**5. Temperature Dependence of Intrinsic** α**-Helix and PPII Propensities**

If we assume Tiffany and Krimm are correct, and the DSE is composed of three main structural states (PPII, α-helix, and unordered), then the PPII and α-helix propensities given in Tables 1 and 2 can be used to model how PPII, α-helix, and unordered populations change with temperature for a generic polypeptide. This is shown in Figure 9A, where populations at different temperatures were modeled by using the integrated van't Hoff equation (Equation (3)), a transition enthalpy for PPII to nonPPII (∆*HPPII*), and a transition enthalpy for α to non-α (∆*Hα*). As discussed above, peptide [46] and IDP studies [37,42] both indicate ∆*HPPII* is ~10 kcal mol−<sup>1</sup> . Calorimetric studies using alanine-rich peptides that adopt α-helix by Bolen and coworkers indicate ∆*H<sup>α</sup>* is ~1 kcal mol−<sup>1</sup> [98]. In this model, because ∆*HPPII* >> ∆*Hα*, PPII populations are highly sensitive to temperature changes, while α-helix populations show reduced temperature sensitivity. Moreover, also because ∆*HPPII* >> ∆*Hα*, PPII populations dominate at very cold temperatures. Unfortunately, the

model predicts α-helix populations that decrease with decreasing temperatures, in stark contrast to the known stabilities of peptide and protein structures. α

<sup>−</sup> <sup>−</sup> Δ ∆ *<sup>α</sup>*

α ≥

α

α

α ∆ *<sup>α</sup>* ∆ *<sup>α</sup>*

Δ

−

∆ *<sup>α</sup>*

α

**α**

α α

α

α

α α ∆ *<sup>α</sup>*

α

Δ ∆ *<sup>α</sup>*

α

Δ <sup>−</sup> <sup>−</sup> <sup>−</sup>

α Δ ∆ *<sup>α</sup>*

Δ <sup>−</sup>

∆ *<sup>α</sup>* Δ

α ∆ *<sup>α</sup>*

α Δ <sup>−</sup> ∆ *<sup>α</sup>* <sup>−</sup> Δ <sup>−</sup> ∆ *<sup>α</sup>* <sup>−</sup> α α −∆ −∆ *<sup>α</sup>* ∆ ∆ *<sup>α</sup> −* − − *α* − *α* **Figure 9.** Temperature effects on PPII, α-helix, and unordered populations in an unfolded polypeptide. (**A**) ∆*HPPII* = 10 kcal mol−<sup>1</sup> and ∆*H<sup>α</sup>* = 1 kcal mol−<sup>1</sup> . (**B**) ∆*HPPII* = 10 kcal mol−<sup>1</sup> and ∆*H<sup>α</sup>* = 11 kcal mol−<sup>1</sup> . To model a generic polypeptide, the PPII and α-helix propensities used the average value from the propensities measured by Hilser and coworkers (column 4, Table 1) and Baldwin and coworkers (column 3, Table 2). Specifically, the PPII propensity was 0.35 at 25 ◦C, while the α-helix propensity was 0.29 at 0 ◦C. To calculate populations, the partition function was determined from *Q* = 1 + e−∆*GPPII/RT* + e−∆*Gα/RT*, with the unordered state as the reference. <sup>∆</sup>*GPPII* and ∆*G<sup>α</sup>* were calculated from the propensities by −*RTln*(*PPII*/1 − *PPII*) and −*RTln*(*α*/1 − *α*), and the temperature dependence of the propensities was calculated with Equation (3). The unordered, α-helix, and PPII populations thus were 1/*Q*, e−∆*Gα/RT*/*Q*, and e−∆*GPPII/RT*/*Q*.

If, instead, ∆*H<sup>α</sup>* is given a value comparable to ∆*HPPII*, the model yields temperaturedependent populations that reasonably agree with experimental results (Figure 9B). Specifically, both PPII and α-helix populations decrease to low levels at high temperatures. Moreover, under cold conditions, PPII dominates, but α-helix is also populated at nonnegligible levels that gradually increase as heat is removed from the system. This result from the model can be explained by assuming that the calorimetry measured ∆*H<sup>α</sup>* is the net heat associated with forming α-helix at the cost of disrupting PPII (i.e., ∆*Hα*~∆*Hcal,<sup>α</sup>* + ∆*HPPII*~1 kcal mol−<sup>1</sup> + 10 kcal mol−<sup>1</sup> = 11 kcal mol−<sup>1</sup> ). In Figure 9B, the transition enthalpies are modeled as 10 kcal mol−<sup>1</sup> and 11 kcal mol−<sup>1</sup> for ∆*HPPII* and ∆*Hα*, respectively. This model is supported by the experimental data obtained for Retro-nuclease (Figure 8). The observed temperature dependence of the Retro-nuclease hydrodynamic size revealed PPII and α-helix intrinsic propensities that changed with temperature in a manner similar to the Figure 9B model.
