Pareto-optimal reversed-phase chromatography separation of three insulin variants with a solubility constraint

With the shift of focus of the regulatory bodies, from fixed process conditions towards flexible ones based on process understanding, model-based optimization is becoming an important tool for process development within the biopharmaceutical industry. In this paper, a multi-objective optimization study of separation of three insulin variants by reversed-phase chromatography (RPC) is presented. The decision variables were the load factor, the concentrations of ethanol and KCl in the eluent, and the cut points for the product pooling. In addition to the purity constraints, a solubility constraint on the total insulin concentration was applied. The insulin solubility is a function of the ethanol concentration in the mobile phase, and the main aim was to investigate the effect of this constraint on the maximal productivity. Multi-objective optimization was performed with and without the solubility constraint, and visualized as Pareto fronts, showing the optimal combinations of the two objectives productivity and yield for each case. Comparison of the constrained and unconstrained Pareto fronts showed that the former diverges when the constraint becomes active, because the increase in productivity with decreasing yield is almost halted. Consequently, we suggest the operating point at which the total outlet concentration of insulin reaches the solubility limit as the most suitable one. According to the results from the constrained optimizations, the maximal productivity on the C₄ adsorbent (0.41 kg/(m³ column h)) is less than half of that on the C₁₈ adsorbent (0.87 kg/(m³ column h)). This is partly caused by the higher selectivity between the insulin variants on the C₁₈ adsorbent, but the main reason is the difference in how the solubility constraint affects the processes. Since the optimal ethanol concentration for elution on the C₁₈ adsorbent is higher than for the C₄ one, the insulin solubility is also higher, allowing a higher pool concentration. An alternative method of finding the suggested operating point was also evaluated, and it was shown to give very satisfactory results for well-mapped Pareto fronts.