Efficient Multiscale Models of Polymer Assembly

A stochastic model for dynamics of FtsZ filaments and the formation of Z -ring

Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the Z -ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces in vitro observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.

Dissecting the Functional Contributions of the Intrinsically Disordered C-terminal Tail of Bacillus subtilis FtsZ

FtsZ is a bacterial GTPase that is central to the spatial and temporal control of cell division. It is a filament-forming enzyme that encompasses a well-folded core domain and a disordered C-terminal tail (CTT). The CTT is essential for ensuring proper assembly of the cytokinetic ring, and its deletion leads to mis-localization of FtsZ, aberrant assembly, and cell death. In this work, we dissect the contributions of modules within the disordered CTT to assembly and enzymatic activity of Bacillus subtilis FtsZ (Bs-FtsZ). The CTT features a hypervariable C-terminal linker (CTL) and a conserved C-terminal peptide (CTP). Our in vitro studies show that the CTL weakens the driving forces for forming single-stranded active polymers and suppresses lateral associations of these polymers, whereas the CTP promotes the formation of alternative assemblies. Accordingly, in full-length Bs-FtsZ, the CTL acts as a spacer that spatially separates the CTP sticker from the core, thus ensuring filament formation through core-driven polymerization and lateral associations through CTP-mediated interactions. We also find that the CTL weakens GTP binding while enhancing the catalytic rate, whereas the CTP has opposite effects. The joint contributions of the CTL and CTP make Bs-FtsZ, an enzyme that is only half as efficient as a truncated version that lacks the CTT. Overall, our data suggest that the CTT acts as an auto-regulator of Bs-FtsZ assembly and as an auto-inhibitor of enzymatic activity. Based on our results, we propose hypotheses regarding the hypervariability of CTLs and compare FtsZs to other bacterial proteins with tethered IDRs.

Quantification of Predictive Uncertainty in Models of FtsZ ring assembly in Escherichia coli

Quantitative predictions of FtsZ protein polymerization are essential for understanding the self-regulating mechanisms in biochemical systems. Due to structural complexity and parametric uncertainty, existing kinetic models remain incomplete and their predictions error-prone. To address such challenges, we perform probabilistic uncertainty quantification and global sensitivity analysis of the concentrations of various protein species predicted with a recent FtsZ protein polymerization model. Our results yield a ranked list of modeling shortcomings that can be improved in order to develop more accurate predictions and more realistic representations of key mechanisms of such biochemical systems and their response to changes in internal or external conditions. Our conclusions and improvement recommendations can be extended to other kinetics models.

Bacterial cell division: modeling FtsZ assembly and force generation from single filament experimental data

The bacterial cytoskeletal protein FtsZ binds and hydrolyzes GTP, self-aggregates into dynamic filaments and guides the assembly of the septal ring on the inner side of the membrane at midcell. This ring constricts the cell during division and is present in most bacteria. Despite exhaustive studies undertaken in the last 25 years after its discovery, we do not yet know the mechanism by which this GTP-dependent self-aggregating protein exerts force on the underlying membrane. This paper reviews recent experiments and theoretical models proposed to explain FtsZ filament dynamic assembly and force generation. It highlights how recent observations of single filaments on reconstituted model systems and computational modeling are contributing to develop new multiscale models that stress the importance of previously overlooked elements as monomer internal flexibility, filament twist and flexible anchoring to the cell membrane. These elements contribute to understand the rich behavior of these GTP consuming dynamic filaments on surfaces. The aim of this review is 2-fold: (1) to summarize recent multiscale models and their implications to understand the molecular mechanism of FtsZ assembly and force generation and (2) to update theoreticians with recent experimental results.

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

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.