Handbook of Size Exclusion Chromatography and Related ...

globular proteins and selected flexible chain polymers were found to elute
predictably when the “viscosity radius”, Rh, (equal to [h]M) was used as the solute
parameter. These authors found that rodlike molecules did not obey this elution
rule, however, and concluded that the universal “SEC radius” had not been found.
This may indeed be true for the broad-based SEC of biomacromolecules; however,
the RSEC (Dubin’s term) must be similar, if not equal, to the effective
hydrodynamic radius proposed by Cassassa and Tagami (34), and must occupy the
effective hydrodynamic volume, Vh. For many proteins, Re may be equivalent to
Rh. Yet,Re may also be calculated from known parameters, such as the molecular
weight (from sedimentation equilibrium or gene sequence), molecular dimensions
(from x-ray crystallography), surface hydration (from titration or modeling), and
partial specific volume (from composition or actual measurement). Following
Oncley’s approach (45), based on an extension of the Stokes relationship for a
perfectly spherical protein, f0 ¼ 6phR0, globular proteins may be described more
accurately than as simple spherical, hydrated structures (34). This frictional
coefficient, f , is defined as:
f ¼ 6ph f
f0
3M(n2 þ d1n 0 1 )
4pN
where f =f0 is the frictional ratio, n2 is the protein partial specific volume, n0 1 is the
pure solvent specific volume, d1 is the protein hydration, and N is Avogadro’s
number. The product of the bracketed quantity in Equation (10) and the shape
factor, fe=fo, is the highly protein-specific radius, Re. If needed, the frictional
ratios may be found from experimental data (s, M, and n2; where s is the sedimentation
coefficient) or from protein dimensional information, assuming best
fit for x-ray structural data to either prolate or oblate spheroids of revolution.
This estimation may be accomplished using the relationships developed long
ago by Perrin (46) and modified by Herzog et al. (47). For prolate ellipsoids
(semi-axes a, b, b)
f
f0
1=3
(1 b
¼
2 =a2 ) 1=2
(b=a) 2=3 ln[1 þ (1 b 2 =a2 ) 1=2 ]=(b=a)
and for oblate ellipsoids (semi-axes a, a, b):
f
f0
(a
¼
2 =b 2
(a=b) 2=3 tan 1 (a2 =b 2
1) 1=2
1) 1=2
where R0 is the radius of a sphere of equal volume to the ellipsoid, that is,
4
3pR3 4
0 ¼ 3ab2 (prolate ellipsoid) or 4
3pa2b (oblate ellipsoid).
Unfortunately, these parameters are known accurately for only a relatively
small group of globular proteins: the 21 globular proteins reported by Squire and
Himmel in 1979 (48). The test of fit for globular protein elution from SEC based
© 2004 by Marcel Dekker, Inc.
(10)
(11)
(12)