Handbook of Size Exclusion Chromatography and Related ...

valuesfork1,k2,anda,theunknownmolecular weightM1 canbecalculatedfrom
Eq. (14):
M1 ¼ k2
k1
{M a2
2 }
1=a1
(14)
where M2 is the molecular weight determined by the peak position calibration
curvemethod,k1 isthecoefficientoftheanalyzedpolymer,k2 isthecoefficientof
the molecular weight standard, and a1 and a2 are the second coefficients of the
polymer and the molecular weight standard, respectively.Equations (15) and (16)
show how kand aare calculated:
k¼6:19 10 9 K 1=3
(15)
a¼ 1
3 (1þa) (16)
where K and aare Mark–Houwink constants that account for the molecular
weight dependence of the intrinsic viscosity.The universal calibration method is
broadly applicable given the availability of Mark–Houwink constants. Reference
86 summarizes Mark–Houwink constants for anumber of common polymers.
Sources of error for the universal calibration method are discussed in Refs 8, 85,
and 87. As can be expected, serious errors occur if mechanisms other than size
exclusion are at work. Cassassa (88) stated that [h]MW is not atrue universal
elution parameter, although both theory and experience indicate good results for
species of similar type. Based on theoretical considerations, Cassassa predicted a
common [h]MW dependence, however, between random coil polymers and
rodlike structures over anarrow range of molecular weight. Indeed, agood fit to
universal calibration for dextrans and some native proteins was found over a
narrow (1 10 6 to1.2 10 7 )molecular weight range (89).
It was mentioned earlier in this section that the hydrodynamic volume and
shape of the standards, in addition to their molecular weight, plays arole in
calibration. Aclaim can be made that the elution behavior of aprotein is better
related to its Stokes radius RS than to its molecular weight (90). However, this
relationship is not widely employed. The plot of RS vs. the inverse error function
erf of (1 KD) can be linear if the pore distribution is Gaussian with respect to
the Stokes radii of the macromolecules. Work with detergent-soluble membrane
proteins emphasizes the need to calibrate with similar standards and the
effectiveness of RS plots (90). Different standards are required for water-soluble
globular and detergent-soluble membrane proteins. Often the membrane proteins
may be excluded or retarded. Asmooth, although nonlinear, relationship was
obtained for the plot of RS vs. erf (1 KD), and ascatter of points was observed
for logMW vs.KD.Detergent-boundproteins behavedifferently,andtheirStokes
radii may be off by 10–30% when calibration curves are based on the elution
volumes of water-soluble proteins. Figure 12 (90) shows the selectivity curve for
© 2004 by Marcel Dekker, Inc.