Intrinsic stiffness and Θ-solvent regime in intrinsically disordered proteins: Implications for liquid-liquid phase...

Liquid-liquid phase separation (LLPS) exhibited by intrinsically disordered proteins (IDPs) depends on the solvation state around the Θ-regime, which separates good from poor solvent. Experimentally, the Θ-solvent regime of the finite length (N) IDPs, as probed by small angle X-ray scattering (SAXS) and single molecular fluorescence resonance energy transfer (smFRET), is in disagreement. Using computer simulations of a coarse-grained IDP model, we address the effect of chain length on the Θ-regime of IDPs with polar side chains (polyglutamine) and hydrophobic side chains (polyleucine) subject to varying concentrations of cosolvents $\left[C\right]$ , urea (denaturant) or trimethylamine N-oxide (protective osmolyte) in water. Due to their intrinsic stiffness, these IDPs are always expanded on short-length scales, independent of the solvent quality. As a result, for short IDP sequences ( $\approx 10$ to 25 residues), their propensity to exhibit LLPS cannot be inferred from single-chain properties. Further, for finite-size IDPs, the cosolvent concentration to attain the Θ-regime ( $\left[C_{\Theta }\right]$ ) extracted from the structure factor emulating SAXS and pair distances mimicking smFRET differs. They converge to the same cosolvent concentration only at large N, indicating that finite size corrections vary for different IDP properties. We show that the radius of gyration ( $R_g$ ) of the IDPs in the Θ-solvent regime satisfies the scaling relation $R_g^2=Nf\left(c\sqrt{N}\right)$ , which can be exploited to accurately extract $\left[C_{\Theta }\right]$ ( $c=\left(\right[C]/[C_{\Theta }]-1)$ ). We demonstrate the importance of finite size aspects originating from the chain stiffness and thermal blob size in analyzing IDP properties to identify the Θ-solvent regime.