Nature of size fluctuations in filamentous cytoskeletal structures

Cells control the size of their cytoskeletal structures, such as microtubule-based cilia and actin cables, by mechanisms that are still not fully understood. Balance-point models of length control, for which there is ample experimental support in a variety of systems ^[1], assume length-dependent rates of filament assembly and/or disassembly. When the two competing rates are equal, then a single, stable fixed-point length is reached. Using a master equation approach, we find that length fluctuations, small deviations in length produced by stochastic addition, and removal of building blocks/fragments during filament assembly and disassembly, are Gaussian independent of the nature of feedback. The variance of the distribution is given by the product of the steady-state filament length and the size of the fragments added or removed. Comparing our calculations to the experimentally measured fluctuations of flagella length in unicellular organisms (Giardia and Chlamydomonas) provides new information about the molecular mechanisms involved in cytoskeletal filament length control. In both, we find that the measured length fluctuations support the idea that assembly and disassembly events occur in bursts, where a large number of proteins (tubulin dimers or short polymers) are added and/or removed at a time.

[1] Mohapatra, Lishibanya, Bruce L. Goode, Predrag Jelenkovic, Rob Phillips, and Jane Kondev. "Design principles of length control of cytoskeletal structures." Annual review of biophysics 45 (2016): 85-116.