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.     

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.     

Non-ideal tracer sedimentation equilibrium: a powerful tool for the characterization of macromolecular interactions in crowded solutions

Non-ideal tracer sedimentation equilibrium is a technique devised to quantify the effect of high concentrations of unrelated macromolecules on the self- or hetero-associations of dilute macromolecules. Principles and experimental techniques are reviewed, and previous experimental work summarized. A new analysis of experimental data is presented that requires no a priori assumptions regarding the nature of weak repulsive interactions between solute species and the concentrated (crowding) species.     

Biochemical characterization of mitochondrial and lysosomal particles in old rat liver

Sedimentation rates, equilibrium densities, and membrane fragility of liver mitochondrial and lysosomal particles were estimated in adult and 36-month-old rats. The sedimentation coefficient and the size of particles were also calculated. The fractionation experiments indicated a similar enzymatic distribution for mitochondrial and lysosomal tracer enzymes in both types of animals. The liver mitochondria of senescent and mature rats were identical in sedimentation rate, sedimentation constants, equilibrium densities, fragility under isotonic conditions, and oxidative phosphorylation. Only in hypotonic media was there a decreased cohesiveness of the external mitochondrial membrane in older animals. In old rats several lysosomal tracer enzymes had lower sedimentation rates and sedimentation coefficients. The equilibrium densities were higher in these animals too. The lysosomal latency in old and mature rats was identical. It can be concluded that in very old age liver lysosomes are smaller in size than those in mature animals.     

A strategy for efficient characterization of macromolecular heteroassociations via measurement of sedimentation equilibrium.

A method is proposed for the selection of experimental conditions for sedimentation equilibrium experiments that will provide maximal information about the values of equilibrium association constants within a given scheme for heteroassociation of two solute components. A discriminator function is proposed that indicates the sensitivity of the experimentally observed gradient or gradients to alterations in the underlying association constants. The value of this function is plotted or tabulated as a function of the concentrations of the two components, over a broad range of solution compositions. It is suggested that experiments performed with loading compositions corresponding to large absolute values of the discriminator function will yield the most information with respect to determination of the underlying association constants. This method was tested by predicting optimal conditions for three different types of sedimentation equilibrium experiments: (i) measurement of total (natural) solute absorbance; (ii) measurement of individual component gradients via measurement of tracer absorbance; and (iii) global analysis of multiple experiments. Experimental data resulting from sedimentation equilibrium experiments carried out under the specified conditions were simulated by addition of realistic levels of random error to calculated equilibrium gradients. The simulated data were then analyzed exactly as real experimental data, i.e., without prior knowledge of the underlying association constants. It was found that the highest accuracy and precision in determination of heteroassociation constants are obtained by global analysis of multiple experiments performed using significantly different loading compositions, each of which is selected from 'sensitive' regions of the discriminator map.     

Variable-Field Analytical Ultracentrifugation: I. Time-Optimized Sedimentation Equilibrium

Sedimentation equilibrium (SE) analytical ultracentrifugation (AUC) is a gold standard for the rigorous determination of macromolecular buoyant molar masses and the thermodynamic study of reversible interactions in solution. A significant experimental drawback is the long time required to attain SE, which is usually on the order of days. We have developed a method for time-optimized SE (toSE) with defined time-varying centrifugal fields that allow SE to be attained in a significantly (up to 10-fold) shorter time than is usually required. To achieve this, numerical Lamm equation solutions for sedimentation in time-varying fields are computed based on initial estimates of macromolecular transport properties. A parameterized rotor-speed schedule is optimized with the goal of achieving a minimal time to equilibrium while limiting transient sample preconcentration at the base of the solution column. The resulting rotor-speed schedule may include multiple over- and underspeeding phases, balancing the formation of gradients from strong sedimentation fluxes with periods of high diffusional transport. The computation is carried out in a new software program called TOSE, which also facilitates convenient experimental implementation. Further, we extend AUC data analysis to sedimentation processes in such time-varying centrifugal fields. Due to the initially high centrifugal fields in toSE and the resulting strong migration, it is possible to extract sedimentation coefficient distributions from the early data. This can provide better estimates of the size of macromolecular complexes and report on sample homogeneity early on, which may be used to further refine the prediction of the rotor-speed schedule. In this manner, the toSE experiment can be adapted in real time to the system under study, maximizing both the information content and the time efficiency of SE experiments.     

Mixed gelation theory. Kinetics, equilibrium and gel incorporation in sickle hemoglobin mixtures.

This paper outlines a theoretical formalism for describing the gelling behavior of sickle cell hemoglobin in mixtures with other hemoglobin and non-hemoglobin proteins. Experimental applications are reported for hybridized and unhybridized mixtures of HbS (sickle hemoglobin), HbA (adult hemoglobin), HbF (fetal hemoglobin), and HbC Harlem. The theory is a general one based on a modification of the sol—gel phase equilibrium equation to take into account the varying tendencies of different hemoglobin species to promote gelation, and specific hemoglobin interactions are encoded in gelling coefficients which quantify gelling capability. Gelling coefficients for the hemoglobin species dealt with here are evaluated by measuring incorporation into the polymer phase in S-A, S-F, and S-C_H mixtures. Given this information, the theory is found to provide accurate prodictions for the equilibrium gelling behavior of the calibrating pairs themselves when they are hybridized or unhybridized, for gelation kinetics in diverse mixtures of these species taken two, three and four at a time, for the anomalous equilibrium and kinetic gelling behavior of A- C_H mixtures, and it also accounts for a variety of results previously published by others. Apparently, given the gelling coefficients for any mutant hemoglobin, one can compute gelling behavior (equilibrium, kinetics, incorporation, etc.) in any specified mixture with any other known hemoglobin(s). The gelling coefficients for any mutant hemoglobin depend upon, and therefore provide information about, gel interactions at the mutant site. From the gelling coefficients one can also obtain the change in free energy of interaction in the gel due to the altered residue. Experimental approaches are described which allow an analysis for the gelling coefficients of any mutant hemoglobin to be performed in a few hours.     

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B(22), the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein-protein and protein-buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B(22) accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.     

Analytical ultracentrifugation for the study of protein association and assembly

Analytical ultracentrifugation remains pre-eminent among the methods used to study the interactions of macromolecules under physiological conditions. Recent developments in analytical procedures allow the high resolving power of sedimentation velocity methods to be coupled to sedimentation equilibrium approaches and applied to both static and dynamic associations. Improvements in global modeling based on numerical solutions of the Lamm equation have generated new sedimentation velocity applications with an emphasis on data interpretation using sedimentation coefficient or molar mass distributions. Procedures based on the use of multiple optical signals from absorption and interference optics for the analysis of the sedimentation velocity and equilibrium behavior of more complex interactions have now been developed. New applications of tracer sedimentation equilibrium experiments and the development of a fluorescence optical system for the analytical ultracentrifuge extend the accessible concentration range over several orders of magnitude and, coupled with the new analytical procedures, provide powerful new tools for studies of both weak and strong macromolecular interactions in solution.     

Sedimentation equilibrium studies on the interaction between cytochrome c and cytochrome c peroxidase

The interaction between cytochrome c and cytochrome c peroxidase was investigated using sedimentation equilibrium at pH 6,20 degrees C, in a number of buffer systems varying in ionic strength between 1 and 100 mM. Between 10 and 100 mM ionic strengths, the sedimentation of the individual proteins was essentially ideal, and sedimentation equilibrium experiments on mixtures of the two proteins were analyzed assuming ideal solution behavior. Analysis of the distribution of mixtures of cytochrome c and cytochrome c peroxidase in the ultracentrifuge cell based on a model involving the formation of a 1:1 cytochrome c-cytochrome c peroxidase complex gave values of the equilibrium dissociation constant ranging from 2.3 +/- 2.7 microM at 10 mM ionic strength to infinity (no detectable interaction) at 100 mM ionic strength. Attempts to determine the presence of complexes involving two cytochrome c molecules bound to cytochrome c peroxidase were inconclusive.     

Sedimentation Equilibrium of a Small Oligomer-forming Membrane Protein: Effect of Histidine Protonation on Pentameric Stability

Analytical ultracentrifugation (AUC) can be used to study reversible interactions between macromolecules over a wide range of interaction strengths and under physiological conditions. This makes AUC a method of choice to quantitatively assess stoichiometry and thermodynamics of homo- and hetero-association that are transient and reversible in biochemical processes. In the modality of sedimentation equilibrium (SE), a balance between diffusion and sedimentation provides a profile as a function of radial distance that depends on a specific association model. Herein, a detailed SE protocol is described to determine the size and monomer-monomer association energy of a small membrane protein oligomer using an analytical ultracentrifuge. AUC-ES is label-free, only based on physical principles, and can be used on both water soluble and membrane proteins. An example is shown of the latter, the small hydrophobic (SH) protein in the human respiratory syncytial virus (hRSV), a 65-amino acid polypeptide with a single α-helical transmembrane (TM) domain that forms pentameric ion channels. NMR-based structural data shows that SH protein has two protonatable His residues in its transmembrane domain that are oriented facing the lumen of the channel. SE experiments have been designed to determine how pH affects association constant and the oligomeric size of SH protein. While the pentameric form was preserved in all cases, its association constant was reduced at low pH. These data are in agreement with a similar pH dependency observed for SH channel activity, consistent with a lumenal orientation of the two His residues in SH protein. The latter may experience electrostatic repulsion and reduced oligomer stability at low pH. In summary, this method is applicable whenever quantitative information on subtle protein-protein association changes in physiological conditions have to be measured.       

Preparation of red-cell-membrane cytoskeletal constituents and characterisation of protein 4.1

A new and rapid method is described for the preparation of protein 4.1, the protein which modulates the interaction between spectrin and actin in the membrane cytoskeleton of the red cell. The method is based on the dissociation of purified membrane cytoskeletons in concentrated Tris at neutral pH, followed by gel filtration in the same medium. This procedure also yields spectrin and actin, as well as the fourth cytoskeletal constituent, protein 4.9, in relatively pure form, and ankyrin. Protein 4.1 is monomeric under our conditions of solvent and protein concentration, with a relative molecular mass, as determined from sedimentation equilibrium, of about 78 000; its sedimentation coefficient and Stokes' radius are those of a globular, though somewhat asymmetric or flexible molecule. It forms a strong complex with F-actin and spectrin. Protein 4.9 is also recovered in active form, and will bind strongly to F-actin.     

Molecular size of nerve growth factor in dilute solution.

Nerve growth factor (NGF) is a protein composed of two identical chains of mass 13,259. An analysis of the sedimentation equilibrium, sedimentation velocity, and gel filtration behavior of dilute solutions of NGF indicates the existence of a rapidly reversible monomer in equilibrium dimer equilibrium and that the association constant K for the reaction at neutral pH is 9.4 X 10(6)M-1. Reaction mixtures consist of equal concentrations of monomer and dimer at a total protein concentration as high as 1.4 mug/ml, and at 1 ng/ml, monomer accounts for greater than 99% of the total. The latter concentration is 20 to 30 times that required for the biological activity of NGF. Several lines of evidence suggest that the dimerization reaction is highly stereospecific, although its biological significance is not known.     

Protein self-association in crowded protein solutions: a time-resolved fluorescence polarization study

The self-association equilibrium of a tracer protein, apomyoglobin (apoMb), in highly concentrated crowded solutions of ribonuclease A (RNase A) and human serum albumin (HSA), has been studied as a model system of protein interactions that occur in crowded macromolecular environments. The rotational diffusion of the tracer protein labeled with two different fluorescent dyes, 8-anilinonaphthalene-1-sulfonate and fluorescein isothiocyanate, was successfully recorded as a function of the two crowder concentrations in the 50-200 mg/mL range, using picosecond-resolved fluorescence anisotropy methods. It was found that apoMb molecules self-associate at high RNase A concentration to yield a flexible dimer. The apparent dimerization constant, which increases with RNase A concentration, could also be estimated from the fractional contribution of monomeric and dimeric species to the total fluorescence anisotropy of the samples. In contrast, an equivalent mass concentration of HSA does not result in tracer dimerization. This different effect of RNase A and HSA is much larger than that predicted from simple models based only on the free volume available to apoMb, indicating that additional, nonspecific interactions between tracer and crowder should come into play. The time-resolved fluorescence polarization methods described here are expected to be of general applicability to the detection and quantification of crowding effects in a variety of macromolecules of biological relevance.     

Studies on 125I-labeled proteins in rat plasma using an air-driven ultracentrifuge: protein-protein interactions and nonideality

The molecular weights of a number of ¹²⁵I-labeled plasma proteins have been determined from an analysis of their sedimentation equilibrium behavior in an air-driven ultracentrifuge. The values obtained agree well with results obtained by other methods. Molecular weights obtained for ¹²⁵I-labeled bovine serum albumin and the rat serum proteins albumin, α₁-acid glycoprotein, and major acute-phase α₁-protein were unaffected by the addition of 7% rat plasma. Direct evidence for protein-protein interactions was obtained for mixtures of ¹²⁵I-labeled rat α₁-acid glycoprotein and the plant lectin concanavalin A and for mixtures of ¹²⁵I-labeled protein A from Staphylococcus aureus and 7% rat plasma. Interactions of a different type were observed when the sedimentation equilibrium profiles of ¹²⁵I-labeled proteins were determined in concentrated solutions of other proteins. Under these conditions the effects of molecular exclusion or nonideality became significant and low estimates were obtained for the molecular weights of the labeled proteins. Analysis of the data obtained for ¹²⁵I-labeled bovine serum albumin in concentrated solutions of bovine serum albumin (20–80 mg/ ml) yielded nonideality coefficients in good agreement with literature values. Analysis of the behavior of ¹²⁵I-labeled rat serum albumin, transferrin, and α₁-acid glycoprotein yielded nonideality coefficients and hence activities of these proteins in undiluted rat plasma.     

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.     

The preparation of human hemoglobin alpha-subunit and a study of its monomer-dimer association.

An improved procedure for the isolation of the alpha-subunit of human hemoglobin is described. The monomer-dimer equilibrium in alpha-subunit solutions has been studied by boundary analysis in gel filtration, sedimentation velocity, sedimentation equilibrium, and cross-linking with dimethyl adipimidate. A dissociation constant has been determined from the sedimentation equilibrium data. The reaction with haptoglobin of cross-linked alpha-subunit showed that the dimer fraction wound form a stable complex.     

Characterization of self-association and heteroassociation of bacterial cell division proteins FtsZ and ZipA in solution by composition gradient-static light scattering

We have characterized the self-association of FtsZ in its GDP-bound state (GDP-FtsZ) and the heteroassociation of FtsZ and a soluble recombinant ZipA (sZipA) lacking the N-terminal transmembrane domain by means of composition gradient-static light scattering (CG-SLS) and by measurement of sedimentation equilibrium. CG-SLS experiments at high ionic strengths and in the presence of 5 mM Mg(2+) show that, while FtsZ self-associates in a noncooperative fashion, sZipA acts as a monomer. CG-SLS data obtained from mixtures of FtsZ (A) and sZipA (B) in the presence of Mg(2+) are quantitatively described by an equilibrium model that takes into account significant scattering contributions from B, A(1), A(2), A(3), A(4), A(5), A(6), A(1)B, A(2)B, A(3)B, and A(4)B. However, in the absence of Mg(2+) (with EDTA), the data are best explained by an equilibrium model in which only B, A(1), A(2), A(3), A(1)B, and A(2)B contribute significantly to scattering. The best-fit molecular weights of monomeric A and B are in good agreement with values calculated from amino acid composition and with values obtained from sedimentation equilibrium. The latter technique also confirmed the interaction between sZipA and GDP-FtsZ. Moreover, the association model that best describes the CG-SLS data is in qualitative agreement with the sedimentation data. From these results, it follows that the binding of sZipA to GDP-FtsZ is of moderate affinity and does not significantly affect the interactions between FtsZ monomers. Under the working conditions used, only one sZipA binds to FtsZ oligomers with a length of six at most. The observed behavior would be compatible with FtsZ fibrils being anchored in vivo to the bacterial inner plasma membrane by substoichiometric binding of membrane-bound ZipA.     

Zone Centrifugation in a Cesium Chloride Density Gradient Caused by Temperature Change

In this communication is described a new technique for the determination of sedimentation coefficients of macromolecules banded in equilibrium density gradients. Initially, the macromolecules are banded in the analytical ultracentrifuge at a low temperature of about 5°C. After equilibrium has been obtained, the temperature is increased to 25°C. The equilibrium band will now sediment to a new equilibrium position in the ultracentrifuge cell: (a) By following the position of the migrating band as a function of time, sedimentation coefficients may be determined. (b) If several species having different sedimentation coefficients are present in the original band, then during the course of the migration the band may split into several new bands which eventually reunite at the final equilibrium position. (c) If different chemical species of macromolecules such as nucleic acids and carbohydrates are present, in general they will exhibit different temperature density relationships, and can move different distances and directions in response to temperature change.