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Description
Many cytoskeletal filaments that drive cellular shape changes and motility, such as actin, FtsZ, and TubZ, undergo treadmilling—a dynamic process in which monomers continuously add to one filament end while dissociating from the other. However, the physical principles that enable treadmilling remain unclear.
Treadmilling requires monomer structure to encode faster binding at one filament end to establish directionality. Hydrolysis, modeled as stochastic bond weakening, promotes depolymerization at the opposite end. Because hydrolysis generates a gradient of weakened monomers, filaments must remain stable in the bulk while disassembling at the ends to avoid fragmentation. How single-stranded filaments (e.g., FtsZ) satisfy these competing constraints is unknown.
To probe the single-filament requirements for treadmilling, we construct a colloidal monomer that polymerises into single-stranded filaments and systematically identify the design features required for sustained treadmilling.
We first investigate how directionality can be encoded at the monomer level by analysing binding to a non-hydrolysing filament whose ends are exposed to monomer pools at constant concentration. We find that a way to encode binding kinetics asymmetry is through geometrically modifying the accessible binding area via polymerization, leading to asymmetric growth rates.
We then incorporate hydrolysis by stochastically weakening binding interfaces within the filament. As monomer–monomer binding strength decreases, analysis of filament stability again shows that a two-state system is necessary to stabilise monomers in the filament interior while permitting end disassembly.
Combining these ingredients yields a monomer architecture that exhibits sustained treadmilling dynamics. These results establish general design principles for engineering treadmilling polymers from simple components.