Analytical Solution to the Flory–Huggins Model

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Abstract
A self-consistent analytical solution for binodal concentrations of the two-component Flory-Huggins phase separation 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 the 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 solute-solvent interaction energies. Moreover, we demonstrate that this strategy allows us to resolve differences in 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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Funding Information
  • Wellcome Trust (203249/Z/16/Z)
  • Frances and Augustus Newman Foundation
  • FP7 Ideas: European Research Council (337969)
  • Biotechnology and Biological Sciences Research Council
  • Laboratory for Molecular Cell Biology, University College London

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