Abstract

Ferritin, a ubiquitous protein complex, plays a critical role in cellular iron homeostasis by sequestering and storing iron in a non-toxic, bioavailable form. This function is contingent upon its precise self-assembly into a hollow, spherical nanocage composed of 24 subunits. Understanding the kinetics of this self-assembly process is vital for elucidating the mechanisms of iron metabolism and for advancing the use of ferritin as a nanobiotechnological platform. In this study, we apply the **Smoluchowski Coagulation Model** to quantitatively investigate the time-dependent aggregation and formation of the ferritin cage. The model, which describes the evolution of particle size distribution in a coagulating system, was adapted to account for the specific biological parameters of ferritin subunit association. We numerically solved the Smoluchowski differential equations to simulate the assembly kinetics under various conditions, including different initial subunit concentrations and temperature profiles. Our key finding is the identification of a critical concentration threshold and a specific set of coagulation kernels that accurately predict the experimentally observed assembly yield and time-scale of the 24-mer complex. This work provides a robust theoretical framework for predicting the self-assembly behavior of multi-subunit protein complexes, offering new insights into the biophysical principles governing protein cage formation and informing the rational design of ferritin-based drug delivery and imaging agents.