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. 1998 Sep;75(3):1503–1512. doi: 10.1016/S0006-3495(98)74069-X

Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation.

P Schuck 1
PMCID: PMC1299825  PMID: 9726952

Abstract

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.

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Selected References

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  1. Beechem J. M. Global analysis of biochemical and biophysical data. Methods Enzymol. 1992;210:37–54. doi: 10.1016/0076-6879(92)10004-w. [DOI] [PubMed] [Google Scholar]
  2. Behlke J., Ristau O. Molecular mass determination by sedimentation velocity experiments and direct fitting of the concentration profiles. Biophys J. 1997 Jan;72(1):428–434. doi: 10.1016/S0006-3495(97)78683-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Cann J. R., Kegeles G. Theory of sedimentation for kinetically controlled dimerization reactions. Biochemistry. 1974 Apr 23;13(9):1868–1874. doi: 10.1021/bi00706a015. [DOI] [PubMed] [Google Scholar]
  4. Claverie J. M., Dreux H., Cohen R. Sedimentation of generalized systems of interacting particles. I. Solution of systems of complete Lamm equations. Biopolymers. 1975 Aug;14(8):1685–1700. doi: 10.1002/bip.1975.360140811. [DOI] [PubMed] [Google Scholar]
  5. Claverie J. M. Sedimentation of generalized systems of interacting particles. III. Concentration-dependent sedimentation and extension to other transport methods. Biopolymers. 1976 May;15(5):843–857. doi: 10.1002/bip.1976.360150504. [DOI] [PubMed] [Google Scholar]
  6. Cox D. J. Computer simulation of sedimentation in the ultracentrifuge. IV. Velocity sedimentation of self-associating solutes. Arch Biochem Biophys. 1969 Jan;129(1):106–123. doi: 10.1016/0003-9861(69)90157-x. [DOI] [PubMed] [Google Scholar]
  7. Cox D. J. Sedimentation of an initially skewed boundary. Science. 1966 Apr 15;152(3720):359–361. doi: 10.1126/science.152.3720.359. [DOI] [PubMed] [Google Scholar]
  8. Demeler B., Saber H. Determination of molecular parameters by fitting sedimentation data to finite-element solutions of the Lamm equation. Biophys J. 1998 Jan;74(1):444–454. doi: 10.1016/S0006-3495(98)77802-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Gabriel O., Gersten D. M. Staining for enzymatic activity after gel electrophoresis, I. Anal Biochem. 1992 May 15;203(1):1–21. doi: 10.1016/0003-2697(92)90036-7. [DOI] [PubMed] [Google Scholar]
  10. Gilbert L. M., Gilbert G. A. Sedimentation velocity measurement of protein association. Methods Enzymol. 1973;27:273–296. doi: 10.1016/s0076-6879(73)27014-3. [DOI] [PubMed] [Google Scholar]
  11. Golz A., Joachims H. Z., Netzer A., Westerman S. T., Gilbert L. M. Pneumoparotitis: diagnosis by computed tomography. Am J Otolaryngol. 1999 Jan-Feb;20(1):68–71. doi: 10.1016/s0196-0709(99)90055-8. [DOI] [PubMed] [Google Scholar]
  12. Holladay L. A. An approximate solution to the Lamm equation. Biophys Chem. 1979 Sep;10(2):187–190. doi: 10.1016/0301-4622(79)85039-5. [DOI] [PubMed] [Google Scholar]
  13. Holladay L. A. Molecular weights from approach-to-sedimentation equilibrium data using nonlinear regression analysis. Biophys Chem. 1979 Sep;10(2):183–185. doi: 10.1016/0301-4622(79)85038-3. [DOI] [PubMed] [Google Scholar]
  14. Holladay L. A. Simultaneous rapid estimation of sedimentation coefficient and molecular weight. Biophys Chem. 1980 Apr;11(2):303–308. doi: 10.1016/0301-4622(80)80033-0. [DOI] [PubMed] [Google Scholar]
  15. MacPhee C. E., Perugini M. A., Sawyer W. H., Howlett G. J. Trifluoroethanol induces the self-association of specific amphipathic peptides. FEBS Lett. 1997 Oct 27;416(3):265–268. doi: 10.1016/s0014-5793(97)01224-6. [DOI] [PubMed] [Google Scholar]
  16. Marque J. Simulation of the time course of macromolecular separations in an ultracentrifuge. II. Controlling the solute concentrations. Biophys Chem. 1992 Jan;42(1):23–27. doi: 10.1016/0301-4622(92)80004-o. [DOI] [PubMed] [Google Scholar]
  17. Minton A. P. Simulation of the time course of macromolecular separations in an ultracentrifuge. I. Formation of a cesium chloride density gradient at 25 degrees C. Biophys Chem. 1992 Jan;42(1):13–21. doi: 10.1016/0301-4622(92)80003-n. [DOI] [PubMed] [Google Scholar]
  18. Philo J. S. An improved function for fitting sedimentation velocity data for low-molecular-weight solutes. Biophys J. 1997 Jan;72(1):435–444. doi: 10.1016/S0006-3495(97)78684-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Sartory W. K., Halsall H. B., Breillatt J. P. Simultation of gradient and band propagation in the centrifuge. Biophys Chem. 1976 Jul;5(1-2):107–135. doi: 10.1016/0301-4622(76)80029-4. [DOI] [PubMed] [Google Scholar]
  20. Schuck P., MacPhee C. E., Howlett G. J. Determination of sedimentation coefficients for small peptides. Biophys J. 1998 Jan;74(1):466–474. doi: 10.1016/S0006-3495(98)77804-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Schuck P., Millar D. B. Rapid determination of molar mass in modified Archibald experiments using direct fitting of the Lamm equation. Anal Biochem. 1998 May 15;259(1):48–53. doi: 10.1006/abio.1998.2638. [DOI] [PubMed] [Google Scholar]
  22. Stafford W. F., 3rd Boundary analysis in sedimentation velocity experiments. Methods Enzymol. 1994;240:478–501. doi: 10.1016/s0076-6879(94)40061-x. [DOI] [PubMed] [Google Scholar]

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