Efficient models of polymerization applied to FtsZ ring assembly in Escherichia coli

Significance Our modeling framework yields accurate and computationally efficient quantitative predictions of complex kinetics of polymerization processes in biological systems. The resulting model consists of 10 differential equations, regardless of the total concentration of proteins. This is in contrast to previous polymerization models, in which the number of equations increases with the total concentrations, reaching into the thousands. Consequently, our model is orders of magnitude faster than its existing alternatives. It can be used to predict polymerization kinetics at high concentrations characteristic of in vivo processes and, especially, their compartmentalized and spatially distributed representations. High protein concentrations complicate modeling of polymer assembly kinetics by introducing structural complexity and a large variety of protein forms. We present a modeling approach that achieves orders of magnitude speed-up by replacing distributions of lengths and widths with their average counterparts and by introducing a hierarchical classification of species and reactions into sets. We have used this model to study FtsZ ring assembly in Escherichia coli. The model’s prediction of key features of the ring formation, such as time to reach the steady state, total concentration of FtsZ species in the ring, total concentration of monomers, and average dimensions of filaments and bundles, are all in agreement with the experimentally observed values. Besides validating our model against the in vivo observations, this study fills some knowledge gaps by proposing a specific structure of the ring, describing the influence of the total concentration in short and long kinetics processes, determining some characteristic mechanisms in polymer assembly regulation, and providing insights about the role of ZapA proteins, critical components for both positioning and stability of the ring.