Physical Principles Underlying Regulation of Size Distributions of Intracellular Condensates*

Condensates play crucial roles in driving biochemical reactions in the cell, and many of these functions depend on condensate size. While previous work has demonstrated that droplet growth is primarily driven by coalescence following fast quench of the system, the size distribution produced by this mechanism has not been described. We first demonstrate that this mechanism produces exponential cluster-size distributions in both optogenetic live-cell experiments and Monte Carlo simulations.  Then, to elucidate the relative effects of quench and coalescence dynamics on size distribution, we analyze Huntingtin polyQ protein aggregation in the cytoplasm, finding that it demonstrates a power-law cluster-size distribution. A similar power-law distribution was recovered by adapting our Monte Carlo simulations to model the case of slow production of condensate components. We demonstrate that these power laws are due to a preferential attachment or “rich get richer” effect. We then describe the transition between a coalescence-limited, exponential regime and a production-limited power-law regime, which can be tuned by the biologically relevant parameters of subdiffusion and material production. Finally, we apply this analysis to endogenous organelles to infer their dynamics.