Fig.2: Procedure (schematic) for the construction of an iso-size/iso-free-mobility nomogram (10). A: A stained Serwer-type gel is evaluated by determining the migration distances of standards and unknown in the first (s1, su1) and second dimensions (s2, su2). B: Particle mobility values are calculated from the migration distances, where mobility is defined as migration velocity (cm/s) divided by field strength (V/cm). The mobility values (two are available for each particle) are used to construct a linear Ferguson plot for each standard (I, II) and the unknown (U). The linear extrapolation of the Ferguson plots to 0 %T (absence of a gel) yields the free mobility for each particle, µo. The retardation coefficient, KR, can be calculated as the absolute value of the slope of the linear Ferguson plot. Please refer to item vi of Assumptions, Section 6.4. C: Fitting equs.1 and 2 to the data using a simultaneous curve-fitting algorithm, the gel is standardized by determining the gel fiber radius, r, and total fiber volume, VF. Further output parameters of the curve fitting are: radius and free mobility for specified centroid of the unknown, values of free mobility for the size standards. XWIDTH and YWIDTH determine the width and height of the box of the nomogram which is scaled by a factor called PLOT MAGNIFICATION to fit the magnified photo of the stained gel pattern. D: After standardization, the nomogram can be constructed. Particles with similar radius are located on the straight diagonal lines (iso-size lines), particles with similar mobility are located on the curved dotted lines (iso-free-mobility lines). It has been shown [Appendix 2 of (10)] that iso-size lines, SL, are given by equ.1. Iso-free-mobility lines, FML, are defined by equ.4. Numbers at the iso-size lines indicate effective particle radii (nm), labels at iso-free-mobility lines specify effective values of free mobility (10^-5 cm^2 V^-1 s^-1). Serwer et al. demonstrated the existence of iso-size lines experimentally (9). E: The nomogram is superimposed on a photograph of the stained gel pattern of the sample to be analyzed. This allows one to characterize each particle position in terms of particle size and free mobility. Procedures of Panels B to D are part of the mainframe program ZWEIDI.DO (10) and the Macintosh program ElphoFit described in this study which allow for a user-friendly evaluation of the gel electrophoretic data. Program GelFit described in two joint studies (16,17) allows one to automate the nomogram overlay (Panel E) and offers a number of additional features, i.e. the transformation of an image from a curvilinear to a rectangular coordinate system representing particle size and free mobility.

Equations:

[equ. 1]: logµ(T) = logµo - KR * T

[equ. 2]: KR = 0.01 * VF/r^2 * (r + R)^2

Abbreviations:

KR, retardation coefficient, absolute value of the slope of a linear Ferguson plot

r, gel fiber radius [nm]

R, radius [nm] of the migrating particle

T, gel concentration [%, g/100 mL]

VF, spezific gel fiber volume [mL/g]

µ, electrophoretic mobility of a migrating particle [migration velocity (cm/s) / field strength (V/cm)]

µo, electrophoretic mobility at T=0

References:

(9) Serwer, P., Hayes, S.J., Griess, G.A., Anal. Biochem. 1986, 152, 339-345.

(10) Tietz, D., Chrambach, A., Electrophoresis 1989, 10, 667-680.

(16) Aldroubi, A., Unser, M., Tietz, D., Trus, B. Electrophoresis 1991, 12, 39-46..