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Toward computational design of protein crystals with improved resolution

Substantial advances have been made in the computational design of protein interfaces over the last 20 years. However, the interfaces targeted by design have typically been stable and high affinity. Here, we report the development of a generic computational design method to stabilize the weak interactions at crystallographic interfaces. Initially, we analyzed structures reported in the Protein Data Bank (PDB) to determine whether crystals with more stable interfaces result in higher resolution structures. We found that, for twenty-two variants of a single protein crystallized by a single individual, Rosetta score correlates with resolution. We next developed and tested a computational design protocol, seeking to identify point mutations that would improve resolution on a highly stable variant of staphylococcal nuclease (SNase Δ+PHS). Only one of eleven initial designs crystallized, forcing us to re-evaluate our strategy and base our designs on an ensemble of protein backbones. Using this strategy, four of the five designed proteins crystallized. Collecting diffraction data for multiple crystals per design and solving crystal structures, we found that designed crystals improved resolution modestly and in unpredictable ways, including altering crystal space group. Post-hoc, in silico analysis showed that crystal space groups could have been predicted for four of six variants (including WT), but that resolution did not correlate with interface stability, as it did in the preliminary results. Our results show that single point mutations can have significant effects on crystal resolution and space group, and that it is possible to computationally identify such mutations, suggesting a potential design strategy to generate high-resolution protein crystals from poorly diffracting ones.

Historically, rational design has been used to overcome various degrees of protein recalcitrance to 48 crystallization, from improving existing crystals to generating new ones 9 . The variety in strategies has 49 been quite broad. Some strategies can be applied when only the protein sequence is known, even before 50 crystal trays are laid; e.g., by deleting loops or regions of low sequence complexity 10 , or by identifying 51 stabilizing mutations from homologous sequences 11 , surface entropy reduction (SER) 12 , or de novo 52 crystal design 13 . Other strategies have focused on improving an existing crystal, such as through the 53 rational engineering of crystal contacts 14,15 . Of the above strategies, all but SER must be tailored to a 54 specific target protein. The necessity for protein-specific approaches is somewhat surprising 55 considering that the underlying physics of crystallization is universal. For example, Fusco et al. 56 identified two generic mechanisms underlying crystal formation in their analysis of 182 proteins in 57 1,536 crystallization conditions 16 . In principle, a reliable and general method for enhancing the 58 resolution of poorly-diffracting crystals through rational and computational design should exist. 59 Here, we report our attempts to develop resolution-enhancing computational design of protein-protein 60 interactions at crystallographic interfaces. We began by identifying physical determinants of high-61 resolution protein crystals. This led us to identify a positive correlation between resolution and crystal 62 lattice 'stability' (the Rosetta-determined score of the asymmetric unit and the unique protein-protein 63 interactions defining the crystal lattice). A Rosetta protocol was then developed to identify stabilizing 64 (resolution-enhancing) point mutations. This protocol was benchmarked in silico against rationally-65 engineered protein crystals 17 . We tested our protocol experimentally by designing, cloning, expressing, 66 purifying, and crystallizing variants of a highly stable form of staphylococcal nuclease (SNase). We 67 found that variants designed on a single, fixed backbone crystallized rarely (1/11), whereas variants 68 designed on an ensemble of backbones crystallized more readily (4/7). Comparison of the highest-69 resolution shells for collected diffraction data (determined by CC1/2) revealed only minor 70 improvements in resolution (~0.05 Å) for three of five designs that crystallized. Surprisingly, two of 71 the resolution-enhancing designs altered the crystal space group. An analysis of our efforts shows that 72 space group changes could have been predicted for three of the five designs, but that crystal lattice 73 stability does not correlate with resolution for our test protein. 74

Materials and Methods 75
All data associated with this paper are available online via Zenodo at the following DOIs: 76

Curation of Crystal Datasets 84
Three protein structure datasets were constructed on October 10 th , 2016, from the Protein Data Bank 4 85 (PDB), termed the: "PDB representative", "SNase", and "Mizutani" sets. 86 To generate the PDB representative set, we first generated three lists of PDB IDs and then took the 87 intersection of the lists. The first list ensured that we only analyzed non-redundant, reasonable-quality 88 protein structures. Using the PISCES server 18 , we generated a list of non-Cα-only X-ray structures in 89 the PDB adhering to the following criteria (culling by chain): 90 • 25% maximum sequence identity, 91 • resolution better than 3.0 Å, 92 • R-value < 0.3, and 93 • Proteins comprising more than 40, but less than 10,000 residues. 94 This list, pisces.txt, contained 10,886 PDB IDs. Next, we generated a second list to limit our analysis 95 to solely crystallographic protein-protein interactions. which was later combined with the energy of the monomer to yield the crystal energy (see Results 3.1). 140 After excluding four structures that could not be modeled with our approach and twelve structures that 141 accidentally included biological interactions in the crystal, 364 PDBs were analyzed from the PDB. 142 These PDBs are listed in: pdb-representative-rosetta.txt. 143 SNase: As above, SNase monomers were downloaded from the PDB and energy minimized using 144 Rosetta v2018.24-dev60250. Unlike above, HETATM records were retained, because the nucleotide 145 analog thymidine-3',5'-diphosphate (THP) bound by the enzyme makes important crystal contacts. 146 The ligand geometry was fixed in simulations and read from the PDB Chemical Components 147 Dictionary. Energy minimization was performed as described above. Individual crystallographic 148 interfaces were not generated and analyzed using EPPIC because SNase is known to be a monomer. 149 Crystals were modeled and crystal energies were computed as described above. similarly to modeling of the PDB and SNase crystal structures, as described above. The only exception 152 being that diphtine synthase is naturally a dimer, so during energy evaluation the two dimeric chains 153 were treated as a monomer and only crystallographic, not biological, interfaces were considered. As 154 with SNase, because the biological state is known, EPPIC was not used to generate or analyze 155 crystallographic interfaces. Crystals were modeled and crystal energies were computed as described 156 above. 157

Forward Design of Diphthine Synthase 158
To determine the computational design approach most likely to be experimentally successful, we tested 159 several strategies on diphthine synthase. Since the resolution is reported for twenty variants, we can 160 ask if a particular design strategy can predict resolution-improving variants. This approach is known as forward design. The energy-minimized structure of wild-type diphthine synthase (PDB ID: 1WNG) 162 was used as input for design. At each position mutated by Mizutani et al. (26,49,54,65,69,79,140,163 142, 146, 171, 173, 187, and 261), each amino acid except cysteine or proline was tested. We attempted 164 to accommodate the mutation by permitting varying degrees of freedom in the wild-type crystal form 165 (simulated by Rosetta Symmetry). These different design strategies ranged from only permitting 166 neighboring side chains to repack to re-docking in the crystal lattice (see Results). All energy 167 calculations were performed in the crystal form and averaged over ten repeats. 168

Computational Design of SNase 169
Design for SNase variants initially followed our most successful diphthine synthase approach: 170 introducing a point mutation at a position followed by repacking of side-chains followed by energy 171 minimization of side-chain and backbone dihedral angles. An energy-minimized structure of Δ+PHS 172 SNase (PDB ID: 3BDC) was used as input. The geometry of the THP ligand was held fixed during the 173 simulation and defined by a Rosetta params file derived from the PDB coordinates. Later, we 174 introduced an ensemble of 200 perturbed backbones generated by Rosetta Backrub 26 as it has been 175 shown that interface ΔΔG prediction is more accurate when using an ensemble of backbones rather 176 than just a single input 27 . The following steps were repeated for each member of the backbone ensemble 177 and for every designable surface position, defined as residues having a Cα-Cα distance under 8 Å 178 across any crystallographic interface. First, the position was mutated to one of eighteen amino acids 179 (cysteine and proline were excluded). Then, the crystal form was generated using Rosetta Symmetry 180 in the wild-type space group and unit cell dimensions. Finally, side-chains were repacked to 181 accommodate the mutation in the crystal form. The error in this modeling was calculated across the 182 ensemble of 200 backbones, instead of by repeating the simulation ten times. 183 immediately flash-cooled in liquid nitrogen. Crystals were stored at 77 K until data collection. 196

Data Collection and Structure Determination 197
All X-ray diffraction data were collected for single crystals at 77 K using a Rigaku FR-E SuperBright 198 rotating anode X-ray generator and a Rigaku DECTRIS PILATUS 200K pixel array detector. 199 Diffraction data were indexed, integrated, and scaled using the XDS program package 31 . Phasing, 200 modeling building and model refining were performed using PHENIX 32 . Phasing was performed by 201 molecular replacement in PHASER 33 using the search model 3BDC, with solvent-exposed or mutated 202 side chains truncated to the Cα position to avoid biasing side-chain placement at crystal contact sites. 203 This is a provisional file, not the final typeset article Side chains were rebuilt using COOT 34 : initial placement was performed using the Mutate and Autofit 204 function and followed by manual refinement. Whole-structure refinement and water placement were 205 performed using phenix.refine 35  Our primary goal in this effort was to develop a broadly applicable, Rosetta-based computational 210 method for crystal contact design, with the goal of systematically predicting single point mutations that 211 could enhance resolution. To this end, we first asked whether or not Rosetta scoring functions might 212 correlate with resolution. 213

Rosetta Score Correlates with Resolution, When Other Variables Are Controlled 214
With over 129,000 crystal structures of biological macromolecules 4 , the PDB provides a trove of data 215 that can be used to determine whether or not Rosetta score correlates with the resolution of protein 216 crystals. To ensure a fair comparison, structures must be first energy-minimized in the Rosetta scoring 217 function using the Rosetta FastRelax protocol 20,21 . As FastRelax runtime scales with protein size, 218 testing every structure in the PDB is not feasible. Furthermore, some structures are overrepresented in 219 the PDB, which might bias analysis. Instead of analyzing all structures, we selected a diverse and 220 representative subset of the PDB containing 364 structures, which had a maximum sequence identity 221 of 25%, a resolution better than 3 Å, R-values less than 0.3, and featured only crystallographic 222 interactions (fully described in Methods 2.1 & 2.2). For every structure in the set, we generated all 223 symmetry-mates within 12 Å using Rosetta Symmetry 22 and energy minimized this "crystal" form ten 224 separate times using the default FastRelax protocol, which features four cycles of minimization each 225 with progressively weaker harmonic constraints to prevent substantial deviation from the starting 226 coordinates. Separately, we energy-minimized the monomeric form of the protein, which was also the 227 asymmetric unit and the biologically-relevant unit. We approximated the energy of the crystal as " = 228 where 〈 % 〉 is the average Rosetta score of ten energy-minimized monomers and 229 ∑ 〈 + 〉 + is the average Rosetta score of interface i in the crystal form, summed over all interfaces within 230 12 Å of the asymmetric unit. Hence, " represents that energy of the minimal unit required to generate 231 the crystal. The relationship between resolution and score is shown in Figure 1A. 232 We initially found a slight anti-correlation between resolution and score for the representative PDB 233 set: higher resolution structures had lower scores. We hypothesized that this unexpected result was 234 caused by our inability to control for the many variables that affect resolution that are not captured by 235 Rosetta score (e.g., how the highest resolution-shell cutoff was decided, user handling of the crystal, 236 the content of the reservoir solution, etc.). To test this hypothesis, we analyzed two additional sets of 237 crystal structures in the same manner as the PDB representative set. The first additional set we analyzed 238 controlled for the protein as a variable. We searched for a small, globular protein, with many structures 239 in the PDB that differed only slightly from each other, but that spanned at least 1 Å in resolution. Of 240 the multiple proteins fulfilling these criteria, we selected SNase, which had 256 crystal structures. We 241 used Rosetta Symmetry and FastRelax to generate ten energy-minimized monomers and crystals, and 242 computed the energy of the crystal as described above. The SNase set did not show a strong correlation 243 between resolution and score ( Figure 1B). To further control extrinsic variables, we analyzed twenty-244 two variants of a single protein (diphthine synthase) that had been previously cloned, expressed, 245 purified, crystallized and the crystal structures solved by one scientist in a crystal engineering study by 246 Mizutani et al. 17 . Despite the variants only differing by a point mutation or two, the crystal structures 247 spanned a range of resolutions from 1.5 Å to 2.3 Å. The structures were energy minimized and the 248 crystal energies calculated in a similar fashion as for the previous two sets. The Mizutani set showed a 249 strong correlation (R 2 = 0.8) between Rosetta score and resolution ( Figure 1C). 250 251   This is a provisional file, not the final typeset article

Rosetta Can Identify Resolution-Enhancing Mutations 260
Since low score corresponded to high resolution for the Mizutani set, we next sought a fast 261 computational design strategy that could identify resolution-enhancing mutations from the wildtype 262 (WT) crystal structure. We tested six strategies on the Mizutani set in an approach known as forward 263 design. Using the energy-minimized crystal form of the wildtype protein as input, we introduced point 264 mutations one-by-one at the positions engineered by Mizutani et al. We then optimized side-chain 265 dihedral angles while keeping the backbone fixed (side-chain repacking) 37 . Following repacking, we 266 tested six design strategies with varying degrees of freedom: (1) we did nothing else before evaluating 267 the score, (2) we applied gradient-based energy minimization on side-chain dihedral angles, (3) we 268 applied gradient-based energy minimization on side-chain and backbone dihedral angles, (4) we 269 applied gradient-based energy minimization on side-chain dihedral angles and the relative 270 position/orientation of the protein and its symmetry mates, (5) we applied gradient-based energy 271 minimization on side-chain and backbone dihedral angles and the relative the relative 272 position/orientation of the protein and its symmetry mates, and (6) we sampled the relative 273 position/orientation of the protein and its symmetry mates, translating in steps of 0.05 Å and rotating 274 in steps of 0.1 degrees, followed by energy minimization as in Strategy 5 over four Monte Carlo cycles. 275 All gradient-based minimization was run until convergence was achieved, defined as a change in 276 Rosetta score of less than 0.00001 following an iteration of minimization, or for 200 iterations. Each 277 strategy was tested ten times to assess error. The forward design results for all strategies are shown in 278 Supplemental Figure 1. 279 We found Strategy 3 (minimizing on side-chain and backbone torsion angles after repacking) to be the 280 most successful. Figure 2 compares the predicted change in score between each variant and WT 281 diphthine synthase for Strategy 3. This approach successfully predicts 6 of 17 (35.3%) resolution-282 enhancing mutations identified in the paper. In addition to these six, this approach predicts 46 other 283 mutations to have lower energy than WT and thus could be potentially resolution-enhancing; however, 284 these were not experimentally characterized by Mizutani et al., so it is unclear if these predictions are 285 correct. Assuming a worst-case scenario where these uncharacterized point mutations do not enhance 286 resolution-enhancing mutations, this design approach would predict 6 resolution-enhancing mutations 287 out of 52 possibilities or 11.5%. Both success rates, 35.3% and 11.5%, compare favorably with 288 historical protein interface design success rates, which are typically under 10% 38 . 289

Rosetta Designed Crystals Do Not Significantly Improve Resolution 290
To determine whether our design approach was applicable to other proteins, we tested it on a model 291 system: Δ+PHS, a well-characterized highly stable variant of staphylococcal nuclease (SNase) 29 . We 292 identified candidate designable residues at crystallographic interfaces as those with a Cα-Cα distance 293 under 8 Å to neighboring symmetry mates. At each position, we introduced a point mutation followed 294 by side-chain repacking and energy minimization of side-chain and backbone dihedral angles. We 295 selected eleven designs for experimental characterization. However, of the eleven, only a single variant 296 crystallized in conditions where the WT protein normally crystallizes. Since we wanted our approach 297 to yield crystals without having to reoptimize crystal growth conditions, we sought to improve the 298 crystallization rate of our designs. To this end, we introduced a step to generate backbone diversity 299 before design. We drew inspiration from recent work showing that interfacial ΔΔG calculations are 300 more accurate when the change in energy is computed across an ensemble of models 27 . Since backbone 301 diversity was introduced beforehand, we were more conservative in our approach and we followed the 302 introduction of point mutations with only side-chain repacking (Strategy 1 from 3.1). From the second 303 round of design we identified seven possible variants, but since two overlapped with those found in the 304 first round, only the five new variants were characterized experimentally. With this design approach, 305 four of the seven variants yielded crystals in WT-like conditions; thus, designing on an ensemble of 306 structures had improved our crystallization rate from 9% to 57%. 307 308  and nucleation significantly, yielding larger crystals across more conditions than the other variants. We 320 then indexed, integrated, and scaled the data sets using XDS. The most likely space group was 321 determined by POINTLESS 39 . For all variants except K64R and K127L, it was the WT space group 322 (P21). We found that K64R crystallized in P212121 and K127L crystallized in P41, the third and second 323 most common space groups for SNase crystals, respectively. In total, we were able to process the data 324 for 37 of the 43 crystal diffraction patterns collected, with the remaining six datasets failing to index 325 due to issues such as ice rings or poor spot profiles. We report a summary of the collected and processed 326 diffraction data in Supplemental Table 1. 327 Following processing with XDS, we identified the highest resolution shell as the shell with the highest 328 resolution still having a significant CC1/2 (t < 0.01). We used CC1/2, or the correlation between 329 intensities when the data is split in half, to select the highest resolution shell because it provides a 330 rigorous statistical cutoff 40 . To compute significance we calculated a t-value, = .
/0) (01 2 , where r is 331 the CC1/2 value and n is the number of reflection pairs (the degrees of freedom), and compared it to 332 Student's t-distribution with the same degrees of freedom 41 . We found that, on average, three of the 333 five designs (60%: Q123D, K64R, and K127L) achieved a higher resolution than WT (Figure 3). 334

Rosetta-Designed Crystals Do Not Behave as Predicted 344
Intrigued by the unexpectedly small variation in resolution between designed variants, we solved the 345 crystal structures of several candidates to ask whether there was an underlying structural basis for the 346 small changes in resolution. We discuss the variants below, grouped by their observed effects on SNase 347 crystallization, and provide a general summary of observations across all variants. 348

Q123D and Q123E 349
In silico, the Q123D design strengthened the crystallographic interface by introducing an electrostatic 350 interaction between D123 in the asymmetric unit and K71 in a neighboring symmetry mate. Upon 351 solving the crystal structure, we found minor changes (less than 0.5 Å RMSD) in the backbone 352 conformation (Supplemental Figure 2). Analysis of the site around the Q123D mutation revealed that 353 residue D123 interacted with residue K84 of a neighboring symmetry mate (with a 3.1 Å distance 354 between the lysine nitrogen and aspartic acid oxygen), instead of K71 (Figure 4). This result is in 355 contrast to the WT structure, where residue K71 interacts with Q123 (3 Å distance between the 356 corresponding oxygen and nitrogen atoms) and K84 solely contacts a phosphate oxygen of THP 357 (Supplemental Figure 3). 358 Although we were unable to solve the crystal structure for the Q123E variant due to twinning and the 359 presence of ice, we expect a similar interaction to be occurring. This supposition is supported by the 360 observed average resolutions, which are quite similar to the WT protein: Q123D slightly improves (by 361 0.01 Å) resolution whereas Q123E slightly worsens resolution (by 0.02 Å). 362

K133M 373
Like Q123E and Q123D, the K133M variant did not significantly alter resolution with respect to the 374 WT protein and resulted in minimal backbone movements (0.17 Å RMSD, Supplemental Figure 2). 375 The design was favored in silico because it replaced an unfavorable electrostatic interaction between 376 K133 and H8 with a van der Waals contact between M133 and H8, while also slightly reducing the 377 entropic cost of forming that crystal contact ( Figure 5). However, the K133M crystal structure revealed 378 that, although the interface had compacted slightly, the side chains were too distant to interact. 379 Compared to the design, the minimum distance between M133 and H8 in the crystal grew from 3.6 Å 380 to 5.3 Å. This lack of interacting side chains likely explains the minimal effect of this mutation on 381 crystal resolution. 382 This is a provisional file, not the final typeset article

K127L and K64R 388
The variant K127L produced the highest-resolution crystals in our study, though it did so in a manner 389 not predicted by design: it altered the crystal space group. The WT protein crystallizes in the space 390 group P21, and, in this crystal form, K127 forms a salt bridge with the THP molecule bound in the 391 neighboring SNase active site ( Figure 6). When this lysine is mutated to leucine, the salt-bridge 392 interaction cannot form, destabilizing the P21 crystal form. Instead, the designed protein crystallizes in 393 P41, a higher symmetry space group, where L127 packs against a neighboring loop by forming 394 backbone interactions with K28 and G29. In this space group, K71 replaces K127 as the interacting 395 partner of the THP in the crystal form, suggesting that the interaction of the substrate phosphate groups 396 with a positively-charged side chain might be useful for SNase crystallization. 397 In addition to the space group change, the K127L variant had the largest backbone motions of all 406 variants. The motions are in the loop region (residues 114-118) that precedes the α-helix containing 407 L127. They occur when residue K116 shifts from contacting the neighboring molecule in the crystal 408 to make contacts to the bound nucleotide analog instead. 409 The other substitution that improved resolution in our study, albeit with a sample size of one, was 410 K64R. Although we were unable to solve a crystal structure due to problems with twinning and the 411 presence of ice, we were able to determine from the diffraction data that K64R (like K127L) resulted 412 in a change in space group, going from P21 to the higher symmetry space group P212121. To gain 413 structural insight as to why this variant and space group might lead to higher resolution, we aligned 414 our K64R model to a different SNase structure crystallized in the same space group (PDB ID: 5KEE) 415 and applied the symmetry operations necessary to generate the neighboring symmetry mates, using 416 unit cell dimensions from the diffraction data. We then used Rosetta's FastRelax protocol to alleviate 417 any clashes that might have been introduced. We observed two possible hydrogen bonding interactions 418 for R64 that might account for this change in space group: one with the carboxylic acid of E135 of a 419 neighboring symmetry mate and another with the backbone carbonyl of the oxygen of the same residue 420 (Figure 7). 421

Retrospectively: Rosetta Score Recovers Space Group Changes, But Not Resolution 422
Since we did not include the possibility of space group changes in our design protocol, yet we observed 423 changes for two variants, we retrospectively asked whether Rosetta could recover the correct space 424 group (Figure 8) by modeling and scoring each variant and the WT in each of the three most popular 425 SNase space groups. For four out of six crystals (including WT), we found that Rosetta could correctly 426 predict the space groups. Rosetta failed to predict the correct space group changes for the K127L 427 variant, yielding P212121 as the lowest scoring space group (when the actual space group was P41), and 428 for the K64R substitution, yielding P21 as the lowest scoring space group (the actual space group was 429 P212121). 430 This is a provisional file, not the final typeset article   Figure 4). Thus, the introduced R64-K78' interaction in the design (green) was intended to be 436 stabilizing.

437
Finally, we asked whether the Rosetta score of the solved crystal structures correlated with the 438 resolution, as we found to be the case for the engineered variants studied by Mizutani et al. 17 (Results  439 3.1). We analyzed the crystal structures of our designs as previously described. Surprisingly, we found 440 an anti-correlation between score and resolution (Figure 9), although it should be noted that our 441 resolution range only spans ~0.1 Å, whereas ~0.8 Å was spanned by the crystal structures from 442 Mizutani et al. (Figure 1). 443   We attempted to develop and validate a generic computational method for protein crystal contact 458 design to engineer crystals that yield high-resolution structural information. Probing the PDB, we 459 found that Rosetta score correlated with crystal resolution when accounting for common external 460 variables relevant to crystallization such as the decision making to select the highest resolution shell, 461 user handling of the crystal, or crystallization conditions. Using data from an existing study in crystal 462 engineering 17 , we developed a design approach that recapitulated resolution-enhancing mutations at a 463 rate of at least 11.5% (and at best 35.3%). We tested our design approach on a model SNase system, 464 Δ+PHS, and found that our initial approach only resulted in one crystallizable variant out of ten, so we 465 improved our approach by designing on an ensemble of backbones to increase this ratio to four in five. 466 Finally, we solved the crystal structures of several of our designs but unfortunately observed little to 467 no improvement in resolution. Post-facto analysis revealed that (1) improvements in resolution came 468 primarily from changes in space group and (2) Rosetta score of designs was not predictive of crystal 469 resolution. 470

Point Mutations Primarily Affected Side-Chain Interactions and Space Groups 471
In general, when all variants were compared to both the WT and predicted design structures, the 472 changes in the fold of SNase were undetectable, but there were detectable changes in side-chain 473 interactions at the crystallographic interfaces. The greatest difference we observed was that two variants crystallized in higher symmetry space groups 484 than WT (P21): K64R crystallized in the space group P212121, and K127L crystallized in the space 485 group P41. Several observed improvements in resolution were seen for this additional symmetry, such 486 as a consistently higher I/σ value (a measure of the information content) over all resolution shells 487 (Supplemental Figure 4). The space group change for K127L was driven by breaking the WT lysine-488 THP contact across one crystallographic interface ( Figure 5), whereas the driver for the space group 489 change of K64R was not definitively determined. The K64R substitution was desired because, in the 490 WT space group (Figure 7), it introduced a putative electrostatic interaction between a terminal amino 491 group of R64 and the carbonyl oxygen of K78 of a symmetry mate,. The mutation did not disrupt any 492 contacts, as K64 was not resolved in the electron density of the WT crystal structure (Supplemental 493 Figure 5); however, this alteration still resulted in a change in space group. Since we were unable to 494 solve a crystal structure for this variant, we resorted to modeling K64R in the new space group. Our 495 models hinted that this space group might be preferred over the WT because R64 can potentially form 496 a hydrogen bond with E135 via both side-chain-side-chain and side-chain-backbone interactions 497 (Figure 7). 498

The Relationship Between Score and Resolution 499
Our initial hypothesis was that crystal interface stability, as captured by Rosetta score, would correlate 500 with crystal resolution. We had two reasons that led us to this hypothesis. First, crystal growth occurs 501 when the rate of protein incorporation into a crystal lattice (attachment) is greater than the rate of 502 protein detachment from the crystal. The rate of attachment depends on the flux of molecules to the 503 growing crystal step, the possible interaction area of the step, and the probability of attachment. The 504 rate of detachment depends on the frequency of detachment events and the detachment probability. 505 Point mutations can affect both the detachment and attachment probabilities. The detachment 506 probability in particular is related to interface stability by the Boltzmann factor: 4 = exp (− + / ) 42 . 507 All other factors being equal, more stable native crystal interfaces will result in lower probabilities of 508 detachment and thus may improve crystal morphology. Second, as interface stability is conferred by 509 favorable molecular interactions and tighter side-chain packing, we reasoned that more stable 510 interfaces would be less dynamic and less mobile, improving the homogeneity of uniform protein 511 positioning within the crystal. Hence, we anticipated that more stable interfaces would result in larger 512 crystals with less mosaicity, which in turn would improve crystal resolution. 513 An initial analysis comparing Rosetta scoring and crystal resolution for a subset of the PDB revealed 514 no relationship between the two. We reasoned that our analysis was obfuscated by many factors that 515 affected resolution, but could not be captured by score alone (e.g. the protein or X-ray source intensity 516 or detector resolution, user handling, etc.). First, we controlled for just the protein by analyzing only 517 structures of SNase in the PDB. We found that controlling for the protein alone was insufficient -518 there was no trend between resolution and score for this set. However, when we controlled for more 519 factors by analyzing the crystal structures of twenty-two variants of a single protein, with all data 520 gathered by the same individual, using the same process, and with the same equipment, we found, as 521 hypothesized, that lower Rosetta scores correlated with higher resolution (Figure 1). Yet, when we 522 repeated the same analysis for crystals of our model protein (again with all experiments conducted  523 identically by one individual), we found an anti-correlation. 524 Why is there an inconsistent behavior between score and resolution? From the PDB, it is apparent that 525 higher resolution crystal structures tend to have better protein geometry, i.e. fewer improbable side-526 chain rotamers, fewer outliers for bond lengths, fewer outliers for bond angles, or fewer atomic/steric 527 clashes 43 . It is possible that because Rosetta represents proteins in internal coordinate space (Φ/Ψ), 528 with fixed bond lengths and angles, it cannot rescue inherently poor geometry and thus better geometry 529 contributes to a lower Rosetta score, even after energy minimization. Then, it is possible that the 530 correlation observed between Rosetta score and resolution for the Mizutani set was a manifestation of 531 the protein geometry improvements that come with higher resolution data, while some external factor, 532 unaccounted for by Rosetta score, affected resolution. If resolution does indeed drive score, then for 533 crystals in a narrow range of resolutions, we would not expect to observe a correlation between Rosetta 534 score and resolution, as was the case for the Δ+PHS variants. In fact, MolProbity 44 , a structure 535 validation software, only compares structures within 0.25 Å bins to account for the improvements in 536 protein geometry offered by higher resolution data. 537

Backrub Improves Design 538
Over the course of this study, we attempted both fixed-backbone design on the WT backbone and 539 fixed-backbone design on a perturbed ensemble of 200 models generated from the WT backbone. To 540 generate the perturbed ensemble, we used an approach known as Backrub 26 that slightly alters the 541 direction of the Cα-Cβ vector to expose the side chain to a new environment while minimally altering 542 the backbone. We found that variants designed using an ensemble of backbones crystallized at a higher 543 This is a provisional file, not the final typeset article rate (4/7) than variants design using the single WT backbone (1/11). We reason that this is because 544 Backrub-generated ensembles capture local backbone fluctuations, whereas fixed-backbone models do 545 not, resulting in a better estimate of point mutation effects, including to interface energy 27 . In general, 546 it is known that proteins are dynamic and are readily capable of incorporating point mutations, 547 especially at protein surface positions 45 , so a fixed-backbone approximation is not sufficient. Hence, 548 we observed an increase in crystallization success rate when we designed on an ensemble of backbones 549 and selected designs scoring well across multiple backbones for experimental characterization. 550

What We Couldn't Predict and Why 551
Of the five designed proteins, only K133M resulted in a crystal structure similar to the design. The 552 designs Q123D and Q123E resulted in the introduction of E/D-K electrostatic interactions, but with a 553 neighboring symmetry mate instead of the one targeted by the design. For these designs, it is not clear 554 how to improve the design algorithm. 555 For the K127L and K64R designs, we observed unpredictable changes in space group. In retrospect, 556 the K127L design should not have scored well in Rosetta, as the K127 amino group clearly makes 557 electrostatic contacts with the phosphate groups of the THP molecule bound by the neighboring 558 symmetry mate. Despite breaking the lysine-THP interaction, the Rosetta score was lower for the 559 variant than the WT protein (in the WT space group), indicating that Rosetta does not correctly weigh 560 the strength of this electrostatic interaction. One possible solution to overcome this issue in the future 561 would be to bias the Rosetta score by the WT electron density, such that eliminating a clearly present 562 interaction is strongly penalized whereas designing residues that are not well-resolved is favored. 563 One possible reason for the failure to improve resolution is that Rosetta is not yet finely tuned for the 564 types of atomic interactions we tried to create. Rosetta was first developed to study protein folding in 565 the context of small, globular domains, before being applied to the inverse challenge, design 46 . Over 566 the years Rosetta has performed best when redesigning protein cores and tightly-packed interfaces 47-567 50 . Our objective here is one of the first attempts to design a loosely-packed interface with a significant 568 amount of water involved. Future work to improve design of solvated interfaces might include 569 explicitly analyzing water interactions the interface either by flooding, as was recently successfully 570 used to dock interfacial waters 51 , or the recently developed HBNet method in Rosetta, which has been 571 used to design hydrogen bonding networks de novo 52 . Multi-state design 53 might also be necessary to 572 prevent undesired changes in space group. 573

Were Our Model Protein Crystals Already Optimal? 574
Initial analyses showed that diffraction patterns collected for the WT control in this study had an 575 average high-resolution limit of 1.77 Å (Figure 3), which agrees with the resolution (1.8 Å) of the 576 PDB-deposited crystal structure of Δ+PHS (3BDC). This value falls firmly in the middle of the 577 distribution of all SNase crystal resolutions (Figure 1) One possible explanation for our designs' minimal improvement in resolution is that our choice in 586 model protein, Δ+PHS, was already optimized for forming high-quality crystals. We selected Δ+PHS 587 as a model system for its high stability (11.8 kcal/mol) 29 , high yield (over 60 mg protein per 1 L of cell 588 culture), and crystallizability (over 300 crystal structures have been deposited in the PDB). We selected 589 for these features so that our model protein would readily incorporate point mutations and so that the 590 corresponding designs would likely express in high quantities and readily crystallize. However, these 591 features also likely pre-selected for a protein that is optimal for crystallization, one for which a majority 592 of point mutations might not be able to yield significant improvements in resolution. Future work might 593 then focus on a protein that is less engineered and may have more room for improvement. 594