Handbook of Size Exclusion Chromatography and Related ...

process may be used to identify the correct association of the protein component.
However,ifadistributionofassociatesispresent,themethoddescribedabovewell
may yield misleading and quantitatively wrong results.
8 BRANCHING
The characterization of branching by MALS has long been an objective
beginning with the seminal paper on the subject by Zimm and Stockmayer (24).
At that time SEC had not been invented. Indeed, the only means of fractionating
asample was by precipitation fractionation, which yielded broad fractions and
rendered attempts to measure distributions present futile. Nevertheless, by
making aplot of log(M)vs. logkr2 gl,even of such crude fractions should reveal
some quantitative elements of the presence of branching. Indeed, this approach
was used later by Podzimek et al. (25) who plotted log(rg) vs. log(M)instead.
Further details of Podzimek’sapproach are discussed in Sec. 10 and in Ref. 25.
The quantitation of branching generally begins from calculation of the
so-called branching ratio
g ¼ 1=M Ð r 2 b dm
1=M Ð r 2 l dm ¼ kr2 gb l
kr 2 gl l
where the mean-square radii are calculated for the branched (b) and linear (l)
molecules at the same molar mass. For the same molar mass, the branched
molecules will be more compact than their linear counterparts and, therefore, the
branching ratio will be less than unity. The ASTRA w software (Wyatt Technology
Corporation, Santa Barbara, California, U.S.A.) provides means to calculate the
average number of branch units per molecule, B, for both trifunctional (three units
joined at one point) and tetrafunctional (four units) branching based on the
corresponding relations (24)
" p # 1
2
B 4B
g3(B) ¼ 1 þ þ (12)
7 9p
and
g4(B) ¼
" p # 1
2
B 4B
1 þ þ
6 3p
(11)
(13)
From these results one may calculate long-chain branching defined as the number
of branches per 100 repeat units. Further details and examples, especially for the
© 2004 by Marcel Dekker, Inc.