Abstract
Cells contain organelles which are dynamic yet coherent structure, but the mechanisms by which
these assemblies form and stably persist are not well understood. Here, we consider the limiting-pool
mechanism which posits that structures grow in a pool of constituents until the pool is depleted. In
order to study experimental signatures of the limiting-pool mechanism, we construct two simple models: first the self-assembly of two linear filamentous structures, and second of two spherical structures.
Using theory and simulations, we analyze the time series of the sizes of the growing structures and make
specific predictions about their autocorrelation functions. We then compare these theoretical results to
synthetic data from stochastic simulations based on the Gillespi algorithm. This approach can be used
in experimental systems to quantitatively test for the limiting-pool mechanism, and can be extended to
other size-control mechanisms.