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Molecular Interactions and Protein Biophysics Resources, Division of Bioengineering and Physical Science, ORS, OD, National Institutes of Health, Bethesda, Maryland 20892, USA
Reprint requests to: Jacob Lebowitz, National Institutes of Health, 13 South Drive, Bldg. 13, Room 3N17, Bethesda, MD 20892, USA; e-mail: lebowitz{at}helix.nih.gov; fax: (301) 480-1242.
Eisenberg has prepared a short paper in this issue entitled "Modern analytical ultracentrifugation in protein science: Look forward, not back," that is critical of our Protein Science review, "Modern analytical ultracentrifugation in protein science: A tutorial review" (Lebowitz et al. 2002). Eisenberg contends that the analytical ultracentrifugation (AU) equations should be developed from multicomponent theory and not the classical Svedberg analysis because the latter is only applicable to two-component systems. We have no argument that multicomponent theory is of importance to understand the effects produced by cosolvents at high concentrations. However, most AU studies are made in buffered dilute salt, and under these conditions, it is usually assumed that the salt/buffer solution is a one-component solvent because preferential interactions either do not occur or generate extremely small errors (Schachman 1959). For the latter case, a simple calculation of the magnitude of the preferential interaction term 
1(1 - 
1) of equation 6 of the Eisenberg paper shows this clearly. Let us assume that we are using PBS at 20°C for a protein sedimentation study, the value is 1.0052 g/mL and 
1 (the reciprocal of the density of water) is 1.0018 mL/g leading to a value of -0.0070 for (1 - 1). Let us select a 
1 value of 0.04 (this is the value for BSA in 1.0 M NaCl from the cited Eisenberg 2000 paper) leading to a value of -0.0003 for 1(1 - 1). Assuming a 2 value of 0.730 mL/g for the protein, the (1 - 2) term needs a correction of 0.1% from the classical treatment. The preferential interaction term 1(1 - 1) has to be very small under dilute buffer/salt conditions because the density of water is very close to the density of the solution.
Based on the above considerations, the classical treatment of sedimentation velocity and equilibrium measurements, under dilute buffer/salt conditions, is valid. This has been the conceptual framework accepted by investigators in the AU field and successfully applied in countless studies. For investigators to implement the multicomponent treatment, density increment d/dc measurements for all protein samples would have to be performed. Eisenberg argues that there are no unusual difficulties or material requirements in the determination of the density increment d/dc. He states that a 1-mL dialyzed solution of the protein at 1 mg/mL is required. In contrast, both Lee et al. (1979) and Durchschlag (1986) propose concentrations of 3–20 and 5–20 mg/mL, respectively, for high precision measurements of d/dc. Assuming that 1 mg/mL is acceptable, what is the error of measuring density using the Paar DMA 5000 density meter? The usual precision for water is ±3.5 x 10-6 g/mL (Durchschlag 1986), and if this is applied to a protein solution of 1 mg/mL, the error in molar mass would be ±1.3%. For dilute solutions, this error is likely to be much greater than the correction for preferential interactions. A question also arises as to the error involved in concentration determinations. We believe that Eisenberg seriously understates both the experimental complications and the amounts of material needed for high precision density meter measurements of protein density increments. Eisenberg overstates the ease of obtaining proteins for biophysical studies. Protein expression difficulties may arise due to formation of inactive and misfolded protein aggregates, leading to low yields of the functional protein. Our review covered work on glycoproteins, membrane proteins, and other proteins that cannot be obtained from recombinant DNA procedures. The material for accurate density increment measurements is generally unavailable in our experience.
A current major focus of analytical ultracentrifugation is the determination of heterogeneous interactions as discussed in our review (Lebowitz et al. 2002). Today, the molar mass is usually known from the primary sequence or can be measured by mass spectrometry. For heterogeneous protein interactions, the buoyant molar mass (the product Md/dc in multicomponent or M[1 - 2] in two-component theory) can be determined separately for each component using sedimentation equilibrium analysis. Because this buoyant molar mass is the primary measured quantity for dilute proteins, it is completely independent of which theoretical framework is used to explain its origin. The correct decomposition into contributions intrinsic to the macromolecule and those from solvation are usually of secondary importance if only the extent of complex formation of the heterogeneous association is the subject of study, because binding constants can be determined based on the measured buoyant molar mass values only (Lebowitz et al. 2002). The measured buoyant molar mass for each component can be used in a separate interpretative step to estimate d/dc and (1 - 2) as described by Eisenberg. We recognize that preferential interactions, and, in general, the solvent conditions, can modulate the strength of macromolecular interactions. The additivity of the buoyant molar mass of the complex, which was used in our review, implies that the buoyancy effect of the preferential solvation of the complex is the weighted sum of those of the components. Any deviations from the additivity should constitute a second-order effect for most situations, and could be detected by pressure dependence if significant (Harrington and Kegeles 1973). With a few exceptions, the overwhelming majority of protein interactions have shown no pressure dependence at the centrifugal fields used in the analytical ultracentrifuge, which indicates that the effect of solvation changes due to complex formation are below measurement error.
Timasheff and coworkers have also focused extensively on preferential interactions, and a statement from their Methods in enzymology paper (Lee et al. 1979) frames the issue. "At this point, it might seem pertinent to ask the under what circumstances are preferential interactions significant? The most general answer is that preferential interactions are significant in all situations in which a chemical process is affected by solvent components, whether they are specific ligands, nonspecific additives, or solvent components, such as glycerol, CsCl, sucrose, urea or alcohol. Probably, the most familiar example of the importance of preferential interaction, is found in the measurement of molecular weights by sedimentation equilibrium in a concentrated denaturant, such as the measurement of the molecular weight of the subunits of an enzyme in 6 M guanidine hydrochloride." Clearly, multicomponent theory does play a very significant role in research by using cosolutes to determine solute/solvent interactions and this provides very important biophysical data. Although Eisenberg and his colleagues have made major contributions, it should be pointed out that others have contributed greatly to this area. The study of preferential interactions is by no means a neglected topic. For example, two treatments of this area of research have recently appeared (Costenaro and Ebel 2002; Timasheff 2002).
In summary, we believe that the inflexible view of Eisenberg regarding our review of AU is counterproductive because, if adopted, it would diminish the use of AU by protein scientists for the characterization of proteins where preferential interactions are negligible. This would occur because investigators would consider sedimentation velocity/equilibrium studies coupled with density increment measurements, as suggested by Eisenberg, as too complex and too costly. The introduction to AU through the development of the classical equations, which hold for buffered dilute salt solutions, has been judged by all authors of educational biophysical texts to be appropriate. Proteomic studies will identify a large number of new interacting systems for characterization, and AU should be able to play an important role in understanding these interactions. We believe that our review, as it stands, helps to meet this future. It should be emphasized that our short tutorial review was intended to introduce analytical ultracentrifugation to a broad range of protein scientists and consequently required a high degree of selectivity in the topics covered. Analytical ultracentrifugation has a 75-year history with exceptional versatility of applications to many biophysical problems that includes the analysis of preferential interactions.
References
Costenaro, L. and Ebel, C. 2002. Thermodynamic relationships between protein–solvent and protein–protein interactions. Acta Cryst. D 58: 1554–1559.[Medline]
Durchschlag, H. 1986. Specific volumes of biological macromolecules and some other molecules of biological interest. In Thermodynamic data for biochemistry and biotechnology (ed. H.-J. Hinz), pp. 45–128. Springer, Berlin.
Harrington, W.F. and Kegeles, G. 1973. Pressure effects in ultracentrifugation of interacting systems. Methods Enzymol. 27: 306–345.[Medline]
Lebowitz, J., Lewis, M.S., and Schuck, P. 2002. Modern analytical ultracentrifugation in protein science: A tutorial review. Protein Sci. 11: 2067–2079.
Lee, J.C., Gekko, K., and Timasheff, S.N. 1979. Measurements of preferential solvent interactions by densimetric techniques. In Methods in enzymology (eds. C.H.W. Hirs and S.N. Timasheff), Vol. 61, pp. 26–49. Academic Press, New York.
Schachman, H.K. 1959. Ultracentrifugation in biochemistry. Academic Press, New York.
Timasheff, S.N. 2002. Protein hydration, thermodynamic binding, and preferential hydration. Biochemistry 41: 13473–13482.[CrossRef][Medline]
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