Attachment and detachment kinetics of FtsZ filaments

An important step in the initialization of bacterial cell division is the formation of the Z-ring. The Z-ring consists of FtsZ (proto)filaments anchored to the cell membrane via linker proteins. FtsZ filaments begin to form in the cytosol and eventually condense near the middle of the cell to form the Z-ring; however, the steps involved are not completely understood and are difficult to observe in experiments. We attempt o break down the process of Z-ring formation in Escherichia coli into a series of simpler processes and use molecular dynamics to gain insight into the details involved. We have developed two different simulations, one to study the attachment of the filament after its collision with the inner membrane and the other to implement the slower reaction-diffusion process that occurs due to many filament attachment and detachment events. We use the LAMMPS package for the former, and for the latter, we use our original C++ code. In the LAMMPS simulations carried out on the Summit supercomputer at ORNL, the FtsZ filaments are modeled as rigid, ball and chain polymers decorated with linkers. Using these linkers, filaments can attach to the cell wall due to an effective potential which combines the effect of interaction between different linker proteins, the filament, and the cell. From this model, we extract the attachment rates of filaments colliding with the membrane at different angles, and compare them to a theoretical model. We also use a modified coarse grain model to estimate the bending energy of a rigid filament and investigate the detachment process. Finally, we present results from further work that integrate these results into a full reaction-diffusion model, where the process of attachment is modeled as a reaction which is rate-limited by the diffusion of the filament to the membrane.