A kinetic master equation formalism can be used to accurately model nanoparticle growth inside LiDps.
During our studies of particle growth in Dps from Listeria innocua (LiDps) using non-covalent mass spectrometry (NCMS), we found that NCMS produced highly quantitative data on the distribution of particle sizes and we looked for a simple model that could explain our findings.
We eventually settled on a kinetic master equation formalism, in which a population of protein cages (initially empty) acquires additional Fe atoms according to a specific set of rules. During the nucleation phase, a small number of Fe2+ ions enter the cage at a constant rate, because their entry rate is limited by their rate of diffusion through the protein cage and binding at the cage interior. During the subsequent growth phase, the particles (assumed spherical) begin to grow at a rate that is proportional to their surface area. This means that larger particles grow faster, leading to the broad particle size distribution observed at later times in the simulation (see right). The model proved to be extremely insensitive to most of its parameters with the exception of the initial Fe/cage ratio -- since this was the experimentally-controlled variable, we were able to reproduce the experimental results with good accuracy without sensitive parameter-tuning.
Perhaps the most exciting result was that the simulations were able to reproduce the bimodal particle size distribution seen at intermediate particle sizes, in which a narrow distribution of particle sizes associated with binding and nucleation (usually only 12 Fe atoms per cage) could be observed alongside the broader distribution resulting from surface-catalyzed particle growth.
