(Contributor: Andreas Chrambach, National Institutes of Health (NIH), Bethesda, MD)
The plot of log(mobility) vs gel concentration is called the Ferguson plot. For proteins in the concentration of crosslinked polyacrylamide (above 3.5%), this plot is linear provided that either absolute mobilities are measured (rarely) or that relative mobilities (Rf values) are correctly evaluated, taking the retardation of the "front" (Rf=1.0) into account (1). In application to agarose gels the plot is convex in view of the change of agarose gel structure with concentration (2).
The Ferguson plot, derived from measurement of migration distance at a given electric field strength, reveals size, shape and net charge of the material migrating as a band in gel electrophoresis (3). Inspection of migration distances on a gel of single concentration cannot provide that information, and measurement of migration distance in a gel of single concentration can provide that information regarding molecular size only for analytes with equal or equalized surface net charge which in the case of SDS-derivatized proteins is widely postulated but in reality non-existent. Size and shape of analytes are given by the slope of the Ferguson Plot, (or on convex plots in agarose gels, the slope as a function of gel concentration). The slope, designated as the retardation coefficient KR, is related to molecular radius, R.
The relation varies depending on the conformational type of the molecule (globular or random-coiled) and on the gel type (categorized as 0-, 1- and 2-dimensional) (4). Commonly, when globular proteins and long-fiber (1-D) gels are used as in PAGE, the square root of KR is proportional to R (R-plot). Thus, when KR is measured for protein standards with known R, the R-plot allows one to evaluate R for unknowns. The slope of the R-plot provides a measure of the length of the gel fiber, the intercept on the R-axis a measure of the radius of that fiber.
- In application to SDS-PAGE (random-coiled molecules and long-fiber gels), KR is proportional to molecular weight (MW). The merit of evaluating MW by that plot, and not by migration distance on a gel of single concentration, is that it avoids the unrealistic assumption of equal charge density for all SDS-proteins.
- The intercept of the Ferguson plot with the log(mobility) axis, designated as Yo, is related to the surface charge density and can be translated, with a considerable number of assumptions, to values of net protons/molecule.
- The statistical evaluation of the Ferguson plot, the R-plot and the calaculation of molecular net charge on the basis of Yo requires a series of computer programs, collectively designated as the PAGE-PACK (5) and ELPHOFIT (6), respectively. The latter is available on the Web at http://www.his.com/~djt/elphoread.html
- Chrambach, A., Rodbard, D.: Polyacrylamide Gel Electrophoresis. Science 172: pp.440-451 (1971).
- Tietz, D., Chrambach, A.: Analysis of Convex Ferguson Plots in Agarose Gel Electrophoresis by Empirical Computer Modeling. Electrophoresis 7: pp.241-250 (1986).
- Rodbard, D., Chrambach, A.: Estimation of Molecular Radius, Free Mobility, and Valence Using Polyacrylamide Gel Electrophoresis. Anal. Biochem. 40: pp.95-134 (1971).
- Rodbard, D., Chrambach, A.: Unified theory of gel electrophoresis and gel filtration. Proc.Nat.Acad.Sci. 65: pp.970-977 (1970).
- Chrambach, A.: The Practice of Quantitative Gel Electrophoresis. (Neuhoff, V. and Maelicke, A., series eds.) VCH Publ., Weinheim FRG 1985, p.50 (1985).
- Tietz, D. and Chrambach, A.: Concave Ferguson plots of DNA fragments and convex Ferguson plots of bacteriophages: Evaluation of molecular and fiber properties, using desktop computers. Electrophoresis 13: pp.286-294 (1992).