Articles
https://doi.org/10.1038/s41594-018-0141-6

De novo design of a non-local β-sheet protein withhigh stability and accuracy
Enrique Marcos 1,2,3,10*, Tamuka M. Chidyausiku1,2,10, Andrew C. McShan4, Thomas Evangelidis5,
Santrupti Nerli4,6, Lauren Carter1,2, Lucas G. Nivón1,2,7, Audrey Davis1,2,8, Gustav Oberdorfer 1,2,9,Konstantinos Tripsianes 5, Nikolaos G. Sgourakis4 and David Baker 1,2*β​-sheet proteins carry out critical functions in biology, and hence are attractive scaffolds for computational protein design.
Despite this potential, de novo design of all-β​-sheet proteins from first principles lags far behind the design of all-α​or mixed-α​β​domains owing to their non-local nature and the tendency of exposed β​-strand edges to aggregate. Through study of loops connecting unpaired β​-strands (β​-arches), we have identified a series of structural relationships between loop geometry, side chain
directionality and β​-strand length that arise from hydrogen bonding and packing constraints on regular β​-sheet structures. We
use these rules to de novo design jellyroll structures with double-stranded β​-helices formed by eight antiparallel β​-strands. The
nuclear magnetic resonance structure of a hyperthermostable design closely matched the computational model, demonstrating accurate control over the β​-sheet structure and loop geometry. Our results open the door to the design of a broad range of
non-local β​-sheet protein structures.

β-​ sheet protein domains are ubiquitous in nature, carrying out awide range of functions: transporting hydrophobic molecules,
recognition and enzymatic processing of carbohydrates, andscaffolding of virus capsids and antibodies, among others. Althoughβ​-sheet protein scaffolds are well suited for incorporating new functions, their design from first principles remains an outstanding
challenge. Recent progress in de novo protein design has enabled
the accurate design of many hyperstable and structurally diverse
proteins, but so far, other than short β​-sheet peptides1–3, all exhibit
either all-α​or mixed-α​β​ folds4. The design of these last has been
considerably facilitated by the derivation of a set of rules describing constraints on the backbone geometry of the loops connecting
secondary structure elements5, but all-β​proteins contain additionalfeatures that are less well understood. All-β​-sheet structures are
particularly challenging to design from scratch6 because a larger
fraction of the interactions are non-local (that is, between residues
distant along the linear sequence), leading to slower folding rates7,
and because β​-strands, particularly at the edges of β​-sheets, canaggregate into amyloid-like structures. Hence, few β​-sheet protein
design studies have sought to generate new backbone structures8,9
and, except for a recent β​-barrel structure with primarily local strand
pairings10, those designs confirmed by high-resolution structure
determination have relied heavily on sequence information11,12 andbackbone structures13,14 from naturally occurring β​-sheet proteins.
So far, the de novo design of β​-sheet loop connections has been
limited to β​-hairpins (two antiparallel β​-strands interacting via
backbone hydrogen bonding and connected through a loop), whichis the most local strand pairing possible and, in principle, the fastest
to fold. However, these structures lack a critical feature of non-local
globular all-β​structures: loops connecting β​-strands not paired toeach other, also known as β​-arches15. These loops connect distinctβ​-sheets and pair β​-strands with larger sequence separation, andthey are essential for enabling the protein fold complexity observedin antibodies, β​-solenoids, jellyrolls and Greek key-containing
structures generally. Here we set out to identify the general principles for designing non-local β​-sheet structures.

Results

Constraints on β-arch geometry. We undertook investigation of
the constraints on the backbone geometry of β​-strands and connecting loops that arise from hydrogen bonding and the requirement for a compact hydrophobic core. We studied side chain
directionality patterns of the two β​-strand residues adjacent toβ​-arch loops (Fig. 1a, left) in naturally occurring protein structures,
defining the side chain orientation of the β​-strand residue preceding
the loop as ‘concave’ (represented by ↓​) if its Cα​Cβ​vector is parallelto the vector d from the first to the second β​-strand, and ‘convex’(represented by ↑​) if the Cα​Cβ​vector is antiparallel to d. For the
residue following the loop, the side chain pattern is described in thesame way, but instead using the vector from the second to the firstβ​-strand (–d) as a reference (Fig. 1a). This results in four possible
β​-arch loop side chain orientation patterns: ↑​↑​, ↑​↓​, ↓​↑​ and ↓​↓​. We
analyzed the side chain patterns and the local backbone geometry(as described with ABEGO torsion bins16) of 5,061 β​-arch loops
from a non-redundant database of natural protein structures (torsion bins A and B are the α​-helix and extended regions; G and E
regions are the positive φ​angle equivalents of A and B; and O is thecis-peptide bond conformation; Supplementary Fig. 1). We foundthat all four side chain orientation patterns frequently occur, and,in contrast to other types of loop connections (that is, α​β​, β​α​ and

Department of Biochemistry, University of Washington, Seattle, WA, USA. 2Institute for Protein Design, University of Washington, Seattle, WA, USA.
Institute for Research in Biomedicine (IRB Barcelona), Barcelona Institute of Science and Technology, Barcelona, Spain. 4Department of Chemistry andBiochemistry, University of California, Santa Cruz, Santa Cruz, CA, USA. 5CEITEC—Central European Institute of Technology, Masaryk University, Brno,
Czech Republic. 6Department of Computer Science, University of California, Santa Cruz, Santa Cruz, CA, USA. 7Present address: Cyrus Biotechnology,
Seattle, WA, USA. 8Present address: Amazon, Seattle, WA, USA. 9Present address: Institute of Biochemistry, Graz University of Technology, Graz, Austria.
10
These authors contributed equally: Enrique Marcos, Tamuka M. Chidyausiku. *e-mail: emarcos82@gmail.com; dabaker@uw.edu
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a

Cα(N)

Cα(C)

d

Cβ(N)

Cβ(C)

β-archβ-hairpin

1

ABB
ABABB
BBG
AB
BBGBB
BB
BG
BBABB
BBGB
A
BAAB
BABB
AAA
G
EB
BGBB
BGB
GB
BBBGB
AAB

CαCβ(N)∙ d>0

CαCβ(N)∙ d<0c

CαCβ(C)∙ –d < 0

400
350
300

Frequency

Loop typesb

CαCβ(C)∙ –d > 0β-arch pattern

250

AB
BAAB

200

A

150
AAB
BBBGB
GB

100
50

BGB

0
0

B

G

ABABB

G
EB

BBG
BBGB

AAA

ABB

BABB

A

B

BBGBB

B

B

B

β-arch patterns
Antiparallel β-arcade
β-arch (2)1β-arch (2) patterns

d

ABABB
BBG

0
β-arch (1)β-arch (1) patterns

Fig. 1 | Constraints on β-arch geometry. a, Side chain directionality in the β​-arch. Comparison between β​-hairpin and β​-arch (left); the Cα​Cβ​ and d vectors
used to define the orientation of the two adjacent side chains are indicated. The four possible side chain directionality patterns are on the right. b, Turntype dependence of β​-arch side chain patterns. Loops on the y axis are described by their ABEGO torsion bins (Supplementary Fig. 1). Most of the loops
adopt only one of the four possible side chain patterns. c, Frequency of the most common loops for each of the four β​-arch side chain patterns. There arestrong preferences: for example, BBGB is strongly associated with the ↓​↑​pattern, whereas ABB is strongly associated with the ↓​↓​pattern (bottom). Only
loops with bending <​120° (see Methods) and containing between 1 and 5 amino acids were considered in this analysis. d, β​-arcades consist of two stacked
β​-arches with in-register strand pairing (left). Because strand pairs of the β​-arcade are in register, the side chains adjacent to one β​-arch loop must havethe same orientation as the paired side chains that are adjacent to the second β​-arch loop, and therefore not all loop pairs are allowed (middle). Example
of a β​-arcade formed by two common β​-arches with compatible side chain patterns (right).

β​-hairpins)5, there was no correlation between β​-arch loop lengthand side chain pattern. Instead, each loop ABEGO type, because of
the way in which it twists and bends the polypeptide chain16, is associated with a specific flanking residue side chain pattern (Fig. 1b).
The most frequently observed turn types (between 1 and 5 aminoacids) for each side chain pattern are listed in Fig. 1c; for example,
ABB, BBGB, BABB and BGB are the most frequent loop types forthe patterns ↓​↓​, ↓​↑​, ↑​↓​ and ↑​↑​, respectively.
The next level of non-local interaction complexity in all-β​ folds
involves strand pairing (parallel or antiparallel) between two β​-arches
forming a β​-arcade (Fig. 1d), a common structural motif in naturally occurring β​-solenoids15,17. Because the β​-arch loops are stacked
in register, the side chains adjacent to one β​-arch loop are likely tohave the same orientation as the side chains adjacent to the second
β​-arch loop; analysis of naturally occurring β​-arcades confirms thatthe side chain patterns of the two β​-arch loops are indeed correlated(Fig. 1d, middle).

Jellyroll design principles. The double-stranded β​-helix can be
regarded as a long β​-hairpin wrapped around an axis perpendicular to the direction of β​-strands, with β​-helical turns formed by thepairing between β​-arcades (Fig. 2a). In the compact folded structure, two antiparallel β​-sheets pack against each other in a sandwich-like arrangement, with the first strand paired to the last, andall β​-strands are connected through β​-arch loops except for the central β​-hairpin. We aimed to design β​-helices with three β​-arcades
forming two antiparallel four-stranded β​-sheets, with the eightβ​-strands connected through six β​-arches and one β​-hairpin. The
non-local character of the structure grows from the first β​-arcade,which starts from the central β​-hairpin, to the last one, where the
N and C termini are paired.
The analysis from Fig. 1 leads to strong constraints on the construction of β​-sheet backbone structures, as the side chain directionality patterns of the β​-strands and loops are coupled in several ways.
First, the directionality patterns of the loops preceding and following
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Double-stranded β-helix

β-arcade 1β-arcade 3β-arcade 2β-sheet 190°

β-sheet 2

b

90°

c

β-sheets in registerβ-sheets out of register

L2
S2

S1

S2

S1

L1
S8

S7
Shift
S3 – S8

L7
S3

S4
L6

S5

S6

S7

β-arcade shift

Shift
S4 – S7S4

S3β-hairpin

L3

S8

L4
S6

S5

L5

d

e

S4 – S 7

S3 – S 8β-arcade shift

Fig. 2 | Double-stranded β-helix topology specification. a, The double-stranded β​-helix fold consists of two four-stranded antiparallel β​-sheets (in blueand green) with six β​-arch and one β​-hairpin connection. Pairs of β​-arches forming the three β​-arcades are highlighted (right). β​-arch loops belonging to
the same β​-arcade are displayed with the same color throughout the figure (β​-arcades 1, 2 and 3 in red, orange and magenta, respectively). b, Topology
diagram of a designed double-stranded β​-helix with all β​-strand pairs in register. The Cα​traces of the first and second β​-sheets are colored in blue andgreen, respectively. Side chain Cβ​positions oriented toward the inner and outer faces of the β​-helix are represented with up and down black arrows withrounded tips, respectively. β​-arch loops are colored as in a. c, Definition of β​-arcade register shift varied during conformational sampling. The β​-arcade
register shift (between β​-arcades 1 and 3) is determined by the register of β​-strand pairs S3/S8 and S4/S7, and the lengths of β​-strands S3, S4, S8 and S7(see Methods). In this example, β​-strand pairs S3/S8 and S4/S7 each have a two-residue register shift, resulting in an overall β​-arcade register shift of four
residues. Loops are omitted to facilitate visualization. d, Example of a design model with all β​-strand pairs in register forming a sandwich-like structure.
e, Example of a design model with register shifts between β​-arcades 1 and 3 (magenta and red) forming a barrel-like structure.

each β​-strand are coupled to the length of the strand (Fig. 2b):for example, a β​-strand with an even number of residues that ispreceded by a ↑​↑​loop must be followed by a ↓​↑​or a ↓​↓​loop, but
not a ↑​↑​ or ↑​↓​loop, owing to the alternating pleating of β​-strands.
Second, because the β​-arcades of the β​-helix have paired β​-strands
and β​-arch loops, the side chains adjacent to one β​-arch loop musthave the same orientation as the paired side chains adjacent to thesecond β​-arch loop (Fig. 1d). Owing to the antiparallel orientationof the β​-arcades, ↓​↓​ and ↑​↑​loops are compatible with loops of thesame type, but ↑​↓​loops are only compatible with ↓​↑​loops (Fig. 1d).
Third, the twist and curvature of the two β​-sheets of the β​-helix areconstrained by the hydrogen-bonding register between β​-arcades
1 and 3 (herein called β​-arcade register), and within β​-strand pairs
S3/S8 and S4/S7, as shown in Fig. 2c.
De novo design of protein structures. We constructed doublestranded β​-helix protein backbones by Monte Carlo fragment
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assembly using blueprints (representations of the target protein
topologies specifying the ordering, lengths and backbone torsion
bins of secondary structure elements and loop connections5) inconjunction with backbone hydrogen-bonding constraints specifying all pairings between β​-strands. We explored strand lengths
between 5 and 7 residues and the most commonly observed β​-archloops between 3 and 5 residues (Fig. 1c). The central β​-hairpin was
designed with two-residue loops following the β​β​ rule5. The register
shifts between pairs of β​-strands from different β​-arcades (1 and 3)
were allowed to range from 0 to 2 and the β​-arcade register shifts
between 0 and 4; strand pairs within the same β​-arcade were kept inregister. A total of 3,673 combinations were enumerated, of which
1,853 had mutually compatible strand lengths and loop types consistent with the constraints summarized in the previous paragraph.
For each of these internally consistent blueprints, we used Rosetta
to build thousands of protein backbones. The resulting ensembleof backbone structures has considerable structural diversity; thoseArticles

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with all strands in register had narrow, sandwich-like structures(Fig. 2d), while those with large register shifts had wider, barrel-likestructures (Fig. 2e).
For each generated backbone, we carried out flexible-sequence
design calculations18,19 to identify low-energy amino acid identities and side chain conformations providing close complementary
packing, side chain–backbone hydrogen bonding in β​-arch loops(to pre-organize their conformation and facilitate folding), and highsequence–structure compatibility. We favored inward-pointing
charged or polar amino acids at the four edge strands to minimize
aggregation propensity20. Loop sequences were designed with consensus profiles obtained from fragments with the same backbone
ABEGO torsion bins21. Because the very large size of the space
sampled by our design procedure limits convergence on optimal
sequence–structure pairs, we carried out a second round of calculations starting from the blueprints yielding the lowest-energy designs,
intensifying sampling at both the backbone and sequence level. For
a subset of designs, we introduced disulfide bonds between pairedβ​-strand positions with high sequence separation (for example,
between the first and last β​-strands) and optimal orientation (seeMethods): disulfide bonds distant in primary sequence decrease
the entropy of the unfolded state and therefore enhance the thermodynamic stability of the native state. To assess compatibility ofthe top-ranked designed sequences with their structures, we characterized their folding energy landscape with biased forward folding simulations21, and those with substantial near-native sampling
were subsequently assessed by Rosetta ab initio structure prediction calculations22,23. Designs with funnel-shaped energy landscapes(where the designed structure is at the global energy minimum andhas a substantial energy gap with respect to alternative conformations) were selected for experimental characterization. Ab initio
structure prediction of natural β​-sheet proteins tends to oversample
local contacts24,25 (that is, favors β​-hairpins over β​-arches), but wesucceeded in designing sequences with the β​-arches sufficiently
strongly encoded that they folded in silico to near the designed target structure.

hydrogen bonding likely favor folding to the correct topology andcontribute to stability by compensating for the loss of interactions
with water of polar groups in the side chains and backbone. These
interactions likely disfavor the competing local strand-pairing
arrangement in which the two strands form a β​-hairpin; this is avery common pathology in ab initio structure prediction25. For
the most stable dimeric design (BH_6), we introduced disulfide bonds to stabilize protein regions having contacts with large
sequence separation (for example, between the N- and C-terminal
strands), but this did not succeed in yielding stable monomers.
Addition of an α​-helix to the C terminus (one of the two extremesof the β​-helix), as a capping domain protecting the strand edges
from intermolecular pairing, also failed to yield stable monomers,
even in combination with disulfide bonds. This suggests that thesequence of the core β​-sheet must strongly encode its structure
independently of disulfide bonds or protecting domains aimed atincreasing stability.

Experimental characterization. For experimental characterization, we chose 19 designs with funnel-shaped energy landscapes
ranging between 70 and 94 amino acids (Supplementary Table 1).
BLAST searches26,27 indicated that the designed sequences had
little or no similarity with native proteins (lowest Expect (E) values ranging from 0.003 to >​10; Supplementary Table 2). Synthetic
genes encoding the designs (design names are BH_n, where BH
stands for β​-helix, n stands for the design number and the _ss suffix
is used if disulfide bonds are present) were obtained; the proteins
were expressed in Escherichia coli and purified by affinity chromatography. Sixteen of the designs expressed well and were soluble,
and two (BH_10 and BH_11) were monomeric (Supplementary
Fig. 2) by size-exclusion chromatography coupled with multiangle light scattering (SEC-MALS) (most of the non-monomericdesigns were either dimers or soluble aggregates). Both monomeric designs had far-ultraviolet circular dichroism spectra (CD) at
25 °C characteristic of β​proteins, a melting temperature (Tm) above
95 °C, and well-ordered structures according to 2D 1H-15N heteronuclear single-quantum coherence (HSQC) spectra (Fig. 3a–c
and Supplementary Fig. 3). For both designs, the number of NMR
peaks matched the number of expected amide resonances based on
the protein sequence, but the higher stability of BH_10 under theconditions of the NMR experiments made it a better candidate for
NMR structure determination.
The two monomeric designs with well-ordered structures wereamong those with better-packed cores and a larger proportion ofβ​-arch loops containing prolines and with backbone polar atoms
making hydrogen bonds (Supplementary Table 3). β​-arch loops thatare structurally preorganized with the polar groups making internal

NMR structure of a de novo–designed β-helix. We succeededin solving the structure of BH_10 by 4D NMR spectroscopy(Fig. 3d, Table 1 and Supplementary Fig. 4), using the 4D-CHAINS/
AutoNOE-Rosetta automated pipeline for resonance assignments
and structure calculation28, and found it to be in very close agreement with the computational model (Cα​r.m.s. deviation (r.m.s.d.)of 0.84 Å, averaged over 10 NMR models). The overall topology
is accurately recapitulated, including all strand pairings, register shifts and loop connections, as supported by 132 long-range
nuclear Overhauser effects (NOEs) between backbone amide andside chain protons (Supplementary Fig. 5). The designed aliphatic
and aromatic side chain packing in the protein core, as well as
salt bridge interactions across the two β​-sheet surfaces, was also
accurately reproduced; three salt bridges between the two paired
β​-arcades and one within the third β​-arcade are well supportedby the observed NOEs (Supplementary Fig. 6). The agreement inboth the backbone conformation and hydrogen-bonding interactions of the loops forming the three β​-arcades is remarkable giventhat these elements are the most flexible parts of the structure andtherefore difficult to design owing to sampling bottlenecks. Theβ​-arcades were designed with pairs of β​-arch loops that interact via
backbone-backbone hydrogen bonds (owing to the complementarity between their backbone conformations) stabilizing loop pairing
and avoiding burial of polar backbone atoms (see Supplementary
Fig. 7 for the BH_10 loop sequences and side chain patterns). For
example, β​-arcade 1 is formed by BBG and ABB loops, and the buried backbone NH group of the G position in the former makes ahydrogen bond with the buried backbone C=​O of the neighboring loop (Fig. 3e). The other two β​-arcades were designed with oneβ​-arch loop containing buried and fully hydrogen-bonded asparagines (four hydrogen bonds in total) that stabilize both loop pairing
and the local β​-arch conformation (of ABABB loops). By design, theasparagine side chain geometry was further stabilized with hydrophobic stacking interactions from the two β​-arch loops of the same
arcade. The high degree of convergence of the designed rotamer in
the NMR ensemble illustrates the high structural preorganization ofthis particular motif (Fig. 3f).
The amino acid sequence of BH_10 is unrelated to any sequencein the NCBI nr database (BLAST found one hit with insignificant
sequence similarity; E value 6.3). We searched the Protein Data
Bank (PDB) for similarities in structure (using the Dali server29
with the lowest-energy NMR model as the query structure) or
sequence (with HHpred30 for sensitive profile-based sequence
search), and identified matches similar in fold but containing additional and irregular secondary structures and longer loops. Thesematches are all homodimers with sheet-to-sheet interface packing(Supplementary Fig. 8) or domains integrated in larger structures,in sharp contrast to the BH_10 monomer.
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0

2

4

6

8

110

N(p.p.m.)

10
0
–10
–20

10 12

115
120
125
130

200 210 220 230 240 250 260

r.m.s.d. (Å)

d

c

20

15

b

–140
–160
–180
–200
–220
–240
–260
–280

Ellipticity (mdeg)

Energy (kcal mol–1)

a10

Design model

9
1

Wavelength (nm)87

H (p.p.m.)

NMR ensemble

BBG
ABABB

BBG
GG

ABABB
ABB

r.m.s.d. 0.8 Å

BBG

e

f

L1
N65
L3
L7

L5
β-arcade 1gβ-arcade 3

h

40
BH_10

35

Residue number

Contact order

25
20
15
10

60
50
Betweenβ-arcades

40
30

Withinβ-arcades

20
10

5
0
30

β-hairpin

70

30

90

150

210

270

330

390

Protein size00

10 20 30 40 50 60 70
Residue number

Fig. 3 | The NMR structure of BH_10 is nearly identical to the design model. a, Calculated BH_10 folding energy landscape. Each dot represents thelowest-energy structure obtained from ab initio folding trajectories starting from an extended chain (red dots), biased forward folding trajectories (bluedots) or local relaxation of the designed structure (green dots); the x axis is the Cα​r.m.s.d. from the designed model and the y axis is the Rosetta all-atomenergy. b, Far-ultraviolet CD spectra (blue, 25 °C; red, 95 °C; green, 25 °C after cooling). c, 1H-15N HSQC spectra obtained at 37 °C at a 1H field of 800 MHz.
d, NMR structure in comparison with the design model. Comparison of core side chain rotamers (NMR structure in gray and design in rainbow) (inset).
Topology diagram showing the ABEGO torsion bins of all loop connections (left). Atomic coordinates for the design model are in Supplementary Dataset 1.
e, Backbone hydrogen bonding of β​-arcade 1 is well preserved across the NMR ensemble. f, Side chain interactions of N65 with backbone and side chainsform a hydrogen-bonded network in β​-arcade 3 that is well recapitulated in the NMR ensemble. g, Contact order of de novo–designed protein domains
confirmed by high-resolution structure determination; all-α​ (blue), α​β​(green) and all-β​(red). The BH_10 design stands out with a contact order of 35.8
for a chain length of 78 residues. The domains are listed in Supplementary Tables 4 and 5. h, Contact map illustrating the large sequence separation of thecontacts present in the BH_10 topology.

Contact order and sequence determinants of the BH_10 fold. The
non-local character of BH_10 is of particular note: a large fractionof the contacting residues are distant along the linear sequence, withextensive strand pairing between the N- and C-terminal β​-strands.
The contact order of the structure (that is, the average separation
along the linear sequence of residues in contact in the 3D structure)
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is higher than that for any previous single-domain protein designed
de novo (Fig. 3g,h). Proteins with high contact order fold more
slowly than those with low contact order as there is a greater loss
in chain entropy for forming the first native interactions, and theytend to form long-lived non-native structures that can oligomerizeor aggregate31. We have overcome the challenges in designingArticles

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Table 1 | NMR and refinement statistics for BH_10
BH_10 (PDB 6E5C)
NMR distance and dihedral constraints
Distance constraints
Total NOE

659

Intraresidue

272

Inter-residue

387

Sequential (|i – j| =​ 1)

222

Medium range (2 ≤​ |i – j| ≤​ 4)

33

Long range (|i – j| ≥​ 5)

132

Intermolecular0

Hydrogen bonds

0

Total dihedral angle restraints

156

φ

78

ψ

78

Structure statistics
Violations (mean ±​ s.d.)0.30 ±​ 0.46

Distance constraints (Å)a
Dihedral angle constraints (°)

9.30 ±​ 2.49

Max. dihedral angle violation (°)b

47.59

Max. distance constraint violation (Å)a

1.32

b

Deviations from idealized geometry
Bond lengths (Å)

0.00 ±​ 0.00

Bond angles (°)

0.00 ±​ 0.00

Impropers (°)

0.00 ±​ 0.00

Average pairwise r.m.s.d. (Å)c
Heavy

0.61 ±​ 0.13

Backbone

0.51 ±​ 0.11

Distance constraint violations in the structural ensemble were calculated using a 7-Å universal
upper distance bound for the NOE restraints assigned by AutoNOE-Rosetta. bDihedral angle
restraints were derived from TALOS-N. The violations were calculated for the core secondary
structural regions of the ten lowest-energy models using a 15° cutoff beyond TALOS-N-predicteddihedral angles. cPairwise r.m.s.d. was calculated among ten refined models for a core secondary
structural region defined by residues 2–8, 11–18, 21–28, 32–36, 39–43, 46–53, 59–65 and 71–75.
anon-local structures by focusing on backbones lacking internalstrain and having maximal internal coherence, and programming β​-strand orientation with highly structured loops.
One of the challenges in achieving high contact order throughβ​-arches is to disfavor formation of more sequence-local β​-hairpins.
To evaluate in silico how each of our design features contributes
to favoring β​-arches over β​-hairpins, we generated folding energy
landscapes for a series of mutants of BH_10 in which loop hydrogenbonding, side chain packing of loop neighbors and loop local geometry were disrupted one at a time. For all conformations generated,
we classified all the β​-strand connections as β​-arch or β​-hairpin
depending on strand-pairing formation, and calculated the overall frequency of β​-hairpin formation for each pair of consecutiveβ​-strands. As shown in Supplementary Fig. 9, disruption of packing
within or between β​-arch loops, removal of side chain–backbonehydrogen-bonding interactions and reducing loop geometry encoding by eliminating prolines all increase sampling of competingβ​-hairpin conformations, and thus substantially decrease samplingof β​-arches and the target designed structure.

Discussion

The design of all-β​globular proteins from first principles hasremained elusive for two decades of protein design research.

We have successfully designed a double-stranded β​-helix de novo,
as confirmed by the NMR structure of the design BH_10, based ona series of rules describing the geometry of β​-arch loops and theirinteractions in more complex β​-arcades. Our work also achieves
two related milestones: the first accurate design of an all-β​ globular protein with exposed β​-sheet edges, and the most non-local
structure yet designed from scratch. Comparison of successful andfailed designs suggests that folding and stabilization of the monomeric structure (and implicitly disfavoring competing topologies
with more local strand pairings) is bolstered by loops containingside chain–backbone and backbone-backbone hydrogen bonds
together with well-packed mixed aliphatic/aromatic side chains in
the protein core, inward-pointing polar amino acids at strand edges
and salt bridges between paired strands. Previous design studies
on β​-propellers11 or parallel β​-helices12 have used naturally occurring backbone structures and consensus sequence information on
the target fold families; this approach, while powerful, sheds lesslight on the key principles underlying β​-sheet structure construction and does not allow the programming of new backbone geometries. The β​-helix fold designed here is well suited for incorporating
metal, ligand-binding and active sites, as illustrated by the broadfunctional diversity of cupin protein domains, which are the closest
naturally occurring structural analogs. With the basic design principles now understood, our de novo design strategy should enable
the construction of a wide range of β​-helix structures tailored to abroad range of target ligands.
Initial advances in protein design were from algorithms thatallowed rapid identification of a very-low-energy sequence fora given backbone structure. In recent years, progress has comefrom the realization that the requirements of burying hydrophobic residues in a core away from solvent while avoiding the burialof backbone polar groups without compensating hydrogen bonds,
together with torsional restrictions on the peptide backbone, considerably constrain overall globular protein backbone geometry,particularly for β​-sheet-containing proteins: it is much harderthan originally expected to construct new backbones that havethese properties. The de novo design of β​-sheet-containing proteins advanced considerably following the elucidation of β​-sheet
design principles for construction of backbones meeting the above
constraints while having desired geometries: for example, principles for controlling the chirality of β​-hairpins5, reducing strain inβ​-strands with glycine kinks10, and combining β​-bulges and register
shifts to curve β​-sheets21. The design rules described here are a considerable further advance as they provide control over β​-arch connections between distinct β​-sheets, and should enable the designof a broad range of β​-protein families beyond the β​-barrel andβ​-helix, with considerable medical and biotechnological potential;
for example, the immunoglobulin fold widely utilized for binding
and loop scaffolding in nature is topologically very similar to the
double-stranded β​-helices designed here, with a larger proportionof β​-hairpins over β​-arches.

Online content

Any methods, additional references, Nature Research reporting
summaries, source data, statements of data availability and associated accession codes are available at https://doi.org/10.1038/
s41594-018-0141-6.
Received: 16 July 2018; Accepted: 11 September 2018;
Published: xx xx xxxx

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Acknowledgements

We thank S. Rettie for mass spectrometry assistance and the rest of the Baker laboratory
members for discussion. We acknowledge computing resources provided by the Hyaksupercomputer system funded by the STF at the University of Washington, and Rosetta@
Home volunteers in ab initio structure prediction calculations. Work carried out at
the Baker laboratory was supported by the Howard Hughes Medical Institute, OpenPhilanthropy, and the Defense Threat Reduction Agency. E.M. was supported by a Marie
Curie International Outgoing Fellowship (FP7-PEOPLE-2011-IOF 298976). G.O. was
supported by a Marie Curie International Outgoing Fellowship (FP7-PEOPLE-2012IOF 332094). This research was financially supported by the Ministry of Education,
Youths and Sports of the Czech Republic within the CEITEC 2020 (LQ1601) project, theGrant Agency of Masaryk University (to K.T.), an R35 Outstanding Investigator Award
to N.G.S. through NIGMS (1R35GM125034-01), and the Office of the Director, NIH,
under High End Instrumentation Grant S10OD018455, which funded the 800-MHz
NMR spectrometer at UCSC. IRB Barcelona is the recipient of a Severo Ochoa
Award of Excellence from the Ministry of Economy, Industry and Competitiveness(government of Spain).

Author contributions

E.M. designed the research, carried out the loop structural analysis, set up the design
method and performed design calculations. T.M.C. carried out design calculations,protein expression, purification and CD experiments. A.C.M. collected 4D NMR data.
T.E. performed 4D-CHAINS analysis. S.N. carried out AutoNOE-Rosetta calculations.
L.C. expressed isotopically labeled proteins and performed SEC-MALS analysis. L.G.N.
designed the research and carried out design calculations. A.D. and G.O. helped inprotein expression and characterization. K.T. and N.G.S. supervised NMR structure
determination. D.B. designed and supervised the research. E.M., and D.B. prepared themanuscript with input from all authors.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/
s41594-018-0141-6.
Reprints and permissions information is available at www.nature.com/reprints.
Correspondence and requests for materials should be addressed to E.M. or D.B.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
© The Author(s), under exclusive licence to Springer Nature America, Inc. 2018

Articles
Methods

Loop analysis. Loop connections between β​-strands were collected from a nonredundant database of PDB structures obtained from the PISCES server32 withsequence identity <​30% and resolution ≤​2 Å. We discarded those loops connectingβ​-strands with hydrogen-bonded pairing (β​-hairpins), and the remaining 5,061
β​-arch loops were subsequently analyzed. The ABEGO torsion bins of eachresidue position were assigned based on the definition shown in Supplementary
Fig. 1, and the side chain directionality pattern of neighboring residues was
defined according to Fig. 1a. The secondary structure of all residue positions was
assigned with DSSP33, and the last β​-strand residue preceding and the first β​-strand
residue following the β​-arch loop were chosen as the critical neighboring residues
determining the side chain pattern of the loop. The loop bending was defined as
the angle between the loop center of mass and the two strand positions adjacentto the loop. Those loops with bending angles larger than 120º were discarded
from the analysis to correctly identify those loops producing a substantial change
in the direction of the two connected β​-strands. The loop dataset is available in
Supplementary Dataset 2.
Backbone generation. We used the Blueprint Builder mover5 of RosettaScripts34
to build protein backbones by Monte Carlo fragment assembly using nine- andthree-residue fragments compatible with the target secondary structure and torsion
bins (ABEGO), as specified in the blueprints of every target topology. We used a
polyvaline centroid representation of the protein and a scoring function accounting
for backbone hydrogen bonding, van der Waals interactions (namely to avoid stericclashes), planarity of the peptide bond (omega score term), and compactness ofstructures (radius of gyration). Thousands of independent folding trajectories were
performed and subsequently filtered. Owing to the non-local character of β​-sheet
contacts, we used distance and angle constraints to favor the correct hydrogenbonded pairing between β​-strand main chain atoms. For every target topology, we
automatically set all pairs of residues involved in β​-strand pairing to generate all
constraints for backbone building. Protein backbones were filtered based on theirmatch with the blueprint specifications (secondary structure, torsion bins andstrand pairing), and subsequently ranked based on backbone hydrogen-bonding
energy (lr_hb score term) and the total energy obtained from one round of allatom flexible-sequence design (see next section).
Flexible-sequence design. Generated protein backbones were subjected toflexible-sequence design calculations with RosettaDesign18,19 using the Rosetta
all-atom energy function Talaris201435 to favor amino acid identities and sidechain conformations with low energy and tight packing. We performed cyclesof fixed backbone design followed by backbone relaxation using the FastDesign
mover36 of RosettaScripts34. Designed sequences were filtered based on total energy,
side-chain packing (measured with RosettaHoles37, packstat and core side-chain
average degree21), side chain–backbone hydrogen bond energy, and secondary
structure prediction (match between the designed secondary structure and thatpredicted by PSPIRED38 based on the designed sequence). Amino acid identities
were restricted based on the solvent accessibility of protein positions, ensuring thathydrophobic amino acids were located in the core and polar ones in the surface.
Further restrictions were imposed to improve sequence-structure compatibility inloop regions. Sequence profiles were obtained for naturally occurring loops withthe same ABEGO string sequence, as previously21.
For those blueprints that yielded the lowest energy designs we performed asecond round with ten times more backbone samples. Backbones generated inthis second round were subjected to more exhaustive sequence design by running
multiple Generic Monte Carlo trajectories optimizing total energy and side chain
average degree simultaneously, and then applied all filters described above.
Design of disulfide bonds and helix capping domain. We used the Disulfidize
mover of RosettaScripts34 to identify pairs of residue positions able to form
disulfide bonds with a good scoring geometry. We searched for disulfide bonds
between residues distant in primary sequence and with a disulfide score <​−​1.0. We
designed a C-terminal helix capping domain (followed with a β​-strand pairing withthe first β​-strand) using the backbone-generation protocol described above but
starting from design BH_6. The structure of BH_6 was kept fixed during fragment
assembly and the C-terminal domain was generated. Then, sequence design was
performed for the C-terminal domain and those neighboring residues within 10 Å.
Sequence–structure compatibility. For assessing the local compatibility between
designed sequences and structures we picked 200 naturally occurring fragments(9- and 3-mers) with sequences similar to the design, and evaluated the structuralsimilarity (by r.m.s.d.) between the ensemble of picked fragments and the local
designed structure. Those with overall low r.m.s.d. fragments, and therefore withhigh fragment quality, were subsequently assessed by Rosetta folding simulations
using the Rosetta energy function ‘ref2015’39. First, biased forward folding
simulations21 (using the three lowest r.m.s.d. fragments and 40 folding trajectories)
were used to quickly identify those designs more likely to have funnel-shaped
energy landscapes. Those designs achieving near-native sampling (r.m.s.d. totarget structure below 1.5 Å) were then assessed by standard Rosetta ab initio
structure prediction22,23.

NaTure STrucTural & MOlecular BiOlOgy
To evaluate the amount of β​-hairpin sampling in each loop connection during
ab initio structure prediction, we first detected all strand pairings formed in eachgenerated decoy and then mapped the residues involved in those strand pairings
to the secondary structure elements of the designed structure. After secondary
structure mapping, pairings between strands consecutive in the sequence werecounted as β​-hairpins. The total count of β​-hairpins sampled in each loop over the
total number of generated decoys is a relative quantity of hairpin sampling allowed
us to compare the β​-hairpin propensity of different loops and mutants(see Supplementary Fig. 9).
Contact order. To evaluate the non-local character of protein structures wecomputed ‘contact order’ as the average sequence separation between pairsof Cα​atoms within a distance of 8 Å and with a sequence separation of threeresidues at least.
Protein expression and purification. Genes encoding the designed sequenceswere obtained from Genscript and cloned into the pET-28b+​  (with N-terminal
6×​His tag and a thrombin cleavage site) expression vectors. Plasmids weretransformed into Escherichia coli BL21 Star (DE3) competent cells, and starter
cultures were grown at 37 °C in LB medium overnight with kanamycin. Overnight
cultures were used to inoculate 500 ml LB medium supplemented with antibiotic,
and cells were grown at 37 °C and 225 r.p.m. until an optical density (OD600) of
0.5–0.7 was reached. Protein expression was induced with 1 mM IPTG at 18 °C
and, after overnight expression, cells were collected by centrifugation (at 4 °C and
4,400 r.p.m. for 10 min) and resuspended in 25 ml of lysis buffer (20 mM imidazole
and PBS). Resuspended cells were lysed in the presence of lysozyme, DNase
and protease inhibitors. Lysates were centrifuged at 4 °C and 18,000 r.p.m. for
30 min, and the supernatant was loaded onto a nickel affinity gravity column preequilibrated in lysis buffer. The column was washed with three column volumesof PBS +​ 30 mM imidazole and the purified protein was eluted with three column
volumes of PBS +​ 250 mM imidazole. The eluted protein solution was dialyzed
against PBS buffer overnight. The expression of purified proteins was assessed by
SDS–PAGE and mass spectrometry, and protein concentrations were determinedfrom the absorbance at 280 nm measured on a NanoDrop spectrophotometer(Thermo Scientific) with extinction coefficients predicted from the amino acidsequences using the ProtParam tool (https://web.expasy.org/protparam/). Proteins
were further purified by fast protein liquid chromatography size-exclusion
chromatography using a Superdex 75 10/300 GL (GE Healthcare) column.
Circular dichroism. Far-ultraviolet CD measurements were carried out with the
AVIV 420 spectrometer. Wavelength scans were measured from 260 to 195 nm at
temperatures between 25 and 95 °C, using a 1-mm path-length cuvette. Protein
samples were prepared in PBS buffer (pH 7.4) at a concentration of 0.2–0.4 mg ml–1.
Size-exclusion chromatography combined with multiple-angle light scattering.
SEC-MALS experiments were performed using a Superdex 75 10/300 GL (GEHealthcare) column combined with a miniDAWN TREOS multi-angle static lightscattering detector and an Optilab T-rEX refractometer (Wyatt Technology). Onehundred-microliter protein samples of 1–3 mg ml–1 were injected onto the column
equilibrated with PBS (pH 7.4) or TBS (pH 8.0) buffer at a flow rate of 0.5 ml min–1.
The collected data were analyzed with ASTRA software (Wyatt Technology) toestimate the molecular weight of the eluted species.
Protein expression of isotopically labeled proteins for NMR structure
determination. Plasmids were transformed using standard heat-shocktransformation into the Lemo21 expression strain of E. coli (NEB) and plated
onto a minimal M9 medium containing glucose and kanamycin to maintain tightcontrol over expression. A single colony was selected, inoculated into 50 ml of LB
containing 50 µ​g ml–1 of kanamycin and grown at 37 °C with shaking overnight.
After approximately 18 h, the 50-ml starter culture was removed and 25 ml wasused to inoculate 500 ml of Terrific Broth (TB) containing 50 µ​g ml–1 kanamycin
and mixed mineral salts40. The TB culture was grown at 37 °C with shaking at
250 r.p.m. until the OD600 reached a value of 1.0. Then, the culture was removed
and the cells were pelleted by centrifugation at 4,000 r.p.m. for 15 min. The TB
broth was removed and the pelleted cells were resuspended gently with 50 ml of
20 mM NaPO4, 150 mM NaCl, pH 7.5. The resuspended cells were transferred intominimal labeling media, containing 15N-labeled ammonium chloride at 50 mM
and 13C-labeled glucose to 0.25% (w/v), as well as trace metals, 25 mM Na2HPO4,
25 mM KH2PO4 and 5 mM Na2SO4. The culture was returned to 37 °C at 250 r.p.m.
for 1 h in order to replace unlabeled nitrogen and carbon with labeled nitrogenand carbon. After 1 h, IPTG was added to 1 mM, the temperature was reduced to
25 °C and the culture was allowed to express overnight. The following morning, theculture was removed and the cells were pelleted by centrifugation at 4,000 r.p.m. for
15 min. The cells were resuspended with 40 ml of lysis buffer (20 mM Tris, 250 mM
NaCl, 0.25% CHAPS, pH 8) and lysed with a Microfluidics M110P Microfluidizer
at 18,000 p.s.i. The lysed cells were clarified using centrifugation at 24,000g for
30 min. The labeled protein in the soluble fraction was purified using immobilized
metal affinity chromatography using standard methods (QIagen Ni-NTA resin).
The purified protein was then concentrated to 2 ml and purified by FPLCNature Structural & Molecular Biology | www.nature.com/nsmb

Articles

NaTure STrucTural & MOlecular BiOlOgy
size-exclusion chromatography using a Superdex 75 10/300 GL (GE Healthcare)column into 20 mM NaPO4, 150 mM NaCl, pH 7.5. The efficiency of labeling was
confirmed using mass spectrometry.
Heteronuclear single-quantum coherence spectra. The designed BH_10(0.81 mM) and BH_11 (0.64 mM) were exhaustively buffer exchanged into NMR
buffer (50 mM NaCl, 20 mM sodium phosphate, pH 6.5, 0.01% (v/v) NaN3, 4 mM
EDTA and 1 U Roche protease inhibitor cocktail) in 95% H2O/5% D2O. 2D 1H-15N
HSQC experiments were acquired at 37 °C with four scans, acquisition times of72 ms (15N) in the indirect dimension and recycle delay of 2 s.
Chemical shift assignment. For chemical shift assignment of BH_10, a set of two
non-uniformly sampled (NUS) 4D NMR experiments, a 4D HC(CC-TOCSY(CO))
NH and 4D 13C-15N edited HMQC-NOESY-HSQC, were acquired at 800 MHz at
37 °C as previously described28. For the 4D HC(CC-TOCSY(CO))NH experiment,
spectrum widths were set to 12,500 (acquisition dimension) ×​  2,100 (15N) ×​  8,000(13C) ×​  7,300 (1H) Hz and acquisition times in the indirect dimensions of 60 ms(15N), 8 ms (13C) and 8 ms (1H) using 16 scans and a recycle delay of 1 s. Spectra
were acquired with 2,000 hypercomplex NUS points distributed over the indirectly
detected dimensions (0.38% sparsity). For the 4D 13C-15N edited HMQC-NOESYHSQC, spectrum widths were set to 12,500 (acquisition dimension) ×​  1,000(15N) ×​  8,000 (13C) ×​  10,000 (1H) Hz, respectively, and acquisition times in theindirect dimensions of 38 ms (15N), 10 ms (13C) and 20 ms (1H) using 8 scans, a
recycle delay of 1 s and a NOESY mixing time of 120 ms. Spectra were acquiredwith 4,000 hypercomplex NUS points distributed over the indirectly detecteddimensions (0.32% sparsity). 4D NUS spectra were processed in NMRPipe41 using
SMILE reconstruction42 and analyzed using NMRFAM-SPARKY43. For every 1
H-15N HSQC peak, the corresponding planes in 4D-HCNH TOCSY and
4D-HCNH NOESY spectra were inspected and peaks were picked manually.
The 4D peak lists were used as input for the 4D-CHAINS algorithm28 to obtain
sequence-specific resonance assignments of backbone and side chain atoms
automatically. The overall assignment completeness reached 92%. No aromatic
resonances were assigned. 4D-CHAINS assignments together with the 4D-HCNH
NOESY peak list were used in AutoNOE-Rosetta for structure determination.
NOE assignment and structure determination using AutoNOE-Rosetta. To
determine the structural models of the BH_10 target protein, we used CS-Rosetta44
that provides AutoNOE-Rosetta45 and RASREC-Rosetta46 protocols. AutoNOERosetta is an iterative NOE assignment method that utilizes RASREC-Rosetta
to model protein structures de novo. These methods make use of valuable
information contained within NMR chemical shifts about secondary and tertiary
structures, and dynamics of proteins, to model targets of interest accurately44,47.
The primary aim of AutoNOE-Rosetta is to label proton atoms to the unassigned
NOESY cross-peaks by mapping their resonance frequencies to the assigned
chemical shift frequencies. The resulting assignments can be utilized to create
NOE-based distance restraints that aid the structure calculation process. The
method begins by creating an initial mapping between the assigned chemical shift
list and the unassigned NOESY cross-peak list. This mapping produces ambiguous
assignments due to possible noise in the NOESY spectra48,49. These assignments
undergo evaluation and filtering. The evaluation criteria rely on the symmetryof cross-peaks, chemical shift compatibility, intermediate structural modelcompatibility (in the subsequent stages of the protocol) and the participation of any
NOE in a network of NOEs (network anchoring)50. The cross-peaks are eliminatedif they lie along the diagonal in the NOESY spectra or their contribution tosome of the evaluation criteria (such as network anchor score) is insignificant.
The intensities of high-scoring NOE peaks are calibrated to produce distance
restraints. These restraints are used to calculate structures within the highly
parallel RASREC-Rosetta, which performs fragment assembly44 using Monte Carlo
methods and additional optimized algorithms46. This process of assigning NOEs
and calculating structures is carried out iteratively across eight distinct stages. The
final stage retains well-converged structural models alongside generated NOE
restraints used for their calculation.
The process of setting up AutoNOE-Rosetta calculations is highly automatedand accessible via a Python interface within the toolbox available at the CS-Rosetta
website (https://csrosetta.chemistry.ucsc.edu). Before setting up NOE assignmentand structure calculation runs, (1) NMR chemical shifts and target sequences areused to predict secondary structure (rigid regions) and flexible end regions fromTALOS-N51, (2) the flexible end regions are trimmed from sequence and chemical
shift files because they cause deterioration of the performance of structure
determination methods by inducing large numbers of degrees of freedom, and(3) the predicted secondary structure, together with trimmed chemical shift
files, is used to select 200 structural fragments of amino acid lengths of three andnine, for each position in the target sequence. On completion of the previous
steps, AutoNOE-Rosetta calculations are set up with target sequence, structural
fragments, chemical shifts and unassigned NOESY cross-peak lists. For the
BH_10 target protein, we obtained NMR chemical shifts from 4D-CHAINS28 andadditionally utilized amide to aliphatic (HCNH) unassigned NOESY cross-peaklists. Thereafter, we performed four rounds of AutoNOE-Rosetta calculations,where each round was supplied with a different restraint weight (standard restraint
Nature Structural & Molecular Biology | www.nature.com/nsmb

weights of 5, 10, 25 and 50 were used). All the calculation runs were evaluatedusing a function that assesses the all-atom energies39 of the structural models andtheir convergence. After selecting the best-scoring restraint weight run, the tenmodels that exhibited the lowest energy within this run were selected. Commands
to set up the calculations were used exactly as provided in the Supplementary
Methods of a previous work28. Molprobity52 was used to compute Ramachandranstatistics for the ten lowest-energy structural models (100% of residues in favoredregions of Ramachandran space, and 99% in favored regions) and deviations fromthe ideal geometry (Table 1).
Salt bridges. We used ESBRI53 to predict salt bridges in the ten lowest-energy
structural models. Out of 19 salt bridges predicted using ESBRI, AutoNOE-Rosetta
recovers four salt bridges in the form of NOE contacts on the surface of the BH_10
protein. To identify salt bridges, we examined the NOE restraints assigned by
AutoNOE-Rosetta between negatively charged glutamic acid or aspartic acid andpositively charged arginine or lysine. We further filtered the restraints based on
the upper distance bound of 4 Å in the ten lowest-energy structures. From thesefilters, we found that the salt bridges recapitulated by the NOE assignment module
between the residue pairs are (15,62), (23,78), (33,64) and (35,62).
Hydrophobic core of BH_10. Buried residues were selected from the ten lowestenergy structural models using a 10 Å2 solvent-accessible surface area threshold.
There are 18 buried residues that contribute up to 70% of the total NOEs assigned
by AutoNOE-Rosetta, and two of them are aromatic residues (F34 and F73).
While 4D-CHAINS does not assign chemical shifts of side chain groups ofaromatic residues (specifically aromatic rings), it provides respective chemical shiftassignments of backbone atoms (Cα​, Hα​, N, H) and the β​-carbon andβ​-proton (Cβ​, Hβ​) atoms. AutoNOE-Rosetta assigned a total of nine NOEs forthe aromatic residues in the hydrophobic core, and the placement of aromatic side
chains was optimized by the Rosetta packer algorithm. On close examination of the
BH_10 structures, we found that the geometry of the two aromatic side chains wasconstrained by neighboring residues with methyl groups placed based on NOEs,
supporting the accuracy of the aromatic side chain placement.
Visualization of protein structures and image rendering. Images of protein
structures were created with PyMOL54.
Reporting Summary. Further information on research design is available in the
Nature Research Reporting Summary linked to this article.
Code availability. The Rosetta macromolecular modeling suite (http://www.
rosettacommons.org/) is freely available to academic and non-commercial
users. Scripts and protocols used in this article for generating protein backbone
blueprints, performing Rosetta design calculations and analyzing protein structures
are all available on GitHub (https://github.com/emarcos/beta_sheet).

Data availability

NMR chemical shifts and NOESY cross-peak lists used to determine structures of
BH_10 have been deposited in the BMRB with accession code 30495. Coordinatesof the ten lowest-energy structures and the restraint lists have been deposited in the
wwPDB as PDB 6E5C. The design model of BH_10 is available as Supplementary
Dataset 1, and the loop dataset used to analyze the side chain patterns of naturally
occurring β​-arches is available in Supplementary Dataset 2. Other data are available
from the corresponding authors upon reasonable request.

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Statistical parameters

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Corresponding author(s): Enrique Marcos, David Baker

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Protein structures used for loop geometric analysis were obtained from a non-redundant database of natural proteins from the Protein
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Analyses on protein structures were carried out with PyRosetta and all design and folding calculations were done with Rosetta.
All NMR analyses were done as described in the methods section with the following programs: NMRPipe, NMRFAM-SPARKY, 4D-CHAINS,
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NMR chemical shifts and NOESY cross-peak lists used to determine structures of BH_10 have been deposited under BMRB ID 30495. Coordinates of ten lowestenergy structures and the restraint lists have been deposited under the PDB ID 6E5C.

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