
==== Front
Nat Struct Mol Biol
Nat Struct Mol Biol
Nature Structural & Molecular Biology
1545-9993
1545-9985
Nature Publishing Group US New York

38177681
1147
10.1038/s41594-023-01147-9
Article
Design of complicated all-α protein structures
http://orcid.org/0000-0003-2083-0979
Sakuma Koya 1
Kobayashi Naohiro 23
http://orcid.org/0000-0003-1716-1241
Sugiki Toshihiko 3
Nagashima Toshio 2
http://orcid.org/0000-0001-7739-3525
Fujiwara Toshimichi 3
http://orcid.org/0000-0001-9467-9728
Suzuki Kano 4
http://orcid.org/0000-0002-6599-1680
Kobayashi Naoya 5
http://orcid.org/0000-0002-5748-4670
Murata Takeshi 467
http://orcid.org/0000-0002-6289-5319
Kosugi Takahiro 158
http://orcid.org/0000-0002-5068-1049
Tatsumi-Koga Rie 5
http://orcid.org/0000-0001-8457-0809
Koga Nobuyasu nkoga@protein.osaka-u.ac.jp

1589
1 https://ror.org/0516ah480 grid.275033.0 0000 0004 1763 208X Department of Structural Molecular Science, School of Physical Sciences, SOKENDAI (The Graduate University for Advanced Studies), Hayama, Japan
2 grid.7597.c 0000000094465255 RIKEN Center for Biosystems Dynamics Research, RIKEN, Yokohama, Japan
3 https://ror.org/035t8zc32 grid.136593.b 0000 0004 0373 3971 Institute for Protein Research, Osaka University, Suita, Japan
4 https://ror.org/01hjzeq58 grid.136304.3 0000 0004 0370 1101 Department of Chemistry, Graduate School of Science, Chiba University, Chiba, Japan
5 grid.250358.9 0000 0000 9137 6732 Protein Design Group, Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of National Sciences, Okazaki, Japan
6 https://ror.org/01hjzeq58 grid.136304.3 0000 0004 0370 1101 Membrane Protein Research Center, Chiba University, Chiba, Japan
7 grid.410794.f 0000 0001 2155 959X Structural Biology Research Center, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Japan
8 grid.467196.b 0000 0001 2285 6123 Research Center of Integrative Molecular Systems, Institute for Molecular Science, National Institutes of National Sciences, Okazaki, Japan
9 https://ror.org/035t8zc32 grid.136593.b 0000 0004 0373 3971 Present Address: Institute for Protein Research, Osaka University, Suita, Japan
4 1 2024
4 1 2024
2024
31 2 275282
10 9 2021
4 10 2023
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
A wide range of de novo protein structure designs have been achieved, but the complexity of naturally occurring protein structures is still far beyond these designs. Here, to expand the diversity and complexity of de novo designed protein structures, we sought to develop a method for designing ‘difficult-to-describe’ α-helical protein structures composed of irregularly aligned α-helices like globins. Backbone structure libraries consisting of a myriad of α-helical structures with five or six helices were generated by combining 18 helix–loop–helix motifs and canonical α-helices, and five distinct topologies were selected for de novo design. The designs were found to be monomeric with high thermal stability in solution and fold into the target topologies with atomic accuracy. This study demonstrated that complicated α-helical proteins are created using typical building blocks. The method we developed will enable us to explore the universe of protein structures for designing novel functional proteins.

Here authors developed a computational method to design complicated all-α structures using typical helix–loop–helix motifs and canonical α-helices, and demonstrated the ability to create complicated all-α proteins.

Subject terms

Biophysics
Proteins
Solution-state NMR
Computational biology and bioinformatics
issue-copyright-statement© Springer Nature America, Inc. 2024
==== Body
pmcMain

Many naturally occurring protein structures are complicated, lacking distinguishable symmetry and regularity. Prominent examples of such complicated proteins are globin-fold structures with eight irregularly packed α-helices; Kendrew referred to the tertiary arrangement of the secondary structures as being difficult to describe in simple terms1 (Fig. 1a). In most parts of globin fold structures, two helices adjacent in the sequence are connected crosswise rather than hairpin-like, and the helix–helix packings deviate from the canonical patterns2,3; this fold does not include internal structural repeats such as α-solenoids4,5. These asymmetric, irregular and nonrepetitive secondary structure arrangements make it difficult to simply describe globin structures, and many naturally occurring proteins as well.Fig. 1 Comparison of the structural complexities of naturally occurring and de novo designed proteins.

a,b, Structures of myoglobin (a) and representative de novo designed all-α proteins (b) (the N- and C-terminals are colored in blue and red, respectively, and the characters represent PDB IDs). The α-helices in the globin structure are irregularly aligned, whereas those of the de novo designs are almost parallelly aligned. c, The order parameter capturing the complexities of α-helical proteins, HO. HO is defined by the average of inner products between helix orientation vectors, ui, for all pairs of N α-helices55. Higher values indicate more ordered, and lower values more complicated. d, HO distributions for naturally occurring and de novo designed proteins with three to eight α-helices. Whereas naturally occurring all-α proteins show broad distributions irrespective of the number of constituent α-helices, previous de novo designed all-α proteins indicated by yellow-ocher bars show relatively higher values in the distributions (for details of the previous designs, see Extended Data Fig. 1). Notably, globin structures indicated by blue bars have quite low values. The all-α proteins created in this study, indicated by red bars, have lower values than the previous designs.

Source data

A wide range of all-α protein structures have been designed, but the designs have been limited to simple and ordered structures consisting of α-helices in almost parallel alignment, such as coiled-coil, bundle and barrel structures (Fig. 1b–d and Extended Data Fig. 1)5–27. Jacobs et al. attempted to design α-helical proteins with more variety15, but their designs were still bundle-like (the two designs with five α-helices in Fig. 1b). However, the distribution of complexity for naturally occurring all-α protein structures is biased to the complicated ones (Fig. 1d). The observed distribution bias is probably due to the fact that all-α proteins with complicated spatial arrangements of α-helices can provide diverse and heterogenous molecular surfaces, enabling specific interactions with binding partners. Moreover, such complicated all-α proteins should make it possible to incorporate a functional site enclosed on nearly all sides by multiple structural elements in three dimensions, like globins. Therefore, the ability to create protein structures with irregularly packed α-helices would contribute to the design of various functional proteins.

In this article, we sought to develop a computational method to design complicated all-α structures by employing helix–loop–helix (HLH) motifs typically observed in naturally occurring proteins. The developed method enabled us to generate a wide range of α-helical protein structure topologies from bundle-like to complicated by combining the typical HLH motifs and canonical α-helices. Finally, we demonstrated the ability to create complicated all-α proteins by de novo design of five distinct topologies.

Strategy for all-α topology building

Although it has been suggested that the overall tertiary arrangements of helices of naturally occurring α-helical proteins can be approximated by a quasi-spherical polyhedral model28, the major obstacle in designing complicated all-α topologies with irregularly aligned α-helices is attributed to the difficulty in determining a priori feasible topologies with their backbone blueprints involving lengths of secondary structures and loops. This is different from the design of αβ-proteins: the topologies are selected in advance by β-strand arrangements (that is, the order and orientations of β-strands in a β-sheet), and the backbone blueprints were derived from a set of rules relating local backbone structures of a few successive secondary structure elements to the preferred tertiary motifs29. Therefore, we attempted to explore all-α topologies, not by preparing them a priori but by generating backbone structure topologies through the combinatorial enumeration of tertiary building blocks (Fig. 2). Moreover, the tertiary building blocks were selected from those typically observed in nature, so that the generated backbone structures are likely to be feasible. Therefore, the question is whether complicated all-α topologies can be generated from typical building blocks.Fig. 2 Strategy for building α-helical backbone structure topologies.

Top: building blocks for generating backbone structures. Canonical α-helices and three types of HLH tertiary motifs typically observed in nature, hairpin (h), v-shaped (v) and corner (c), are used. Helices range from 5 to 35 residues, and each motif type comprises six patterns (Fig. 3a). The motif types were classified on the basis of the bending angle between the constituent helices in HLH motifs. Middle: secondary-structure element ordering to build α-helical proteins with five helices. According to the ordering, globular backbone structures without steric clashes are exhaustively explored by combining the building blocks, with the constraint of total residue length. Bottom: examples for generated α-helical backbone structure topologies. Poorly packed structures (lower) are discarded, whereas globularly folded structures (upper) are collected.

A typical set of HLH motifs as building blocks

We first attempted to collect a set of HLH tertiary motifs that are typically observed in nature as building blocks. The HLH units consisting of two α-helices and the connecting loop of one to five residues in length were extracted from naturally occurring proteins, then clustered into 18 subgroups based on the five-dimensional feature vectors representing the HLH tertiary geometries30 (Extended Data Figs. 2 and 3 and Methods). The representative 18 HLH motifs corresponding to each cluster density peak exhibited a broad range of bending angles between two helices, such as left- or right-handed helix–turn–helix, helix–corner–helix and kinked helices (Fig. 3a and Extended Data Figs. 3 and 4); the amino acid preference for each motif is shown in Extended Data Fig. 5: Gly at the residues with positive phi backbone torsion angle, helix capping residues immediately before helices such as Asp, Asn, Thr or Ser (refs. 31,32), and hydrophobic periodicity of helix residues specific to each motif are observed. The 18 HLH motifs are classified into three classes according to the magnitude of the bending angle: hairpin (h), v-shaped (v) and corner (c). The 18 representative HLH motifs were used as building blocks (Fig. 2, top) for generating α-helical backbone structure topologies.Fig. 3 18 HLH tertiary motifs and generated α-helical backbone structures.

a, Identified 18 HLH tertiary motifs typically observed in nature. The motifs are classified based on the bending angle between the two helices in the motifs: hairpin (h), v-shaped (v) and corner (c), which are presented in order of the magnitude of the bending angle, with the ABEGO backbone torsion pattern for the connecting loop. The residues with the backbone torsion angle, A, B, E and G, in the ABEGO torsion representation (‘A’ corresponds to the right-handed α-helix region in the Ramachandran map, ‘B’ to the β-strand region, ‘E’ to the extended region with a positive phi angle, and ‘G’ to a left-handed α-helix) are shown in red, blue, yellow and green, respectively. b, HO distributions for generated backbone structures with six helices. The black, gray and white bars respectively represent the distributions for the ensemble generated using only hairpin motifs (h), hairpin and v-shaped (h + v) motifs, and all three motifs (h + v + c). Incorporation of v-shaped and corner loops yields lower HO structures. c, Examples for the generated backbone structures. The used motif type strings and the HO values are indicated for each structure. The N- and C-terminals are colored in blue and red, respectively.

Source data

Generation of all-α topologies by combinatorial enumeration

Next, we investigated whether complicated topologies are produced using these typical tertiary motifs. Helical backbone structures composed of five and six helices were built with 90 and 110 residues in the total length, respectively, by combining the set of 18 HLH motifs and canonical α-helices ranging from 5 to 35 residues. The backbone structures were generated by enumerating all the combinations and selecting compact and steric-clash-free structures (Methods): 1,159,937,910 five-helix and 20,878,882,380 six-helix structures were enumerated, and 1,899,355 and 380,869 structures were then selected for each. The resulting topologies exhibited a broad spectrum ranging from helical bundle-like to complicated globular structures, demonstrating that complicated α-helical topologies are created from the typical tertiary motifs and canonical α-helices (Fig. 3b, white bar; Fig. 3c and Extended Data Fig. 6); the helix lengths were also widely distributed in the generated structures (Extended Data Fig. 7). Moreover, we found that the complexities of the generated topologies increase, as tertiary motifs with larger bending angles are included (black, gray and white bars in Fig. 3b). These results highlight the importance of corner-type motifs33 in building complicated α-helical topologies.

Design of complicated α-helical topologies

From the generated myriad backbone structure topologies, we selected five for de novo design, H5_fold-0, H6_fold-C, H6_fold-Z, H6_fold-U and H7_fold-K (the Arabic numeral after ‘H’ indicates the number of helices) (Fig. 4 and Supplementary Fig. 1), in the following way. We first selected three topologies exhibiting extremely low helix order (HO) values (for the definition, see Fig. 1c and Methods): H5_fold-0, H6_fold-C and H6_fold-Z (Fig. 1d). Next, to test whether all identified HLH motifs could be used for de novo design, we selected H6_fold-U and H7_fold-K, which include all of the HLH motifs not used in the first three and still exhibit lower HO values (Fig. 1d). For all target folds except H5_fold-0, the lengths of the terminal helices were manually elongated to ensure sufficient packing interactions. None of these backbone structures is similar to any known protein structures; H5_fold-0, H6_fold-C, H6_fold-Z and H6-fold-U show a TM-score <0.6, using TM-align34 against the ECOD database35, and H6_fold-K shows a score of 0.610, with a structure of e2bnlA1 (Extended Data Fig. 8). The details of the selected topologies are described in Supplementary Text. For each backbone structure, amino acid sequences were designed through iterations of fixed-backbone sequence optimization and fixed-sequence structure optimization using Rosetta design calculations36,37. Designs with low energy, tight core packing38 and high compatibility between local sequences and structures29 were selected, and their energy landscapes were explored by 10,000 independent Rosetta ab initio structure prediction simulations starting from an extended conformation39. Ninety-one percent (75 of 82 designs) for H5_fold-0, 45% (18 of 40 designs) for H6_fold-C, 68% (27 of 40 designs) for H6_fold-Z, 67% (60 of 90 designs) for H6_fold-U, and 40% (36 of 90 designs) for H7_fold-K, showed funnel-shaped energy landscapes. Among the designs having funnel-shaped energy landscapes, we selected approximately ten designs for each topology (for the details, see Methods).Fig. 4 Backbone structures for the five design target topologies.

The design target backbone structures. H1–7 represents the first to seventh helices. The letter string next to a loop indicates the ABEGO torsion pattern and the character within a bracket indicates the motif type. The loop residues are colored in the ABEGO torsion representation, same as Fig. 3a. The HO value and radius of gyration (Rg) are indicated for each structure.

Experimental characterization of designed proteins

We obtained synthetic genes encoding ten designs for H5_fold-0, seven for H6_fold-C, seven for H6_fold-Z, eight for H6_fold-U and eight for H6_fold-K. Some designs (H6_fold-Z, 2; H6_fold-U, 1; H7_fold-K, 2) have weak sequence similarity to known proteins with blast E-value <0.005, but the structures are unknown (Supplementary Table 1). The proteins were expressed in Escherichia coli and purified using a Ni2+-NTA affinity column. The purified proteins were then characterized by circular dichroism (CD) spectroscopy and size-exclusion chromatography combined with multi-angle light scattering (SEC–MALS). For all design target topologies, 34 of 40 designed proteins were found to be well expressed and highly soluble, and showed CD spectra typical of α-helical proteins; 27 out of the 34 designs were found to be monomeric by SEC–MALS (Supplementary Tables 2–6). Furthermore, the monomeric designs were characterized by 1H-15N heteronuclear single quantum coherence (HSQC) nuclear magnetic resonance (NMR) spectroscopy, and 23 designs showed well-dispersed sharp peaks (Supplementary Tables 2–6 and Supplementary Fig. 2). The experimental results for all the designs are summarized in Extended Data Table 1. For each topology, we selected one monomeric design with well-dispersed sharp NMR peaks for NMR structure determination (Fig. 5 and Supplementary Fig. 3). All the designs were found to be highly stable from thermal denaturation up to 170 °C by CD (Fig. 5b,c). The NMR structures were solved at high quality using MagRO-NMRViewJ40,41 (Table 1, Supplementary Text, Supplementary Figs. 4 and 5 and Supplementary Table 7), and the solved structures were consistent with the design models (Fig. 6 and Supplementary Table 8). For H5_fold-0, one of the designs was solved by X-ray crystallography and was nearly identical to the design model except for the domain swapping in the crystallized condition (Fig. 6, Table 2 and Supplementary Fig. 5). Despite the inclusion of noncanonical helix–helix packing arrangements in each design, the sidechains from distant α-helices were found to be coherently packed to constitute a single hydrophobic core similar to the design model. Notably, the bulky hydrophobic sidechains from the loops and neighboring α-helices also contributed largely to the core: they spiked the core and pinned the loops to the target conformations (Extended Data Fig. 9; for the importance of hydrophobic residues in the HLH motifs on energy landscapes of the designs, see Supplementary Fig. 6b,e). Interestingly, the N- and C-terminal helices of H6-FoldU_Nomur was found to be fluctuated despite the helix formation (Supplementary Figs. 7–9). Furthermore, in the thermal denaturation, the helical content of H6-FoldU_Nomur was gradually decreased before the transition (the second from the bottom in Fig. 5c), and in the chemical denaturation, the m-value, which represents the cooperativity, was lower than those of the other designs (Fig. 5d; note that m-values also depend on protein size, with larger proteins having larger m-values42; therefore, the H5_fold-0_Elsa and Chantal, which are smaller in size than the other designs, show lower m-values). These results would be attributed to the low hydrophobicity for the core-forming residues of the C-terminus: almost all of the residues are Ala (Supplementary Fig. 8). We also compared the loop geometries of all HLH motifs at the ABEGO level in the design models and experimental structures (Supplementary Fig. 10 and Supplementary Table 9) (for the importance of helix capping residues in the HLH motifs on energy landscapes of the designs, see also Supplementary Fig. 6c,f). Except for the loop immediately before the C-terminal helix of H6-FoldU_Nomur, all loop geometries of the experimental structures agreed with those of the design models. These results indicate that the difficult-to-describe α-helical proteins are designable with typical building blocks.Fig. 5 Characterization of designed proteins.

a, Energy landscapes from Rosetta ab initio structure prediction simulations. The y axis represents Rosetta all-atom energy and the x axis represents the Cα RMSD from the design model. Black points represent the lowest energy structures obtained in independent Monte Carlo structure prediction trajectories starting from an extended chain for each sequence; red points represent the lowest energy structures obtained in trajectories starting from the design model. b, Far-ultraviolet CD spectra at 30 °C, the temperatures close to the melting temperature Tm, and 170 °C. The CD spectra were recorded under the pressure of 10 bar. c, Thermal denaturation measured at 222 nm under the pressure of 10 bar. For each design, the data were fitted to a two-state model (black solid line) to obtain the Tm. d, Chemical denaturation with GuHCl (square brackets denote concentration) measured at 222 nm and 25 °C. For each design, the data were fitted to a two-state model (black solid line) to obtain the free energy of unfolding ΔG and its dependency on the denaturant, m-value. e, Two-dimensional 1H-15N HSQC spectra at 25 °C and 600 MHz.

Table 1 NMR constraints and structure statistics of the five designed structures

Design ID	H5_fold-0_Chantal	H6_fold-C_Rei	H6_fold-Z_Gogy	H6_fold-U_Nomur	H7_fold-K _Mussoc	
PDB ID	7BQM	7BQN	7BQQ	7BQS	7BQR	
BMRB entry	36,335	36,336	36,337	36,339	36,338	
NMR distance and dihedral constraints						
Distance constraints						
 Total NOE	2,098 (100.0%)	3,018 (100.0%)	2,771 (100.0%)	2,515 (100.0%)	2,934 (100.0%)	
Intra-residue	425 (20.3%)	596 (19.7%)	551 (19.9%)	436 (17.3%)	484 (16.5%)	
Inter-residue						
Sequential (|i − j| = 1)	555 (26.5%)	727 (24.1%)	620 (22.4%)	578 (23.0%)	661 (22.5%)	
Medium range (1 < |i − j| < 5)	617 (29.4%)	983 (32.6%)	867 (31.3%)	801 (31.8%)	906 (30.9%)	
Long range (|i − j| ≥ 5)	501 (23.9%)	712 (23.6%)	733 (26.5%)	700 (27.8%)	883 (30.1%)	
Total dihedral angle restraints	132	206	232	195	220	
ϕ	66	103	116	97	110	
ψ	66	103	116	98	110	
Structure statistics						
Violations (mean and s.d.)†						
Distance constraints (Å)	0.024 ± 0.068 (0.10 ± 0.28)	0.000 ± 0.000 (0.00 ± 0.00)	0.192 ± 0.059 (1.20 ± 0.70)	0.318 ± 0.071 (1.50 ± 0.59)	0.219 ± 0.020 (1.20 ± 0.43)	
Dihedral angle constraints (°)	0.000 ± 0.000 (0.00 ± 0.00)	1.006 ± 4.273 (0.05 ± 0.21)	21.473 ± 0.262 (0.90 ± 0.26)	2.056 ± 5.853 (0.10 ± 0.28)	4.336 ± 7.772 (0.20 ± 0.35)	
Max. distance constraint violation (Å)	0.243	0.186	0.413	0.416	0.278	
Max. dihedral angle violation (°)	18.782	20.114	29.059	21.092	23.562	
Deviations from idealized geometry‡						
Bond lengths (Å)	0	0	0	0	0	
Bond angles (°)	0	0	0	0	0	
Impropers (°)	0	0	0	0	0	
Average pairwise RMSD* (Å)						
Heavy	1.34 ± 0.11	1.26 ± 0.12	1.19 ± 0.08	1.15 ± 0.10	1.14 ± 0.10	
Backbone	0.39 ± 0.09	0.47 ± 0.10	0.39 ± 0.06	0.35 ± 0.06	0.27 ± 0.05	
†Mean and s.d. values are derived from 20 models of Amber refined structures. The averaged number of violations for dihedral angle constraints (>20°) and distance constraints (>0.2 Å) across 20 models, and the s.d. are indicated in parentheses.

‡No geometrical outliers are found in all models.

*Averaged RMSD and deviation of backbone and heavy atoms for all pair of models in ensemble (20 × 20), are calculated by MolMol53, fitted on the residues in ordered region (H5_fold-0_Chantal: 4–85; H6-fold-C_Rei: 2–15, 24–39, 69–91, 97–112; H6_fold-Z_Gogy: 4–118; H6_fold-U_Nomur: 5–19, 21–36, 38–96, 99–107; H7_fold-K_Mussoc: 8–25, 27–48, 52–121) identified by Filt_Robot54.

Fig. 6 Comparison of computational models with experimentally determined structures.

Design structures (left) and NMR structures (a crystal structure for H5_fold-0_Elsa) (right); the N- and C-terminals are colored in blue and red, respectively. The Cα RMSD between them is indicated (for H5_fold-0_Elsa, of which crystal structure is domain-swapped dimer, the Cα RMSD was calculated using MICAN56).

Table 2 X-ray crystallography data collection and refinement statistics

	H5_fold-0_Elsa	
Data collection		
Space group	P21	
Cell dimensions		
a, b, c (Å)	45.98, 33.66, 58.38	
α, β, γ (°)	90.00, 93.11, 90.00	
Resolution (Å)	45.9–2.33 (2.47–2.33)*	
Rmerge	0.090 (0.483)	
I/σI	13.63 (2.54)	
Completeness (%)	98.7 (92.3)	
Redundancy	6.4 (4.5)	
Refinement		
Resolution (Å)	45.9–2.33	
No. reflections	49,835	
Rwork/Rfree	0.2066/0.2469	
No. atoms		
Protein	1,422	
Ligand/ion	6	
Water	16	
B-factors		
Protein	57.59	
Ligand/ion	84.02	
Water	45.80	
RMSD		
Bond lengths (Å)	0.003	
Bond angles (°)	0.517	
*Statistics for the highest resolution shell are shown in parentheses. PDB ID: 7DNS.

Discussion

De novo designs of α-helical proteins have focused on structures consisting of parallelly aligned α-helices (Fig. 1), many of which are based on helical structure models such as the helical wheel43 and Crick’s parameterization44. We sought to develop a computational method for designing difficult-to-describe α-helical protein structures. We first identified the 18 HLH motifs typically observed in naturally occurring proteins. We then demonstrated that a wide range of globular all-α backbone structure topologies from bundle-like to complicated are generated by combining the 18 typical HLH motifs and canonical α-helices. The key to building complicated α-helical topologies is to include HLH motifs with larger bending angles such as corner-type motifs. The approach of this developed method is regarded as the reverse of blueprint-based design: design target topologies are searched by the combinations of HLH motifs in this approach, whereas design target topologies are predetermined and then local backbone structures favoring the topologies are selected in blueprint-based design.

We succeeded in designing complicated α-helical protein structures with five distinct topologies, three of which, H5_fold-0, H6_fold-C and H6_fold-Z, exhibited structural complexities comparable to the globin fold. The design success rate was as high as that of previous de novo designs, and the design exhibited high solubility and thermal stability, similarly to previous designs29,45–49. Moreover, the loop geometries of almost all HLH motifs were formed as designed, which must have enabled the designed proteins to fold into the target topologies. These de novo design results indicate that the compact and steric-clash free backbone structures generated by using the typical HLH motifs are probably designable. In this regard, however, one of the questions is whether all or how much of the generated backbone structures can have tight core packing of sidechains. We have demonstrated that the selected five backbone structures are packable through de novo design, but the packability for the other backbone structures has not been clarified, which should be addressed in next works.

The computationally generated myriad of complicated all-α structures should provide diverse and heterogeneous molecular surfaces for engineering functions such as binding, enzymatic activity and self-assembly into symmetric oligomers. The myriad of generated structures, which are presumably highly soluble and stable, coupled with the recently developed massive gene synthesis50,51 and parallel high-throughput screening17,18,26,52, should make it possible to create proteins with optimal structures for specific functions17,26.

Methods

Definition of HO

HO is the order parameter that captures the complexities of α-helical proteins. HO is defined by the average of inner products between helix orientation vectors, ui, for all pairs of N α-helices55:HO=2N(N−1)∑i=1i<jN(ui⋅uj)2.

Higher values indicate more ordered and lower values, more complicated.

Analysis of all-α protein structures for de novo designed and naturally occurring proteins

Twenty-two de novo designed all-α protein structures were collected from Protein Data Bank (PDB). To this end, de novo designs were searched by the keyword ‘de novo’ or ‘de-novo’ in PDB as of November 2020, and then all-α structures containing no β-strands were extracted on the basis of the secondary structure assignments by the DSSP algorithm57 (for the PDB structures including multiple chains or NMR models, the first chain or model was used). The following four classes of de novo designed proteins were excluded from the dataset: (1) designed proteins created on the basis of backbone structures of naturally occurring proteins, and those with sequence similarity higher than 0.90 (as an exception, the three-helix bundle structure designs (PDB code: 6DS9 and 2A3D) were both included because of their structural dissimilarity); (2) assemblies composed of one or two α-helices (for example, 3R3K and 1U7J); (3) repetitive structures such as α-solenoids (for example, 1MJ0 and 5K7V); (4) membrane proteins.

For naturally occurring all-α protein structures, 7,352 representative structures found in the mainly-α class in the CATH database58 with sequence identity less than 40% were used.

For calculating the HO values of the collected structures, secondary structure elements and loops were assigned by DSSP57 (α-helices are defined for the residue regions composed of at least five successive residues assigned as ‘H’ by the DSSP calculation). Note that the secondary structure assignments by DSSP are not always consistent with those originally defined by the authors. For example, the number of α-helices in the structures (PDB codes: 4TQL and 1P68) respectively designed with three and four α-helices were defined as four and five due to partially distorted α-helices.

Clustering of HLH units using the five features representing a HLH geometry

A total of 13,667 HLH structures were extracted from 7,280 X-ray structures (secondary structures were assigned by DSSP57), obtained from the PISCES server59, with resolution ≤2.5 Å, R-factor ≤0.3, sequence length more than or equal to 40, and ≤25% sequence identity. We then classified the HLH structures by their loop residue lengths and extracted 13,510 HLH structures in total with loop of one to five residues in length. The extracted HLH structures were clustered for each loop length from one to five using the density clustering algorithm30 (Extended Data Fig. 3), with the five features representing a HLH geometry (Extended Data Fig. 2).

Building backbone structures

α-Helical backbone structures were built using Rosetta by exhaustive sampling for the conformations with steric-clash free (Rosetta vdw score <4.0 using the weight value, 0.1) and smaller radius of gyration (<14 Å) (the threshold value corresponds to the peak of the distribution of the radius of gyration for naturally occurring proteins; Supplementary Fig. 11) by combining canonical α-helices ranging from 5 to 35 residues (backbone torsion angles, phi, psi and omega, were set to −60.0, −45.0 and 180.0, respectively) and the identified 18 HLH motifs (Main and Fig. 3a), with length constraints of 90 and 110 residues for the five- and six-helix proteins, respectively. For generating five-helix structures, 64,440,995 steric-clash free four-helix structures with 70 residues were first generated, and then an α-helix with 18 types of connecting loops was appended to the C-terminal of the generated four-helix structures so that the total length becomes 90 residues. For generating six-helix structures, an α-helix with 18 types of connecting loops was appended to the N-terminal of the generated five-helix structures so that the total length becomes 110 residues. From these structures, the globular five- and six-helix structures were collected on the basis of the radius of gyration.

Selection of designs for experimental characterization based on the shapes of energy landscapes

We set three criteria for the selection by the shapes of energy landscapes. First, the overall shape of the landscape should be funnel-like with an apparent and sharp ‘neck’ reaching low-root mean square deviation (RMSD) and low-energy region, which is the hallmark of the foldability specifically into the target conformation. This is the most important criterion on the selection of energy landscape plots: for ill-designed sequences, all conformations remain in the high-RMSD and high-energy regions and do not have such a ‘neck’. Second, the funnel should not have subminima that indicate that the protein has alternative folded states. This is a criterion to exclude the possibility of misfolding and avoid a rugged energy landscape. Third, the ensemble of lowest-RMSD and lowest-energy conformations at the bottom of the funnels should not be away from, and ideally should overlap with, the conformational ensemble in the simulations starting from the target structure. This criterion is not mandatory, but consistency between fragment assembly simulations that offer global sampling and near-native relax simulations helps us to rank the designs with the similar quality in terms of the first and second criteria.

Expression and purification of designed proteins

The genes encoding the designed sequences were synthesized and inserted into pET21b vectors. The whole plasmid constructs were purchased from FASMAC or Eurofins Genomics. The target proteins were overexpressed by IPTG induction in E. coli BL21 Star (DE3) cells cultured in MJ9 minimal media including 15N ammonium sulfate as the sole nitrogen source and 12C glucose as the sole carbon source60. The expressed uniformly (U-)15N-labeled proteins with a 6xHis tag at the C-terminus were purified by Ni2+-affinity columns. The purified proteins were then dialyzed against phosphate-buffered saline (PBS) buffer, 137 mM NaCl, 2.7 mM KCl, 10 mM Na2HPO4 and 1.8 mM KH2PO4, at pH 7.4; this buffer was used for all the experiments except NMR structure determination. The expression level, solubility and purity of each designed protein were evaluated by sodium dodecyl sulfate–polyacrylamide gel electrophoresis. To further confirm them, the samples were analyzed by mass spectroscopy (Bruker Daltonics REFLEX III and Thermo Scientific Orbitrap Elite).

Experiments to identify designed proteins exhibiting folding ability

The following three experiments were conducted to evaluate the folding ability of designed sequences: CD spectroscopy, size exclusion chromatography with multi-angle light scattering (SEC–MALS) and 1H-15N HSQC NMR spectroscopy. Supplementary Tables 2–6 present the results of the evaluations for each designed sequence for each fold.

CD spectroscopy under 1-bar pressure

Far-UV CD spectra was measured to study whether the designs show the characteristic spectra of α-helical proteins, by scanning from 260 to 200 nm at 20 °C for ∼15 μM protein samples in PBS buffer on a JASCO J-1500 CD spectrometer. The measurements were performed four times and then averaged.

SEC–MALS

Oligomeric states for the designs in solution were studied by SEC–MALS with miniDAWN TREOS static light scattering detector (Wyatt Technology Corp.) combined with a high-performance liquid chromatography system (1260 Infinity LC, Agilent Technologies) with a Shodex KW-802.5 column (Showa Denko K.K.) for H5_fold-0_Chantal and H6_fold-C_Rei or a Superdex 75 increase 10/300 GL column (GE Healthcare) for H5_fold-0_Elsa, H6_fold-Z_Gogy and H7_fold-K_Mussoc. After the equilibration of the column with PBS buffer, 100 µl of the samples after purification by Ni2+-affinity columns were injected. The absorbance at 280 nm was measured by the high-performance liquid chromatography system to give the protein concentrations and intensity of light scattering at 659 nm was measured at angles of 43.6°, 90.0° and 136.4°. These data were analyzed by the ASTRA software (version 6.1.2, Wyatt Technology) using a change in the refractive index with concentration, a dn/dc value, 0.185 ml g−1, to estimate the molecular weight of dominant peaks.

1H-15N HSQC NMR spectroscopy

Whether the designs fold into well-packed structures or not was evaluated by 1H-15N HSQC 2D-NMR spectroscopy. The purified protein samples were concentrated to 0.2–1.0 mM, and mixed with their 10% volume of D2O. The experiments were performed at 25 °C on a JEOL JNM-ECA 600 MHz spectrometer, and data were analyzed by JEOL Delta (version 5.3.1).

High-pressure CD spectroscopy for melting temperature (Tm) estimation

For the designs that were evaluated to have the folding ability in the above experiments (one design for each target topology was selected), thermal denaturation was studied by using high-pressure CD spectroscopy. JASCO J-1500 CD spectrometer was equipped with additional pressure instruments so that temperature of the solution samples can be scanned from 30 °C to 170 °C under 10 bar. Temperature was increased 1 °C per minute for ∼15 μM protein samples. Fixed wavelength measurements at 222 nm were performed at every 1 °C, and wavelength scanning measurements (260 to 200 nm) were performed at 30, 40, 60, 80, 90, 100, 110, 120, 130, 140, 150, 160 and 170 °C. Thermal denaturation was measured once. Tm was estimated by nonlinear fitting to thermal denaturation CD curve at 222 nm. The nonlinear least-squares analysis was performed by nls function in R language, given a two-state unfolding and linear extrapolation model. After this fitting, we obtained Tm at which the estimated populations of folded and unfolded states become equal.

CD spectroscopy for chemical denaturation

Chemical denaturation with GuHCl was monitored at 222 nm for 2–3 μM protein samples in PBS buffer (pH 7.4) at 25 °C in a 1-cm path length cuvette. The GuHCl concentration was automatically controlled by a JASCO ATS-530 titrator. Chemical denaturation was measured once. The chemical denaturation curves were fit by nonlinear least-squares analysis using a two-state unfolding and linear extrapolation model61. The free energy change, ΔG, for the unfolding transition and its dependency on the denaturant, m-value, were obtained from the fitting.

Sample preparation for NMR structure determination

The most promising design for each target topology was overexpressed by IPTG induction in E. coli BL21 Star (DE3) cells cultured in MJ9 minimal media containing 15N ammonium sulfate as the sole nitrogen source and 13C glucose as the sole carbon source60. The expressed U-15N,U-13C-enriched proteins were purified by Ni2+-affinity columns, and dialyzed against PBS buffer. The protein samples were further purified by gel filtration chromatography on an ÄKTA Pure 25 FPLC (GE Healthcare) using a Superdex75 or Superdex75 increase 10/300 GL column (GE Healthcare), which also replaced the PBS buffer at pH 7.4 with the customized buffer for NMR spectroscopy. The following 95% H2O/5% D2O buffer conditions for each sample were used: 100 mM NaCl, 5.6 mM Na2HPO4, 1.1 mM KH2PO4, at pH 7.4 for H5_fold-0_Chantal; 50 mM NaCl, 5.5 mM Na2HPO4, 4.5 mM KH2PO4, at pH 6.9 for H6_fold-C_Rei; 50 mM NaCl, 3.2 mM Na2HPO4, 4.5 mM KH2PO4, at pH 6.5 for H6_fold-Z_Gogy; 155 mM NaCl, 3.0 mM Na2HPO4, 1.1 mM KH2PO4, 10 μM ethylenediaminetetraacetic acid, 0.02% NaN3, cOmplete protease inhibitor cocktail (Roche), at pH 7.4 for H6_fold-U_Nomur; and 155 mM NaCl, 3.0 mM Na2HPO4, 1.1 mM KH2PO4, at pH 7.4 for H7_fold-K_Mussoc.

Solution structure determination by NMR

NMR measurements

NMR measurements were performed on Bruker AVANCE III NMR spectrometers equipped with QCI cryo-Probes at 303 K. The spectrometers with 600, 700 and 800 MHz magnets were used for the signal assignments and nuclear Overhauser effect (NOE)-related measurements, while 700, 900 and 950 MHz ones, for residual dipolar coupling (RDC) experiments. For the signal assignments, 2D 1H-15N HSQC (echo/anti-echo), 1H-13C Constant-Time HSQC for aliphatic and aromatic signals, 3D HNCO, HN(CO)CACB and 3D HNCACB for backbone signal assignments, while BEST pulse sequence was applied to the triple resonance measurements for H6_fold-C_Rei. For structure determination, 3D 15N-edited NOESY and 3D 13C-edited NOESY for aliphatic and aromatic signals (mixing time 100 ms) were performed. For H6_fold-U_Nomur, additional 3D HN(CA)CO, HN(CO)CA, HNCA, HBHA(CO)NH, HBHANH, H(CCCO)NH, CC(CO)NH, 3D 13C-HSQC (13C-t1) NOESY 13C-HSQC, 3D 13C-HSQC (13C-t1) NOESY 15N-HSQC and 4D 13C-HSQC NOESY 13C-HSQC were measured. Except for 3D-edited NOESY, all the other spectra were performed using non-uniform sampling (NUS) for H6_fold-U_Nomur and H7_fold-K_Mussoc. For NUS, sampling ratio was set at 25% for 3D and 6% for 4D with a fixed random seed. The NUS spectra were reconstructed by iteratively re-weighted least squares for 3D while iterative soft thresholding for 4D spectra with virtual-echo technique using qMDD tool62.

For the RDC experiments, 2D in-phase and anti-phase (IPAP) 1H-15N HSQC using water-gate pulses for water suppression were measured with or without 6–10 mg ml−1 of Pf1 phage (ASLA Biotech). For confirming the positions of 1H-15N signals in the 2D IPAP 1H-15N HSQC, 3D HNCO at the identical buffer condition containing Pf1 phage were measured. The α- and β-states of 15N signals split by 1H-15N 1J-coupling were separately identified for the protein in the isotropic and weakly aligned states, to obtain 1-bond RDC 1D1H/15N values. For the sample H6_fold-U_Nomur, 3D J-HNCO (without 1H decoupling for 15N evolution) was measured at 25% NUS, which were used for confirming α- and β-states of 15N signal positions overlapped in 2D IPAP spectra. 3D J-HN(CO)CA spectrum was also measured for H6_fold-U_Nomur to obtain 1D1Hα/13Cα for appending an additional number of alignment data at the identical magnetic field and alignment tensor.

NMR signal assignments

All NMR signals were identified in a fully automated manner using MagRO-NMRViewJ (upgraded version of Kujira40), in which noise peaks were filtered by deep-learning methods using Filt_Robot41. FLYA module was used for fully automated signal assignments and structure calculation63 to obtain roughly assigned chemical shifts (Acs), and then trustworthy ones were selected into the MagRO Acs table. After confirmation and correction of the Acs by visual inspection using MagRO, TALOS+64 calculations were performed to predict phi/psi dihedral angles, which were then converted to angle constraints for the CYANA format.

Structure calculation

Several CYANA65 calculations were performed using the Acs table, NOE peak table and dihedral angle constraints. The Acs table was exported by the MagRO CYANA module, and then the aliased chemical shifts were automatically calculated depending on the spectrum width of responsible NOESY spectra. For dihedral angle constraints, phi and psi, with deviation were derived from TALOS+ prediction using chemical shifts of 15N, 13C′, 13Cα and 13Cβ, with high prediction score noted by ‘Good’. The minimal angle deviation was set at 20°. After several iterations of CYANA calculations, dihedral angle constraints derived from TALOS+64 revealing large violation for nearly all models in structure ensemble were eliminated.

After the averaged target function of the ensemble reached to less than 2.0 Å2, refinement calculations by Amber12 were carried out for 20 models with lowest target functions. The coordinates of final.pdb calculated by CYANA, distance constraints (final.upl), dihedral angle constraints derived from TALOS+ prediction were converted into Amber format and topology file using Sander Tools. Firstly, 500 steps of minimization (250 steps of steepest decent, 250 steps of conjugate gradient) were carried out without electrostatic potential and NMR constraints. Second, molecular dynamics simulations with the ff99SB force field using implicit water system (0.1 M of ionic strength, 18.0 Å of cutoff) were performed, in which the temperature was gradually increased from 0.0 K to 300.0 K by 1,500 steps, followed by the simulation with 28,500 steps at 300.0 K (1.0 fs time step, total 30 ps). Finally, 2,000 steps for minimization (1,000 steps for steepest decent and 1,000 steps for conjugate gradient) with constraints of distance and dihedral angle were applied at the same condition used in the molecular dynamics simulations.

NMR structure validation

The RMSD values were calculated for the 20 structures overlaid to the mean coordinates for the ordered regions, automatically identified by Filt_Robot using multi-dimensional nonlinear scaling54.

The RDC back-calculation was performed by PALES66 using experimentally determined values of RDC. The averaged correlation between the simulated and experimental values was obtained using the signals except the residues on overlapped regions in 1H-15N HSQC and the ones in low-order parameters less than 0.8 predicted by TALOS+. For the validation of H6_fold-U_Nomur, a lot of signals were overlapped in 2D IPAP-HSQC spectra. To overcome this problem, 1JHN−15N split 3D HNCO (without 1H-decoupling scheme in 15N evolution period) spectra in isotropic and anisotropic states were measured by NUS (25% data point reduction) to obtain signal positions of α- and β-states of 15N spins at resolution of 0.3 Hz. 1JHα/13Cα split 3D HN(CO)CA spectra at the same conditions were also measured to obtain 1D1Hα/13Cα at resolution of 0.2 Hz. Initially the RDC reproducibility of H6_fold-U_Nomur were examined using separately 1DHN−15N and 1DHα−13Cα tables by PALES for all models to confirm that the averaged correlation coefficients are greater than 0.9, and then final correlation coefficients were calculated with two merged tables.

Solution structural dynamics of H6_fold-U_Nomur measured by NMR

15N R1, R2 and 15N-{1H} NOE experiments

The 15N R1, R2 and 15N-{1H} NOE measurements were performed for a uniformly 15N-labeled H6_fold-U_Nomur protein sample with a concentration of 0.78 mM, which is the same condition as the solution used for the structure determination. These were conducted at 303 K on Bruker 700 MHz Avance-III NMR spectrometer equipped with cryogenic probe, using the 4-mm-diameter NMR Shigemi-tube. The 15N R1 and R2 were obtained by measuring 2D 1H-15N HSQC with the inversion-recovery technique and with the temperature-compensated CPMG method, respectively67. Steady-state 15N-{1H} NOE was obtained by measuring 2D 1H-15N HSQC spectra with and without saturation pulse in each of the retardation time acquired by the interleaved method. The 2D 1H-15N peaks were automatically identified and assigned using the MagRO software40. Some assignments were corrected with visual inspection. The 15N-{1H} NOE values were estimated as the peak intensity ratio I/I0 derived from the 2D HSQC spectra with (I) and without (I0) saturation pulse. The I/I0 data were fitted by using an exponential equation, I/I0 = exp(−R × t) with delay time t (s) to obtain the 15N relaxation rate constant R (s−1).

2D 1H-15N CLEANEX-PM FHSQC experiments

The uniformly 15N-labeled protein sample of H6_fold-U_Nomur was lyophilized, and then 2D 1H-15N HSQC data were collected immediately after dissolving the lyophilized sample in 100% D2O. However, protons of the amide groups of most residues were promptly replaced by deuterium within 10 min after the dissolution, probably due to the high pH of the sample solvent (pH 7.4). This prevented us to obtain practical H–D exchange rates. Therefore, the exchange rates between the water and amide protons were obtained using the 2D 1H-15N CLEANEX-PM FHSQC68,69 scheme. In this method, the exchange ratio depends only on kopen in the protein folding/unfolding. The amide group would be in the EX1 limit due to the relatively high pH of 7.4, namely kclose « k, where kclose is the global and/or local folding rate of a protein and k is the exchange rate of amide group in the unfolded state, the observable solvent exchange rate kex would be obtained as the global and/or local unfolding rate of a protein, kopen. The 2D 1H-15N FHSQC data without applying spin-lock pulse was also measured under the same condition to obtain the reference, I0. For 2D 1H-15N CLEANEX-PM FHSQC spectra with different spin-lock time tm and the reference spectrum, the observed peaks were automatically identified and assigned by MagRO40 with manual correction to obtain a normalized list of signal intensities for each residue. The following equation was used to obtain kobs for each residue:II0=kexkex+R1A−R1B×exp−R1B×tm−exp−R1A+kex×tm,

where R1B is the apparent longitudinal relaxation rate of water molecules, and R1A is a mixture of the apparent longitudinal and transverse relaxation rates on the rotational frame for the residue of interest. The values of R1A and kex for each residue with error values were obtained by curve-fitting by this equation, with the assumption, R1B = 0.6 (s−1).

X-ray structure determination of H5_fold-0_Elsa

Sample preparation for X-ray structure determination

The gene encoding the designed sequence of H5_fold-0_Elsa in pET21b vector was digested at the NdeI and XhoI restriction sites and cloned into pET15b-TEV vector with cleavable sites by TEV protease instead of thrombin (original) between the designed sequence and the N-terminal 6xHis tag. Designed protein was expressed in E. coli BL21 Star (DE3) cells, and purified by a Ni2+-affinity column. The N-terminal His tag was then cleaved by TEV protease, and removed through a Ni2+-affinity column. The protein samples without a His tag were purified by an anion-exchange chromatography (HiTrapQ HP 1-ml column, GE Healthcare) followed by gel filtration chromatography (Superdex 75 10/300 GL column) on an ÄKTA Pure 25 FPLC. Mass spectroscopy was performed to confirm that a His tag was successfully cleaved.

To assess the effect of the tag cleavage on the oligomeric state and stability, we performed SEC–MALS and thermal denaturation CD experiments under high pressure for the original and tag-cleaved samples of H5_fold-0_Elsa. The solvent was exchanged to PBS at pH 7.4 before these experiments. The results showed that the tag-cleaved protein was also monomeric and had nearly identical denaturation temperature (the second row in Fig. 5c, 106 °C) as the original sample with the C-terminal His tag (Supplementary Fig. 12, 105 °C), which indicates that the removal of tag and slight differences in flanking amino-acid sequences do not largely change the stability and oligomeric state of the designed protein in solution.

Crystallization and X-ray structure determination

The protein samples of H5_fold-0_Elsa at the concentration of 12 mg ml−1 (1.07 mM) was crystallized in the solution of 0.4 M MgCl2, 0.1 M Tris–HCl (pH 7.5) and 30% PEG 3350, using the sitting-drop vapor diffusion method at 296 K. The obtained crystals were soaked in the solution of 0.4 M MgCl2, 0.1 M Tris–HCl (pH 7.5), 30% PEG 3350 and 10% glycerol, mounted on cryo-loops (Hampton Research), flash-cooled and stored in liquid nitrogen.

X-ray diffraction data of the crystal were collected with BL-1A beamline (λ = 1.1000 Å) at Photon Factory, and processed to 2.3 Å by XDS70. After phase determination by molecular replacement using the design model by Molrep71 in the CCP4 suite, the molecular model was constructed and refined using Coot72 and Phenix Refine73. Translation/Libration/Screw refinement was performed in late stages of refinement. The refined structures were validated with RAMPAGE74. Ramachandran plot statistics showed that 98.8% and 0.00% of residues were in favored and outlier regions, respectively. The crystallographic data collection is summarized in Table 2.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41594-023-01147-9.

Supplementary information

Supplementary Information Supplementary Text, Figs. 1–12 and Tables 1–9.

Reporting Summary

Peer Review File

Supplementary Data 1 Computational design models of the designed all-α proteins.

Supplementary Data 2 Source data for Supplementary Fig. 11.

Source data

Source Data Fig. 1 Statistical source data.

Source Data Fig. 3 Statistical source data.

Source Data Extended Data Fig. 1 Statistical source data.

Source Data Extended Data Fig. 3 Statistical source data.

Source Data Extended Data Figs. 4 and 5 Statistical source data.

Source Data Extended Data Fig. 6 Statistical source data.

Source Data Extended Data Fig. 7 Statistical source data.

Extended data

Extended Data Fig. 1 Twenty-two de novo designed proteins collected from Protein Data Bank (PDB).

a, Structures and their PDB IDs of the twenty-two de novo designed proteins collected from PDB. b, The helix order (HO) values of the designs were plotted in the HO histograms for naturally occurring all-α proteins (these histograms are identical to those in Fig. 1).

Source data

Extended Data Fig. 2 The five features representing the HLH tertiary geometry.

a-d, For representing tertiary geometries of HLH units, the following angles, θN, θC, ϕNC, ϕNL, and ϕCL, were identified using the VN, VC, VL, VHN, and VHC vectors (these vectors are calculated using Cα atoms). a, The definitions of θN and θC. VN and VC respectively represent the helix vectors for the N- and C- terminal helices in a HLH geometry, which are calculated using the equations proposed by Krissinel et al.53. VL is the loop vector from the last Cα atom (blue) in the N-terminal helix to the first Cα atom (red) in the C-terminal helix. θΝ was identified as the angle between the VN and VL vectors; θC, was identified as the angle between the VC and VL vectors. b, The definitions of ϕNC· ϕNC was identified as the dihedral angle between the plane defined with the VN and VL vectors and that with the VC and VL vectors. c, The definition of ϕNL· VHN is the helix spiral vector at the end of the N-terminal helix, which was identified as the vector pointed to the last Cα atom (blue) in the N-terminal helix from the Cα atom immediately before the last Cα atom (white). ϕNL was identified as the dihedral angle between the plane defined with the VHN and VL vectors and that with the VHN and VN vectors. d, The definition of ϕCL· VHC is the helix spiral vector at the beginning of the C-terminal helix, which was identified as the vector from the first Cα atom (red) in the C-terminal helix to the Cα atom immediately after the first Cα atom (yellow). ϕCL was identified as the dihedral angle between the plane defined with the VC and VHC vectors and that with the VL and VHC vectors.

Extended Data Fig. 3 Statistical analysis of HLH motifs of naturally occurring proteins.

HLH structures collected from naturally occurring protein structures were clustered for each loop length from one to five based on the pairwise Euclidean distance between the five-dimensional vectors of the features shown in Extended Data Fig. 2, using the density clustering algorithm30. For each loop length, decision graphs to determine density peaks of clusters are shown, in which rho represents the local density of a point in the five-dimensional feature vector space and delta represents the minimum distance between a point to any other point with higher density; for the point with highest density, delta is calculated as the maximum distance to any other points.

Source data

Extended Data Fig. 4 Mapping of 18 representative HLH motifs on the ϕNC-ϕNL plane.

The loop numbers with their ABEGO torsion patterns correspond to the 18 representative HLH motifs shown in Extended Data Fig. 3.

Source data

Extended Data Fig. 5 ABEGO-based loop geometries and amino acid sequence preferences of the cluster that each HLH motif belongs to.

(Left) The 18 representative HLH motifs are shown as in Extended Data Fig. 3. (Middle) ABEGO torsion patterns of the loop. This result suggests that the relative arrangements of adjacent helices strongly limit the torsion patterns of the connecting loop. (Right) Amino acid sequence preferences of each HLH motif. The first residue of the loop is indicated by an arrow.

Source data

Extended Data Fig. 6 Examples of compact structures obtained from the enumeration of six-helix structures.

The structures are sorted by their HO values from top left to bottom right. The top left structure shows the smallest HO value and has irregularly packed α-helices, whereas the bottom right one shows the highest HO value and has parallelly aligned α-helices. The five designed topologies are shown together by enclosed squares.

Source data

Extended Data Fig. 7 Distribution of the helix lengths for the generated backbone structures with four-helix and 70 residues, five-helix and 90 residues, and six-helix and 110 residues.

Left: The distribution of mean helix lengths for the generated backbone structures. For each backbone structure, the mean helix length was calculated by averaging lengths of the helices in the structure. Middle: The distribution of standard deviation of helix lengths for the generated backbone structures. For each backbone structure, the standard deviation of lengths of the helices in the structure was calculated. Right: The two-dimensional distribution of the mean and standard deviation of helix lengths. The width of the distribution of the standard deviation was in the order of the four-helix, five-helix, and six-helix structures. This is because the four-helix structures were not subject to the Rg constraint, and the five- and six- helix structures were the ones with Rg < 14 Å. Since the same threshold value for the Rg constraint was used, the distribution width for the five-helix structures is slightly wider than that of the six-helix structures. The helix lengths of the designs chosen for experimental characterization correspond to the vicinity of the peaks of the distributions.

Source data

Extended Data Fig. 8 Comparison of designed structures and the most similar naturally occurring proteins.

The designed structures (left) and the most similar ones (right) with pdb ids and TM-score values.

Extended Data Fig. 9 Comparison of computational models (left) with experimentally determined structures (right).

Hydrophobic core residues are shown in stick. Bulky hydrophobic side chains from loops and the neighboring α-helices, which spiked the core and pinned the loops to the target conformations, are shown in yellow.

Extended Data Table 1 Summary of experimental results for designed proteins

The second column shows the number of designs experimentally tested for the fold in the leftmost column. The subsequent columns give the number of designs that satisfy each experimental characterization, which was performed sequentially from the left to the right. The successful designs are defined as those that satisfy all criteria and are expected to fold into correct fold. The details of the results are shown in Supplementary Tables 2-6.

†Expression and solubility were assessed by SDS-PAGE and mass spectrometry.

‡SEC-MALS was used to determine oligomerization state. The number of designs in which the main peak of the absorbance at 280 nm corresponds to the monomeric state was counted.

*1H-15N HSQC spectra were collected.

Extended data

is available for this paper at 10.1038/s41594-023-01147-9.

Supplementary information

The online version contains supplementary material available at 10.1038/s41594-023-01147-9.

Acknowledgements

We thank RIKEN Yokohama NMR Facility for NMR measurements, the Functional Genomics Facility, NIBB Core Research Facilities, especially Y. Makino, for mass spectrometry analysis, and the Instrument Center, Okazaki, Japan, especially M. Nakano, for HSQC spectra measurements. We also thank M. Yamamoto for experimental assistance, S. Minami for advice on structure similarity comparison and useful discussions, and Y. Ishii and S. Akiyama for valuable comments on the paper. The computations were performed using the Research Center for Computational Science (RCCS), Okazaki, Japan (Project: 21-IMS-C174, 20-IMS-C157, 19-IMS-C175, 18-IMS-C155, 17-IMS-C147, 16-IMS-C129 and 15-IMS-C180). Three-dimensional structure determination was supported by Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS) from AMED under grant numbers JP19am0101072 and JP20am0101083. The synchrotron radiation experiments were performed at Photon Factory (proposals 2016G-048). We also thank the beamline staff at BL1A of Photon Factory (Tsukuba, Japan) for help during data collection. This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grants-in-Aid for Scientific Research 15H05592 to N. Koga, 18H05420 to T.K. and N. Koga, 18H05425 to T.M. and 18K06152 to Naohiro K., the Japan Science and Technology Agency (JST) Precursory Research for Embryonic Science and Technology (PRESTO, grant number JPMJPR13AD to N. Koga) and the JST-Mirai Program (JPMJMI17A2 to Naohiro K.). K. Sakuma was also supported by JSPS KAKENHI Grant-in-Aid for JSPS Research Fellow 15J02427.

Author contributions

K. Sakuma and N. Koga designed the research. K. Sakuma analyzed natural proteins and performed computational design work. K. Sakuma wrote the program code. K. Sakuma, T.K. and R.T.-K. expressed, purified, characterized the designed proteins by biochemical assay, and prepared protein samples for NMR: H5_fold-0, H6_fold-C and H6_fold-Z, by K. Sakuma, and H6_fold-U and H7_fold-K, by T.K. and R.T.-K. For NMR structure determination, Naohiro K., T.S. and T.N. collected data: H5_fold-0_Chantal, H5_fold-C_Rei and H6_fold-Z_Gogy, by T.S., and H6_fold-U_Nomur and H7_fold-K_Mussoc, by Naohiro K. and T.N. Naohiro K. performed structural analysis. For NMR structural dynamics of H6_fold-U_Nomur, Naohiro K. and T.N. collected and analyzed data. For crystal structure determination, Naoya K. prepared protein samples and K. Suzuki, with advice from T.M., performed crystallization and structural analysis. K. Sakuma, Naohiro K., T.F., K. Suzuki, T.M., T.K., R.T.-K. and N. Koga wrote the paper.

Peer review

Peer review information

Nature Structural & Molecular Biology thanks John Anderson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available. Primary Handling Editor: Sara Osman, in collaboration with the Nature Structural & Molecular Biology team.

Data availability

The solution NMR structures of the five designs have been deposited in the PDB under the accession numbers 7BQM (H5_fold-0_Chantal), 7BQN(H6_fold-C_Rei), 7BQQ (H6_fold-Z_Gogy), 7BQS (H6_fold-U_Nomur) and 7BQR (H7_fold-K_Mussoc). The NMR data have been deposited in the Biological Magnetic Resonance Data Bank under the accession numbers 36335(H5_fold-0_Chantal), 36336 (H6_fold-C_Rei), 36337 (H6_fold-Z_Gogy), 36339 (H6_fold-U_Nomur) and 36338 (H7_fold-K_Mussoc). The crystal structure of H5_fold-0_Elsa has been deposited in the PDB under the accession number 7DNS. The computational design models are presented as Supplementary Data 1. The generated compact and steric-clash-free five-helix (1,899,355) and six-helix (380,869) structures are available at https://github.com/kogalab21/all-alpha_design. The plasmids encoding the designed sequences are available through Addgene under the accession numbers 201825 (H5_fold-0_Elsa), 201826(H5_fold-0_Chantal), 201827 (H6_fold-C_Rei), 201828 (H6_fold-Z_Gogy), 201829(H6_fold-U_Nomur) and 201830 (H7_fold-K_Mussoc). Source data are provided with this paper.

Code availability

The code for building and analyzing helical structures has been implemented into Rosetta at https://github.com/RosettaCommons/main/tree/koga/all-alpha_design. The demo for building helical structures is available at https://github.com/kogalab21/all-alpha_design.

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

These authors contributed equally: Koya Sakuma, Naohiro Kobayashi.
==== Refs
References

1. Kendrew JC A three-dimensional model of the myoglobin molecule obtained by x-ray analysis Nature 1958 181 662 666 10.1038/181662a0 13517261
Kendrew, J. C. et al. A three-dimensional model of the myoglobin molecule obtained by x-ray analysis. Nature 181, 662–666 (1958).13517261 10.1038/181662a0
2. Crick FHC The packing of α-helices: simple coiled-coils Acta Crystallogr. 1953 6 689 697 10.1107/S0365110X53001964
Crick, F. H. C. The packing of α-helices: simple coiled-coils. Acta Crystallogr. 6, 689–697 (1953).10.1107/S0365110X53001964
3. Chothia C Levitt M Richardson D Structure of proteins: packing of alpha-helices and pleated sheets Proc. Natl Acad. Sci. USA 1977 74 4130 4134 10.1073/pnas.74.10.4130 270659
Chothia, C., Levitt, M. & Richardson, D. Structure of proteins: packing of alpha-helices and pleated sheets. Proc. Natl Acad. Sci. USA 74, 4130–4134 (1977).270659 10.1073/pnas.74.10.4130
4. Kobe B Kajava AV When protein folding is simplified to protein coiling: the continuum of solenoid protein structures Trends Biochem. Sci. 2000 25 509 515 10.1016/S0968-0004(00)01667-4 11050437
Kobe, B. & Kajava, A. V. When protein folding is simplified to protein coiling: the continuum of solenoid protein structures. Trends Biochem. Sci. 25, 509–515 (2000).11050437 10.1016/S0968-0004(00)01667-4
5. Doyle L Rational design of alpha-helical tandem repeat proteins with closed architectures Nature 2015 528 585 588 10.1038/nature16191 26675735
Doyle, L. et al. Rational design of alpha-helical tandem repeat proteins with closed architectures. Nature 528, 585–588 (2015).26675735 10.1038/nature16191
6. Walsh ST Cheng H Bryson JW Roder H DeGrado WF Solution structure and dynamics of a de novo designed three-helix bundle protein Proc. Natl Acad. Sci. USA 1999 96 5486 5491 10.1073/pnas.96.10.5486 10318910
Walsh, S. T., Cheng, H., Bryson, J. W., Roder, H. & DeGrado, W. F. Solution structure and dynamics of a de novo designed three-helix bundle protein. Proc. Natl Acad. Sci. USA 96, 5486–5491 (1999).10318910 10.1073/pnas.96.10.5486
7. Dai QH Structure of a de novo designed protein model of radical enzymes J. Am. Chem. Soc. 2002 124 10952 10953 10.1021/ja0264201 12224922
Dai, Q. H. et al. Structure of a de novo designed protein model of radical enzymes. J. Am. Chem. Soc. 124, 10952–10953 (2002).12224922 10.1021/ja0264201
8. Wei Y Kim S Fela D Baum J Hecht MH Solution structure of a de novo protein from a designed combinatorial library Proc. Natl Acad. Sci. USA 2003 100 13270 13273 10.1073/pnas.1835644100 14593201
Wei, Y., Kim, S., Fela, D., Baum, J. & Hecht, M. H. Solution structure of a de novo protein from a designed combinatorial library. Proc. Natl Acad. Sci. USA 100, 13270–13273 (2003).14593201 10.1073/pnas.1835644100
9. Go A Kim S Baum J Hecht MH Structure and dynamics of de novo proteins from a designed superfamily of 4-helix bundles Protein Sci. 2008 17 821 832 10.1110/ps.073377908 18436954
Go, A., Kim, S., Baum, J. & Hecht, M. H. Structure and dynamics of de novo proteins from a designed superfamily of 4-helix bundles. Protein Sci. 17, 821–832 (2008).18436954 10.1110/ps.073377908
10. Calhoun JR Solution NMR structure of a designed metalloprotein and complementary molecular dynamics refinement Structure 2008 16 210 215 10.1016/j.str.2007.11.011 18275812
Calhoun, J. R. et al. Solution NMR structure of a designed metalloprotein and complementary molecular dynamics refinement. Structure 16, 210–215 (2008).18275812 10.1016/j.str.2007.11.011
11. Huang PS High thermodynamic stability of parametrically designed helical bundles Science 2014 346 481 485 10.1126/science.1257481 25342806
Huang, P. S. et al. High thermodynamic stability of parametrically designed helical bundles. Science 346, 481–485 (2014).25342806 10.1126/science.1257481
12. Murphy GS Computational de novo design of a four-helix bundle protein–DND_4HB Protein Sci. 2015 24 434 445 10.1002/pro.2577 25287625
Murphy, G. S. et al. Computational de novo design of a four-helix bundle protein–DND_4HB. Protein Sci. 24, 434–445 (2015).25287625 10.1002/pro.2577
13. Brunette TJ Exploring the repeat protein universe through computational protein design Nature 2015 528 580 584 10.1038/nature16162 26675729
Brunette, T. J. et al. Exploring the repeat protein universe through computational protein design. Nature 528, 580–584 (2015).26675729 10.1038/nature16162
14. Boyken SE De novo design of protein homo-oligomers with modular hydrogen-bond network-mediated specificity Science 2016 352 680 687 10.1126/science.aad8865 27151862
Boyken, S. E. et al. De novo design of protein homo-oligomers with modular hydrogen-bond network-mediated specificity. Science 352, 680–687 (2016).27151862 10.1126/science.aad8865
15. Jacobs TM Design of structurally distinct proteins using strategies inspired by evolution Science 2016 352 687 690 10.1126/science.aad8036 27151863
Jacobs, T. M. et al. Design of structurally distinct proteins using strategies inspired by evolution. Science 352, 687–690 (2016).27151863 10.1126/science.aad8036
16. Bhardwaj G Accurate de novo design of hyperstable constrained peptides Nature 2016 538 329 335 10.1038/nature19791 27626386
Bhardwaj, G. et al. Accurate de novo design of hyperstable constrained peptides. Nature 538, 329–335 (2016).27626386 10.1038/nature19791
17. Chevalier A Massively parallel de novo protein design for targeted therapeutics Nature 2017 550 74 79 10.1038/nature23912 28953867
Chevalier, A. et al. Massively parallel de novo protein design for targeted therapeutics. Nature 550, 74–79 (2017).28953867 10.1038/nature23912
18. Rocklin GJ Global analysis of protein folding using massively parallel design, synthesis, and testing Science 2017 357 168 175 10.1126/science.aan0693 28706065
Rocklin, G. J. et al. Global analysis of protein folding using massively parallel design, synthesis, and testing. Science 357, 168–175 (2017).28706065 10.1126/science.aan0693
19. Polizzi NF De novo design of a hyperstable non-natural protein–ligand complex with sub-A accuracy Nat. Chem. 2017 9 1157 1164 10.1038/nchem.2846 29168496
Polizzi, N. F. et al. De novo design of a hyperstable non-natural protein–ligand complex with sub-A accuracy. Nat. Chem. 9, 1157–1164 (2017).29168496 10.1038/nchem.2846
20. Studer S Evolution of a highly active and enantiospecific metalloenzyme from short peptides Science 2018 362 1285 1288 10.1126/science.aau3744 30545884
Studer, S. et al. Evolution of a highly active and enantiospecific metalloenzyme from short peptides. Science 362, 1285–1288 (2018).30545884 10.1126/science.aau3744
21. Koebke KJ Clarifying the copper coordination environment in a de novo designed red copper protein Inorg. Chem. 2018 57 12291 12302 10.1021/acs.inorgchem.8b01989 30226758
Koebke, K. J. et al. Clarifying the copper coordination environment in a de novo designed red copper protein. Inorg. Chem. 57, 12291–12302 (2018).30226758 10.1021/acs.inorgchem.8b01989
22. ElGamacy M Coles M Lupas A Asymmetric protein design from conserved supersecondary structures J. Struct. Biol. 2018 204 380 387 10.1016/j.jsb.2018.10.010 30558718
ElGamacy, M., Coles, M. & Lupas, A. Asymmetric protein design from conserved supersecondary structures. J. Struct. Biol. 204, 380–387 (2018).30558718 10.1016/j.jsb.2018.10.010
23. Chen Z Programmable design of orthogonal protein heterodimers Nature 2019 565 106 111 10.1038/s41586-018-0802-y 30568301
Chen, Z. et al. Programmable design of orthogonal protein heterodimers. Nature 565, 106–111 (2019).30568301 10.1038/s41586-018-0802-y
24. Silva DA De novo design of potent and selective mimics of IL-2 and IL-15 Nature 2019 565 186 191 10.1038/s41586-018-0830-7 30626941
Silva, D. A. et al. De novo design of potent and selective mimics of IL-2 and IL-15. Nature 565, 186–191 (2019).30626941 10.1038/s41586-018-0830-7
25. Xu C Computational design of transmembrane pores Nature 2020 585 129 134 10.1038/s41586-020-2646-5 32848250
Xu, C. et al. Computational design of transmembrane pores. Nature 585, 129–134 (2020).32848250 10.1038/s41586-020-2646-5
26. Cao L De novo design of picomolar SARS-CoV-2 miniprotein inhibitors Science 2020 370 426 431 10.1126/science.abd9909 32907861
Cao, L. et al. De novo design of picomolar SARS-CoV-2 miniprotein inhibitors. Science 370, 426–431 (2020).32907861 10.1126/science.abd9909
27. Sesterhenn F De novo protein design enables the precise induction of RSV-neutralizing antibodies Science 2020 368 eaay5051 10.1126/science.aay5051 32409444
Sesterhenn, F. et al. De novo protein design enables the precise induction of RSV-neutralizing antibodies. Science 368, eaay5051 (2020).32409444 10.1126/science.aay5051
28. Murzin AG Finkelstein AV General architecture of the α-helical globule J. Mol. Biol. 1988 204 749 769 10.1016/0022-2836(88)90366-X 3225849
Murzin, A. G. & Finkelstein, A. V. General architecture of the α-helical globule. J. Mol. Biol. 204, 749–769 (1988).3225849 10.1016/0022-2836(88)90366-X
29. Koga N Principles for designing ideal protein structures Nature 2012 491 222 227 10.1038/nature11600 23135467
Koga, N. et al. Principles for designing ideal protein structures. Nature 491, 222–227 (2012).23135467 10.1038/nature11600
30. Rodriguez A Laio A Machine learning. Clustering by fast search and find of density peaks Science 2014 344 1492 1496 10.1126/science.1242072 24970081
Rodriguez, A. & Laio, A. Machine learning. Clustering by fast search and find of density peaks. Science 344, 1492–1496 (2014).24970081 10.1126/science.1242072
31. Richardson JS Richardson DC Amino acid preferences for specific locations at the ends of α helices Science 1988 240 1648 1652 10.1126/science.3381086 3381086
Richardson, J. S. & Richardson, D. C. Amino acid preferences for specific locations at the ends of α helices. Science 240, 1648–1652 (1988).3381086 10.1126/science.3381086
32. Doig AJ Baldwin RL N- and C-capping preferences for all 20 amino acids in α-helical peptides Protein Sci. 1995 4 1325 1336 10.1002/pro.5560040708 7670375
Doig, A. J. & Baldwin, R. L. N- and C-capping preferences for all 20 amino acids in α-helical peptides. Protein Sci. 4, 1325–1336 (1995).7670375 10.1002/pro.5560040708
33. Efimov AV A novel super-secondary structure of proteins and the relation between the structure and the amino acid sequence FEBS Lett. 1984 166 33 38 10.1016/0014-5793(84)80039-3 6692923
Efimov, A. V. A novel super-secondary structure of proteins and the relation between the structure and the amino acid sequence. FEBS Lett. 166, 33–38 (1984).6692923 10.1016/0014-5793(84)80039-3
34. Zhang Y Skolnick J TM-align: a protein structure alignment algorithm based on the TM-score Nucleic Acids Res. 2005 33 2302 2309 10.1093/nar/gki524 15849316
Zhang, Y. & Skolnick, J. TM-align: a protein structure alignment algorithm based on the TM-score. Nucleic Acids Res. 33, 2302–2309 (2005).15849316 10.1093/nar/gki524
35. Cheng H ECOD: an evolutionary classification of protein domains PLoS Comput. Biol. 2014 10 e1003926 10.1371/journal.pcbi.1003926 25474468
Cheng, H. et al. ECOD: an evolutionary classification of protein domains. PLoS Comput. Biol. 10, e1003926 (2014).25474468 10.1371/journal.pcbi.1003926
36. Kuhlman B Design of a novel globular protein fold with atomic-level accuracy Science 2003 302 1364 1368 10.1126/science.1089427 14631033
Kuhlman, B. et al. Design of a novel globular protein fold with atomic-level accuracy. Science 302, 1364–1368 (2003).14631033 10.1126/science.1089427
37. Leaver-Fay A ROSETTA3: an object-oriented software suite for the simulation and design of macromolecules Methods Enzymol. 2011 487 545 574 10.1016/B978-0-12-381270-4.00019-6 21187238
Leaver-Fay, A. et al. ROSETTA3: an object-oriented software suite for the simulation and design of macromolecules. Methods Enzymol. 487, 545–574 (2011).21187238 10.1016/B978-0-12-381270-4.00019-6
38. Sheffler W Baker D RosettaHoles2: a volumetric packing measure for protein structure refinement and validation Protein Sci. 2010 19 1991 1995 10.1002/pro.458 20665689
Sheffler, W. & Baker, D. RosettaHoles2: a volumetric packing measure for protein structure refinement and validation. Protein Sci. 19, 1991–1995 (2010).20665689 10.1002/pro.458
39. Rohl CA Strauss CE Misura KM Baker D Protein structure prediction using Rosetta Methods Enzymol. 2004 383 66 93 10.1016/S0076-6879(04)83004-0 15063647
Rohl, C. A., Strauss, C. E., Misura, K. M. & Baker, D. Protein structure prediction using Rosetta. Methods Enzymol. 383, 66–93 (2004).15063647 10.1016/S0076-6879(04)83004-0
40. Kobayashi N KUJIRA, a package of integrated modules for systematic and interactive analysis of NMR data directed to high-throughput NMR structure studies J. Biomol. NMR 2007 39 31 52 10.1007/s10858-007-9175-5 17636449
Kobayashi, N. et al. KUJIRA, a package of integrated modules for systematic and interactive analysis of NMR data directed to high-throughput NMR structure studies. J. Biomol. NMR 39, 31–52 (2007).17636449 10.1007/s10858-007-9175-5
41. Kobayashi N Noise peak filtering in multi-dimensional NMR spectra using convolutional neural networks Bioinformatics 2018 34 4300 4301 10.1093/bioinformatics/bty581 29985974
Kobayashi, N. et al. Noise peak filtering in multi-dimensional NMR spectra using convolutional neural networks. Bioinformatics 34, 4300–4301 (2018).29985974 10.1093/bioinformatics/bty581
42. Myers JK Pace CN Scholtz JM Denaturant m values and heat capacity changes: relation to changes in accessible surface areas of protein unfolding Protein Sci. 1995 4 2138 2148 10.1002/pro.5560041020 8535251
Myers, J. K., Pace, C. N. & Scholtz, J. M. Denaturant m values and heat capacity changes: relation to changes in accessible surface areas of protein unfolding. Protein Sci. 4, 2138–2148 (1995).8535251 10.1002/pro.5560041020
43. Schiffer M Edmundson AB Use of helical wheels to represent the structures of proteins and to identify segments with helical potential Biophys. J. 1967 7 121 135 10.1016/S0006-3495(67)86579-2 6048867
Schiffer, M. & Edmundson, A. B. Use of helical wheels to represent the structures of proteins and to identify segments with helical potential. Biophys. J. 7, 121–135 (1967).6048867 10.1016/S0006-3495(67)86579-2
44. Crick FHC The Fourier transform of a coiled-coil Acta Crystallogr. 1953 6 685 689 10.1107/S0365110X53001952
Crick, F. H. C. The Fourier transform of a coiled-coil. Acta Crystallogr. 6, 685–689 (1953).10.1107/S0365110X53001952
45. Lin YR Control over overall shape and size in de novo designed proteins Proc. Natl Acad. Sci. USA 2015 112 E5478 E5485 10.1073/pnas.1509508112 26396255
Lin, Y. R. et al. Control over overall shape and size in de novo designed proteins. Proc. Natl Acad. Sci. USA 112, E5478–E5485 (2015).26396255 10.1073/pnas.1509508112
46. Huang PS De novo design of a four-fold symmetric TIM-barrel protein with atomic-level accuracy Nat. Chem. Biol. 2016 12 29 34 10.1038/nchembio.1966 26595462
Huang, P. S. et al. De novo design of a four-fold symmetric TIM-barrel protein with atomic-level accuracy. Nat. Chem. Biol. 12, 29–34 (2016).26595462 10.1038/nchembio.1966
47. Marcos E Principles for designing proteins with cavities formed by curved beta sheets Science 2017 355 201 206 10.1126/science.aah7389 28082595
Marcos, E. et al. Principles for designing proteins with cavities formed by curved beta sheets. Science 355, 201–206 (2017).28082595 10.1126/science.aah7389
48. Marcos E De novo design of a non-local β-sheet protein with high stability and accuracy Nat. Struct. Mol. Biol. 2018 25 1028 1034 10.1038/s41594-018-0141-6 30374087
Marcos, E. et al. De novo design of a non-local β-sheet protein with high stability and accuracy. Nat. Struct. Mol. Biol. 25, 1028–1034 (2018).30374087 10.1038/s41594-018-0141-6
49. Dou J De novo design of a fluorescence-activating β-barrel Nature 2018 561 485 491 10.1038/s41586-018-0509-0 30209393
Dou, J. et al. De novo design of a fluorescence-activating β-barrel. Nature 561, 485–491 (2018).30209393 10.1038/s41586-018-0509-0
50. Klein JC Multiplex pairwise assembly of array-derived DNA oligonucleotides Nucleic Acids Res. 2016 44 e43 10.1093/nar/gkv1177 26553805
Klein, J. C. et al. Multiplex pairwise assembly of array-derived DNA oligonucleotides. Nucleic Acids Res. 44, e43 (2016).26553805 10.1093/nar/gkv1177
51. Plesa C Sidore AM Lubock NB Zhang D Kosuri S Multiplexed gene synthesis in emulsions for exploring protein functional landscapes Science 2018 359 343 347 10.1126/science.aao5167 29301959
Plesa, C., Sidore, A. M., Lubock, N. B., Zhang, D. & Kosuri, S. Multiplexed gene synthesis in emulsions for exploring protein functional landscapes. Science 359, 343–347 (2018).29301959 10.1126/science.aao5167
52. Basanta B An enumerative algorithm for de novo design of proteins with diverse pocket structures Proc. Natl Acad. Sci. USA 2020 117 22135 22145 10.1073/pnas.2005412117 32839327
Basanta, B. et al. An enumerative algorithm for de novo design of proteins with diverse pocket structures. Proc. Natl Acad. Sci. USA 117, 22135–22145 (2020).32839327 10.1073/pnas.2005412117
53. Koradi R Billeter M Wuthrich K MOLMOL: a program for display and analysis of macromolecular structures J. Mol. Graph 1996 14 51 55 10.1016/0263-7855(96)00009-4 8744573
Koradi, R., Billeter, M. & Wuthrich, K. MOLMOL: a program for display and analysis of macromolecular structures. J. Mol. Graph 14, 51–55 (1996).8744573 10.1016/0263-7855(96)00009-4
54. Kobayashi N A robust method for quantitative identification of ordered cores in an ensemble of biomolecular structures by non-linear multi-dimensional scaling using inter-atomic distance variance matrix J. Biomol. NMR 2014 58 61 67 10.1007/s10858-013-9805-z 24384868
Kobayashi, N. A robust method for quantitative identification of ordered cores in an ensemble of biomolecular structures by non-linear multi-dimensional scaling using inter-atomic distance variance matrix. J. Biomol. NMR 58, 61–67 (2014).24384868 10.1007/s10858-013-9805-z
55. Krissinel E Henrick K Secondary-structure matching (SSM), a new tool for fast protein structure alignment in three dimensions Acta Crystallogr D 2004 60 2256 2268 10.1107/S0907444904026460 15572779
Krissinel, E. & Henrick, K. Secondary-structure matching (SSM), a new tool for fast protein structure alignment in three dimensions. Acta Crystallogr D 60, 2256–2268 (2004).15572779 10.1107/S0907444904026460
56. Minami S Sawada K Chikenji G MICAN: a protein structure alignment algorithm that can handle multiple-chains, inverse alignments, C α only models, alternative alignments, and non-sequential alignments BMC Bioinf. 2013 14 24 10.1186/1471-2105-14-24
Minami, S., Sawada, K. & Chikenji, G. MICAN: a protein structure alignment algorithm that can handle multiple-chains, inverse alignments, C α only models, alternative alignments, and non-sequential alignments. BMC Bioinf. 14, 24 (2013).10.1186/1471-2105-14-24
57. Kabsch W Sander C Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features Biopolymers 1983 22 2577 2637 10.1002/bip.360221211 6667333
Kabsch, W. & Sander, C. Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 22, 2577–2637 (1983).6667333 10.1002/bip.360221211
58. Orengo CA CATH–a hierarchic classification of protein domain structures Structure 1997 5 1093 1108 10.1016/S0969-2126(97)00260-8 9309224
Orengo, C. A. et al. CATH–a hierarchic classification of protein domain structures. Structure 5, 1093–1108 (1997).9309224 10.1016/S0969-2126(97)00260-8
59. Wang, G. & Dunbrack, R. L. Jr. PISCES: a protein sequence culling server. Bioinformatics 19, 1589–1591 (2003).
60. Jansson M High-level production of uniformly N-15- and C-13-enriched fusion proteins in Escherichia coli J. Biomol. NMR 1996 7 131 141 10.1007/BF00203823 8616269
Jansson, M. et al. High-level production of uniformly N-15- and C-13-enriched fusion proteins in Escherichia coli. J. Biomol. NMR 7, 131–141 (1996).8616269 10.1007/BF00203823
61. Santoro MM Bolen DW Unfolding free energy changes determined by the linear extrapolation method. 1. Unfolding of phenylmethanesulfonyl α-chymotrypsin using different denaturants Biochemistry 1988 27 8063 8068 10.1021/bi00421a014 3233195
Santoro, M. M. & Bolen, D. W. Unfolding free energy changes determined by the linear extrapolation method. 1. Unfolding of phenylmethanesulfonyl α-chymotrypsin using different denaturants. Biochemistry 27, 8063–8068 (1988).3233195 10.1021/bi00421a014
62. Hassanieh H Mayzel M Shi L Katabi D Orekhov VY Fast multi-dimensional NMR acquisition and processing using the sparse FFT J. Biomol. NMR 2015 63 9 19 10.1007/s10858-015-9952-5 26123316
Hassanieh, H., Mayzel, M., Shi, L., Katabi, D. & Orekhov, V. Y. Fast multi-dimensional NMR acquisition and processing using the sparse FFT. J. Biomol. NMR 63, 9–19 (2015).26123316 10.1007/s10858-015-9952-5
63. Schmidt E Guntert P A new algorithm for reliable and general NMR resonance assignment J. Am. Chem. Soc. 2012 134 12817 12829 10.1021/ja305091n 22794163
Schmidt, E. & Guntert, P. A new algorithm for reliable and general NMR resonance assignment. J. Am. Chem. Soc. 134, 12817–12829 (2012).22794163 10.1021/ja305091n
64. Shen Y Delaglio F Cornilescu G Bax A TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts J. Biomol. NMR 2009 44 213 223 10.1007/s10858-009-9333-z 19548092
Shen, Y., Delaglio, F., Cornilescu, G. & Bax, A. TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts. J. Biomol. NMR 44, 213–223 (2009).19548092 10.1007/s10858-009-9333-z
65. Guntert P Buchner L Combined automated NOE assignment and structure calculation with CYANA J. Biomol. NMR 2015 62 453 471 10.1007/s10858-015-9924-9 25801209
Guntert, P. & Buchner, L. Combined automated NOE assignment and structure calculation with CYANA. J. Biomol. NMR 62, 453–471 (2015).25801209 10.1007/s10858-015-9924-9
66. Zweckstetter M Bax A Prediction of sterically induced alignment in a dilute liquid crystalline phase: aid to protein structure determination by NMR JACS 2000 122 3791 3792 10.1021/ja0000908
Zweckstetter, M. & Bax, A. Prediction of sterically induced alignment in a dilute liquid crystalline phase: aid to protein structure determination by NMR. JACS 122, 3791–3792 (2000).10.1021/ja0000908
67. Farrow NA Backbone dynamics of a free and phosphopeptide-complexed Src homology 2 domain studied by 15 N NMR relaxation Biochemistry 1994 33 5984 6003 10.1021/bi00185a040 7514039
Farrow, N. A. et al. Backbone dynamics of a free and phosphopeptide-complexed Src homology 2 domain studied by 15 N NMR relaxation. Biochemistry 33, 5984–6003 (1994).7514039 10.1021/bi00185a040
68. Hwang TL Mori S Shaka AJ vanZijl PCM Application of phase-modulated CLEAN chemical EXchange spectroscopy (CLEANEX-PM) to detect water–protein proton exchange and intermolecular NOEs JACS 1997 119 6203 6204 10.1021/ja970160j
Hwang, T. L., Mori, S., Shaka, A. J. & vanZijl, P. C. M. Application of phase-modulated CLEAN chemical EXchange spectroscopy (CLEANEX-PM) to detect water–protein proton exchange and intermolecular NOEs. JACS 119, 6203–6204 (1997).10.1021/ja970160j
69. Hwang TL van Zijl PC Mori S Accurate quantitation of water-amide proton exchange rates using the phase-modulated CLEAN chemical EXchange (CLEANEX-PM) approach with a Fast-HSQC (FHSQC) detection scheme J. Biomol. NMR 1998 11 221 226 10.1023/A:1008276004875 9679296
Hwang, T. L., van Zijl, P. C. & Mori, S. Accurate quantitation of water-amide proton exchange rates using the phase-modulated CLEAN chemical EXchange (CLEANEX-PM) approach with a Fast-HSQC (FHSQC) detection scheme. J. Biomol. NMR 11, 221–226 (1998).9679296 10.1023/A:1008276004875
70. Kabsch W Xds Acta Crystallogr. D 2010 66 125 132 10.1107/S0907444909047337 20124692
Kabsch, W. Xds. Acta Crystallogr. D 66, 125–132 (2010).20124692 10.1107/S0907444909047337
71. Vagin A Teplyakov A Molecular replacement with MOLREP Acta Crystallogr. D 2010 66 22 25 10.1107/S0907444909042589 20057045
Vagin, A. & Teplyakov, A. Molecular replacement with MOLREP. Acta Crystallogr. D 66, 22–25 (2010).20057045 10.1107/S0907444909042589
72. Emsley P Cowtan K Coot: model-building tools for molecular graphics Acta Crystallogr. D 2004 60 2126 2132 10.1107/S0907444904019158 15572765
Emsley, P. & Cowtan, K. Coot: model-building tools for molecular graphics. Acta Crystallogr. D 60, 2126–2132 (2004).15572765 10.1107/S0907444904019158
73. Adams PD PHENIX: a comprehensive Python-based system for macromolecular structure solution Acta Crystallogr. D 2010 66 213 221 10.1107/S0907444909052925 20124702
Adams, P. D. et al. PHENIX: a comprehensive Python-based system for macromolecular structure solution. Acta Crystallogr. D 66, 213–221 (2010).20124702 10.1107/S0907444909052925
74. Lovell SC Structure validation by Cα geometry: ϕ,ψ and Cβ deviation Proteins 2003 50 437 450 10.1002/prot.10286 12557186
Lovell, S. C. et al. Structure validation by Cα geometry: ϕ,ψ and Cβ deviation. Proteins 50, 437–450 (2003).12557186 10.1002/prot.10286
