Population balance modelling case studies for protein crystallisation: Workflows addressing impurities and heterogeneous seeding

In this study, a population balance modelling (PBM) workflow for protein crystallisation is introduced and applied to two case studies, modelling lysozyme crystallisation in the presence of protein impurities (thaumatin and bovine serum albumin (BSA)) and heterogeneous silica seeds. The workflow systematically applies engineering judgement to identify phenomena (nucleation, growth, and enhancement/inhibition by foreign species), incorporates linear and exponential empirical adjustments to traditional kinetic models, and employs sequential kinetic parameter estimation to quantify phenomena. Across the two studies, workflow applicability was demonstrated for different crystalliser configurations (static/orbital shaking), buffer systems, foreign species, and scale-up (1 to 5 mL), whilst also overcoming experimental and solubility data limitations often encountered in high-cost crystallisation experiments. Although some calibrated parameters were uncertain with the 95% t -value smaller than the reference (attributed to a need for larger datasets), the workflow not only increased system knowledge but also revealed a critical knowledge gap: the complex, protein impurity-dependent behaviour of ternary lysozyme-silica-impurity systems, which traditional kinetic models proved unable to capture. The proposed workflow is broadly applicable to other peptides, proteins, or even small molecules, positioning it as a potential method for accelerating process design and understanding.