Advancing HIC method development: Retention-time modeling and tuning selectivity with ternary mobile-phase systems

The use of a ternary mobile-phase system comprising ammonium sulphate, sodium chloride, and phosphate buffer was explored to tune retention and enhance selectivity in hydrophobic interaction chromatography. The accuracy of the linear solvent-strength model to predict protein retention with the ternary mobile-phase system based on isocratic scouting runs is limited, as the extrapolated retention factor at aqueous buffer conditions (k₀) cannot be reliably established. The Jandera retention model utilizing a salt concentration averaged retention factor (k¯₀) in aqueous buffer for ternary systems overcomes this bottleneck. Gradient retention factors were derived based on isocratic scouting runs after numerical integration of the isocratic Jandera model, leading to retention-time prediction errors below 11 % for linear gradients. Furthermore, an analytical expression was formulated to predict HIC retention for both linear and segmented linear gradients, considering the linear solvent-strength (LSS) model within ternary salt systems, relying on a fixed k₀. The approach involved conducting two gradient scouting runs for each of the two binary salt systems to determine model parameters. Retention-time prediction errors for linear gradients were below 12 % for lysozyme and 3 % for trypsinogen and α-chymotrypsinogen A. Finally, the analytical expression for a ternary mobile-phase system was used in combination with a genetic algorithm to tune the HIC selectivity. With an optimized segmented ternary gradient, a critical-pair separation for a mixture of 7 proteins was achieved within 15 min with retention-time prediction errors ranging between 0.7 and 15.7 %.