Cytoskeletal filaments, such as actin, microtubules, and FtsZ, are active cellular components exhibiting treadmilling—a dynamic process where filaments grow at one end and shrink at the other due to nucleotide hydrolysis. While previous models often simplified this as self-propulsion, this approach overlooks the constant turnover of components. This paper focuses on understanding the self-organization mechanisms of treadmilling polymers, particularly FtsZ, a crucial protein in bacterial cell division responsible for forming the Z-ring, a structure that orchestrates this process. The study aims to elucidate the role of treadmilling in the self-organization of FtsZ into the Z-ring, a process vital for bacterial cell division and potentially relevant to other cytoskeletal processes. Treadmilling has been shown to be essential for cell division in various bacteria, but how it contributes to the large-scale structure of the Z-ring remains unclear. This research seeks to address this gap using a combination of computational modeling and in vitro and in vivo experiments.

The literature extensively discusses treadmilling in various cytoskeletal filaments. Previous studies have examined treadmilling in actin, microtubules, and FtsZ, highlighting its role in cellular processes. While single-filament dynamics are relatively well-understood, the collective behaviour and self-organization mechanisms of treadmilling filaments remain less explored. Existing models often employ self-propulsion, which may overestimate forces and fail to capture the turnover aspect of treadmilling. The role of treadmilling in FtsZ-ring formation has been suggested, but the detailed mechanisms remain unclear. Studies have shown that treadmilling is essential for bacterial cell division, but the link between treadmilling and Z-ring organization requires further investigation. This research builds upon previous work by developing a more realistic computational model to explore the collective dynamics of treadmilling filaments and directly comparing the results to experimental data. This approach improves upon previous modeling efforts by incorporating the inherent dynamics of growth, shrinkage, and turnover associated with treadmilling.

The researchers developed a coarse-grained computational model of treadmilling filaments as polymers of spherical beads on a 2D plane with periodic boundary conditions. The model incorporates filament nucleation, growth, and shrinkage kinetics, dynamically creating and deleting monomers. Filament polymerization is only allowed if free space is available. Tail depolymerization probability is modeled using a time-dependent function that accounts for nucleotide hydrolysis and monomer dissociation. Two key parameters govern treadmilling: the head polymerization rate (r_on) and the monomer detachment time (τ_det). Simulations were performed for a range of (r_on, τ_det) values. In vitro experiments involved reconstituting *E. coli* FtsZ filaments on supported lipid bilayers (SLBs) and imaging using total internal reflection fluorescence microscopy. Filament lengths and velocities, as well as monomer lifetimes, were measured. High-speed atomic force microscopy (HS-AFM) was used to image reconstituted FtsZ filaments to study collective ordering. In vivo experiments involved imaging the Z-ring formation in *B. subtilis* cells. To model the in vivo Z-ring formation, the model incorporated a curvature-sensing mechanism, where filaments align along the cell circumference, a spatial modulation of FtsZ polymerization rates, and attractive interfilament interactions (mimicking cross-linking).

The computational model accurately reproduced single-filament treadmilling dynamics, matching in vitro experimental data. Collective simulations revealed three regimes depending on filament size: a quasi-empty regime, an unstable treadmilling regime, and a highly stable, nematically ordered regime. Nematic ordering is driven by the preferential death of misaligned filaments. High-speed AFM images of *E. coli* FtsZ filaments showed a striking resemblance to simulation snapshots, with a clear transition to high nematic order at higher density. A FtsZ mutant with reduced GTPase activity showed reduced nematic order, further supporting the model. The model successfully captured the rapid condensation and slow maturation dynamics of the Z-ring in *B. subtilis*, matching in vivo experimental data. The rapid condensation is attributed to the rapid dissolution of filaments in growth-inhibited regions. Slow maturation is due to the replacement of misaligned filaments with aligned ones, leading to increasing filament velocity in mature rings. Arresting treadmilling in simulations mimicked the in vivo effects of impaired treadmilling, demonstrating its crucial role in Z-ring formation and stability.

The study's findings demonstrate a novel mechanism for the self-organization of cytoskeletal filaments through treadmilling, where filament mortality plays a central role. This contrasts with previously studied self-organizing systems. The model quantitatively explains the dynamics of Z-ring formation, revealing the interplay between filament curvature, spatial modulation of polymerization rates, and interfilament interactions. The rapid response to chemical cues and the ability to heal defects highlight the potential of treadmilling filaments in synthetic biology and active matter research. The model provides insights into the functional FtsZ assemblies and the dynamics of the Z-ring, suggesting implications for understanding bacterial cell wall synthesis and division. The model also has implications for the broader field of active matter, expanding our understanding of ordering mechanisms in energy-consuming systems.

This research reveals a new self-organization mechanism for cytoskeletal filaments driven by treadmilling and filament mortality. The model accurately predicts both in vitro and in vivo observations of FtsZ behavior. Future research should explore the model's applicability to other cytoskeletal systems and investigate the detailed interactions between the Z-ring and other components of the bacterial cell division machinery. Further investigation into the physical properties of treadmilling filaments as active matter, especially their response to obstacles and perturbations, would also be beneficial.

The model is a 2D simplification of a 3D biological process. While the model captures key aspects of Z-ring formation, it may not fully account for all complexities of the in vivo system. The model's parameters were fitted to specific experimental conditions, and their generalizability to other bacterial species or conditions requires further investigation. The study focused primarily on FtsZ, and the role of other proteins involved in cell division was not explicitly modeled.