Treadmilling and length distributions of active polar filaments

The cytoskeleton is a network of filamentous proteins, notably, actin filaments and microtubules. These filaments are active as their assembly is driven by the hydrolysis of nucleotides bound to the constituting protomers. In addition, the assembly kinetics differs at the two respective ends, making them active polar filaments. Experimental evidence suggests, that, in vivo, actin filaments and microtubules can grow at one and shrink at the other end at the same rate, a state that is known as treadmilling. In this work, we use a generic discrete two-state model for active polar filaments to analyze the conditions leading to treadmilling. We find that a single filament can self-organize into the treadmilling state for a broad range of monomer concentrations. In this regime the corresponding length distribution has a pronounced maximum at a finite value. We then extend our description to consider specifically the dynamics of actin filaments. We show that actin treadmilling should be observable in vitro in the presence of appropriate depolymerization promoting factors.