Scaling of  CG Transition Point

Intrinsically disordered proteins (IDPs) exhibit liquid-liquid phase separation (LLPS) close to the Theta solvent conditions where the single IDP chains undergo a coil-to-globule-like transition. We address the effect of chain length and amino acid composition on the  Theta state in the IDPs with the changes in cosolvent conditions. To probe the  Theta state in polypeptides, we studied the behavior of polyleucine and polyglutamine with six different chain lengths (N = 16 to 512) in various urea (denaturant) and trimethylamine N-oxide (TMAO) (protective osmolyte) concentrations using a coarse-grained IDP model and computer simulations. The Flory scaling exponent (nu) of polyleucine (polyglutamine) undergoes a transition from nu ~  0.6 (0.6) to 0.3 (0.5) with increasing N in water. We observed that the Theta condition for both the IDPs strongly depends on N and varies as 1/N^{0.5}. Depending on N, polyglutamine (polyleucine) chains reach the Theta state at different cosolvent concentrations, confirming that in addition to chain length, the amino acid composition also influences the Theta solvent condition for the IDPs. Moreover, the Theta state for smaller chain lengths (N = 16 to 64) calculated using the structure factor mimicking the small-angle X-ray scattering (SAXS) experiments and using pair distances mimicking fluorescence resonance energy transfer (FRET) experiments are in disagreement. The Theta state computed using the structure factor and pair distances converges to the same point only at large N. As the Theta state is correlated with the conditions of observing LLPS for IDPs, we predict that IDP's LLPS propensity will increase with N. 

Scaling exponent, nu as a function of cosolvent concentration, [cosolvent] extracted from three methods - critical ratio (red circle), FRET (green square) and SAXS (violet triangle) for (A) polyQ, (B) polyL. The green and cyan shaded regions correspond to various concentrations of cosolvent TMAO and urea, respectively. The grey horizontal dotted line denotes the CG transition point or  Theta condition where nu = 0.5. The three vertical dashed lines correspond to the Coil-Globule transition concentration from three different methods - critical ratio (red),  FRET (green), and SAXS (violet).

The required cosolvent concentration to induce Coil-Globule transition , Theta as a function of chain length N for (A) polyglutamine and (B) polyleucine calculated using three different methods - critical ratio (red circle), pair distances mimicking FRET (green square) and structure factor mimicking SAXS (violet triangle). The shaded region green and cyan correspond to cosolvent TMAO and urea, respectively. The dotted lines are guides to the eyes.