Molecular weight distribution of interacting proteins calculated by multiple regression analysis from sedimentation equilibrium data: An interpretation of α s1-κ-casein interaction

Abstract

Multiple regression analysis in four series with exponentially spaced molecular weight scales shifted by a factor of 2 1 4 between series was applied to sedimentation equilibrium data for determination of the molecular weight distribution of synthesized model systems consisting of up to three components which represented heterogeneous associating systems. Negative weight fractions of the components which were frequently encountered during multiple regression analysis were forced to zero by successively eliminating from the regression matrix the corresponding molecular weights in order of the magnitude of negative t values. The simplex optimization technique in conjunction with a prohibit-trespassing routine was used to maximize F values obtained from multiple regression analysis in search of the best fit values of component molecular weights. The quantitative information relating molecular weights and relative concentrations obtained by simplex optimization supplemented the regression matrix for calculation of the molecular weight distribution to improve the resolution of the molecular weight distribution patterns. This multiple regression method when carried out in conjunction with the simplex optimization provided a better fit to the data than the linear programming method of Scholte. When applied to mixtures of three standard proteins, the simplex optimization routine yielded values of molecular weights and relative concentrations of the component proteins which were in good agreement with the known values of the original mixtures. The molecular weight distribution calculated from sedimentation equilibrium data of α s1-κ-casein mixtures using a uv scanner indicated that κ-casein readily dissociated to an oligomer, probably up to trimer, and interacted with the monomer or dimer of α s1-casein forming a complex of approximately 400,000 molecular weight. This dissociation of κ-casein was promoted in the presence of ovalbumin, a nonmilk protein. © 1979.