Hybrid Kinetic Modelling of Protein Crystallization: Hanging Drop and Langmuir–Blodgett Conditions

The understanding and control of protein crystallization are crucial in structural biology, drug development, and biomaterial design. This study introduces a unified framework for modeling and comparing crystallization kinetics using selected growth functions. Experimental datasets from the literature for four proteins, Lysozyme, Thaumatin, Ribonuclease A, and Proteinase K, under Hanging Drop and Langmuir–Blodgett conditions were analyzed. Five kinetic models, Avrami, Kashchiev, Hill, Logistic, and Generalized Sigmoid (GSM), were fitted to size–time data of the four benchmark proteins. From each fit, four descriptors were extracted: crystallization half-time, time of maximum growth, width at half-maximum, and peak growth rate. These metrics summarize crystallization dynamics and enable cross-comparison of proteins and methods. Langmuir–Blodgett templating accelerated onset and improved synchrony, though the effect varied by protein and model. Logistic, Hill, and GSM models provided consistent fits across most conditions, while Avrami and Kashchiev were more sensitive to early or late deviations. Notably, descriptor extraction remained reliable even with limited or uneven sampling, revealing kinetic regimes such as synchrony, asymmetry, or prolonged nucleation, not evident in raw data. This transferable analytical framework supports quantitative evaluation of crystallization behavior, aiding screening, process optimization, and time-resolved structural studies.