TY - JOUR T1 - Exact length distribution of filamentous structures assembled from a finite pool of subunits JF - bioRxiv DO - 10.1101/042184 SP - 042184 AU - David Harbage AU - Jané Kondev Y1 - 2016/01/01 UR - http://biorxiv.org/content/early/2016/03/02/042184.abstract N2 - Self-assembling filamentous structures made of protein subunits are ubiquitous in cell biology. These structures are often highly dynamic, with subunits in a continuous state of flux, binding to and falling off the filament. In spite of this constant turnover of their molecular parts, many cellular structures seem to maintain a well-defined size over time, which is often required for their proper functioning. One widely discussed mechanism of size regulation involves the cell maintaining a finite pool of protein subunits available for assembly. This finite pool mechanism can control the length of a single filament by having assembly proceed until the pool of free subunits is depleted to the point when assembly and disassembly are balanced. Still, this leaves open the question whether the same mechanism can provide size control for multiple filamentous structures that are assembled from a common pool of protein subunits, as is often the case in cells. We address this question by solving the steady-state master equation governing the stochastic assembly and disassembly of multi-filament structures made from a shared, finite pool of subunits. We find that, while the total number of subunits within a multi-filament structure is well defined, individual filaments within the structure have a wide, power-law distribution of lengths. We also compute the phase diagram for two multi-filament structures competing for the same pool of subunits and identify conditions for coexistence when both have a well-defined size. These predictions can be tested in cell experiments in which the size of the subunit pool or the number of filaments with a multifilament structure is tuned within a cell. ER -