Sol-gel transition in heteroassociative RNA-protein solutions: A quantitative comparison of coarse-grained simulations and the Semenov-Rubinstein theory

TL;DR

This study combines molecular dynamics simulations and Semenov-Rubinstein theory to analyze sol-gel transitions in RNA-protein solutions, revealing complex behaviors like double reentrance and highlighting the role of binding site saturation.

Contribution

It provides a detailed comparison between coarse-grained simulations and the Semenov-Rubinstein theory, identifying limitations of the mean-field approximation in dilute regimes.

Findings

Identified sol-gel transition without phase separation

Observed double reentrant behavior with concentration changes

Quantitatively compared simulation results with theoretical predictions

Abstract

Protein RNA-binding domains selectively interact with specific RNA sites, a key interaction that determines the emergent cooperative behaviors in RNA-protein mixtures. Through molecular dynamics simulations, we investigate the impact of the specific binding interactions on the phase transitions of an examplary RNA-protein system and compare it with predictions of the Semenov-Rubinstein theory of associative polymers. Our findings reveal a sol-gel (percolation) transition without phase separation, characterized by double reentrant behavior as the RNA or protein concentration increases. We highlight the crucial role of bridge formations in driving these transitions, particularly when binding sites are saturated. The theory quantitatively predicts the binding numbers at equilibrium in the semidilute regime, but it significantly overestimates the size of the concentration range where percolation is observed. This can partly be traced back to the fact that the mean-field assumption in the theory is not valid in the dilute regime, and that the theory neglects the existence of cycles in the connectivity graph of the percolating cluster at the sol-gel transition. Our study enriches the understanding of RNA-protein phase behaviors, providing valuable insights for the interpretation of experimental observations.