species, which will sediment slower. However, if the protein is present in a variety of oligomers that do not interconvert, then dilution will have no effect whatsoever on the proportion of oligomers. Hence, a dilution series is essential to characterizing any protein in solution. Indeed, one SV experiment (of three dilutions) will very quickly tell the experimentalist in a matter of hours whether their protein sample undergoes a complex set of self-associations of exquisite biological necessity, or that the protein is an aggregated mess, and another sample preparation is needed.

The protein purity should be >95%, and it is recommended to perform size-exclusion chromatography as the last preparative step. With regard to the buffer requirements, it is useful to include at least 20 mM salts to suppress electrostatic interactions. Obviously, no solvent component should interfere with the optical detection, and reference buffer precisely matched in volume and composition is needed for experiments with the IF system. For most proteins under common experimental conditions, the effective partial-specific volume can be predicted with sufficient precision from the amino acid sequence, for example, using the software SEDNTERP, which also permits to calculate the solvent density and viscosity from tabulated data. Greater care must be used with proteins containing non-amino acid components (e.g., glycoproteins, proteins with prosthetic groups, detergent-solubilized proteins), or buffer conditions containing glycerol, sucrose or other components increasing the density and potentially leading to preferential solvation.

(Continues…)Excerpted from Analytical Ultracentrifugation by David J. Scott, Stephen E. Harding, Arthur J. Rowe. Copyright © 2005 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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