Computer simulation of transport patterns of associating macromolecules : with special attention to the electrophoresis of αS1- and β-casein

The anomalous boundaries occurring during free electrophoresis or ultracentrifugation of interacting biopolymers are investigated. As is already known from the early studies of LONGSWORTH and MACINNES (1942), such interactions can give rise to abnormal velocities and areas of the migrating peaks in transport patterns.In this thesis in particular the complex formation between α _S1 - and β-casein two major proteins from milk, was studied. The importance of such complex formation for the cohesion of the natural casein micelles in milk has been stressed repeatedly.Complex formation between these proteins was easily recognizable from the different number of moving peaks on both sides of the electrophoretic channel.Application of the moving boundary theory (Chapter 2) leads to the conclusion that the constituent mobility of α _S1 -casein is fairly high, which indicates the presence of complexes of a high stoichiometric ratio α _S1 /β.The development of the reaction boundaries during electrophoresis was simulated in the ALGOL-programs presented in Chapter IV. In the computations the self-polymerization of α _S1 -casein under the experimental conditions and the simultaneous formation of the various complexes was taken into account. The results of such a simulation was found to be consistent with the conclusions of the moving boundary theory.The simulation (Chapter 3) is brought about by dividing the electrophoretic channel into a large number of small boxes of equal length. The development of the reaction boundary then was simulated by means of alternate rounds of transport of material from one box to the next and subsequent re-equilibration. Only the transport due to the velocity is accounted for, which makes the procedure a simplification of GOAD's method for the numerical solution of the conservation-of- mass equation of a system of migrating and interacting macromolecules. By reducing the calculation in this way a diffusion-like error is introduced which is used to advantage to imitate the diffusional flux. It is shown that this procedure is essentially identical to the countercurrent analog developed by BETHUNE and KEGELES to account for the effect of diffusion on the transport pattern of interacting proteins.The adjustment of the simulated diffusion coefficients to their actual values is discussed and the results of different calculations compared. It is shown that in agreement with expectation diffusional spreading had only a minor influence on the development of a reaction boundary in prolonged experiments.