Self-consistent solution to the Flory-Huggins model and applications in protein liquid-liquid phase separation

Qian, D.; Michaels, T. C. T.; Knowles, T. P. J.

doi:10.1101/2022.04.23.489256

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bioRxiv · 10.1101/2022.04.23.489256

Self-consistent solution to the Flory-Huggins model and applications in protein liquid-liquid phase separation

Qian, D.·Michaels, T. C. T.·Knowles, T. P. J.

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Abstract

A self-consistent analytical solution for binodal concentrations of the two-component Flory-Huggins model is derived. We show that this form extends the validity of the Ginzburg-Landau expansion away from the critical point to cover the whole phase space. Furthermore, this analytical solution reveals an exponential scaling law of the dilute phase binodal concentration as a function of interaction strength and chain length. We demonstrate explicitly the power of this approach by fitting experimental protein liquid-liquid phase separation boundaries to determine the effective chain length and the solute-solvent interaction energy. Moreover, we demonstrate that this strategy allows us to resolve the differences in the interaction energy contributions of individual amino acids. This analytical framework can serve as a new way to decode the protein sequence grammar for liquid-liquid phase separation.

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Qian, D., Michaels, T. C. T., Knowles, T. P. J.. 2022-04-23. Self-consistent solution to the Flory-Huggins model and applications in protein liquid-liquid phase separation. https://doi.org/10.1101/2022.04.23.489256

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