Analytical Ultracentrifugation: Sedimentation Velocity and Sedimentation Equilibrium
Introduction
For over 75 years, analytical ultracentrifugation (AUC) has proven to be a powerful method for characterizing solutions of macromolecules and an indispensable tool for the quantitative analysis of macromolecular interactions (Cole 1999, Hansen 1994, Hensley 1996, Howlett 2006, Scott 2005). Because it relies on the principle property of mass and the fundamental laws of gravitation, AUC has broad applicability and can be used to analyze the solution behavior of a variety of molecules in a wide range of solvents and over a wide range of solute concentrations. In contrast to many commonly used methods, during AUC, samples are characterized in their native state under biologically relevant solution conditions. Because the experiments are performed in free solution, there are no complications due to interactions with matrices or surfaces. Because it is nondestructive, samples may be recovered for further tests following AUC. For many questions, there is no satisfactory substitute method of analysis.
Two complementary views of solution behavior are available from AUC. Sedimentation velocity (SV) provides first‐principle, hydrodynamic information about the size and shape of molecules (Howlett 2006, Laue 1999, Lebowitz 2002). Sedimentation equilibrium (SE) provides first‐principle, thermodynamic information about the solution molar masses, stoichiometries, association constants, and solution nonideality (Howlett 2006, Laue 1995). Different experimental protocols are used to conduct these two types of analyses. This chapter will cover the fundamentals of both velocity and equilibrium AUC.
AUC provides useful information on the size and shape of macromolecules in solution with very few restrictions on the sample or the nature of the solvent. The fundamental requirements for the sample are (1) that it has an optical property that distinguishes it from other solution components, (2) that it sediments or floats at a reasonable rate at an experimentally achievable gravitational field, and (3) that it is chemically compatible with the sample cell. The fundamental solvent requirements are its chemical compatibility with the sample cell and its compatibility with the optical systems. The range of molecular weights suitable for AUC exceeds that of any other solution technique from a few hundred Daltons (e.g., peptides, dyes, oligosaccharides) to several hundred‐million Daltons (e.g., viruses, organelles).
Different sorts of questions may be addressed by AUC depending on the purity of the sample. Detailed analyses are possible for highly purified samples with only a few discrete macromolecular components. Some of the thermodynamic parameters that can be measured by AUC include the molecular weight, association state, and equilibrium constants for reversibly interacting systems. AUC can also provide hydrodynamic shape information. For samples containing many components, or containing aggregates or lower molecular weight contaminants, or high concentration samples, size distributions and average quantities may be determined. While these results may be more qualitative than those from more purified samples, the dependence of the distributions on macromolecular concentration, ligand binding, pH, and solvent composition can provide unique insights into macromolecular behavior.
Section snippets
Basic Theory
Mass will redistribute in a gravitational field until the gravitational potential energy exactly balances the chemical potential energy at each radial position. If we monitor the rate at which boundaries of molecules move during this redistribution, then we are conducting a SV experiment. If we determine the concentration distribution after equilibrium is reached, then we are conducting an equilibrium sedimentation experiment.
Dilute Solution Measurements
For dilute solutions containing a single macromolecular component, detailed information is available from both SE and SV analysis (Cole 1999, Hansen 1994, Hensley 1996, Howlett 2006, Laue 1999, Lebowitz 2002, Scott 2005). What constitutes a dilute solution depends somewhat on the nature of the macromolecule being studied and the solvent it is in. For this review, we will consider a system dilute if there is not significant hydrodynamic or thermodynamic nonideality (below), and if gradients in
Concentrated and Complex Solutions
If a solution contains a single macromolecular component at high concentration, then one may use SE analysis to extract thermodynamic information. In particular, the concentration dependence of the apparent molecular weight, Mapp, divided into the actual molecular weight (i.e., M/Mapp) yields the activity coefficient, γ. The product of the activity coefficient and weight concentration yields the chemical activity (or apparent concentration). For an ideal solution, γ = 1, and the apparent
Instrumentation and Optical Systems
The analytical ultracentrifuge is similar to a high‐speed preparative centrifuge in that a spinning rotor provides a gravitational field large enough to make molecular‐sized particles sediment. What distinguishes the Beckman Coulter (Fullerton, CA) XLI analytical ultracentrifuge from a high‐speed preparative centrifuge is the specialized rotors, sample holders and optical systems that permit the observation of samples during sedimentation. To view the sample, the analytical rotor has holes
Sample Requirements
Often, the first question that we face when planning an AUC experiment is “do we have enough material?” The sample requirements for AUC typically lie somewhere between crystallography/NMR and biochemical assays, but they can vary greatly depending on the nature of the experiment, the optical detection system, and the extinction coefficient. The sample volumes required for AUC analysis are quite low. SV experiments are generally performed using two‐sector cells that require 420 μl/sample, but for
Sample Preparation
The admonition from the late Efraim Racker “Don't waste clean thinking on dirty enzymes” (Schatz, 1996) applies well to AUC. Rather than trying to interpret complicated and ambiguous AUC data obtained using impure or heterogeneous samples, we find that the time is much better spent on improved purification protocols. In practice, proteins should be at least 95% pure by SDS–polyacrylamide gel electrophoresis and the mass spectrum should correspond to a single species consistent with the
Instrument Operation and Data Collection
SV experiments are carried out in two‐channel cells with sector‐shaped compartments (Fig. 1) in order to prevent convection, which would occur if the cell walls were not parallel to radial lines. The usual protocol in our laboratories is to run three sample concentrations spanning at least an order of magnitude, for example, 0.1, 0.3, and 1.0 mg/ml.
For SV experiments using absorbance optics, the cells are assembled using standard double‐sector centerpieces and quartz windows. The cells are
Sedimentation Equilibrium
The big advantage of SE is that it removes all hydrodynamic effects, so that purely thermodynamic analysis is possible. The requirements for sample purity and homogeneity are much stricter for SE measurements that for velocity experiments. In the latter case, the boundaries associated with each species separate during the sedimentation run so that it is possible to isolate contaminants from the species of interest. In contrast, different species are incompletely fractionated in an SE gradient.
Discussion and Summary
AUC is a versatile and rigorous technique for characterizing the molecular mass, shape, and interactions of biological molecules in solution. In particular, the size distribution analysis available with SV is more flexible, is applicable to more chemical systems, spans a much wider range of sizes, and provides higher resolution than size exclusion chromatography. The hydrodynamic information available with SV is complemented by thermodynamic analysis by SE. The availability of interference
Acknowledgment
This work was supported by grant numbers RR‐18286 and AI‐53615 from the NIH to J.L.C.
References (89)
- et al.
Improved ultracentrifuge cells for high‐speed sedimentation equilibrium studies with interference optics
Anal. Biochem.
(1970) - et al.
Calculation of the partial specific volume of proteins in concentrated salt and amino acid solutions
Methods Enzymol.
(1985) - et al.
Molecular mass determination by sedimentation velocity experiments and direct fitting of the concentration profiles
Biophys. J.
(1997) Construction of hydrodynamic bead models from high‐resolution X‐ray crystallographic or nuclear magnetic resonance data
Biophys. J.
(1997)Hydrodynamic bead modeling of biological macromolecules
Methods Enzymol.
(2000)Analysis of heterogeneous interactions
Methods Enzymol.
(2004)Analysis of weight average sedimentation velocity data
Methods Enzymol.
(2000)- et al.
Calculating sedimentation coefficient distributions by direct modeling of sedimentation velocity concentration profiles
Methods Enzymol.
(2004) - et al.
Sedimentation velocity analysis of heterogeneous protein‐protein interactions: Sedimentation coefficient distributions c(s) and asymptotic boundary profiles from Gilbert‐Jenkins theory
Biophys. J.
(2005) - et al.
Sedimentation velocity analysis of heterogeneous protein‐protein interactions: Lamm equation modeling and sedimentation coefficient distributions c(s)
Biophys. J.
(2005)