**6. Discussion**

Structural and energetic characterization of the DSE is required for a molecularlevel understanding of both protein stability and fold specificity. Historically, short peptides [11–13] and the protein coil library [27–30] have been used as the principal models from which to investigate the DSE. For these two models, there is good quantitative agreement in the sense that the protein coil library, when compared to peptide results, has been found to reproduce the intrinsic conformational preferences of the amino acids for helix, sheet, and PPII [29], as well as the effects on the conformational preferences from neighboring residues [31]. This agreement between two independent models indicates that the magnitudes and types of intrinsic biases in unstructured polypeptides are reasonably well-known. The role of the temperature in describing DSE structure, however, is less well understood. Heat indeed modulates the populations of unstructured states, which is evidenced by the large temperature-dependent changes in hydrodynamic size exhibited by IDPs [39–41]. Moreover, the ability of a protein to fold [2], phase separate [99], or recognize its binding partner [69] is also temperature-dependent.

Recently, we demonstrated that the enthalpy, entropy, and magnitude of DSE conformational bias can be elucidated by analyzing heat effects on the mean *R<sup>h</sup>* of IDPs [37]. The sequence dependence of IDP hydrodynamic size yields an independent measure of the intrinsic bias for PPII, because PPII-rich structures are extended [43]. Additionally, as the PPII bias is driven by a favorable enthalpy [46], the effect of increased temperature is to populate nonPPII states at the expense of PPII. Thus, the enthalpy and entropy of the PPII–nonPPII transition can be determined from the heat-induced changes to the mean *R<sup>h</sup>* . Our analysis of the sequence dependence on IDP hydrodynamic size revealed amino acid-specific preferences for PPII that are in good quantitative agreement with both calorimetry-measured values from short peptides and those inferred by a survey of the protein coil library (Figure 7). Modeling the effects of heat on IDP hydrodynamic size yields an enthalpy and entropy of PPII formation that were quantitatively similar to the peptide-measured values [37,46]. It is important to note that these three DSE models (i.e., peptides, the coil library, and IDPs) universally report that the allowed regions of Ramachandran space are unevenly sampled, and that PPII is the predominant denatured state conformation under normal conditions.

When interpreting the effects of the PPII bias on the mean *R<sup>h</sup>* of unstructured proteins, the population of the α backbone conformation has consequences that must be considered. The α basin of the Ramachandran map of Φ and Ψ dihedral angles is among the most populated regions in the coil library distribution [27,30], and is shared with turn structures [29]. Because of the backbone geometry of the α configuration, whereby sparse sampling at dispersed positions can produce turns, and heavy sampling among contiguous positions yields helices, the effect of a PPII bias on the mean *R<sup>h</sup>* can be either compaction or expansion. This is demonstrated in Figure 8C. The codependence of DSE mean *R<sup>h</sup>* on both the α and PPII biases predicts that intrinsic α preferences, and its corresponding thermodynamic parameters, can be estimated from low-temperature studies that compare experimental *R<sup>h</sup>* to computer-simulated DSE trends (Figure 8A). Specifically, for some unstructured proteins, the intrinsic α bias at low temperatures may be sufficiently strong that its magnitude, sequence dependence, and enthalpy and entropy of formation can be measured from the effect on the mean *R<sup>h</sup>* . It remains to be seen if this strategy can be successful, and if the resultant intrinsic α propensities as measured in IDPs compare favorably to those obtained from short peptides (Table 2) and surveys of the protein coil library [27–30].

**Author Contributions:** S.T.W. conceived and coordinated this work; E.A.P., K.A.L. and S.T.W. cowrote the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the National Institutes of Health, grant numbers R15GM115603, R25GM102783, and R15GM119096.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data presented in this study are openly available and cited in the references.

**Conflicts of Interest:** The authors declare no conflict of interests.
