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.

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.

Mathematical models of microbial growth and metabolism: a whole-organism perspective

We review the principles underpinning the development of mathematical models of the metabolic activities of micro-organisms. Such models are important to understand and chart the substantial contributions made by micro-organisms to geochemical cycles, and also to optimise the performance of bioreactors that exploit the biochemical capabilities of these organisms. We advocate an approach based on the principle of dynamic allocation. We survey the biological background that motivates this approach, including nutrient assimilation, the regulation of gene expression, and the principles of microbial growth. In addition, we discuss the classic models of microbial growth as well as contemporary approaches. The dynamic allocation theory generalises these classic models in a natural manner and is readily amenable to the additional information provided by transcriptomics and proteomics approaches. Finally, we touch upon these organising principles in the context of the transition from the free-living unicellular mode of life to multicellularity.

Efficient Multiscale Models of Polymer Assembly

Protein polymerization and bundling play a central role in cell physiology. Predictive modeling of these processes remains an open challenge, especially when the proteins involved become large and their concentrations high. We present an effective kinetics model of filament formation, bundling, and depolymerization after GTP hydrolysis, which involves a relatively small number of species and reactions, and remains robust over a wide range of concentrations and timescales. We apply this general model to study assembly of FtsZ protein, a basic element in the division process of prokaryotic cells such as Escherichia coli, Bacillus subtilis, or Caulobacter crescentus. This analysis demonstrates that our model outperforms its counterparts in terms of both accuracy and computational efficiency. Because our model comprises only 17 ordinary differential equations, its computational cost is orders-of-magnitude smaller than the current alternatives consisting of up to 1000 ordinary differential equations. It also provides, to our knowledge, a new insight into the characteristics and functioning of FtsZ proteins at high concentrations. The simplicity and versatility of our model render it a powerful computational tool, which can be used either as a standalone descriptor of other biopolymers' assembly or as a component in more complete kinetic models.

Beyond the Discovery Void: New targets for antibacterial compounds

Antibiotics save many lives, but their efficacy is under threat: overprescription, population growth, and global travel all contribute to the rapid origination and spread of resistant strains. Exacerbating this threat is the fact that no new major classes of antibiotics have been discovered in the last 30 years: this is the "discovery void." We discuss the traditional molecular targets of antibiotics as well as putative novel targets.

Biological Insights from a Simulation Model of the Critical FtsZ Accumulation Required for Prokaryotic Cell Division

A simulation model of prokaryotic Z-ring assembly, based on the observed behavior of FtsZ in vitro as well as on in vivo parameters, is used to integrate critical processes in cell division. According to the model, the cell's ability to divide depends on a "contraction parameter" (χ) that links the force of contraction to the dynamics of FtsZ. This parameter accurately predicts the outcome of division. Evaluating the GTP binding strength, the FtsZ polymerization rate, and the intrinsic GTP hydrolysis/dissociation activity, we find that inhibition of GTP-FtsZ binding is an inefficient antibacterial target. Furthermore, simulations indicate that the temperature sensitivity of the ftsZ84 mutation arises from the conversion of FtsZ to a dual-specificity NTPase. Finally, the sensitivity to temperature of the rate of ATP hydrolysis, over the critical temperature range, leads us to conclude that the ftsZ84 mutation affects the turnover rate of the Z-ring much less strongly than previously reported.

Bacterial cell division: experimental and theoretical approaches to the divisome

Cell division is a key event in the bacterial life cycle. It involves constriction at the midcell, so that one cell can give rise to two daughter cells. This constriction is mediated by a ring composed offibrous multimers of the protein FtsZ. However a host of additional factors is involved in the formation and dynamics of this "Z-ring" and this complicated apparatus is collectively known as the "divisome". We review the literature, with an emphasis on mathematical modelling, and show how such theoretical efforts have helped experimentalists to make sense of the at times bewildering data, and plan further experiments.