Universal length fluctuations of actin structures found in cells

Actin is a key cytoskeletal protein that forms filaments that bundle into linear structures in vivo, which are involved in motility, signaling, and cell division. Despite the rapid turnover of individual actin monomers, these structures are often maintained at a specific length, which is important for their function. Length control is commonly attributed to length-dependent assembly or disassembly of the structure, whereby a stable length is achieved when the two opposing processes are balanced. Here we show that regardless of the nature of the length-dependent feedback, such "balance point" models predict a Gaussian distribution of lengths with a variance that is proportional to the steady state length. Contrary to this prediction, a reexamination of experimental measurements on the lengths of stereocilia, microvilli, actin cables, and filopodia reveals that the variance scales with the square of the steady state length. We propose a model in which the individual filaments in bundles undergo independent assembly dynamics, and the length of the bundle is set by the length of the longest filament. This model predicts a non-Gaussian distribution of bundle lengths with a variance that scales with the square of the steady state length. Our theory underscores the importance of crosslinking filaments into networks for size control of cytoskeleton structures.