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Molecular Sieve Studies of Interacting Protein Systems

II. ENUMERATION OF COMPONENTS AND DETERMINATION OF MOLECULAR SIZE DISTRIBUTIONS

From the ¹ From the Department of Biochemistry, University of Virginia, Charlottesville, Virginia 22901

Studies of chemically reacting systems of macromolecules by conventional transport experiments are subject to inherent ambiguities. These uncertainties often prohibit an unequivocal determination of the explicit reactions which give rise to the average properties being measured. Such difficulties may be circumvented with molecular sieve chromatography in which subunit dissociation curves are obtained on columns of different gel porosity. From such data, procedures are described for enumeration of components in a complex reaction mixture and for determination of their molecular size distribution. For a system having k components data must be obtained on at least 2k - 1 columns of different porosity to obtain the weight fractions of all components in the system. If the equilibria are shifted by variation in some parameter, such as total concentration, and the distributions are determined at various resulting states of the equilibria, it is possible to calculate stoichiometries between all components and to determine the equilibrium constants for the system. Additional information that can be obtained with these procedures includes the weight average degree of polymerization and the molecular weight of monomer.

These procedures depend on the fact that molecular sieve partition coefficients are linearly independent functions of both the molecular size and calibration constants (porosity) of the gel. Experimental data are presented in support of this linear independence. Feasibility of the mathematical procedures has been shown by calculations carried out for a hypothetical dissociation reaction in which random errors have been applied to the ideal dissociation curves, and the resulting data have been used to calculate the stoichiometry and equilibrium constant for the reaction.

In order to minimize the effort involved in multiple column experiments and to obtain an overdetermined system for calculations, the methods can be extended to a single column in which an arbitrary gradient of gel porosity is established. The basic features of this molecular sieve gradient chromatography technique are outlined and its potential use in determining molecular size distributions has been described. These methods are applicable to multicomponent systems in which the various species are in rapidly reversible equilibrium, in slow equilibrium, or are noninteracting.

The use of columns having more than one gel porosity provides a stringent test for the assumption that the column bed material does not itself perturb the chemical equilibria being studied.

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