A scale-invariant log-normal droplet size distribution below the transition concentration for protein phase separation

Abstract

Many proteins have been recently shown to undergo a process of phase separation that leads to the formation of biomolecular condensates. Intriguingly, it has been observed that some of these proteins form dense droplets of sizeable dimensions already below the transition concentration, which is the concentration at which phase separation occurs. To understand this phenomenon, which is not readily compatible with classical nucleation theory, we investigated the properties of the droplet size distributions as a function of protein concentration. We found that these distributions can be described by a scale-invariant log-normal function with an average that increases progressively as the concentration approaches the transition concentration from below. These results suggest the existence of a universal behaviour independent of the sequences and structures of the proteins undergoing phase separation, which is typically observed for second-order phase transitions. Based on these observations, we show that it is possible to use the scale invariance to estimate the critical concentration for phase separation.