Parameter estimation of a size-exclusion simulated moving bed for protein purification via meta-heuristic methods with estimability analysis and uncertainty evaluation

• Parameter estimation was successfully applied to an SMB mathematical model. • Local estimability analysis enhances data validation before estimation. • A thorough uncertainty quantification method was used to better characterize the results. • PSO demonstrated high effectiveness in solving optimization problems. • The methodology proved to be efficient in using data from multiple experiments. This study aims to enhance the modelling of myoglobin (Mb) and bovine serum albumin (BSA) separation in size-exclusion gel systems by leveraging experimental data and computational methods. The objective is to estimate the parameters of a mathematical model that accurately represents this separation process. To achieve this, optimization problems with adequate objective functions are solved via Particle Swarm Optimization (PSO), which has been shown to be more efficient than comparable deterministic methods Comprehensive estimability and uncertainty analyses were also conducted to thoroughly assess the model’s reliability and accuracy. The initial phase of the study involved estimating parameters for a fixed bed system. During this phase, it was discerned through estimability analysis that the mass transfer coefficient parameters, denoted as k h , had minimal impact on the model’s outputs, leading to their exclusion from subsequent estimations. The focus then shifted to refining the model parameters to simultaneously fit both the fixed bed and Simulated Moving Bed (SMB) experimental data. The comparative analysis between these parameters and the fixed bed parameters highlighted notable differences, particularly in the axial dispersion parameter ( D ax ) and the BSA size exclusion constant ( K SEC , B S A ). An uncertainty evaluation was successfully executed after completing this study, providing confidence intervals for each parameter, and propagating the uncertainty to the prediction of the developed model. This comprehensive approach ensures a more accurate and reliable understanding of the separation dynamics in size-exclusion gel processes for Mb and BSA.