Measuring Protein‐Protein Interactions by Equilibrium Sedimentation

Andrea Balbo1, Patrick H. Brown1, Emory H. Braswell2, Peter Schuck2

1 National Institutes of Health, Bethesda, Maryland, 2 University of Connecticut, Storrs, Connecticut
Publication Name:  Current Protocols in Immunology
Unit Number:  Unit 18.8
DOI:  10.1002/0471142735.im1808s79
Online Posting Date:  November, 2007
GO TO THE FULL TEXT: PDF or HTML at Wiley Online Library


This unit describes basic principles and practice of sedimentation equilibrium analytical ultracentrifugation for the study of reversible protein interactions, such as the characterization of self‐association, heterogeneous association, and binding stoichiometry, as well as the determination of association constants. Advanced tools such as mass conservation analysis, multiwavelength analysis, and global analysis are introduced and discussed in the context of the experimental design. A detailed protocol guiding the investigator through the experimental steps and the data analysis is available as an internet resource. Curr. Protoc. Immunol. 79:18.8.1‐8.18.28. © 2007 by John Wiley & Sons, Inc.

Keywords: sedimentation equilibrium; sedimentation velocity; chemical equilibria; reversible interactions; multi‐protein complex; analytical ultracentrifugation

PDF or HTML at Wiley Online Library

Table of Contents

  • Introduction
  • Basic Principles
  • Strategies for the Analysis of Reversible Interactions
  • Experimental Considerations
  • Summary
  • Literature Cited
  • Figures
PDF or HTML at Wiley Online Library


PDF or HTML at Wiley Online Library



Literature Cited

   Adams, E.T., Jr., and Lewis, M.S. 1968. Sedimentation equilibrium in reacting systems. VI. Some applications to indefinite self‐associations: Studies with beta‐lactoglobulin A. Biochemistry 7:1044‐1053.
   Advant, S.J., Braswell, E.H., Kumar, C.V., and Kalonia, D.S. 1995. The effect of pH and temperature on the self‐association of recombinant human interleukin‐2 as studied by equilibrium sedimentation. Pharm. Res. 12:637‐641.
   Ansevin, A.T., Roark, D.E., and Yphantis, D.A. 1970. Improved ultracentrifuge cells for high‐speed sedimentation equilibrium studies with interference optics. Anal. Biochem. 34:237‐261.
   Arisaka, F. 1999. Applications and future perspectives of analytical ultracentrifugation. Tanpakushitsu Kakusan Koso 44:82‐91.
   Arkin, M. and Lear, J.D. 2001. A new data analysis method to determine binding constants of small molecules using equilibrium analytical ultracentrifugation with absorption optics. Anal. Biochem. 299:98‐107.
   Balbo, A. and Schuck, P. 2005. Analytical ultracentrifugation in the study of protein self‐association and heterogeneous protein‐protein interactions. In Protein‐Protein Interactions. (E. Golemis and P.D. Adams, eds.) pp. 253‐277. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, New York.
   Berkowitz, S.A. 2006. Role of analytical ultracentrifugation in assessing the aggregation of protein biopharmaceuticals. AAPS J. 8:E590‐E605.
   Bevington, P.R. and Robinson, D.K. 1992. Data Reduction and Error Analysis for the Physical Sciences. McGraw‐Hill, New York.
   Boulant, S., Vanbelle, C., Ebel, C., Penin, F., and Lavergne, J.P. 2005. Hepatitis C virus core protein is a dimeric alpha‐helical protein exhibiting membrane protein features. J. Virol. 79:11353‐11365.
   Braswell, E. and Lary, J. 1981. Equilibrium‐sedimentation studies of some self‐associating cationic dyes. J. Phys. Chem. 85:1573.
   Burgess, B.R., Schuck, P., and Garboczi, D.N. 2005. Dissection of merozoite surface protein 3, a representative of a family of Plasmodium falciparum surface proteins, reveals an oligomeric and highly elongated molecule. J. Biol. Chem. 280:37236‐37245.
   Burrows, S.D., Doyle, M.L., Murphy, K.P., Franklin, S.G., White, J.R., Brooks, I., McNulty, D.E., Scott, M.O., Knutson, J.R., Porter, D., Young, P.R., and Hensley, P. 1994. Determination of the monomer‐dimer equilibrium of interleukin‐8 reveals it is a monomer at physiological concentrations. Biochemistry 33:12741‐12745.
   Center, R.J., Earl, P.L., Lebowitz, J., Schuck, P., and Moss, B. 2000. The human immunodeficiency virus type 1 gp120 V2 domain mediates gp41‐independent intersubunit contacts. J. Virol. 74:4448‐4455.
   Center, R.J., Schuck, P., Leapman, R.D., Arthur, L.O., Earl, P.L., Moss, B., and Lebowitz, J. 2001. Oligomeric structure of virion‐associated and soluble forms of the simian immunodeficiency virus envelope protein in the pre‐fusion activated conformation. Proc. Natl. Acad. Sci. U.S.A. 98:14877‐14882.
   Chatelier, R.C. 1988. A parameterized overspeeding method for the rapid attainment of low‐speed sedimentation equilibrium. Anal. Biochem. 175:114‐119.
   Chatelier, R.C. and Minton, A.P. 1987. Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. II. Two protein components. Biopolymers 26:1097‐1113.
   Cole, J.L. 2004. Analysis of heterogeneous interactions. Meth. Enzymol. 384:212‐232.
   Correia, J.J. and Yphantis, D.A. 1992. Equilibrium sedimentation in short solution columns. In Analytical Ultracentrifugation in Biochemistry and Polymer Science. (S.E. Harding, A.J. Rowe, and J.C. Horton, eds.) pp. 231‐252. The Royal Society of Chemistry, Cambridge, U.K.
   Dall'Acqua, W., Goldman, E.R., Eisenstein, E., and Mari uzza, R.A. 1996. A mutational analysis of the binding of two different proteins to the same antibody. Biochemistry 35:9667‐9676.
   Dam, J., Guan, R., Natarajan, K., Dimasi, N., Chlewicki, L.K., Kranz, D.M., Schuck, P., Margulies, D.H., and Mari uzza, R.A. 2003. Variable MHC class I engagement by Ly49 NK cell receptors revealed by the crystal structure of Ly49C bound to H‐2Kb. Nat. Immunol. 4:1213‐1222.
   Dam, J., Baber, J., Grishaev, A., Malchiodi, E.L., Schuck, P., Bax, A., and Mari uzza, R.A. 2006. Variable dimerization of the Ly49A natural killer cell receptor results in differential engagement of its MHC class I ligand. J. Mol. Biol. 362:102‐113.
   Darawshe, S. and Minton, A.P. 1994. Quantitative characterization of macromolecular associations in solution via real‐time and postcentrifugation measurements of sedimentation equilibrium: A comparison. Anal. Biochem. 220:1‐4.
   Darawshe, S., Rivas, G., and Minton, A.P. 1993. Rapid and accurate microfractionation of the contents of small centrifuge tubes: Application in the measurement of molecular weights of proteins via sedimentation equilibrium. Anal. Biochem. 209:130‐135.
   Datta, S.A., Zhao, Z., Clark, P.K., Tarasov, S., Alexandratos, J.N., Campbell, S.J., Kvaratskhelia, M., Lebowitz, J., and Rein, A. 2007. Interactions between HIV‐1 Gag molecules in solution: An inositol phosphate‐mediated switch. J. Mol. Biol. 365:799‐811.
   Davis, A.J., Perugini, M.A., Smith, B.J., Stewart, J.D., Ilg, T., Hodder, A.N., and Handman, E. 2004. Properties of GDP‐mannose pyrophosphorylase, a critical enzyme and drug target in Leishmania mexicana. J. Biol. Chem. 279:12462‐12468.
   Dölle, F. and Schubert, D. 1997. Dye‐labelling as a means to study ternary protein complexes by analytical ultracentrifugation: The band 3/ankyrin/aldolase complex from erythrocyte membranes. Prog. Colloid Polym. Sci. 107:77‐81.
   Durchschlag, H. 1986. Specific volumes of biological macromolecules and some other molecules of biological interest. In Thermodynamic data for biochemistry and biotechnology. (H.‐J. Hinz, ed.) pp. 45‐128. Springer, Berlin.
   Edelstein, J. and Schachman, H. 1967. Simultaneous determination of partial specific volumes and molecular weights with microgram quantities. J. Biol. Chem. 242:306‐311.
   Fairman, R., Fenderson, W., Hail, M.E., Wu, Y., and Shaw, S.‐Y. 1999. Molecular weights of CTLA‐4 and CD80 by sedimentation equilibrium ultracentrifugation. Anal. Biochem. 270:286‐295.
   Fernandez, M.M., Bhattacharya, S., De Marzi, M.C., Brown, P.H., Kerzic, M., Schuck, P., Mariuzza, R., and Malchiodi, E.L. 2007. Superantigen natural affinity maturation revealed by the crystal structure of staphylococcal enterotoxin G and its binding to T‐cell receptor Vbeta8.2. Proteins 68:389‐402.
   Fleming, K.G., Ackerman, A.L., and Engelman, D.M. 1997. The effect of point mutations on the free energy of transmembrane alpha‐helix dimerization. J. Mol. Biol. 272:266‐275.
   Ghirlando, R., Keown, M.B., Mackay, G.A., Lewis, M.S., Unkeless, J.C., and Gould, H.J. 1995. Stoichiometry and thermodynamics of the interaction between the Fc fragment of human IgG1 and its low‐affinity receptor FcγRIII. Biochemistry 34:13320‐13327.
   Guan, R., Malchiodi, E.L., Wang, Q., Schuck, P., and Mariuzza, R. 2004. Crystal structure of the C‐terminal peptidoglycan‐binding domain of human peptidoglycan recognition protein Ialpha reveals sodium‐mediated receptor dimerization. J. Biol. Chem. 279:31873‐31882.
   Hanlon, S., Lamers, K., Lauterbach, G., Johnson, R., and Schachman, H.K. 1962. Ultracentrifuge studies with absorption optics. I. An automatic photoelectric scanning absorption system. Arch. Biochem. Biophys. 99:157‐174.
   Harrington, W.F. and Kegeles, G. 1973. Pressure effects in ultracentrifugation of interacting systems. Meth. Enzymol. 27:106‐345.
   Haschemeyer, R.H. and Bowers, W.F. 1970. Exponential analysis of concentration or concentration difference data for discrete molecular weight distributions in sedimentation equilibrium. Biochemistry 9:435‐445.
   Hoiland, H. 1986. Partial molar volumes of biochemical model compounds in aqueous solution. In Thermodynamic Data for Biochemistry and Biotechnology. (H.‐J. Hinz, ed.) pp.17‐44. Springer, Berlin.
   Holladay, L.A. and Sohpianolpoulos, A.J. 1972. Nonideal associating systems. I. Documentation of a new method for determining the parameters from sedimentation equilibrium data. J. Biol. Chem. 247:427‐439.
   Holtzer, M.E., Braswell, E.H., Angelleti, R.H., Mints, L., Zhu, D., and Holtzer, A. 2000. Ultracentrifuge and CD studies of folding equilibria in a retro‐GCN4‐like leucine zipper. Biophys. J. 78:2037‐2048.
   Horan, T.P., Martin, F., Simonet, L., Arakawa, T., and Philo, J.S. 1997. Dimerization of granulocyte‐colony stimulating factor receptor: The Ig plus CRH construct of granulocyte‐colony stimulating factor receptor forms a 2:2 complex with a ligand. J. Biochem. 121:370‐375.
   Houtman, J.C., Brown, P.H., Bowden, B., Yamaguchi, H., Appella, E., Samelson, L.E., and Schuck, P. 2007. Studying multisite binary and ternary protein interactions by global analysis of isothermal titration calorimetry data in SEDPHAT: Application to adaptor protein complexs in cell signaling. Protein Sci. 16:30‐42.
   Howlett, G.J. 1992. Sedimentation analysis of membrane proteins. In Analytical Ultracentrifugation in Biochemistry and Polymer Science. (S.E. Harding, A.J. Rowe, and J.C. Horton, eds.) pp. 470‐483. The Royal Society of Chemistry, Cambridge, U.K.
   Howlett, G.J. and Jeffrey, P.D. 1973. Theoretical behavior of interacting protein systems in density gradients at sedimentation equilibrium. J. Phys. Chem. 77:1250‐1258.
   Howlett, G.J., Minton, A.P., and Rivas, G. 2006. Analytical ultracentrifugation for the study of protein association and assembly. Curr. Opin. Chem. Biol. 10:430‐436.
   Ikemizu, S., Gilbert, R.J., Fennelly, J.A., Collings, A.V., Harlos, K., Jones, E.Y., Stuart, D.I., and Davis, S.J. 2000. Structure and dimerization of a soluble form of B7‐1. Immunity 12:51‐60.
   Johnson, M.L. 1983. Evaluation and propagation of confidence intervals in nonlinear, asymmetrical variance spaces. Biophys. J. 44:101‐106.
   Johnson, M.L. and Straume, M. 1994. Comments on the analysis of sedimentation equilibrium experiments. In Modern Analytical Ultracentrifugation. (T.M. Schuster and T.M. Laue, eds.) pp. 37‐65. Birkhäuser, Boston.
   Jones, I.I., Vullev, V., Braswell, E.H., and Zhu, D. 2000. Multi‐step photoinduced electron transfer in a de novo helix bundle: Multimer self‐assembly of peptide chains including a chromophore special pair. J. Am. Chem. Soc. 122:388‐389.
   Junghans, R.P., Stone, A.L., and Lewis, M.S. 1996. Biophysical characterization of a recombinant soluble interleukin 2 receptor (Tac). J. Biol. Chem. 271:10453‐10460.
   Kim, K.‐S., Rajarathnam, K., Clark‐Lewis, I., and Sykes, B.D. 1996. Structural characterization of a monomeric chemokine: Monocyte chemoattractant protein‐3. FEBS Lett. 395:277‐282.
   Laue, T.M. 1999. Analytical centrifugation: Equilibrium approach. Curr. Protoc. Protein Sci. 18:20.3.1‐20.3.13.
   Laue, T.M., Shah, B.D., Ridgeway, T.M., and Pelletier, S.L. 1992. Computer‐aided interpretation of analytical sedimentation data for proteins. In Analytical Ultracentrifugation in Biochemistry and Polymer Science. (S.E. Harding, A.J. Rowe, and J.C. Horton, eds.) pp. 90‐125. The Royal Society of Chemistry, Cambridge.
   Laue, T.M., Senear, D.F., Eaton, S., and Ross, J.B. 1993. 5‐hydroxytryptophan as a new intrinsic probe for investigating protein‐DNA interactions by analytical ultracentrifugation: Study of the effect of DNA on self‐assembly of the bacteriophage lambda cI repressor. Biochemistry 32:2469‐2472.
   Laue, T.M., Anderson, A.L., and Weber, B.W. 1997. Prototype fluorimeter for the XLA/XLI analytical ultracentrifuge. In Ultrasensitive Biochemical Diagnostics II. SPIE Proceedings. (G.E. Cohn and S.A. Soper, eds.) pp. 196‐204. SPIE, Bellingham, Wash.
   Lebowitz, J., Lewis, M.S., and Schuck, P. 2002. Modern analytical ultracentrifugation in protein science: A tutorial review. Protein Sci. 11:2067‐2079.
   Lebowitz, J., Lewis, M.S., and Schuck, P. 2003. Back to the future: A rebuttal to Henryk Eisenberg. Protein Sci. 12:2649‐2650.
   Leder, L., Llera, A., Lavoie, P.M., Lebedeva, M.I., Li, H., Sékaly, R.‐P., Bohach, G.A., Gahr, P.J., Schlievert, P.M., Karjalainen, K., and Mariuzza, R.A. 1998. A mutational analysis of the binding of staphylococcal enterotoxins B and C3 to the T cell receptor β chain and major histocompatibility complex class II. J. Exp. Med. 187:823‐833.
   Leong, S.R., Lowman, H.B., Liu, J., Shire, S., Deforge, L.E., Gillece‐Castro, B.L., McDowell, R., and Hébert, C.A. 1997. IL‐8 single‐chain homodimers and heterodimers: Interactions with the chemokine receptors CXCR1, CXCR2, and DARC. Protein Sci. 6:609‐617.
   Lewis, M.S. and Youle, R.J. 1986. Ricin subunit association. J. Biol. Chem. 261:11572‐11577.
   Lewis, M.S. and Junghans, R.P. 2000. Ultracentrifugal analysis of the molecular mass of glycoproteins of unknown or ill‐defined carbohydrate composition. Meth. Enzymol. 321:136‐149.
   Lewis, M.S., Shrager, R.I., and Kim, S.‐J. 1993. Analysis of protein‐nucleic acid and protein‐protein interactions using multi‐wavelength scans from the XL‐A analytical ultracentrifuge. In Modern Analytical Ultracentrifugation. (T.M. Schuster and T.M. Laue, eds.) pp. 94‐115. Birkhäuser, Boston.
   Li, Y., Li, H., Dimasi, N., McCormick, J.K., Martin, R., Schuck, P., Schlievert, P.M., and Mari uzza, R.A. 2001. Crystal structure of a superantigen bound to the high‐affinity, zinc‐dependent site on MHC class II. Immunity 14:93‐104.
   Li, H., Zhao, Y., Guo, Y., Li, Z., Eisele, L., and Mourad, W. 2007a. Zinc induces dimerization of the class II major histocompatibility complex molecule that leads to cooperative binding to a superantigen. J. Biol. Chem. 282:5991‐6000.
   Li, H., Zhao, Y., Guo, Y., Vanvranken, S.J., Li, Z., Eisele, L., and Mourad, W. 2007b. Mutagenesis, biochemical, and biophysical characterization of Mycoplasma arthritidis–derived mitogen. Mol. Immunol. 44:763‐773.
   Lindenthal, S. and Schubert, D. 1991. Monomeric erythrocyte band 3 protein transports anions. Proc. Natl. Acad. Sci. U.S.A. 88:6540‐6544.
   Liu, J., Reitz, B., Fox, J., and Shire, S.J. 1997. Determination of the average molecular weights of antibody and its complexes in serum using a preparative ultracentrifuge. Pharm. Res. 14:348.
   Lustig, A., Engel, A., Tsiotis, G., Landau, E.M., and Baschong, W. 2000. Molecular weight determination of membrane proteins by sedimentation equilibrium at the sucrose or Nycodenz‐adjusted density of the hydrated detergent micelle. Biochim. Biophys. Acta 1464:199‐206.
   MacGregor, I.K., Anderson, A.L., and Laue, T.M. 2004. Fluorescence detection for the XLI analytical ultracentrifuge. Biophys. Chem. 108:165‐185.
   Malchiodi, E.L., Eisenstein, E., Fields, B.A., Ohlendorf, D.H., Schlievert, P.M., Karjalainen, K., and Mari uzza, R.A. 1995. Superantigen binding to a T cell receptor β chain of known three‐dimensional structure. J. Exp. Med. 182:1833‐1845.
   Mancheno, J.M., Tateno, H., Goldstein, I.J., Martinez‐Ripoll, M., and Hermoso, J.A. 2005. Structural analysis of the Laetiporus sulphureus hemolytic pore‐forming lectin in complex with sugars. J. Biol. Chem. 280:17251‐17259.
   Mayer, G., Ludwig, B., Muller, H.W., van den Broek, J.A., Friesen, R.H.E., and Schubert, D. 1999. Studying membrane proteins in detergent solution by analytical ultracentrifugation: Different methods for density matching. Prog. Colloid Polym. Sci. 113:176‐181.
   McLellan, J.S., Yao, S., Zheng, X., Geisbrecht, B.V., Ghirlando, R., Beachy, P.A., and Leahy, D.J. 2006. Structure of a heparin‐dependent complex of Hedgehog and Ihog. Proc. Natl. Acad. Sci. U.S.A. 103:17208‐17213.
   Morris, M. and Ralston, G.B. 1989. A thermodynamic model for the self‐association of human spectrin. Biochemistry 28:8561‐8567.
   Natarajan, K., Boyd, L.F., Schuck, P., Yokoyama, W.M., Eilat, D., and Margulies, D.H. 1999. Interaction of the NK cell inhibitory receptor Ly49A with H‐2Dd: Identification of a site distinct from the TCR site. Immunity 11:591‐601.
   Paliwal, V., Ptak, W., Sperl, J., Braswell, E., and Askenase, P.W. 1997. Recombinant soluble alpha beta T cell receptors protect T cells from immuno suppresion: Requirement for aggregated multimeric, disulfide‐linked alpha beta heterodimers. J. Immunol. 159:1718‐1727.
   Perugini, M.A., Griffin, M.D., Smith, B.J., Webb, L.E., Davis, A.J., Handman, E., and Gerrard, J.A. 2005. Insight into the self‐association of key enzymes from pathogenic species. Eur. Biophys. J. 34:469‐476.
   Philo, J.S. 2000. Sedimentation equilibrium analysis of mixed associations using numerical constraints to impose mass or signal conservation. Meth. Enzymol. 321:100‐120.
   Philo, J.S., Aoki, K.H., Arakawa, T., Narhi, L.O., and Wen, J. 1996. Dimerization of the extracellular domain of the erythropoietin (EPO) receptor by EPO: One high‐affinity and one low‐affinity interaction. Biochemistry 35:1681‐1691.
   Pörschke, D. and Labuda, D. 1982. Codon‐induced transfer ribonucleic acid association: Quantitative analysis by sedimentation equilibrium. Biochemistry 21:53‐56.
   Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. 1992. Numerical Recipes in C, 2nd (corrected) ed. University Press, Cambridge.
   Rajarathnam, K., Kay, C.M., Dewald, B., Wolf, M., Baggiolini, M., Clark‐Lewis, I., and Sykes, B.D. 1997. Neutrophil‐activating peptide‐2 and melanoma growth‐stimulatory activity are functional as monomers for neutrophil activation. J. Biol. Chem. 272:1725‐1729.
   Ralston, G.B. 1994. The concentration dependence of the activity coefficient of the human spectrin heterodimer: A quantitative test of the Adams‐Fujita approximation. Biophys. Chem. 52:51‐61.
   Reynolds, J.A. and McCaslin, D.R. 1985. Determination of protein molecular weight in complexes with detergent without knowledge of binding. Meth. Enzymol. 117:41‐53.
   Richards, E.G. and Schachman, H.K. 1959. Ultracentrifuge studies with Rayleigh interference optics. I. General applications. J. Phys. Chem. 63:1578‐1591.
   Richards, E.G., Teller, D.C., and Schachman, H.K. 1968. Ultracentrifuge studies with Rayleigh interference optics. II. Low‐speed sedimentation equilibrium of homogeneous systems. Biochemistry 7:1054‐1076.
   Rivas, G., Stafford, W., and Minton, A.P. 1999. Characterization of heterologous protein‐protein interactions via analytical ultracentrifugation. Methods 19:194‐212.
   Rivas, G., Lopez, A., Mingorance, J., Ferrandiz, M.J., Zorrilla, S., Minton, A.P., Vicente, M., and An dreu, J.M. 2000. Magnesium‐induced linear self‐association of the FtsZ bacterial cell division protein monomer: The primary steps for FtsZ assembly. J. Biol. Chem. 275:11740‐11749.
   Roark, D.E. 1976. Sedimentation equilibrium techniques: Multiple speed analyses and an overspeed procedure. Biophys. Chem. 5:185‐196.
   Rosovitz, M.J., Schuck, P., Varughese, M., Chopra, A.P., Mehra, V., Singh, Y., McGinnis, L.M., and Leppla, S.H. 2003. Alanine‐scanning mutations in domain 4 of anthrax toxin protective antigen reveal residues important for binding to the cellular receptor and to a neutralizing monoclonal antibody. J. Biol. Chem. 278:30936‐30944.
   Schachman, H.K. 1959. Ultracentrifugation in Biochemistry. Academic Press, New York.
   Schachman, H.K., Gropper, L., Hanlon, S., and Putney, F. 1962. Ultracentrifuge studies with absorption optics. II. Incorporation of a monochromator and its application to the study of proteins and interacting systems. Arch. Biochem. Biophys. 99:175‐190.
   Schmidt, B. and Riesner, D. 1992. A fluorescence detection system for the analytical ultracentrifuge and its application to proteins, nucleic acids, viroids and viruses. In Analytical Ultracentrifugation in Biochemistry and Polymer Science. (S.E. Harding, A.J. Rowe, and J.C. Horton, eds.) pp. 176‐207. The Royal Society of Chemistry, Cambridge.
   Schönfeld, H.‐J., Pöschl, B., and Müller, F. 1998. Quasi‐elastic light scattering and analytical ultracentrifugation are indispensable tools for the purification and characterization of recombinant proteins. Biochem. Soc. Trans. 26:753‐758.
   Schubert, D. and Schuck, P. 1991. Analytical ultracentrifugation as a tool for studying membrane proteins. Progr. Colloid Polym. Sci. 86:12‐22.
   Schubert, D., Tziatzios, C., Broeck, J.A.v.d., Schuck, P., Germeroth, L., and Michel, H. 1994. Determination of the molar mass of pigment‐containing complexes of intrinsic membrane proteins: Problems, solutions and application to the light‐harvesting complex B800/820 of Rhodospirillum molischianum. Progr. Colloid. Polym. Sci. 94:14‐19.
   Schuck, P. 1994. Simultaneous radial and wavelength analysis with the Optima XL‐A analytical ultracentrifuge. Progr. Colloid. Polym. Sci. 94:1‐13.
   Schuck, P. 2003. On the analysis of protein self‐association by sedimentation velocity analytical ultracentrifugation. Anal. Biochem. 320:104‐124.
   Schuck, P. 2007. Sedimentation equilibrium analytical ultracentrifugation for multi‐component protein interactions. In Protein Interactions: Biophysical Methods for Complex Systems. (P. Schuck, ed.) pp. 289‐316. Springer, New York.
   Schuck, P. and Millar, D.B. 1998. Rapid determination of molar mass in modified Archibald experiments using direct fitting of the Lamm equation. Anal. Biochem. 259:48‐53.
   Schuck, P., Radu, C.G., and Ward, E.S. 1999. Sedimentation equilibrium analysis of recombinant mouse FcRn with murine IgG1 and Fc fragment. Mol. Immunol. 36:1117‐1125.
   Scott, D.J. and Schuck, P. 2005. A brief introduction to the analytical ultracentrifugation of proteins for beginners. In Modern Analytical Ultracentrifugation: Techniques and Methods. (D.J. Scott, S.E. Harding, and A.J. Rowe, eds.) pp. 1‐25. The Royal Society of Chemistry, Cambridge.
   Servillo, L., Brewer, H.B., and Osborne, J.C. 1981. Evaluation of the mixed interaction between apolipoproteins A‐II and C‐I by equilibrium sedimentation. Biophys. Chem. 13:29‐38.
   Shi, J., Ghirlando, R., Beavil, R.L., Beavil, A.J., Keown, M.B., Young, R.J., Owens, R.J., Sutton, B.J., and Gould, H.J. 1997. Interaction of the low‐affinity receptor CD23/FcɛRII lectin domain with the Fcɛ3‐4 fragment of human immunoglobulin E. Biochemistry 36:2112‐2122.
   Shire, S. 1992. Determination of molecular weight of glycoproteins by analytical ultracentrifugation. Beckman Instruments, Palo Alto, Calif.
   Shire, S. 1994. Analytical ultracentrifugation and its use in biotechnology. In Modern Analytical Ultracentrifugation. (T.M. Schuster and T.M. Laue, eds.) pp. 261‐297. Birkhäuser, Boston, Mass.
   Silkowski, H., Davis, S.J., Barclay, A.N., Rowe, A.J., Harding, S.E., and Byron, O. 1997. Characterization of the low affinity interaction between rat cell adhesion molecules CD2 and CD48 by analytical ultracentrifugation. Eur. Biophys. J. 25:455‐462.
   Svedberg, T. and Pedersen, K.O. 1940. The Ultracentrifuge. Oxford University Press, London.
   Tanford, C. and Reynolds, J.A. 1976. Characterization of membrane proteins in detergent solutions. Biochim. Biophys. Acta 457:133‐170.
   Ucci, J.W. and Cole, J.L. 2004. Global analysis of non‐specific protein‐nucleic interactions by sedimentation equilibrium. Biophys. Chem. 108:127‐140.
   van Holde, K.E. and Baldwin, R.L. 1958. Rapid attainment of sedimentation equilibrium. J. Phys. Chem. 62:734‐749.
   Vistica, J., Dam, J., Balbo, A., Yikilmaz, E., Mariuzza, R.A., Rouault, T.A., and Schuck, P. 2004. Sedimentation equilibrium analysis of protein interactions with global implicit mass conservation constraints and systematic noise decomposition. Anal. Biochem. 326:234‐256.
   Weber, A.N., Moncrieffe, M.C., Gangloff, M., Imler, J.L., and Gay, N.J. 2005. Ligand‐receptor and receptor‐receptor interactions act in concert to activate signaling in the Drosophila toll pathway. J. Biol. Chem. 280:22793‐22799.
   Wills, P.R., Comper, W.D., and Winzor, D.J. 1993. Thermodynamic nonideality in macromolecular solutions: Interpretation of virial coefficients. Arch. Biochem. Biophys. 300:206‐212.
   Wills, P.R., Nichol, L.W., and Siezen, R.J. 1980. The indefinite self‐association of lysozyme: Consideration of composition‐dependent activity coefficients. Biophys. Chem. 11:71‐82.
   Yphantis, D.A. 1964. Equilibrium ultracentrifugation of dilute solutions. Biochemistry 3:297‐317.
   Yphantis, D.A., Lary, J.W., Stafford, W.F., Liu, S., Olsen, P.H., Hayes, D.B., Moody, T.P., Ridgeway, T.M., Lyons, D.A., and Laue, T.M. 1994. On‐line data acquisition for the Rayleigh interference optical system of the analytical ultracentrifuge. In Modern analytical ultracentrifugation. (T.M. Schuster and T.M. Laue, eds.) pp. 209‐226. Birkhäuser, Boston.
   Yu, I.M., Gustafson, C.L., Diao, J., Burgner, J.W. 2nd, Li, Z., Zhang, J., and Chen, J. 2005. Recombinant severe acute respiratory syndrome (SARS) coronavirus nucleocapsid protein forms a dimer through its C‐terminal domain. J. Biol. Chem. 280:23280‐23286.
   Zorrilla, S., Jiménez, M., Lillo, P., Rivas, G., and Minton, A.P. 2004. Sedimentation equilibrium in a solution containing an arbitrary number of solute species at arbitrary concentrations: Theory and application to concentrated solutions of ribonuclease. Biophys. Chem. 108:89‐100.
Key References
   Balbo and Schuck, 2005. See above.
  The above publications are general reviews on analytical ultracentrifugation.
   Howlett et al., 2006. See above.
  The above are references on special topics related to long‐column SE.
   Lebowitz et al., 2002. See above.
  The above are references on data analysis in analytical ultracentrifugation.
   Schachman, 1959. See above.
  The above publications present Some experimental alternatives in regard to analytical ultracentrifugation.
   Schuck, 2007. See above.
   Scott and Schuck, 2005. See above.
   Svedberg and Pedersen, 1940. See above.
   Ansevin et al., 1970. See above.
   Durchschlag, 1986. See above.
   Eisenberg, H. 2003. Modern analytical ultracentrifugation in protein science: Look forward, not back. Protein Sci. 12:2657‐2650.
   Howlett, 1992. See above.
   Lebowitz et al., 2003. See above.
   Schubert and Schuck, 1991. See above.
   Tanford and Reynolds, 1976. See above.
   Vistica et al., 2004. See above.
   Johnson and Straume, 1994. See above.
   Lewis et al., 1993. See above.
   Minton, A.P. 1997. Alternative strategies for the characterization of associations in multicomponent solutions via measurement of sedimentation equilibrium. Progr. Colloid Polym. Sci. 107:11‐19.
   Philo, 2000. See above.
   Schuck, 1994. See above.
   Servillo et al., 1981. See above.
  Vistica et al., 2004. See above.
   Correia et al., 1992. See above.
   Darawshe and Minton, 1994. See above.
   Lebowitz, J., Teale, M., and Schuck, P.W. 1998. Analytical band centrifugation of proteins and protein complexes. Biochem. Soc. Transact. 26:745‐749.
Internet Resources
  SEDPHAT download page (Dr. Peter Schuck) at NIH.
  SEDPHAT home page.
  References on SE analysis.
  Online protocol for SE (Andrea Balbo, Patrick Brown, and Peter Schuck).
PDF or HTML at Wiley Online Library