Scaling law and universal drop size distribution of coarsening in conversion-limited phase separation

Phase separation is not only ubiquitous in diverse physical systems, but also plays an important organizational role inside biological cells. However, experimental studies of intracellular condensates (drops with condensed concentrations of specific collections of proteins and nucleic acids) have challenged the standard coarsening theories of phase separation. Specifically, the coarsening rates observed are unexpectedly slow for many intracellular condensates. Recently, Folkmann et al. [Science 373, 1218 (2021)] argued that the slow coarsening rate can be caused by the slow conversion of a condensate constituent between the state in the dilute phase and the condensate state. One implication of this conversion-limited picture is that standard theories of coarsening in phase separation (Lifshitz-Slyozov-Wagner theory of Ostwald ripening and drop coalescence schemes) no longer apply. Surprisingly, I show here that the model equations of conversion-limited phase separation can instead be mapped onto a grain growth model in a single-phase material in three dimensions. I further elucidate the universal coarsening behavior in the late stage using analytical and numerical methods.

Automated summary

Phase separation is a common phenomenon in various physical systems and biological cells. Recent experimental studies have found that the coarsening rates of intracellular condensates are unexpectedly slow, possibly due to the slow conversion of condensate constituents. Traditional theories of phase separation are no longer applicable, but the conversion-limited phase separation model can be mapped onto a grain growth model in three-dimensional materials.