Theory of Complexation of Two Oppositely Charged Intrinsically Disordered Proteins: Application of Polyelectrolyte Physics to Explain Experimental Results*

We present an analytical polymer model of polyelectrolyte complexation (PEC)[1,2], based on the Edwards-Muthukumar Hamiltonian[3,4] and counterion condensation and release[1,2], to quantitatively describe the driving forces of complexation of prothymosin alpha (ProTα) and histone (H1), two intrinsically disordered proteins with opposite net charges. This model of PEC takes into account conformational properties of the individual IDPs, counterions associated to the IDPs, and the free salt ions, resulting in several free energy contributions of enthalpic and entropic origin. Free volume entropy of the condensed and released counterions, Coulomb energy of the bound ion-pairs - both of the counterion-protein and protein-protein types, and electrostatic correlations of free charges are found to contribute most significantly to the thermodynamics, whereas the excluded volume or site-specific interactions seem overwhelmed by electrostatic interactions. The dielectric mismatch between the bulk solvent and regions close to the proteins plays a crucial role in the energetics of the complexation. The model captures the thermodynamics of protein complexation, both in terms of the reaction enthalpy and free energy for different salt concentrations, as well as the salt concentration dependent chain dimensions, with only four adjustable parameters[5]. The model quantitatively matches with the experimental finding[5] that the entropy gain from the released counterions is the primary thermodynamic driving force of the complexation, whereas an enthalpy loss opposes the process.

[1] Mitra, Kundagrami, (2023), J. Chem. Phys. 158, 014904. [2] Ghosh et al., (2023), J. Chem. Phys. 158, 204903.  [3] Edwards, Singh, (1979), J. Chem. Soc. Faraday Trans. 275, 1001-1019. [4] Muthukumar, (1987), J. Chem. Phys. 86, 7230-7235. [5] Chowdhury et al., (2023), Proc Natl Acad Sci USA., 120, e2304036120.