**4. IDP Model of the DSE**

The results of many studies (reviewed above) revealed a significant bias toward PPII in the unstructured states of proteins, even when no prolines are present in the sequence. This indicates that the PPII conformation is a dominant component of the DSE, and potentially an important structural descriptor for understanding the properties associated with IDPs and intrinsically disordered regions (IDRs). Although intrinsic PPII propensities have been determined for the common amino acids (see Tables 1 and 3), the ability of these experimentally determined propensities to quantitatively reproduce ID structural behavior in biological proteins has been difficult to establish.

An experimental system was designed to address this issue and provide an independent measure of the amino acid-specific bias for PPII in IDPs. Based on the hypothesis that the magnitude of a PPII preference in the disordered conformational ensemble can affect its population-weighted hydrodynamic size [41,44,45], it has been shown that intrinsic PPII propensities can be obtained by analyzing the sequence dependence of the mean hydrodynamic radius, *R<sup>h</sup>* , of IDPs [37]. This method relies on two assumptions we demonstrate are reasonable. First, that PPII effects on mean *R<sup>h</sup>* follow a simple power law scaling relationship [41,44,45], and second, that the protein net charge also can influence the hydrodynamic size [38,76].

To establish the relationship linking mean *R<sup>h</sup>* to chain bias for PPII in an ensemble, a computer algorithm based on the hard sphere collision (HSC) model was used to generate polypeptide structures through a random search of conformational space [48,49]. The HSC model has no intrinsic bias for PPII, which was demonstrated previously [49], and thus a PPII sampling bias could be added to the algorithm as a user-defined parameter [41].

Briefly, in this model, individual conformers are generated by using the standard bond angles and bond lengths [77], and a random sampling of the backbone dihedral angles Φ, Ψ, and Ω. (Φ, Ψ) is restricted to the allowed Ramachandran regions [78]; the peptide bond dihedral angle, Ω, is given 100% the *trans* form for nonproline amino acids, while prolines sample the *cis* form at a rate of 6–10%, depending on the identity of the preceding amino acid [79]. The positions of side chain atoms are determined from sampling rotamer libraries [80]. Van der Waals atomic radii [47,81] are used as the only scoring function to eliminate grossly improbable conformations. To calculate state distributions typical of protein ensembles, a structure-based energy function parameterized to solvent-accessible surface areas is used to determine the population weight of the generated structures [82–90]. Random structures are generated until the population-weighted structural size, <*L*>, becomes stable [41]. *L* is the maximum Cα–C<sup>α</sup> distance in a state, and <*L*> is considered stable when its value changes by less than 1% upon a 10-fold increase in the number of ensemble states. <*L*>/2 is used to approximate the mean *R<sup>h</sup>* of an ensemble.

Figure 3A shows the effect on simulated mean *R<sup>h</sup>* (i.e., <*L*>/2) from increasing the applied PPII sampling bias, *SPPII*, which is obtained by weighting the random selection of Φ and Ψ. For example, a 30% sampling bias for PPII had 30% of the paired (Φ, Ψ) values for any residue randomly distributed in the region of (−75◦ ± 10◦ , +145◦ ± 10◦ ). The remaining 70% of paired (Φ, Ψ) were distributed in the allowed Ramachandran regions outside of (−75◦ ± 10◦ , +145◦ ± 10◦ ). In this figure, each data point represents a computergenerated poly-alanine conformational ensemble (typically >10<sup>8</sup> states). These results are mostly insensitive to steric effects originating from the side chain atoms when biological sequences are used instead of poly-alanine [38]. Unusual sequences, such as all proline or all glycine, cause deviations from the poly-alanine trend.

The simulations revealed that increasing chain propensity for PPII gives rise to increased mean *R<sup>h</sup>* , which is expected because PPII is an extended structure [43]. The dependence of mean *R<sup>h</sup>* on chain length at each sampling bias was fit to the power law scaling relationship, *R<sup>h</sup>* = *Ro*·*N<sup>v</sup>* , where *N* is chain length in number of residues, *R<sup>o</sup>* the pre-factor, and *v* the polymer scaling exponent. Individual fits at a given *SPPII* are shown by lines in Figure 3A, obtained by nonlinear least squares methods. *Ro*, on average, was 2.16 Å,

Φ Ψ

−

except when the sampling bias was 100% PPII (Figure 3B). When *R<sup>o</sup>* is held at 2.16 Å, the resulting *v* shows a logarithmic dependence on *SPPII* (Figure 3C).

Φ Ψ Φ Ψ

α α

−

∙ − **Figure 3.** PPII bias expands the structural dimensions of the DSE. (**A**) The effect of an applied PPII sampling bias (*SPPII*) on mean *R<sup>h</sup>* (i.e., <*L*>/2) for poly-alanine at different *N*. Filled circles represent no preferential bias, while open circles, triangles, and squares show when *SPPII* is 40%, 80%, and 100%, respectively. (**B**) *SPPII* effects on fit parameter *Ro*. Average *R<sup>o</sup>* for *SPPII* range of 0–90% is 2.16 Å, indicated by the stippled line. (**C**) *SPPII* effects on fit parameter *v* when *R<sup>o</sup>* is held constant at 2.16 Å. Line is from nonlinear least squares fit of these data to the logarithmic equation, *v* = *v<sup>o</sup>* + *a*·*ln*(1 − *SPPII*).

∙ Because most computer-generated random structures have steric conflicts, and thus are removed by the hard sphere filter, the applied PPII bias, *SPPII*, does not necessarily equal the population-weighted fractional number of residues in the PPII conformation in an ensemble of allowed states. By using *fPPII* = <*NPPII*>/*N* to account for this difference, where *NPPII* is the number of residues in the PPII conformation in a state, and <*NPPII*> is the population-weighted value for the ensemble (i.e., <*NPPII*> = ∑*NPPII,i*·*P<sup>i</sup>* with *P<sup>i</sup>* the Boltzmann probability of state *i*), the simulation trends in Figure 3 can be combined into a simple relationship,

$$R\_h = (2.16\ A) \cdot \text{N}^{0.503 - 0.11 \cdot \ln(1 - f\_{PPII})} \tag{1}$$

Additional simulations found that Equation (1) is independent of the specific pattern of PPII propensities in the polypeptide chain [45].

∑ ∙ ܴ ൌ ൫2.16 Å൯ ∙ ܰ.ହଷି.ଵଵ∙ሺଵିುು<sup>ሻ</sup> To test Equation (1) directly, mutational effects on experimental *R<sup>h</sup>* were measured for an IDP [44]. Apparent changes in *fPPII* were determined from amino acid substitutions, following the strategy shown in Figure 4. These experiments used the N-terminal end of the p53 tumor suppressor protein, a prototypical IDP consisting of 93 residues, p53(1-93). The apparent net charge, *Qnet*, calculated from sequence for p53(1-93), is −17. Thus, this test was conducted in the background of potentially strong intramolecular charge–charge interactions that were unaccounted for. Nonetheless, experiments with P→G and A→G substitutions applied to p53(1-93) gave reasonable results, indicating a per-position average PPII bias change of 0.76 at each proline site (i.e., relative to the intrinsic PPII bias of glycine) and 0.48 at each alanine site. These results are evidence of significant conformational bias for PPII in IDPs, even at nonproline positions.

Equation (1) was also used to predict *R<sup>h</sup>* from sequence for a database of IDPs, using the experimental PPII propensities in Table 1 [45]. For each IDP, *fPPII* was calculated by ∑ *PPIIi*/*N*, where *PPII<sup>i</sup>* is the PPII propensity of amino acid type *i*, and the summation is over the protein sequence containing *N* number of amino acids. Figure 5A shows *R<sup>h</sup>* predicted when using PPII propensities from Hilser and coworkers (column 4, Table 1). Compared to the null model where PPII is not strongly preferred and the chain is an unbiased statistical coil, Equation (1) indeed captures the overall experimental trend. Repeating these predictions using the PPII scales measured by Creamer or Kallenbach (columns 2 and 3, Table 1), both yield *R<sup>h</sup>* values that are consistently larger than in the experiment [45], indicating these two scales may be overestimated, at least for describing structural preferences in prototypical IDPs. Moreover, the error from predicting *R<sup>h</sup>* by Equation (1) when using the Hilser-measured PPII scale was found to trend strongly

with *Qnet* when *Qnet* was normalized to chain length (Figure 5B), more so than >500 other physicochemical properties that can be calculated from the primary sequence [38]. The linear trend in prediction error to *Qnet* (determined from sequence as number of K and R minus number of D and E) was used to modify Equation (1), yielding − → →

$$R\_h = (2.16 \text{ A}) \cdot \text{N}^{0.503 - 0.11 \cdot \ln(1 - f\_{ppm})} + 0.26 \cdot |Q\_{\text{net}}| - 0.29 \cdot \text{N}^{0.5} \tag{2}$$

∑

→ → → → **Figure 4.** Using mutational effects on IDP *R<sup>h</sup>* to estimate changes in chain bias for PPII. Computed *R<sup>h</sup>* dependence on *fPPII* for a 93-residue polypeptide, using Equation (1). Arrows show results from experimental *R<sup>h</sup>* measured by both dynamic light scattering (DLS) and size exclusion chromatography (SEC) methods for wild type p53(1-93) and the P→G and A→G substitution mutants. In total, 22 proline (*NPRO*) and 12 alanine residues (*NALA*) in the wild type sequence were substituted to glycine in the P→G and A→G mutants, respectively.

ܴ ൌ ൫2.16 Å൯ ∙ ܰ.ହଷି.ଵଵ∙ሺଵିುು<sup>ሻ</sup> 0.26 ∙ |ܳ௧| െ 0.29 ∙ ܰ.ହ **Figure 5.** Predicting IDP *R<sup>h</sup>* from sequence using experimental PPII propensities. (**A**) *R<sup>h</sup>* predicted by Equation (1) compared to experimental *R<sup>h</sup>* for 34 IDPs. Predicted values (black circles) were determined from sequence using experimental PPII propensities measured in peptides by Hilser and coworkers (column 4, Table 1). Red squares show *R<sup>h</sup>* predictions when using a null model where PPII is not preferentially populated [45]. (**B**) Size-normalized error, (predicted—experimental *Rh* )/*N*0.5, compared to size-normalized *Qnet* (i.e., |*Qnet*|/*N*0.5) for each IDP in panel A. (**C**) Equation (2) predicted *R<sup>h</sup>* compared to experimental *R<sup>h</sup>* for 34 IDPs. The identity, primary sequence, and experimental *R<sup>h</sup>* for the IDPs used to generate data in this Figure are provided in ref. [37]. In each plot, R<sup>2</sup> is the coefficient of determination.

κ Equation (2), which amends Equation (1) for *Qnet* effects on the hydrodynamic size, is highly accurate in predicting *R<sup>h</sup>* from sequence for many IDPs (Figure 5C). Further, in this set of IDPs, mean *R<sup>h</sup>* did not trend with κ [38], which is a measure of the mixing of positive and negative charges in the primary sequence [91]. This justified using *Qnet* to modify Equation (1) and obtain Equation (2), because mean *R<sup>h</sup>* was independent of sequence organization of the charged side chains.

To further test Equation (2) and its ability to describe PPII effects on IDP *R<sup>h</sup>* , random PPII scales were generated and tested for accuracy at predicting experimental *R<sup>h</sup>* [37]—thus establishing the sensitivity of Equation (2) to scale variations. Briefly, each random scale, where the 20 common amino acids were individually assigned random values between 0 and 1, was used to predict *R<sup>h</sup>* by Equation (1), and was then compared to experimental

*Rh* , an example of which is shown Figure 5A for the peptide-based PPII scale measured by Hilser and coworkers. Next, the linear trend in prediction error to size-normalized *Qnet* was determined, as in Figure 5B. These two steps generate two correlations (R<sup>2</sup> ), which were used to evaluate each random scale (Figure 6A). Because the slope and intercept from the error trend with size-normalized *Qnet* provides the coefficients preceding |*Qnet*| and *N*0.5 in Equation (2), each scale yields a unique empirical modification to Equation (1) that corrects for net charge effects on mean *R<sup>h</sup>* . The results from analyzing 10<sup>6</sup> randomly generated scales in this manner are given in Figure 6A. Each data point represents a PPII scale. The color, from black to purple, red, and through yellow, is the average error in predicting *R<sup>h</sup>* from sequence after correcting for net charge effects on hydrodynamic size (i.e., after using scale-specific Equation (2) to predict *R<sup>h</sup>* ). The abscissa is the correlation (R<sup>2</sup> ) of Equation (1)-predicted *R<sup>h</sup>* with the experiment for a scale. The ordinate is the correlation (R<sup>2</sup> ) of size-normalized Equation (1) error with size-normalized *Qnet*.

**Figure 6.** Using experimental *R<sup>h</sup>* from IDPs to determine amino acid-specific intrinsic PPII propensities. (**A**) Ability of experimental PPII propensity scales (from Table 1) to describe the sequence dependence on IDP *R<sup>h</sup>* compared to 10<sup>6</sup> random PPII propensity scales. Missing amino acids from scales measured by Kallenbach (column 3, Table 1) and Creamer (column 2, Table 1) were given the scale average (bottom value, Table 1). Compared as well is the result from using a coil library scale (Table 3). In panels A and B, results from using scales from Hilser and coworkers, Kallenbach and coworkers, Creamer and coworkers, and the coil library are labeled "H", "K", "C", and "coil", respectively. (**B**) Histogram of error distribution in the boxed region of panel A. Small errors are better. (**C**) Average scale value calculated for each of the 20 common amino acids using the "best" performing random PPII propensity scales (red bars). Average scale value using the "best" performing random scales that also maintain correct rank order for the nonpolar amino acids (blue bars), yielding an experimental PPII propensity scale based on IDPs. Error bars report standard deviations.

Two key observations are immediately apparent in the data given in Figure 6A. First, there is a set of random PPII propensity scales that are better than typical at predicting mean *Rh* from sequence when using *fPPII*, *Qnet*, and *N*. These scales, highlighted by the boxed area, predict IDP *R<sup>h</sup>* with good correlation with experimental *R<sup>h</sup>* (R<sup>2</sup> > 0.7; *x*-axis) and a prediction error that also trends with *Qnet* (R<sup>2</sup> > 0.4; *y*-axis). Second, the experimental PPII propensities determined calorimetrically from host–guest analysis of the binding energetics of the Sos peptide (i.e., the peptide-based scale measured by Hilser and coworkers) outperform almost all random scales in their ability to describe sequence effects on mean hydrodynamic size when using only conformational bias and net charge considerations. This is particularly evident when comparing error magnitudes (Figure 6B).

To determine if Equation (2) is sufficiently sensitive to discern the differences in PPII bias of the amino acids, the average scale value for each amino acid type was computed from the "best" performing random scales. The "best" scales were defined as those in the boxed area of Figure 6A with the smallest error (i.e., less than the distribution mode; see Figure 6B). The computed averages, unfortunately, report a somewhat trivial specificity except for distinguishing proline and nonproline types (red bars, Figure 6C), most likely owing to the low representation of some amino acid types in the IDP dataset, specifically the nonpolar amino acids [92]. When substitution effects on mean *R<sup>h</sup>* were measured experimentally in p53(1-93) to determine rank order in PPII propensities among

the nonpolar amino acid types [37], and then used to restrict the "best" random scales to those that also maintain this rank order, the average scale value by amino acid type (blue bars, Figure 6C) exhibited strong correlations with the other experimental PPII scales (Figure 7). These amino acid-specific average scale values (blue bars, Figure 6C), which were obtained solely from analyzing sequence effects on IDP *R<sup>h</sup>* , represent an independent measure of the intrinsic PPII bias in the ID states of biological proteins.

**Figure 7.** Comparison of experimental PPII propensities. (**A**) Correlation of the peptide-measured PPII scale from Hilser and coworkers (column 4, Table 1) with the IDP-measured PPII propensities (blue bars, Figure 6C). (**B**) Correlation of the coil library (Table 3) and IDP scales. In both plots, each blue circle represents an amino acid type.

Because ID has sequence characteristics that show fundamental disparities when compared to nonID sequences, using IDPs as a DSE model for folded protein is not fully supported. For example, unlike the heterogeneous composition of amino acids and the weak repetition found in the sequences of folded proteins [93,94], IDPs and IDRs have a lower sequence complexity [95] with strong preferences for hydrophilic and charged amino acid side chains over aromatic and hydrophobic side chains [92,96]. These disparate properties of the primary sequence suggest potentially disparate structural behavior. To investigate this issue, protein sequence reversal was used to gain experimental access to the disordered ensemble of a protein with a composition of L-amino acids and pattern of side chains identical to those of a conventional folded protein [42]. Using staphylococcal nuclease for these studies, the unaltered wild type adopts a stable native structure consisting of three α-helices and a five-stranded, barrel-shaped β-sheet [97]. The protein variant with reversed sequence directionality, Retro-nuclease, was found to be an elongated monomer, and exhibits the structural characteristics of intrinsic disorder [42]. At 25 ◦C, the mean *R<sup>h</sup>* of Retro-nuclease was found to be 34.0 ± 0.5 Å by DLS techniques. Sedimentation analysis by analytical ultracentrifugation (AUC) and SEC methods gave similar results under similar conditions (33.0 Å at 20 ◦C by AUC, and 33.7 Å at ~23 ◦C by SEC). Equation (2), for comparison, predicts 33.1 Å using the Retro-nuclease primary sequence, which is close to the observed experimental values.

The hydrodynamic size of Retro-nuclease is highly sensitive to temperature changes (Figure 8A), which is consistent with observations from other IDPs [39–41]. The enthalpy and entropy of the PPII to nonPPII transition have been measured in short alanine peptides by monitoring heat effects on structure over a broad temperature range [46]. The results from CD spectroscopy, which monitored the change in the CD signal at 215 nm, gave

∆*HPPII* and ∆*SPPII* of ~10 kcal mol−<sup>1</sup> and 32.7 cal mol−<sup>1</sup> K −1 , respectively, while NMR measurements, using heat effects on <sup>3</sup> *JHNα*, gave ~13 kcal mol−<sup>1</sup> and 40.9 cal mol−<sup>1</sup> K −1 . Δ Δ <sup>−</sup> <sup>−</sup> <sup>−</sup> *α* − − −

α β

α ∆ <sup>−</sup> α **Figure 8.** Temperature, α, and PPII effects on DSE hydrodynamic size. (**A**) Open circles show Retro-nuclease mean *R<sup>h</sup>* measured using DLS methods from 5 to 65 ◦C. The dashed line was calculated with Equation (2) and modeling temperature effects on the intrinsic PPII propensities by Equation (3) and with ∆*HPPII* = 13 kcal mol−<sup>1</sup> . Temperature-dependent changes to the amino acid PPII propensities, from Equation (3), cause the Equation (2)-predicted *R<sup>h</sup>* to change accordingly. (**B**,**C**) Simulated effects on population-weighted size from α and PPII bias. Fractional change in mean *R<sup>h</sup>* (i.e., <*L*>/2) was used to normalize simulation results for chain length. In panel C, open circles represent experimental *R<sup>h</sup>* measured for IDPs and normalized relative to the simulated size of an unbiased ensemble [37], as explained in the main text. *fPPII* for each IDP was calculated from sequence using the IDP experimental PPII scale (blue bars, Figure 6C).

Because the PPII bias is noncooperative [46] and locally determined [72], the effect from temperature changes can be modeled at the level of individual residue positions using the integrated van't Hoff equation,

$$\ln\left(K\_{PPII}(T)\right) = \left(\frac{\Delta H\_{PPII}}{R}\right)\left(\frac{1}{(298\text{ K})} - \frac{1}{T}\right) + \ln\left(K\_{PPII}(298\text{ K})\right) \tag{3}$$

∆ − Δ where *KPPII* is the equilibrium between PPII and nonPPII states, *T* is temperature, and *R* is the gas constant. ∆*HPPII* is assumed to be constant. If PPII is the lone dominant conformation, then *KPPII* for each amino acid type can be estimated from experimental PPII propensities at 25 ◦C as *KPPII,i* = (1 − *PPII<sup>i</sup>* )/*PPII<sup>i</sup>* . The importance of Equation (3) is that it provides another check on the ability of the DSE to be described from the results of peptide studies. Moreover, these two values, ∆*HPPII* and *PPII<sup>i</sup>* , give access to the entropy from the relationship (*∂G*/*∂T*)<sup>P</sup> = −*S*. Using IDP-measured intrinsic PPII propensities (blue bars, Figure 6C), we found that ∆*HPPII*~13 kcal mol−<sup>1</sup> captures the decrease in Retro-nuclease mean *R<sup>h</sup>* from 25 to 65 ◦C (Figure 8A). For alanine, using its IDP-measured PPII propensity at 25 ◦C (0.32) and ∆*HPPII* = 13 kcal mol−<sup>1</sup> yields ∆*SPPII* = 45.1 cal mol−<sup>1</sup> K −1 .

Although the predicted and experimental mean *R<sup>h</sup>* agree at 25 and 65 ◦C, experimental and Equation (2)-predicted values at 5, 15, 35, and 45 ◦C show obvious differences (Figure 8A). At 35 and 45 ◦C, the experimental mean *R<sup>h</sup>* values were larger than predicted, whereas at 5 and 15 ◦C, they were smaller. The analysis of heat effects on *R<sup>h</sup>* using Equation (3) assumed PPII to be the lone dominant DSE conformation, which is not necessarily correct. Indeed, the Retro-nuclease CD spectrum reported a cold-induced local minimum at 222 nm for *T* < 25 ◦C [42], revealing temperature-dependent population of the α backbone conformation. By including the effects of an α bias in simulations of DSE hydrodynamic size, both the over- and underpredictions of mean *R<sup>h</sup>* at 5, 15, 35, and 45 ◦C can be explained.

Briefly, preferential sampling of main chain dihedral angles for Φ and Ψ associated with α-helix can cause changes in the structural dimensions of the DSE [38]. Monitored from the population-weighted mean size, *R<sup>h</sup>* ~ <*L*>/2, computer-generated ensembles that sample (Φ, Ψ) in the α region (−64◦ ± 10◦ , −41◦ ± 10◦ ) show compaction under modest preferences, and elongated sizes at higher α sampling rates (Figure 8B). Specifically, when (Φ, Ψ) sampling for α is weakly preferred, the probability of contiguous stretches

of residues in the α state is low, and turn structures are more likely than helical segments that form when the α bias is higher. Because the effect of the α bias on the mean *R<sup>h</sup>* of the DSE can be accentuated by the PPII bias, whereby ensembles with high PPII propensities show increased sensitivity to changes in the α bias, the consequences of both the α and PPII biases for mean *R<sup>h</sup>* must be considered. For example, the average chain propensity for PPII in our IDP database is ~0.4 when estimated from sequence. Thus, the IDP trend of mean *R<sup>h</sup>* with α bias should follow the red line in Figure 8B, and not the black line. Likewise, the effect of PPII bias on mean *R<sup>h</sup>* is codependent on the α bias (Figure 8C). When PPII is the dominant conformation, the structural dimensions of the denatured state follow the relationship given by Equation (1) (black line in Figure 8C). If, instead, PPII is not the dominant conformation, and moderate α preferences are present, then the *R<sup>h</sup>* dependence on PPII bias changes. More precisely, the result of increasing the chain preference for α is to suppress the effect of PPII on mean *R<sup>h</sup>* (blue line in Figure 8C). When the α bias is stronger than the PPII bias (i.e., α is the dominant conformation), then the effect of the PPII bias is compaction (red line in Figure 8C).

The comparison of experimental IDP *R<sup>h</sup>* to the curves in Figure 8C (open circles in the figure) confirms that PPII is the dominant backbone conformation in IDP ensembles [37]. Here, fractional ∆*R<sup>h</sup>* was calculated as (experimental *Rh*—simulated *R<sup>h</sup>* )/simulated *R<sup>h</sup>* , where simulated *R<sup>h</sup>* refers to the size of an unbiased ensemble that has been corrected for net charge effects. In the figure, a majority of the IDPs are found to have experimental mean *R<sup>h</sup>* values slightly larger than expected based upon the sequence-calculated value of *fPPII*. This suggests that the amino acid preferences for PPII may be underestimated by the IDP-based scale, and the values for *fPPII* in this figure should be shifted to the right. The possibility of a larger intrinsic PPII bias cannot be eliminated because PPII effects on mean *R<sup>h</sup>* are suppressed by the presence of an α bias. The magnitude and sequence dependence to the α bias in the protein DSE is currently unknown, although it has been estimated in short alanine-rich peptides [22].

The idea that PPII propensities are underestimated possibly explains some of the Retronuclease data shown in Figure 8A. An underestimated PPII bias gives an underestimated predicted mean *R<sup>h</sup>* at 35 and 45 ◦C. At 5 and 15 ◦C, the disagreement between theory and experiment is likely caused by the α bias detected in the Retro-nuclease CD spectrum [37,38]. To obtain the sequence dependence of both the α and PPII biases in the DSE and test these assumptions, the analysis of sequence effects on IDP mean *R<sup>h</sup>* reviewed above could simply be repeated at both colder and warmer temperatures. Higher temperatures reduce α effects on mean *R<sup>h</sup>* and isolate the effects of the PPII bias. Colder temperatures give access to the α bias. Just as the sequence dependence of mean *R<sup>h</sup>* at *T* ≥ 25 ◦C yields the amino acid-specific biases for PPII from the comparison of experimental *R<sup>h</sup>* to simulated coil values that omit PPII effects, the sequence dependence of mean *R<sup>h</sup>* at T < 25 ◦C can yield the amino acid bias for the α conformation via comparison to the theoretical treatment that omits the α effects.
