Size regulation of multiple organelles competing for a shared subunit pool

How cells regulate the size of intracellular structures and organelles, despite continuous turnover in their component parts, is a longstanding question. Recent experiments suggest that size control of many intracellular assemblies is achieved through the depletion of a limiting subunit pool in the cytoplasm. While the limiting pool model ensures organelle size scaling with cell size, it does not provide a mechanism for robust size control of multiple co-existing structures. Here we propose a kinetic theory for size regulation of multiple structures that are assembled from a shared pool of subunits. We demonstrate that a negative feedback between the growth rate and the size of individual structures underlies size regulation of a wide variety of intracellular assemblies, from cytoskeletal filaments to three-dimensional organelles such as centrosomes and the nucleus. We identify the feedback motifs for size control in these structures, based on known molecular interactions, and quantitatively compare our theory with available experimental data. Furthermore, we show that a positive feedback between structure size and growth rate can lead to bistable size distributions arising from autocatalytic growth. In the limit of high subunit concentration, autocatalytic growth of multiple structures leads to stochastic selection of a single structure, elucidating a mechanism for polarity establishment.