Application of Multiple Regression Analysis to Sedimentation Equilibrium Data of αs1- and κ-caseins Interactions for the Calculation of Molecular Weight Distribution

Multiple regression analysis was applied to sedimentation equilibrium data for determination of the molecular weight distribution (MWD) of model systems consisting of up to 3 components. Negative weight fractions which were frequently encountered during multiple regression analysis were forced to zero by sequentially eliminating from the regression matrix the corresponding molecular weights in order of the magnitude of negative t -values. The simplex optimization of Morgan & Deming (1974), modified by incorporating a prohibit–range– trespassing routine, was used to search for the best fit values for weight average molecular weights and relative concentrations of the components. This method almost quantitatively reproduced the molecular weights and concentrations of the original model systems. This quantitative information supplemented the multiple regression matrix to improve the resolution of MWD. A direct comparison using model systems revealed that the multiple regression method in conjunction with the simplex optimization routine was more quantitative than the linear programming method of Scholte (1969). When applied to mixtures of standard proteins (ribonuclease A; ovalbumin; γ-globulin and ovalbumin; γ-globulin; apoferritin), the simplex optimization routine yielded values for average molecular weights and relative concentrations of the component proteins which were in good agreement with the known values in the original mixtures. The MWD of α s1 - k -casein mixtures at an ionic strength of 0.1 suggested that k -casein was readily dissociated to the monomer (or the dimer) and interacted with the monomer (or the dimer) of α s1 -casein forming a complex of approximately 400000.