We present a population balance model for enzyme deactivation and aggregation kinetics with a limited number of physically relevant parameters and use this model to analyse the experimental data for thermal inactivation of jack bean urease. The time dependence of the relative enzymatic activity was found to follow the second order kinetics, which was consistent with pre-equilibrated folding/unfolding of the native enzyme, followed by irreversible cluster–cluster aggregation of the non-native enzyme resulting in gradual and permanent loss of enzymatic activity. Monomer–cluster aggregation scenario was considered but was not consistent with the observed kinetic order of monomer disappearance at longer times. We analysed time evolution of the average hydrodynamic radius obtained from dynamic light scattering measurements and by fitting these data with our model, we were able to estimate the value of the unfolding equilibrium constant with a reasonable accuracy (Kc around 0.05 at 80 degrees C). We were also able to make order of magnitude estimates of the maximum number of enzyme molecules in the aggregated clusters (hundreds)as well as the aggregation rate constant of the non-native enzyme.
Grancic, P., Illeova, V., Polakovic, M., & Sefcik, J. (2012). Thermally induced inactivation and aggregation of urease: experiments and population balance modelling. Chemical Engineering Science, 70, 14–21. https://doi.org/10.1016/j.ces.2011.07.050