Percolation physics and density transition frameworks converge in biomolecular condensation

TLDR: Kar et al. as mentioned in this paper proposed a percolation-based model of biomolecular condensates and showed that protein clusters follow a heavytailed distribution, with low abundance of larger mesoscale clusters and distributions changing with total protein concentration.

Abstract: A rapidly growing body of work in recent years has resulted in exciting advances in our understanding of the importance of biomolecular condensates (or, more generally, various forms of mesoscale to macroscale biological matter) and their transitions in biology and disease (1–3). At first glance, the physics of how liquids percolate through porous/granular materials or related concepts in network connectivity may not seem relevant to furthering our mechanistic understanding of biomolecular condensates. Interestingly, however, percolation theory has been extensively used in the related areas of polymer physics (4, 5) and phase transitions (as well as in numerous other fields). Now, in an exciting advance, Kar et al. (6) describe a combination of experimental, conceptual, and computational work that explores the connection between percolation physics and an important class of biomolecular condensation with links to neurodegenerative diseases. Conceptual understanding in the biomolecular condensate field has been extensively guided by simple forms of nucleation and Flory–Huggins-type theories. A prediction of this type of theory is that, below a saturation concentration (csat) of a single macromolecule (e.g., protein) in a solvent, the macromolecule will exist mainly as monomers and very small clusters, because there is a size-dependent energy penalty for cluster formation. It is only above the saturation concentration that phase separation (a density transition) will occur, resulting in the formation of a dense phase (aka micrometer-sized droplets). Now, Kar et al. (6) describe a broad set of data that can provide a test of this prediction. The proteins studied in this work are FET (FUS, EWSR1, TAF15) family proteins, with links to neurodegenerative disease, which have been extensively investigated in the field. Using a combination of imaging, dynamic light scattering (DLS), and single-particle (tracking, multiparameter fluorescence, and microfluidics-based) experiments, Kar et al. (6) show that, while phase separation is not observed in solutions below an effective csat, subsaturated solutions of these proteins contain a range of nanoscale clusters. The data indicate that clusters follow a heavytailed distribution, with low abundance of larger mesoscale clusters and distributions changing with total protein concentration. It is only above csat that larger micrometer-sized bodies that display coarsening appear. Fluorescence resonance energy transfer/DLS data show that cluster formation is reversible, and that protein exchanges between clusters. Together, these data draw a sharp contrast with the predictions based on nucleation theory discussed above. The authors then go on to invoke percolation theory–based ideas to offer an explanation for these observations, building on their and other previous work (4, 5, 7, 8). In percolation theory, there exists a critical connectivity probability (pc) at which the system undergoes a connectivity (geometric) transition, forming a system-spanning network (Fig. 1A). In the present work, the proteins are represented in a stickers and spacers model of associative polymers, with stickers contributing specific protein–protein interactions and spacers contributing generalized excluded volume/ solvation effects. In the framework of the percolation model, this system can undergo a percolation-type connectivity transition (via specific sticker–sticker interactions) at a critical protein concentration cperc (Fig. 1B). Thus, specific sticker– sticker interactions give rise to an additional energy scale class that contributes to system behavior. As previously described by the Pappu laboratory (8), this scenario can give rise to an interesting coupling between density and percolation transitions if the system/conditions result in cperc being greater than csat but less than the dense phase concentration cden. Under these conditions, a density transition results in a coupled percolation transition in the dense phase, since cden is greater than cperc. How does this relate to the authors’ experimental findings of molecular clusters below csat (6)? The key result from the percolation approach is that, even below the percolation threshold, smaller network clusters are still formed (Fig. 1), and the size distribution of these clusters shifts to larger sizes as the connectivity (concentration) is increased. As noted above, this is just what was observed in the authors’ measurements. The authors then looked at ways to test the coupling between the two types of transitions. Indeed, using small-molecule solutes or mutations as perturbations, they find either coupled or differential effects on formation of clusters and macroscopic phase separation. These results are consistent with the existence of separate types of interactions governing generalized solubility and specific connectivity effects, and the idea that these can be perturbed selectively but can also be coupled. The above work is also complemented with simulations whose results are in keeping with the above model. Overall, the work serves to inspire a number of lines of thinking and inquiry.