Abstract
A method for fitting experimental sedimentation velocity data to finite-element solutions of various models based on the Lamm equation is presented. The method provides initial parameter estimates and guides the user in choosing an appropriate model for the analysis by preprocessing the data with the G(s) method by van Holde and Weischet. For a mixture of multiple solutes in a sample, the method returns the concentrations, the sedimentation (s) and diffusion coefficients (D), and thus the molecular weights (MW) for all solutes, provided the partial specific volumes (v) are known. For nonideal samples displaying concentration-dependent solution behavior, concentration dependency parameters for s(sigma) and D(delta) can be determined. The finite-element solution of the Lamm equation used for this study provides a numerical solution to the differential equation, and does not require empirically adjusted correction terms or any assumptions such as infinitely long cells. Consequently, experimental data from samples that neither clear the meniscus nor exhibit clearly defined plateau absorbances, as well as data from approach-to-equilibrium experiments, can be analyzed with this method with enhanced accuracy when compared to other available methods. The nonlinear least-squares fitting process was accomplished by the use of an adapted version of the "Doesn't Use Derivatives" nonlinear least-squares fitting routine. The effectiveness of the approach is illustrated with experimental data obtained from protein and DNA samples. Where applicable, results are compared to methods utilizing analytical solutions of approximated Lamm equations.
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Selected References
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- 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]
- 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]
- 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]
- Cohen R., Claverie J. M. Sedimentation of generalized systems of interacting particles. II. Active enzyme centrifugation--theory and extensions of its validity range. Biopolymers. 1975 Aug;14(8):1701–1716. doi: 10.1002/bip.1975.360140812. [DOI] [PubMed] [Google Scholar]
- Demeler B., Saber H., Hansen J. C. Identification and interpretation of complexity in sedimentation velocity boundaries. Biophys J. 1997 Jan;72(1):397–407. doi: 10.1016/S0006-3495(97)78680-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Georgel P., Demeler B., Terpening C., Paule M. R., van Holde K. E. Binding of the RNA polymerase I transcription complex to its promoter can modify positioning of downstream nucleosomes assembled in vitro. J Biol Chem. 1993 Jan 25;268(3):1947–1954. [PubMed] [Google Scholar]
- 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]
- 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]
- Johnson M. L., Faunt L. M. Parameter estimation by least-squares methods. Methods Enzymol. 1992;210:1–37. doi: 10.1016/0076-6879(92)10003-v. [DOI] [PubMed] [Google Scholar]
- 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]
- Stafford W. F., 3rd Boundary analysis in sedimentation transport experiments: a procedure for obtaining sedimentation coefficient distributions using the time derivative of the concentration profile. Anal Biochem. 1992 Jun;203(2):295–301. doi: 10.1016/0003-2697(92)90316-y. [DOI] [PubMed] [Google Scholar]
- Todd G. P., Haschemeyer R. H. General solution to the inverse problem of the differential equation of the ultracentrifuge. Proc Natl Acad Sci U S A. 1981 Nov;78(11):6739–6743. doi: 10.1073/pnas.78.11.6739. [DOI] [PMC free article] [PubMed] [Google Scholar]