Predictive optimization and scale-up of dynamic binding capacity for C-phycocyanin from Spirulina platensis in packed-bed chromatography

Background Dynamic binding capacity at 5% breakthrough (DBC 5% ) is a key performance parameter in packed-bed chromatography because it determines the effective working capacity of the adsorbent and directly influences process productivity under dynamic-flow conditions. Methods This study presents a systematic methodology for the predictive optimization and scale-up of DBC 5% for C-phycocyanin (CPC) purification from Spirulina platensis using a sequential design of experiments (DoE) approach. A 2⁴ full factorial design with two center points (2⁴ + 2) was first employed to identify the significant operating variables, followed by a central composite design (CCD) to evaluate potential nonlinear responses. Significant findings The 2⁴ + 2 factorial model exhibited superior predictive performance, achieving an R² of 98.97% and a predicted R² of 94.82%, compared with corresponding values of 91.04% and 48.50%, respectively, for the CCD model. The optimized operating conditions (pH 6.0, 10% (w/v) feed concentration, 1.6 cm bed height, and a flow rate of 10.0 mL/min) yielded a predicted DBC 5% of 10.51 mg/mL, which was experimentally validated by an observed value of 10.45 mg/mL, corresponding to a relative error of 2.9%. Furthermore, scale-up from 1.6 cm to 5.0 cm internal-diameter columns while maintaining hydrodynamic similarity successfully preserved DBC 5% , demonstrating consistent adsorption performance across the investigated scales. Although the developed regression model is specific to the chromatographic system investigated, the proposed DoE-based optimization framework and hydrodynamic scale-up strategy provide a practical methodology that can be applied to other packed-bed chromatography systems following appropriate experimental calibration and validation.