The influence of ionic strength and pH on the aggregation properties of zinc‐free insulin studied by static and dynamic laser light scattering
Authors: Kadima W. , Øgendal L. , Bauer R. , Kaarsholm N. , Brodersen K. , Hansen J. F. , Porting P. 
Published: December 2004

The aggregation properties of zinc‐free insulin have been studied using static and dynamic light scattering. The aggregation has been investigated as a function of three parameters, the concentration of sodium chloride (in the range 10–100 mM), the pH value (in the range pH 7.5–10.5), and the insulin concentration (1.8–13.4 mg/mL). The measured homodyne autocorrelation function was used to determine the apparent mean hydrodynamic diameter as well as the apparent weight‐averaged molar mass of the insulin species in solution. A method of data analysis was employed, which allows the separation of light scattering contributions from the insulin oligomers and from irrelevant macromolecules and possible impurities present in the sample solutions. Also, a simple phenomenological equilibrium model describing the association of oligomers of insulin is presented. One aspect of this model is that it makes it possible to determine weight average molar masses corrected for virial effects on the Rayleigh ratio. This was necessary because virial effects cannot be isolated and corrected for by dilution since this would change the equilibrium distribution of oligomers. The basis of the model is a positive contribution to Gibbs free energy from charge repulsion depending on the protein charge and the number of monomers in the oligomers, and an assumed constant negative contribution to Gibbs free energy arising from either an entropic gain or hydrogen bonding upon association. The equilibrium model gives a good description of both the apparent weight average molar masses and the apparent hydrodynamic diameters, when the effect of the insulin concentration is taken into account by including virial effects arising from charge–charge repulsion (Donnan effect). The result shows that the association of insulin as a function of pH and ionic strength can be described by an effective charge equal to the charge derived from proton titration reduced by the number of sodium ions binding to insulin. At the lowest pH and highest salt concentration (pH 7.5, 100 mM NaCl, 12 mg/mL insulin), the weight average molar mass is close to that of the hexamer, and at the highest pH and lowest salt concentration (pH 10.5, 10 mM NaCl, 1.9 mg/mL), the weight average molar mass is close to that of the monomer. In all cases, however, a distribution of oligomers is present with a relative Gaussian width of about 30%. Neglecting the positive term in Gibbs free energy, an upper bound to the association constant for insulin can be calculated: The negative term in Gibbs free energy corresponds to an association constant of (0.8 ± 0.3)·105M−1, which is in agreement with published values for the monomer‐to‐monomer association. The satisfactory agreement between theory and experiments for the weight average molar mass suggests that it should be possible to predict the aggregational properties of mutant forms of insulin. © 1993 John Wiley & Sons, Inc.