Data Analysis And Interpretation

The primary data are supplied as text files containing a two-line header with information about the conditions of the run followed by columns of data (i.e., radius and concentration) and sometimes a third column of standard errors of the concentration data. These concentration profile data may be analyzed by various methods to extract the hydrodynamic and thermodynamic information that the investigator desires.

There are several software packages available that either transform the data into suitable visual form or that fit the profiles directly by least-squares techniques (Table 20.7.1).

Before applying any of these techniques, distinctions must be made between the different types of system likely to be encountered, in order to choose the appropriate type of analysis. In general, systems can be divided into either ideal or nonideal, interacting or non-interacting, monodisperse or polydisperse, and single-component or multicomponent. An example of a single-component, monodisperse, ideal system is a globular protein near its isoelectric point at an ionic strength of 0.1, at about 1 mg/ml and not undergoing self-association. An example of a single-component, polydisperse ideal system is a monomer-dimer-tetramer self-associating system in rapidly reversible equilibrium near its isoelectric point, at an ionic strength of 0.1 at ~1 mg/ml. An example of a two-component, polydisperse, ideal system is a weakly binding antigen-antibody system composed of four species—free antibody, free antigen, singly ligated antigen, and doubly ligated antigen—at an ionic strength of 0.1 at ~1 mg/ml.

Experimental Design

Starting with a sample of unknown properties, a run should be performed with three or four cells covering a wide range of loading concentrations. With interference optics, a typical protocol is to start with either 1 mg/ml or 0.3 mg/ml as the highest concentration and make 3-fold serial dilutions spanning a 27-fold range. With absorption optics, use a starting absorbance of 1.0 absorbance units. This initial run will provide information about both the polydispersity and possible concentration dependence. If concentration dependence can be ruled out at this stage, the system can be analyzed as either a monodisperse system or a polydisperse system composed of independent species. If concentration dependence is observed, it will be a combination of either association or nonideality, or both. Association is manifested as a weight-average sedimentation coefficient that increases with concentration, while nonideality is manifested as a weight average sedimentation coefficient that decreases with concentration. A nonideal, mono-or polydisperse system can be analyzed as the sum of nonideal independent components. An interacting system, which is composed of a reaction boundary, must be analyzed by taking mass action into account during sedimentation. The distinction made above between ideal, nonideal, interacting, and independent species will determine which method of analysis must be employed. Use of DCDT-g(s*) or least-squares-g(s*) analysis would be appropriate for the initial characterization and as a way of visualizing the general behavior of the system.

Data Analysis

There is a wide range of software available for analysis of sedimentation velocity data. The reader is referred to Table 20.7.1 for a list of the most commonly used software packages. The g(s*) methods are model-independent and provide estimates of the range of sedimentation coefficient, number of species, their relative amounts, and degree of concentration dependence. In the absence of concentration dependence, one could use any one of the curve-fitting methods that use either approximate or numerical solutions to the Lamm equation to estimate number of components as well as their sedimentation and diffusion coefficients, relative amounts, and molecular weights. In the case of negative concentration-dependent single species—non-ideal systems—hydrodynamic non-ideality and second virial coefficients can be estimated (Solovyova et al., 2001). For the

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