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allows the selection of the sedimentation analysis model.
Sedfit contains numerous models and methods for data analysis. Central are the direct boundary models. They follow the strategy of expressing all sedimentation processes by the underlying equations, and of directly modeling the raw data by least-squares regression. When necessary, the noise structure of the data is also explicitly modeled by least squares. Because this concept makes it necessary to specify the type of sedimentation process, many different models are needed to accommodate the different experimental situations encountered. Also, different models can be used reflecting the different knowledge about the sample (e.g., number of species).
In the following, a brief overview of the models is given, but reading the more specific information following the links below is highly recommended.
Most of the models are based on numerical solutions of the Lamm equation1, which is the partial differential equation describing the evolution of concentration distribution with time (see introduction to Lamm equation solutions). The Lamm equation is very general, and can be used to analyze species as small as salts up to virtually unlimited size, can describe sedimentation and flotation, allows the incorporation of the rotor acceleration into the model, allows modeling of experiments using layering techniques, and more. The numerical algorithms for solving the Lamm equation are optimized for speed and precision, and do not require any user intervention (although all relevant parameters are available for change for the interested user). They use the finite element technique. For small s-values, it follows the strategy originally described by Claverie2, but combined with a Crank-Nicholson scheme3 for increased precision and a more efficient adaptive driver of the time-steps. Details can be found in ref. 4. For higher precision and speed at large s-values, Sedfit uses a new finite element approach with a moving frame of reference5 , also combined with Crank-Nicholson scheme. There is an automatic switchover between the methods. Systematic noise is calculated algebraically6.
Models are available for independent ideal species, species with a continuous size-distribution, species in rapid self-association equilibrium (monomer-dimer, monomer-trimer, monomer-dimer-tetramer, and monomer-tetramer-octamer), or non-ideal concentration-dependent sedimentation of the type s(c) = s0/(1+kc) (including terms for the concentration dependence of D).
For the independent ideal species, either a known discrete number of species can be used, or distribution functions for an unknown number of species are available7. There is a large variation of the distribution functions that can be selected according to the different prior knowledge available. Such prior can be knowledge of the approximate shape of the molecules, their diffusion coefficient, partial-specific volume, the molar mass for molecules that can undergo a conformational change, etc. Further, the distribution can be either a sedimentation coefficient (or flotation coefficient) distribution c(s) or a molar mass distribution c(M)7.
In a typical scenario with a previously uncharacterized sample, one would for example do a c(s) analysis first, using some knowledge about the nature of the molecules to obtain information on purity, s-values, number of species and relative amounts. (For a detailed description on how to perform this analysis, see the help-page of this model). Usually, it is very useful to run the same sample at a range of concentrations and at different rotor speeds. This will reveal if the molecules can be described as ideal non-interacting particles, or if there is a concentration dependence for an associating system, and the presence of hydrodynamic nonideality. After that, for non-interacting species, one would use the information on the number of species and switch to the discrete species Lamm equation model. Here, the s-values from the c(s) analysis can be used, and either constraining the molar mass to that known from sequence (or hypothesized for the oligomers) or fitting for the molar mass. (If the molar mass is the quantity of interest, a relatively low rotor speed is most useful because it allows for considerable diffusional spreading, while highest resolution and precision in the sedimentation coefficient (and molecular shape) is usually obtained at the highest possible rotor speed.) Alternatively, if there is knowledge on the molecules, their self-association, conformational change, etc, one would of course choose one of the specific models.
In part for comparison with previous sedimentation analysis strategies, and to complete the tool-box for velocity analysis, the g*(s) method and the van Holde-Weischet G(s)8 is available. While I would recommend using direct boundary modeling for quantitative analysis whenever possible, the g*(s) and G(s) transformations can be very useful as additional tools, for example, for diagnostic purpose and semi-quantitative description of the data, in particular where an appropriate explicit boundary model is not yet available.
The g*(s) method is calculated in Sedfit by least squares and direct boundary modeling, termed ls-g*(s)9. This method is not limited to small data sets, as no approximation of dcdt is involved, and can therefore be used conveniently with both absorbance and interference data. ls-g*(s) is a very good model for the sedimentation of very large particles where diffusion can be neglected. The extrapolation of ls-g*(s) to infinite time10 is a link between g*(s) and G(s), and can be considered an extension of the van Holde-Weischet method to interference data containing systematic noise components.
Some other methods closely related to conventional sedimentation velocity analysis are also included in Sedfit. These are those for analytical zone centrifugation11 (sedimentation velocity using a synthetic boundary layering technique), dynamic light scattering (substituting the Lamm equation solutions by appropriate decaying exponentials for the autocorrelation functions), and electrophoresis (obeying a Lamm equation in linear geometry with constant force). Finally, some special modifications for time-dependent sedimentation are available.
References:
1) O. Lamm. (1929) Die Differentialgleichung der Ultrazentrifugierung. Ark. Mat. Astr. Fys. 21B:1-4
2) J.-M. Claverie, H. Dreux and R. Cohen. (1975) Sedimentation of generalized systems of interacting particles. I. Solutions of systems of complete Lamm equations. Biopolymers 14:1685-1700
3) J. Crank and P. Nicholson. (1947) A practical method for numerical evaluation of solutions of partial differential equations of the heat-conducting type. Proc. Cambridge Philos. Soc. 43:50-67
4) P. Schuck, C.E. McPhee, and G.J. Howlett. (1998) Determination of sedimentation coefficients for small peptides. Biophysical Journal 74:466-474.
5) P. Schuck (1998) Sedimentation analysis of non-interacting and self-associating solutes using numerical solutions to the Lamm equation. Biophysical Journal 75:1503-1512.
6) P. Schuck and B. Demeler (1999) Direct sedimentation analysis of interference-optical data in analytical ultracentrifugation. Biophysical Journal 76:2288-2296.
7) P. Schuck (2000) Size distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and Lamm equation modeling. Biophysical Journal 78:1606-1619.
8) K.E. van Holde and W.O. Weischet. (1978) Boundary analysis of sedimentation velocity experiments with monodisperse and paucidisperse solutes. Biopolymers 17:1387-1403.
9) P. Schuck and P. Rossmanith (2000) Determination of the sedimentation coefficient distribution g*(s) by least-squares boundary modeling. Biopolymers 54:328-341.
10) in preparation
11) J. Lebowitz, M. Teale, and P.W. Schuck (1998) Analytical band centrifugation of proteins and protein complexes. Biochemical Society Transactions 26:745-749.