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Algorithms have been developed for the analysis of sedimentation equilibrium data by fitting to arbitrary reaction schemes. These have been implemented within the framework of a larger program called Sedanal, which until inclusion of equations for fitting equilibrium data was capable of treating only sedimentation velocity data (Stafford and Sherwood, Biophys Chem 108:231–243, 2004) A predecessor to this program, called NONSIM (first used by Margossian and Stafford, Biochemistry, 1982), forms the basis for the algorithms used in Sedanal. Fitting to the equilibrium equations is carried out by minimization with respect to either the L1 norm (average absolute value of the residuals) using the simplex method of Nelder and Mead (1965) or the L2 norm using the Levenberg-Marquardt method. In cases involving more than one macromolecular component (i.e., hetero-associations or self-associating systems involving nonparticipating species), conservation of mass is invoked, and weight fractions of the components become fitting parameters. Thus, it is possible to fit directly for the weight fraction of incompetent species in a self-associating system without resorting to further mathematical treatment of apparent equilibrium constants. Global fitting of data spanning multiple speeds and loading concentrations (and multiple optical systems) allows the determination of both equilibrium constants for the interacting species and the weight fractions of the several components. Because the weight fraction of components must remain constant upon dilution while the distribution of individual species will vary characteristically with local concentration according to the law of mass action, these types of mixed systems can be resolved as long as data from a sufficiently wide range of loading concentrations and speeds can be combined in a global fit. A large array of arbitrary reaction schemes can be represented using the Model Editor, which is part of Sedanal. |
