Mechanistic Modeling of Reversed-Phase Chromatography of Insulins within the Temperature Range 10-40 °C

In the many published theories on the retention in reversed-phase chromatography (RPC), the focus is generally on the effect of the concentration of the mobile phase modulator(s), although temperature is known to have a significant influence both on the retention and on the selectivity between the adsorbates. The aim of this study was to investigate and model the combined effects of the temperature and the modulator concentrations on RPC of three insulin variants. KCl and ethanol were used as mobile phase modulators, and the experiments were performed on two different adsorbents, with C₁₈ and C₄ ligands. The temperature dependence was investigated for the interval 10-40 °C and at two different concentrations of each modulator. The model is derived from the expression for the adsorption equilibrium, which assumes that ethanol is adsorbed to the ligands and displaced by the insulin molecules, similar to the displacement of counterions in the steric mass-action model for ion-exchange chromatography. A good model fit to the new linear-range retention data was achieved by only adding and calibrating three parameters for the temperature dependence of the equilibrium. We found that a lower temperature results in a longer retention time for all adsorbates, adsorbents, and modulator concentrations used in this study, indicating that the adsorption process is enthalpy-driven. A comparison of the different contributions to the temperature dependence revealed that the large contribution from the equilibrium constant is dampened by the significant contributions of the opposite sign from the changes in activity coefficients of insulins and ethanol. Neglect of these effects when comparing different adsorbents and modulators might yield incorrect conclusions because the equilibrium constant varies with both, whereas the activity coefficients should be independent of the adsorbent. As expected, the conditions that promote higher retention also give a higher selectivity between the adsorbates. Nonetheless, in relation to its effect on the retention, the influence of the KCl concentration on the selectivity was significantly stronger than that of the temperature or that of the ethanol concentration.