Using ¹H^N amide temperature coefficients to define intrinsically disordered regions: An alternative NMR method

Abstract

This report describes a cost‐effective experimental method for determining an intrinsically disordered protein (IDP) region in a given protein sample. In this area, the most popular (and conventional) means is using the amide (¹H^N) NMR signal chemical shift distributed in the range of 7.5–8.5 ppm. For this study, we applied an additional step: analysis of ¹H^N chemical shift temperature coefficients (¹H^N‐CSTCs) of the signals. We measured ¹H–¹⁵N two‐dimensional NMR spectra of model IDP samples and ordered samples at four temperatures (288, 293, 298, and 303 K). We derived the ¹H^N‐CSTC threshold deviation, which gives the best correlation of ordered and disordered regions among the proteins examined (below −3.6 ppb/K). By combining these criteria with the newly optimized chemical shift range (7.8–8.5 ppm), the ratios of both true positive and true negative were improved by approximately 19% (62–81%) compared with the conventional “chemical shift‐only” method.

Abbreviations

CS

chemical shift

CSTC

chemical shift temperature coefficient

heteroNOE

heteronuclear Overhauser effect

HSQC

heteronuclear single quantum coherence

IDP

intrinsically disordered protein

IDR

intrinsically disordered region

MCC

Matthews's correlation coefficient

NMR

nuclear magnetic resonance

PDB

Protein Data Bank

RDC

residual dipolar coupling

ROC

receiver operating characteristic

SOFAST‐HMQC

band‐selective optimized flip angle short transient‐heteronuclear multi quantum coherence

Introduction

Intrinsically disordered protein (IDP)1 is an emerging key idea for the protein sequence–function relationship.2, 3, 4, 5, 6 Even under physiological conditions, IDPs (and intrinsically disordered regions, IDRs) do not adopt unique and compact three‐dimensional (3D) structures overall or in the part of the polypeptide chain. Growing interest in IDPs has led to an increasing number of reports describing that they possess various physiological functions. Such functions include transcription, translation, and signaling cascades. A unique biological feature of IDPs is believed to be structural polymorphism among the free and multiple target‐bound states with their biological partner proteins. It is particularly interesting that IDP–IDP interaction happens to exhibit ultrahigh picomolar affinity between linker histone H1 and prothymosin α, both of which remain in a full disordered state, even in complex.7 We built a database, IDEAL, in which the protein segments (ProS) in IDPs, which are important for interaction with their targets, were annotated extensively.8, 9 Recent reports describe that IDPs from tardigrades contribute to resistance against drought by IDP's unique vitrification mechanism.10, 11 More recently, we have discovered a sequence‐independent function of human‐genome derived IDPs as a cryoprotectant against other enzymes and non‐enzymatic proteins.12 Consequently, methods for experimental discrimination of IDPs from non‐IDPs are expected to become increasingly important.

To date, two major experimental methods have been used to confirm the presence of disordered regions in a given polypeptide chain: X‐ray crystallography and solution NMR. Because substantial difficulty underlies X‐ray crystallography of IDPs in theory, solution NMR methodology becomes indispensable for physicochemical studies of IDPs.13, 14, 15 The conventional NMR method to ascertain whether the residue of interest belongs to either an IDP region (IDR) or a structured domain (non‐IDR), and probably the simplest, is to acquire ¹H‐¹⁵N HSQC spectrum of the sample and to measure the dispersion of amide ¹H chemical shift (¹H^N‐CS). Because ¹H^N‐CS is sensitive to its local environment of the amide groups in the 3D structure, a typical HSQC of a folded protein sample shows a widely dispersed spectrum in the range of 6–11 ppm on the ¹H axis. By contrast, a sample consisting only of an IDR might show a very narrow range of ¹H^N‐CS: 7.5–8.5 ppm. However, this tendency does not suggest a theory. As a result, some amide protons of the residues within the structured domain region might eventually give a chemical shift at 7.5–8.5 ppm. For example, ubiquitin and the mouse ZO1 PDZ1 domain, both of which we selected as folded protein examples, respectively possess 13 (out of 70) and 16 (out of 90) amide signals (Table 1).¹⁶ Consequently, although ¹H^N‐CS is a good indicator of protein residues for IDR/non‐IDR discrimination, room for improvement remains.

Table 1.

Amino‐Acid Sequences of Proteins Used for this Study. Residues Showing Well‐Separated Signals Used for the CSTC Analysis Are Underlined

Protein name	Total residues	Used signals
Training dataset (IDP)
B3 (thymosin)	44	38a	MADKPDMGEIASFDKAKLKKTETQEKNTLPTKETIEQEKRSEIS
C1 (WWOX)	36	33	MAALRYAGLDDTDSEDELPPGWEERTTKDGWVYYAK
Training dataset (structured)
hUb	76	64	MQIFVKTLTGKTITLEVEPSDTIENVKAKIQDLEGIPPDQQRLIFAGLQL
			EDGRTLSDYNIQKESTLHLVLRLRGG
mZO1‐PDZ1	100	84	GPLGSDHIWEQHTVTLHRAPGFGFGIAISGGRDNPHFQSGETSIVISDVL
			KGGPAEGQLQENDRVAMVNGVSMDNVEHAFAVQQLRKSGKNAKITIRRKK
hVps4b‐MIT	81	68	GSDHMSSTSPNLQKAIDLASKAAQEDKAGNYEEALQLYQHAVQYFLHVVK
			YEAQGDKAKQSIRAKCTEYLDRAEKLKEYLK
Evaluation dataset
hSUMO1	97	93	MSDQEAKPSTEDLGDKKEGEYIKLKVIGQDSSEIHFKVKMTTHLKKLKES
			YCQRQGVPMNSLRFLFEGQRIADNHTPKELGMEEEDVIEVYQEQTGC
hSUMO2	93	88	MADEKPKEGVKTENNDHINLKVAGQDGSVVQFKIKRHTPLSKLMKAYCER
			QGLSMRQIRFRFDGQPINETDTPAQLEMEDEDTIDVFQQQTGG

^aChemical shifts were not assigned. Thirty‐eight well‐separated signals were used for the analysis.

We have specifically examined the parameter ¹H^N chemical shift temperature coefficients (¹H^N‐CSTCs).16, 17 Actually, ¹H^N‐CSTC can be readily estimated from a small number of additional HSQC measurements at different temperatures (at least two). Strong correlation between ¹H^N‐CSTC and formation of intramolecular hydrogen bonds has been reported in the relevant literature.18, 19, 20, 21 Consequently, it seems promising that the additional use of ¹H^N‐CSTC for IDR/non‐IDR discrimination can improve accuracy, although the border line between IDR and non‐IDR definition is not equivalent to the absence or presence of intramolecular hydrogen bonds. To evaluate this idea, we designed the following experiments: 1 preparation of a dataset of ¹H^N‐CSTC of proteins for method development, for which residues had been classified as either IDR or non‐IDR; 2 defining a single ¹H^N‐CSTC threshold value that gives the best Matthew's correlation coefficient (MCC) upon IDR/non‐IDR discrimination; 3 evaluating the method by its application to sample realistic IDR/non‐IDR discrimination problems, human SUMO1 and SUMO2 cases (the method was also evaluated by comparing the orthodox ¹H^N‐CS criteria); 4 evaluating the combinatorial use of the ¹H^N‐CSTC method and the conventional ¹H^N‐CS criterion and comparing it with the single use of each two criteria.

Results

Experimental design

For this study, we started to obtain an amide chemical shift temperature coefficient (¹H^N‐CSTC) data for statistical analysis. We analyzed the amide temperature coefficients of two IDP samples with 30–50 residues: IDP‐B3 and IDP‐C1 [Fig. 1(a,b), S1, and Table 1]. Among them, backbone signals of 33 out of 36 residues (92%) were assigned for IDP‐C1, whereas 38 well‐separated backbone signals out of 44 residues (86%) of IDP‐B3 were used for this analysis without assignment. We were unable to assign IDP‐B3 because of a poor signal‐to‐noise ratio of 3D experiments. These samples were confirmed as unstructured in solution by our membrane fusion‐based systematic IDP assessment22 as well as CD (Supporting Information Fig. S1). Subsequently, we analyzed ¹H^N‐CSTC of hUb, mZO1‐PDZ1, and hVps4b^MIT [Fig. 1(c–e)] as a control of the structured protein domains. For the IDP samples, all residues were classified as disordered. For the structured proteins, the residues were classified into two classes (structured regions and disordered regions) using Ota's criteria to identify IDP regions from the NMR structure ensemble23 (Table 1). For all these residues, ¹H–¹⁵N SOFAST‐HMQC spectra,24 instead of HSQC, were recorded at four temperatures to calculate ¹H^N‐CSTC: 288, 293, 298, and 303 K. These data were then used for statistical analyses (histogram and Matthew's correlation). Finally, two proteins including both the structured and disordered parts of the polypeptides (hSUMO1 and hSUMO2) were used to evaluate the proposed ¹H^N‐CSTC method [Fig. 1(f, g)].

Figure 1.

SOFAST‐HMQC spectra of the analyzed proteins recorded at four temperatures: (a) IDP‐B3, (b) IDP‐C1, (c) hUb, (d) mZO1‐PDZ1, (e) hVps4b^MIT, (f) hSUMO1, and (g) hSUMO2. For all spectra, signals of 288, 293, 298, and 303 K are shown, respectively, as cyan, green, orange, and red.

Histogram of ¹H^N‐CSTC but not ¹⁵N‐CSTC showed deviation between ordered and disordered regions

We selected 211 and 76 residues, respectively, as structured and IDR residue datasets. We then measured SOFAST‐HMQC spectra of the corresponding NMR samples at four temperatures and calculated ¹H^N‐CSTCs and ¹⁵N^H‐CSTCs of the structured and IDR residues. The average and the standard deviation for ¹H^N‐CSTCs of the IDR and non‐IDR (structured) residues were, respectively, −5.62 ±1.56 and − 3.19 ±2.58 ppb/K. Similarly, the average and the standard deviation for ¹⁵N^H‐CSTCs of the IDR and non‐IDR residues were, respectively, −7.09 ±9.52 and 3.25 ±12.63 ppb/K. Figure 2(a, b) represents histograms of ¹H^N‐CSTC and ¹⁵N^H‐CSTC for the residues classified in both the structured and IDR residues. The histogram of ¹H^N‐CSTC showed clear deviation between the two datasets, in which ¹H^N of the ordered region showed large (small negative) CSTCs, whereas that of the disordered region showed small (large negative) CSTCs. This tendency was readily confirmed from the SOFAST‐HMQC spectra of hSUMO1. Actually, hSUMO1 includes 16 IDR residues at its N‐terminus, whereas hSUMO2 has 12 IDR residues. Typical chemical shift changes of the amide signals upon temperature shift taken from 2D NMR spectra of hSUMO1 are shown [Fig. 1(f)]. Although a similar tendency of the histogram of ¹⁵N^H‐CSTC was obtained, we abandoned the use of ¹⁵N^H‐CSTC for IDR/non‐IDR discrimination because the standard deviation for non‐IDR residues was too large [12.63 ppb/K, Fig. 2(b)].

Figure 2.

Histograms of (a) ¹H^N‐CSTC and (b) ¹⁵N^H‐CSTC for residues classified in both structured (light gray) and IDR (black) residues.

Defining the threshold of ¹H^N‐CSTC for order/disorder discrimination and redefinition of ¹H^N‐CS range

We calculated the MCC²⁶ only for any given ¹H^N‐CSTCs [Eq. (3)]. By changing the threshold value in 0.1 ppb/K increments, we sought the threshold that produced the maximum MCC for discriminating the structured and IDR states in the evaluation dataset of ¹H^N‐CSTCs. We chose the threshold value with care. For instance, had we chosen a small (large negative) threshold, the denominator would have been zero. All residues in the NMR structure would have been labeled as being ordered. Consequently, N(*, D) will be zero. For all 287 residues, we were able to calculate all the MCCs (i.e., denominators were non‐zero) when we adjusted the threshold value within −4.5 to −3.0 ppb/K. Results demonstrated that threshold values between −3.6 and − 3.9 ppb/K gave almost maximum MCC values (greater than 0.55) [Fig. 3(a)]. The calculated MCC at −3.6 ppb/K was the highest (0.626). Therefore, we set −3.6 ppb/K as the ¹H^N‐CSTC threshold (CSTC_TH) used to label structured and IDR residues based on NMR spectra. We also calculated the receiver operating characteristic (ROC) curve of this defined CSTC_TH against the training dataset [Fig. 3(b)].

Figure 3.

(a) MCC curve of IDP discrimination by change of the ¹H^N‐CSTC threshold. (b) ROC curve of IDP discrimination by ¹H^N‐CSTC < −3.6 ppb/K as IDR.

Evaluation of the new IDP/non‐IDP discrimination method against naturally occurring examples, hSUMO1 and hSUMO2

We then evaluated the usefulness the new IDR discrimination method with the ¹H^N‐CSTC criterion (¹H^N‐CSTC < −3.6 ppb/K as IDR) against the evaluation dataset of mixture of IDR and non‐IDR in naturally occurring proteins (hSUMO1 and hSUMO2). Both proteins contain N‐terminal disordered regions followed by compactly folded ubiquitin‐like domains (Ubl). We compared the new method with the orthodox IDR criterion of ¹H^N‐chemical shift distribution range (¹H^N‐CS), which is in the range of 7.5–8.5 ppm. When applying the ¹H^N‐CS criterion alone, the discrimination method accuracy was 62% (Table 2); the score closely resembled that of using only ¹H^N‐CSTC (59%). In detail, the numerous false positive residues that were judged as IDR residues, although they were non‐IDR, impaired the accuracy. For example, 67 false‐positive IDR residues were judged by the ¹H^N‐CS criterion, whereas 72 false positives were judged by ¹H^N‐CSTC. These results demonstrate that the ¹H^N‐CSTC criterion alone is not useful.

Table 2.

Results of the Two Naturally Occurring, Mixed Examples of IDP/Non‐IDP Residues, hSUMO1 and hSUMO2, by the Indicated IDP Discrimination Methods. Numbers of the Predicted Residues Are Shown. CS Shows the IDP Discrimination Only by the ¹H^N‐CS Range of 7.5–8.5 ppm, Whereas CSTC Shows IDP Discrimination Only by ¹H^N‐CSTC with −3.6 ppb/K as the CSTC Threshold

	CS	CSTC	CS†/CSTC
True
Positive (a)	28	30	28
Negative (b)	84	77	118
Total (%)	112 (62)	107 (59)	146 (81)
False
Positive (c)	67	74	33
Negative (d)	2	0	2
Total	69 (38%)	74 (41%)	35 (19%)
Positive total (a + c)	95	104	61
Negative total (b + d)	86	77	120

^{† 1}H^N chemical shift range of IDP is defined between 7.5 ppm and 8.5 ppm.

Subsequently, we combined the two criteria: ¹H^N‐CS and ¹H^N‐CSTC. Only when a residue fulfills both the criteria is the residue judged as IDR, otherwise non‐IDR. This combinatorial use of CS and CSTC drastically improved the accuracy to 81%, which was 19% higher than that of the orthodox method alone (7.5–8.5 ppm criterion). This improvement was driven by marked reduction of false positives (67–33). It is noteworthy that the number of the true‐positives was unchanged. Finally, we inferred that the combinatorial use of ¹H^N‐CSTC and ¹H^N‐CS was helpful for discriminating IDR residues from the NMR HSQC spectra of naturally occurring IDR/non‐IDR mixed case of proteins.

Re‐assessment of ¹H^N‐chemical shift range for IDP/non‐IDP discrimination

Next, we reassessed the threshold values (upper and lower limits of ¹H^N‐CS) for discriminating structured and IDR/non‐IDR residues. Historically, the chemical shift ranges of 7.5–8.5 ppm or 7.6–8.6 ppm have been used to confirm that residues with ¹H^N chemical shift in the range belong to IDR, when the NMR samples are entirely disordered. However, if the protein sample of interest includes both ordered and IDRs in one polypeptide, then the signals raised from the ordered region might eventually appear in the chemical shift range. Therefore, we calculated the ratio of true positive residues by changing the upper and lower threshold values of the chemical shift in 0.1 ppm when this criterion was used in combination with the previously determined ¹H^N‐CSTC threshold (−3.6 ppb/K). Results demonstrate that ¹H^N‐CS of 7.8–8.5 ppm gave the best result for discriminating ordered/IDR residues, providing accuracy of 83%, which was 2% higher than that of the previous CS/CSTC combination.

Discussion

For this study, we introduced ¹H^N‐CSTC as another experimental indicator for IDR/non‐IDR discrimination. We defined the threshold value CSTC_TH as −3.6 ppb/K. Our approach was fundamentally based on earlier findings about the relation between ¹H^N‐CSTC and hydrogen bond formation inside a protein molecule. First, weak correlation between ¹H^N‐CSTC and the secondary structures of peptides or proteins had been reported respectively by Andersen et al.²⁷ and by Baxter et al.16 Cierpicki et al. subsequently reported strong correlation between 1H^N‐CSTC and intramolecular hydrogen bonding N–H···O=C.19, 20 This fact was rediscovered and analyzed further by Bouvignies et al.18 and by Tomlinson and Williamson.17 An advanced study by Hong et al. combining NMR and parallel MD simulations demonstrated that ¹H^N‐CSTC originates from thermal expansions of intramolecular N–H···O=C hydrogen bonding distances.25 However, thermal expansion of hydrogen bonding distances more likely occurs between protein backbone amide groups and solvent water rather than intramolecular hydrogen bonds. Based on this knowledge, we attempted to use ¹H^N‐CSTC as an indication of IDRs.

The threshold value of ¹H^N‐CSTC for discriminating hydrogen‐bonded and solvent‐exposed ¹H^N was found to be as −4.6 ppb/K.19, 20 The value was slightly smaller than our discrimination threshold for IDR/non‐IDR residues, CSTC_TH as −3.6 ppb/K, because most IDR residues are assumed to be fully exposed to the solvent, whereas non‐IDR residues might still contain solvent‐exposed residues at the surface of compactly folded domains. Accordingly, we decided not to use ¹H^N‐CSTC alone as the criterion for IDR, but to use a combination of two criteria: the ¹H^N‐CS range and ¹H^N‐CSTC. This approach improved the discrimination accuracy. Nevertheless, our determined ¹H^N‐CSTC threshold of −3.6 ppb/K might still estimate non‐IDR residues erroneously in solvent‐exposed β‐strands as IDR. Therefore, we tested the application of an additional rule further as follows:

If one residue of “state D” is sandwiched by two residues of “state O”, then the “state D” residue is changed to “state O”.[Rule α]

The use of this additional Rule α improved IDR/non‐IDR discrimination further, producing results as high as 92% for our evaluation datasets hSUMO1/hSUMO2 (Table 3). This Rule α was only applicable to limited cases in which all the amide signals have been assigned sequentially. By contrast, the combinatorial use of ¹H^N‐CS range (7.8–8.5 ppm) and ¹H^N‐CSTC was easier because the method did not require signal assignment.

Table 3.

Results of the Two Naturally Occurring, Mixed Examples of IDP/Non‐IDP Residues, hSUMO1 and hSUMO2, Obtained Using the Indicated IDP Discrimination Methods. Numbers of Predicted Residues Are Shown. CS Shows the IDP Discrimination Only by the Refined ¹H^N‐CS Range of 7.8–8.5 ppm, Whereas CSTC Shows the IDP Discrimination Only by ¹H^N‐CSTC with −3.6 ppb/K as the CSTC Threshold; α Denotes That the Rule α (see the text) was Additionally Applied

	CS†	CS†/CSTC	CS†/CSTC/α‡
True
Positive (a)	28	28	28
Negative (b)	97	123	139
Total	125 (69%)	151 (83%)	167 (92%)
False
Positive (c)	54	28	12
Negative (d)	2	2	2
Total	56 (31%)	30 (17%)	14 (8%)
Positive total (a + c)	82	56	40
Negative Total (b + d)	99	125	141

^{† 1}H^N chemical shift range of IDP is defined between 7.8 ppm and 8.5 ppm.

^‡ The additional Rule α was applied.

Some alternative NMR techniques are useful for discriminating IDR/non‐IDR residues: 13C secondary chemical shifts,26, 27, 28, 29 the ¹H–¹⁵N heteronuclear Overhauser effect (heteroNOE30), and residual dipolar coupling (RDC14, 31, 32). The 13C secondary chemical shifts of Cα, Cβ, and CO, which are differences of the chemical shifts from those of a random coil state, were shown to be sensitive to its backbone φ and ψ torsion angles, thereby being useful for ascertaining the secondary structure of proteins.26, 28, 29 This technique is also useful for discriminating IDR residues from non‐IDR residues.27 The major shortcoming of this approach, however, is to complete sequential assignments of backbone signals; otherwise the secondary chemical shifts cannot be calculated. For this purpose, long NMR measuring time (at least two 3D datasets, HNCACB, and HN(CA)CO) with a 13C/¹⁵N‐labeled protein sample, and an effort to assign the signals, are required. Accordingly, neither the use of ¹H–¹⁵N heteroNOE nor of RDC requires signal assignment. Both are 2D‐based experiments. The measurement time is shorter than that of 3D experiments. Although no comprehensive threshold of ¹H–¹⁵N heteroNOE exists for discriminating IDR residues, we found in our earlier study that ¹H–¹⁵N heteroNOE <0.5 showed a reasonable confidence.23 However, ¹H–¹⁵N heteroNOE experiments require a long measuring time: typically 1 day (with a reference spectrum). Furthermore, measurement of RDC requires a special medium for the NMR sample preparation, as reviewed in an earlier report.33 In contrast, our proposed method is simpler, requiring only additional measurements of HSQC spectra at other temperatures. We evaluated it in naturally occurring protein cases, with or without amide signal assignment.

Conclusion

In summary, we introduced amide chemical shift temperature coefficients as an additional simple parameter to assess whether the protein region of interest fits the criteria of IDPs. In addition to a narrow dispersion of overall ¹H‐¹⁵N HSQC (and SOFAST‐HMQC) spectra in the ¹H axis, large negative temperature dependency (large up‐field change) of its chemical shift was shown to be a good indication of IDPs. If the region is intrinsically disordered, then it merely shows a state transition from ordered to disordered upon temperature increase. It remains disordered because it must be intrinsically disordered by definition. Results show that most of the amide chemical shifts might also exhibit linear change upon the temperature shift. This tendency suggests that only two HSQC spectra at the different temperature points are sufficient to drive ¹H^N‐CSTC, thereby assessing the disordered region.

Materials and Methods

Protein sample preparation

We selected three proteins (including protein domains), human ubiquitin (hUb, 76 aa), MIT domain from human Vps4B (Residues 1–77, hVps4b^MIT, 81 aa), and the first PDZ domain of mouse zonula occludens 1 (Residues 18–110, mZO1‐PDZ1, 100 aa) as mainly folded protein examples. We then selected two IDPs from our in‐house human genome derived IDP library,22 IDP‐B3 (thymosin β10, 44 aa) and IDP‐C1 (WWOX Isoform 3, 33 aa) as the well‐characterized IDPs. All five of these proteins were used as the training dataset for method development. Finally, we chose human SUMO1 (hSUMO1, 97 aa) and SUMO2 (hSUMO2, 93 aa) as the validation set for the method developed in this study. Among them, chemical shift assignments of the main‐chain amide group (NH) signals for hUb20, 21 and hSUMO134, 35 were obtained from the literature. The NH signals of hVps4b^MIT 36 and mZO1‐PDZ137 were assigned and reported by us. The NH signals of IDP‐C1 and hSUMO2 were found (this study, see below). The NH signals of IDP‐B3 were used without assignment.

Isotopically labeled proteins for NMR study were generated in Escherichia coli BL21(DE3) grown in 1 or 2 L M9 minimal medium culture, respectively, in the presence of [13C]‐glucose and [¹⁵N]‐NH₄Cl as the sole carbon and nitrogen sources. Recombinant expression and purification of hUb, mZO1‐PDZ1, and hVps4b^MIT were done according to the protocols.37, 38 ¹⁵N‐labeled proteins of IDP‐B3 and IDP‐C1 were expressed using an N^PRO(EDDIE)‐fusion protein expression system39 and were purified according to our slightly modified protocol.40 13C/¹⁵N‐labeled IDP‐C1 was also prepared and used for NH signal assignment.

For hSUMO1 and hSUMO2, the plasmids harboring the genes of N‐terminally GST‐tagged SUMOs, pET‐GST‐SUMO1/2, were transformed to BL21(DE3). After induction of protein expression by IPTG, the cells from 2 L M9 medium were harvested. Then the cells were suspended in lysis buffer (50 mM Tris–HCl, pH 7.4, 200 mM NaCl, 2 mM DTT) and were disrupted by sonication. The supernatant was applied to a DEAE–Sepharose (GE Healthcare, Little Chalfont, UK) column. The pass‐through was used for glutathione affinity column chromatography (3 mL bed/volumes, GST‐Accept®, Nacalai Tesque Inc., Tokyo, Japan). The GST‐tag was removed by addition of thrombin on beads. The crude protein was passed through benzamidine sepharose (GE Healthcare, Little Chalfont, UK) and was subsequently concentrated to a small volume. Finally, the sample was purified by gel filtration (Superdex® 75 pg; GE Healthcare, Little Chalfont, UK), concentrated to approximately 0.2 mM, and was dialyzed against 25 mM phosphate buffer (pH 6.25) containing 75 mM NaCl and 2 mM DTT.

NMR experiments

NMR experiments were conducted using an NMR spectrometer (600 MHz, Avance III; Bruker AXS GmbH, Karlsruhe, Germany) equipped with a cryogenic triple‐resonance probe. To determine ¹H^N‐CSTCs, approximately 100 μM protein samples were dissolved in the NMR measurement buffer (25 mM phosphate buffer (pH 6.25) containing 75 mM NaCl and 2 mM DTT). Then, to shorten the experimental time, the ¹H–¹⁵N SOFAST‐HMQC spectra instead of HSQC to shorten experimental time were measured at 288, 293, 298, and 303 K. For all the well‐dispersed NH signals, ¹H^N‐CSTCs were found following the equation of

$${}^1{\mathrm{H}}^{\mathrm{N}}-\mathit{\text{CSTC}}=\mathrm{\Delta }{\mathrm{\delta }}_{\mathrm{H}}/\mathrm{\Delta }T,$$ (1)

where δ_H is the ¹H^N chemical shift and T is the temperature. ¹⁵N^H‐CSTC was ascertained similarly as

$${}^{15}{\mathrm{N}}^{\mathrm{H}}-\text{CSTC}=\mathrm{\Delta }{\mathrm{\delta }}_{\mathrm{N}}/\mathrm{\Delta }T,$$ (2)

where δ_N represents the ¹⁵N^H chemical shift.

Signal assignment

For the assignment of backbone ¹H, 13C, and ¹⁵N resonances of IDP‐C1 and hSUMO2, ¹H‐¹⁵N HSQC, HNCACB, CBCA(CO)NH, HNCO, and HN(CA)CO spectra were recorded. All 2D and 3D spectra were processed using NMRPipe41 and were analyzed with the Sparky program.42

Dataset preparation

For all ¹H^N‐CS, ¹⁵N^H‐CS, ¹H^N‐CSTC, and ¹⁵N^H‐CSTC data, we regarded that each residue belongs to either IDRs (D state, representing “disordered” state) or non‐IDRs (O state, representing “ordered” state). The states of respective residues were assigned based on results obtained from our earlier study.23 Briefly, it was defined from their Cα’s atomic co‐ordinate deviations as RMSD in the corresponding solution structures, which were retrieved from the Protein Data Bank (PDB). The following structures were used for the corresponding NMR data, PDB ID: 1D3Z (hUb), 2RRM (mZO1‐PDZ1), 1WR0 (hVps4b^MIT), 1A5R (hSUMO1), and 2AWT (hSUMO2). If the deviation was larger than Ota's threshold, 3.2 Å, then the residue was classified as disordered, or part of an IDR (d), and as ordered (O) otherwise.23 Before analyzing the method, each coordinate entry of 1A5R and 2AWT was pre‐fitted to the first entry of each ensemble, particularly addressing their structured ubiquitin‐like regions. All the states for the residues from IDP‐B3 and IDP‐C1 were designated as D because they were confirmed by two experiments: CD spectra (manuscript in preparation, Supporting Information Fig. S1) and indirect systematic NMR assessment.22 Simultaneously, the O/D states for the same residues were determined by ¹H^N‐CSTC (and ¹⁵N^H‐CSTC). If the CSTC was smaller (larger negative value) than a given threshold of CSTC (CSTC_TH), then the residue was designated as D, and otherwise as O.

We attempted to optimize the value for CSTS_TH as described below. We compared the two O/D states of each residue using two methods: one found using Ota's method based on PDB data and another defined by the new CSTC method (this study). When the state of a residue defined by PDB was A, and when that of CSTC was B, then we designated the state of the residue as (A, B), where A and B represent one of O or D. We evaluated the agreement of the residues’ states between the two ways by PDB and by CSTC using Matthews's correlation coefficient (MCC),43 defined as

$$\mathit{MCC}=\frac{N\left(O,O\right)\times N\left(D,D\right)-N\left(O,D\right)\times N\left(D,O\right)}{\sqrt{N\left(O,*\right)\times N\left(*,O\right)\times N\left(D,*\right)\times N\left(*,D\right)}},$$ (3)

where N(A, B) represents the number of residues in state (A, B) in a protein, and

$$N\left(A,*\right)=N\left(A,A\right)+N\left(A,B\right).$$ (4)

Conflict of Interest

The authors declare that they have no conflict of interest in relation to this study or contents of this report describing it.

Supporting information

Appendix S1: CD spectra of each IDP.

Supplementary Figure S1. CD spectra of the selected human genome‐derived IDP samples. Spectra were measured at 278K (circle), 293K (triangle), and 308K (square).