Handbook of Size Exclusion Chromatography and Related ...

column before the protein emerges in maximum concentration was plotted as a
function of the logarithm of protein molecular weight. The agreement was
considered,atthetime, tobesurprisinglygood.Alsointheearly1960s,Whitaker
(26)reportedgoodcorrelationsbetweentheratiooftheelutionvolumetothevoid
volume, V=V0, and the logarithm of the molecular weight. Anewelution volume
parameter, Kav, based on comparisons with the void and total column volumes,
was soon derived (7,27,28).
Kav ¼ Ve V0
Vt V0
The relationship described as Kav was recommended by Pharmacia (Uppsala,
Sweden) as the method of choice for column calibration from the earliest days of
Sephadex w use. These results, and others like them, set the stage for aunique
analytical tool at the time, one capable of predicting the molecular weights of
unknown proteins. The elution of 37 purified proteins and two small solutes was
plotted by this method and is shown in Fig. 1.
Modern theoretical models used to describe SEC elution behavior must
allow for possible variations in both the solute and bead pore size and shape, while
remaining consistent with current concepts regarding SEC as an equilibriumcontrolled
process. The shape of the “pore” in SEC is important in the prediction
of elution behavior. Gel pores were originally described in terms of the
penetrability of “hard-sphere” solutes, and extensions of this model are still
employed today. Early theories of hard sphere solute models, in chronological
order of appearance in the literature, are the random-spheres pore model of Ogston
(29), the randomly occurring cones, cylinders, and crevices pore model of Squire
(30), and the random-rod pore model of Laurent and Killander (31). The model
proposed by Squire for the description of pores in Sephadex w for a solute eluting
at Ve was given as
Ve ¼ V0 þ kV0 1
þ k 00 V0 1
(2)
r
R
3
(cones) þ k 0 V0 1
r
R
2
(cylinders)
r
(crevices)
R
(3)
where r is the protein radius. The cones and cylinders are of radius R, and the
crevices of width 2R. An arbitrary assignment of the distribution of these pores,
k 00 ¼ 9g, k 0 ¼ 9g 2 , and k ¼ 3g 3 , leads to the simplified equation describing the
contribution of all pore types to elution volume:
© 2004 by Marcel Dekker, Inc.
Ve
V0
h
r
i3 ¼ 1 þ g 1
R
(4)