General Multimodal Protein Design Enables DNA-Encoding of Chemistry

Problem

• Existing enzyme-engineering campaigns require an initial protein with measurable activity, leaving many new-to-nature chemistries without obvious biological starting points.Finding such starting proteins is largely dependent on chemical intuition and what evolution has already sampled.Source: Introduction · p. 2

Limitations

• Current computational pipelines constrain enzyme design by pre-specifying active-site geometries and by sequentially generating backbones before inverse-folding sequences, preventing joint use of sequence and structure objectives.These limitations impede discovery of reactions without known motifs or precise mechanisms and novel active-site geometries.Source: Introduction · p. 2

DISCO framework

• DISCO simultaneously designs protein sequences and 3D structures de novo around arbitrary biomolecules, using a multimodal Feynman-Kac corrector to jointly optimize sequence and structure objectives without inverse folding.The framework co-folds designs with arbitrary biomolecules and does not require pre-defined residue motifs.Source: Introduction · p. 2

Experimental catalysis

• DISCO generates diverse, evolvable carbene transferases with novel active sites whose activities surpass typical starting points for directed evolution and, in selected cases, extensively evolved variants.The system was applied experimentally to new-to-nature catalysis.Source: Introduction · p. 2

Broader protein design

• Beyond catalysis, DISCO achieves state-of-the-art in silico binder generation for diverse biomolecular targets with fine-grained property control.This result demonstrates the framework’s broader multimodal protein-design scope.Source: Introduction · p. 2

Multimodal protein generation with DISCO

• DISCO jointly denoises masked sequences and continuous atomic coordinates, using bidirectional cross-modal conditioning so sequence and structure adapt to each other during generation.Training uses unimodal diffusion losses, while inference adds sequence self-correction, temperature smoothing, and noisy guidance; approximately 90% of unconditional sequences refold within 2 Å RMSD of designed backbones.Source: Multimodal protein generation with DISCO · pp. 2, 4

Conditioning on arbitrary biomolecular contexts

• DISCO generated the highest proportion of diverse, co-designable complexes for 178 of 179 ligands and also supported multi-ligand, DNA, and RNA conditioning.Co-designability required protein-backbone and ligand-centroid RMSD < 2 Å after Chai-1 refolding; DNA- and RNA-binding designs outperformed existing models.Source: Conditioning on arbitrary biomolecular… · pp. 4, 6

Multimodal inference steering using Feynman-Kac Correctors

• FKC-MM enriched disulfide and cation-π properties, while FKC-SG improved separation between on-target and off-target complexes over best-of-N filtering.The top 2% of designable 100-amino-acid FKC-MM proteins contained six disulfide bonds, matching only the top 0.2% of comparable training proteins.Source: Multimodal inference steering using… · p. 6

DISCO designs exhibit realistic protein features with novel, complementary motifs

• DISCO produced realistic proteins with natural compositions, diverse structures, favorable geometries, native-like surface properties, and complex long-range topologies.These realistic designs also formed ligand-responsive pockets, appropriate cofactor coordination sites, sterically suitable cavities, and valid alternative ligand conformers.Source: DISCO designs exhibit realistic… · pp. 6, 8
• Over 90% of DISCO-generated binding motifs were cluster-diverse, while most co-designable motifs lacked natural AlphaFoldDB homologs and many folds lacked close Protein Data Bank homologs.Novel motifs were defined as having no match or RMSD > 3 Å in Folddisco searches for coordination spheres of up to ten residues.Source: DISCO designs exhibit realistic… · p. 8

Design strategy

• DISCO was conditioned on DFT-derived heme–carbene intermediate geometries and bonding patterns, allowing co-folding to sample protein-compatible conformations without fixing a transition state or catalytic residue motif.This bypasses theozyme-based design, which can be difficult to generalize when mechanisms for new-to-nature reactions are uncertain.Source: Designing enzymes for new-to-nature… · pp. 8–9

Design landscape

• From approximately 10^4 generated sequence–structure pairs, filtering yielded 90 experimental designs whose active sites were predominantly geometrically novel, with more than 80% exceeding 3 Å RMSD across five nearest residues.The designs included both reference-like and divergent conformations, often involving rotation about the iron–carbenoid bond.Source: Designing enzymes for new-to-nature… · p. 9

Screening and diversity

• The 90 designs were highly diverse, with no pair sharing more than 50% sequence identity and 75 distinct structural clusters at TM-score below 0.5.All designs were screened in whole-cell Escherichia coli across cyclopropanation, B–H insertion, C(sp3)–H insertion, and spirocyclopropanation, using TrpB as a background-reactivity control.Source: Designing enzymes for new-to-nature… · p. 9

Catalytic performance

• 72% yield, 4,050 TTN, and 99:1 diastereomeric ratio were achieved for cyclopropanation, while B–H insertion reached 98% yield and 5,170 TTN, exceeding reported benchmarks.C(sp3)–H insertion reached 42% yield and 2,360 TTN, rivaling evolved P411-CHF catalysts; spirocyclopropanation showed fewer active variants with modest activity.Source: Designing enzymes for new-to-nature… · pp. 9, 11, Figure 4 · p. 10

Evolvability

• A single error-prone-PCR round on dCT-H11 produced approximately 35 improved variants among roughly 700 mutants, increasing enantioselectivity from +35% to +49% ee or inverting it to +35% to -35% ee.Improving substitutions were distributed across the protein, consistent with long-range epistatic effects during enzyme evolution.Source: Designing enzymes for new-to-nature… · p. 11

Structural novelty

• Selected designs repurposed unrelated folds for heme binding and carbene transfer, including dCT-H11 with 21% identity to its closest structural match and dCT-F9 with 5% identity.dCT-H11’s closest active-site motif differed by more than 7 Å RMSD, while several designs lacked corresponding motifs in AlphaFoldDB.Source: Designing enzymes for new-to-nature… · pp. 11–12

• From just 90 genes, top designs achieved 98% yield for B–H insertion and >2,300 TTN for C(sp3)–H insertion, exceeding previously evolved biocatalysts.The designs also had novel active-site residues, stereoselectivity, and accessible fitness landscapes supporting subsequent evolution.Source: General biomolecular design unlocks… · p. 12
• DISCO couples sequence and 3D-structure generation, using cross-modal recycling, self-correction, entropy regularization, and inference-time steering to enable controllable, diverse protein design.These methods produced high-quality proteins that outperformed existing co-generation approaches.Source: General biomolecular design unlocks… · p. 12
• Conditioning solely on reaction intermediates produced promiscuous carbene transferases across four new-to-nature reactions without transition-state calculations, theozyme scaffolding, or extensive wet-lab screening.The platform provides global discovery of diverse, evolvable enzymes, but the demonstrated reactions cover only a small subset of synthetically valuable transformations absent from nature.Source: General biomolecular design unlocks… · p. 12

A.1 Notation

• The notation defines proteins as length-L paired sequence and backbone-coordinate objects, with amino acids drawn from a vocabulary containing a specialized mask token.Diffusion time uses τ = 0 for data and τ = 1 for noise, while separate structure and sequence times are denoted t(τ) and r(τ).Source: §A.1 · p. 20, §A.2 · p. 20

A.2 Theoretical foundations

• The theoretical foundations treat multimodal systems by first defining separate continuous and discrete diffusion processes, then combining them over sequence and structure spaces.Protein data are modeled as paired sequence and backbone coordinates with independently defined modality noise processes.Source: §A.2 · p. 20, §A.1 · p. 20, §A.2.1 · p. 20

A.2.1 Continuous-space diffusion modeling

• The continuous structure process destroys information with a forward SDE and generates samples by reversing a learned score-based denoising SDE.The drift and diffusion are chosen so the terminal distribution is approximately N(0, I), and a denoising network parameterizes reverse-time generation.Source: §A.2.1 · pp. 20–21

A.2.2 Discrete-Space diffusion modeling

• The discrete sequence process independently masks amino-acid tokens according to a schedule, then trains a denoiser with a weighted cross-entropy objective over masking levels.The schedule sets α0 = 1 and α1 = 0, interpolating between original and fully masked tokens.Source: §A.2.2 · pp. 21–22
• Standard discrete denoising lacks generation-order control and permanently commits unmasked tokens, preventing correction of earlier mistakes.These limitations motivate alternative reverse-time processes for discrete generation.Source: §A.2.2 · p. 22
• Path planning addresses both discrete-diffusion limitations by planning unmasking order and remasking previously unmasked tokens before denoising them again.In practice, uniform planners are used because confidence-dependent remasking reduces structural diversity.Source: §A.2.2 · p. 22

A.2.3 Multi-modal diffusion modeling

• DISCO combines separate structure and sequence diffusion processes to perform joint protein sequence–structure cogeneration.Proteins are represented by sequence and backbone-structure components, with modality-specific forward processes combined for multimodal generation.Source: §A.2.3 · pp. 22–23
• A single denoiser Dθ operates on partially noised sequence and structure, enabling reverse inference along any trajectory of paired noise levels from (1, 1) to (0, 0).Training combines independent modality losses on jointly noised inputs, while inference ties the two schedules through a unified variable τ.Source: §A.2.3 · p. 23

A.3 Data pipeline

• The data pipeline uses a weighted PDB dataset processed with AlphaFold 3 procedures, sampling chains or interfaces whose minimum heavy-atom separation is below 5 Å.The dataset is capped at 2021-09-30, with weights βchain = 0.5, βinterface = 1, αprot = 3, αnuc = 3, and αligand = 1; cropping uses 20% contiguous, 40% spatial, and 40% spatial-interface crops.Source: §A.3 · p. 24

A.4 Model architecture

• DISCO adapts AlphaFold 3’s conditional diffusion architecture for co-design by removing template and MSA modules, replacing MSA features with DPLM 650M, and using atom-level tokenization for nonprotein molecules.Each amino acid and nucleotide is one token, while each heavy atom of other molecules is separately encoded.Source: §A.4 · p. 24

A.4.1 Denoiser architecture

• The denoiser iteratively updates sequence and pair representations over four cycles, combining cross-modal states, DPLM 650M evolutionary features, skip connections, and a reduced 8-block Pairformer.The first-cycle outputs are cached for later modules, and a final CrossModalEncode precedes diffusion-based sequence and structure estimates.Source: §A.4.1 · pp. 24–25

A.4.2 Cross-modal encoding

• CrossModalEncode promotes sequence–structure self-consistency by encoding noisy and denoised sequences with frozen DPLM 650M and structures with a trainable LigandMPNN-based message-passing encoder.A distance map from the denoised structure estimate is injected into pair representations through a distance one-hot encoder.Source: §A.4.2 · p. 25

A.4.3 Diffusion module

• The DiffusionModule conditions trunk representations on structure and sequence noise, compresses atom-level geometry with AtomAttentionEncoder, processes tokens through a 24-block full-attention DiffusionTransformer, and decodes separate sequence and structure outputs.The structure update is rescaled and combined with noisy input positions according to a schedule equation.Source: §A.4.3 · pp. 25–26

A.4.4 Diffusion conditioning

• DiffusionConditioning embeds structure and sequence noise separately, concatenating pair features with relative positions and projecting single representations before transition processing.Structure noise uses logarithmic Fourier embedding, whereas sequence noise is embedded directly.Source: §A.4.4 · p. 26

A.4.5 Atom attention decoder

• The AtomAttentionDecoder broadcasts token features to atoms, adds atom-level skip connections, applies a 3-block, 4-head cross-attention AtomTransformer, and projects the final outputs.In sequence mode, updated atomic features are scatter-added back to tokens before layer normalization and bias-free linear projection.Source: §A.4.5 · p. 26

A.5 Training

• DISCO has 888 million parameters, including 235 million trainable parameters, and trains for 160,000 steps across 32 L40S GPUs over 11 days.Dropout is applied only in Pairformer, while pretrained DPLM 650M weights remain fully frozen.Source: §A.5 · p. 26
• The training pipeline uses cross-modal encoding, diffusion conditioning, token-level self-attention, and atom-attention decoding to jointly process noisy structure and sequence representations.The diffusion module includes 24 transformer blocks with 16 attention heads and returns structure outputs or sequence logits.Source: §A.5 · pp. 27–28

A.5.1 Structure diffusion losses

• Structure diffusion uses a weighted aligned MSE loss after rigidly aligning predicted and ground-truth structures, excluding unresolved atomic positions.DNA and RNA receive αdna = αrna = 5, while ligands receive αligand = 10.Source: §A.5.1 · p. 30
• Smooth LDDT evaluates differentiable pairwise-distance accuracy within 30 Å for nucleic acids and 15 Å for other atoms, with zero loss indicating perfect coordinate recovery.The full structure objective combines Smooth LDDT with MSE, and unresolved positions are excluded.Source: §A.5.1 · p. 30
• Structure noise is sampled as 16 · exp(−1.2 + 1.5 · N(0, 1)), and losses use σdata = 16 after optimal ground-truth chain assignment.The chain assignment follows the procedure described in the AlphaFold 3 supplementary information.Source: §A.5.1 · p. 30

A.5.2 Sequence diffusion losses

• Unlike structure training, the sequence diffusion head uses only the masked diffusion loss, with a linear schedule αr = 1 − r and uniformly sampled sequence time r.This objective is attributed to.Source: §A.5.2 · p. 30
• Sequence losses mask residues with low backbone occupancy, unresolved backbone atoms, or membership in histidine tags defined as runs of at least five histidines.The SUBS parameterization from prevents predicting mask tokens, and all reference and sequence features are masked to prevent amino-acid information leakage.Source: §A.5.2 · pp. 30–31

A.5.3 Full training loss

• The full training objective combines sequence, structure, and AlphaFold 2-identical distogram losses, weighted by αseq = 1, αMSE = 4, αsmooth_lddt = 4, and αdistogram = 0.03.Source: §A.5.3 · p. 31

A.5.5 Model selection; A.6 Inference

• Co-designability scales from 16% to 88% with the same checkpoint solely through inference settings, demonstrating that inference is critical for model performance.The final checkpoint is 160k, selected for superior co-designability–structural-diversity tradeoffs as later training overfits.Source: §A.5.5 · p. 32, §A.6 · p. 33

A.6.1 Inference sampling; A.6.2 Sequence self-correction

• Random remasking enables sequence self-correction during diffusion, allowing errors to be corrected at critical structural residues where standard masked inference performs poorly.The method is motivated by the requirement that standard masked diffusion keep unmasked tokens fixed throughout inference.Source: §A.6.2 · p. 34

A.6.3 Entropy adaptive sequence temperature

• Entropy-adaptive temperature flattens overconfident early residue predictions, and its combination with global temperature control is critical for performance.The entropy term approaches zero as sequence time approaches zero, while the global logit temperature is maintained separately.Source: §A.6.3 · pp. 34–35

A.6.4 Inference schedule; A.6.7 Inference hyperparameters

• Inference schedules trade co-designability against structural diversity, with mask_rate = t^1.5 encouraging diversity and λ = 0.1 providing the best reported balance between plausibility and diversity.Unconditional and conditional benchmarks use different hyperparameters because they occupy different points on the Pareto frontier.Source: §A.6.4 · pp. 35–36, Figure S2 · p. 36, §A.6.7 · p. 38

A.6.5 Conditional generation

• Conditional generation jointly denoises protein sequence and structure around ligand or nucleic-acid features, requiring no additional training or fine-tuning.The conditioning molecule participates in attention and pairformer computations while its coordinates are denoised through the reverse trajectory.Source: §A.6.5 · p. 36

A.6.6 Noisy guidance; 13: # Sequence noisy guidance: corrupt structure

• Noisy guidance uses partially noised conditions in a multimodal diffusion model, with logit-space interpolation for sequences and standard-deviation rescaling for continuous structure scores.Guidance can also be applied to unconditional joint generation by adaptively choosing the noise level for the other modality.Source: §A.6.6 · p. 36, §13 · p. 38

A.7 Inference steering; A.7.1 Feynman-Kac Correctors - Specificity Guidance

• Feynman-Kac Correctors steer samples toward target distributions by updating states, accumulating log-weights, and resampling particles; specificity guidance uses β < 0 to favor on-target binding and repel off-target binding.Because protein states lack rotational and translational invariance, on- and off-target scores are aligned with Kabsch transformations before guidance, while steering acts on protein state and uses ligand state for conditioning.Source: §A.7 · pp. 40–41, §A.7.1 · pp. 41–42

A.7.2 FKC-SG experimental details

• FKC-SG performed best with β = −0.5, resample = false at τ = 0.6, and K = 4 for valine/proline or K = 8 for the other ligand pairs.The tested pairs were valine/proline, aldosterone/cortisone, and biotin/PLP.Source: §A.7.2 · p. 43

A.7.3 FKC-SG evaluation

• Specific sequences were identified by retaining max-reward samples, refolding each sequence three times per target, and requiring a minimum ligand-centroid RMSD above 6 Å across nine comparisons.Designability required ligand-centroid and protein RMSDs below 2 Å before off-target separation was assessed.Source: §A.7.3 · p. 43

A.7.4 Feynman-Kac Correctors - Multimodal

• The multimodal Feynman–Kac corrector extends reward tilting to continuous and discrete modalities using modality-specific time schedules, drift terms, rate matrices, and weights.The derivation treats a one-dimensional discrete case and follows unimodal FKC results from and [22].Source: §A.7.4 · pp. 43–44

A.7.5 FKC-MM reward functions

• FKC-MM rewards couple residue identities with geometry through soft contact counts and log-sum aggregation, exemplified by disulfide-bond and cation-π interactions.The disulfide reward uses d0 = 4.5 Å, τ = 0.3 Å, and Δmin = 3; the cation-π reward uses d0 = 8.0 Å, τ = 0.5 Å, and Δmin = 4.Source: §A.7.5 · p. 47

A.8.1 Unconditional protein generation

• Unconditional DISCO generation sampled 100 structures at lengths 70, 100, 200, and 300, classifying co-designability by ESMFold backbone RMSD < 2.0 Å.pLDDT was averaged across residues, while novelty and diversity analyses were restricted to co-designable samples.Source: §A.8.1 · p. 48

A.8.2 Sequence diversity and novelty

• Sequence diversity was the number of MMseqs2 clusters divided by 400, while sequence novelty was the average of 1 − seq. identity against UniRef50.ProteinMPNN generated eight candidate sequences per backbone for inverse-folding comparisons.Source: §A.8.2 · p. 48, §A.8.1 · p. 48

A.8.3 Structural diversity and novelty

• Structural diversity was the number of Foldseek clusters divided by 400, and structural novelty was the average of 1 − TM-score from searches against the PDB.Both analyses used co-designable backbones.Source: §A.8.3 · pp. 48–49

A.8.4 Conditional evaluation of small-molecule ligands

• 179 chemically diverse molecules spanning cofactors, metals, drug-like compounds, fluorophores, saccharides, pollutants, and metabolites formed the STUDIO-179 benchmark.Source: §A.8.4 · p. 49
• 50 protein–ligand complexes were generated for each molecule at target lengths of 150, 200, and 250 residues using DISCO.Ligand inputs combined RDKit ETKDG bond information with GFN2-xTB-optimized geometries.Source: §A.8.4 · p. 49
• Co-designability was assessed by refolding each complex with Chai-1, requiring backbone RMSD below 2.0 Å and an additional supplied criterion.For multi-ligand systems, the associated condition was required independently for every ligand.Source: §A.8.4 · p. 49
• Protein–ligand steric clashes were flagged when protein and ligand heavy atoms were closer than the van der Waals-radius threshold, with a 0.5 Å tolerance for minor overlap.Source: §A.8.4 · p. 49
• Binding-site analyses defined the pocket as residues with backbone atoms within 10 Å of any ligand heavy atom, retaining up to the 10 closest residues.This definition was used for logP and pocket hydrophobicity analyses.Source: §A.8.4 · p. 49

A.8.5 Conditional evaluation: nucleic acid binding

• Nucleic-acid complexes used post-training-cutoff DNA/RNA targets, 100 samples per target, and a 2.0 Å co-designability threshold after Chai-1 refolding.DNA chains were cropped to 10 nucleotides, with lengths sampled uniformly from 50 to 80; phosphorus atoms anchored nucleotide alignment.Source: §A.8.5 · pp. 49–50

A.8.6 Baseline methods

• Conditional-generation benchmarks compared DISCO with RFdiffusion3 and BoltzGen, adding RFDiffusion All-Atom for small-molecule conditioning under identical downstream evaluation.Unconditional monomer generation additionally used La-Proteina[48], ProteinGenerator[49], ESM3[50], and LigandMPNN[15] for RFDiffusion All-Atom sequences.Source: §A.8.6 · p. 50

A.8.7 Binding motif novelty

• Binding motifs were searched with Folddisco[24] in refolded co-designable complexes and classified as novel when unmatched or when matched-residue RMSD exceeded 3.0 Å.The search used the afdb_swissprot_v4 Foldcomp database and motifs defined by the k residues nearest the ligand.Source: §A.8.7 · p. 50

A.8.8 Binding motif diversity

• Motif diversity was quantified using nearest-neighbour distances across Cα-RMSD, chemical-spatial cost, 1 − lDDT, Frobenius distance, and cluster ratio metrics.Cluster diversity used complete-linkage clustering at t = 2.0 Å, with r = nclusters/ndesigns indicating structural distinctness.Source: §A.8.8 · pp. 50–51

A.9 Density Functional Theory calculations

• DFT modeled triplet-state heme carbene-insertion intermediates with unrestricted B3LYP/def2-TZVP calculations, SMD ethyl acetate solvation, and NEB-TS transition states.A 5-methylimidazole axial ligand represented the heme cofactor during electronic-structure calculations and was removed during design.Source: §A.9 · p. 51

A.10 Design filtering for enzymes

• Enzyme campaigns generated on the order of 10^4 sequence–structure pairs and filtered them through Chai-1 and AlphaFold 3 co-designability checks.Retained designs additionally required contact, burial, coordination, hydrophobicity, charge, confidence-cutoff, and sequence- and structure-clustering criteria.Source: §A.10 · pp. 51–53

• Unconditional samples have very high co-designability, and filtering for co-designability produces no qualitative changes in amino-acid, secondary-structure, radius-of-gyration, or relative-contact-order distributions.Source: §A.11.1 · p. 54
• Table S4 identifies co-designable structural and sequence diversity as the most informative unconditional-generation metrics because they capture sample quality and the absence of mode collapse.The table cautions that co-designability should not be maximized alone because folding models cannot refold every PDB protein within 2 Å RMSD.Source: Table S4 · p. 54
• Unconditional analyses further examine co-designability across sampling settings and protein lengths, amino-acid and long-range-contact distributions, radius of gyration, and disulfide-bond counts against PDB-based references.Figure S4 varies the number of steps and recycles with noisy guidance disabled; Figures S5–S9 provide the distributional analyses and references.Source: Figure S4 · p. 54, Figure S5 · p. 55, Figure S7 · p. 56

A.11.2 Additional conditional generation results

• Co-designability was lower than in unconditional generation, but filtering generally caused no qualitative changes except in secondary-structure distributions.Analyses were otherwise evaluated without co-designability filtering; co-designability may be biased because current folding methods refold only about 60% of PDB training structures.Source: §A.11.2 · p. 57, Figure S13 · p. 61
• DISCO generated the highest proportion of diverse, co-designable sequence–structure pairs for every ligand in the remaining STUDIO-179 benchmark.The benchmark spans natural to non-natural ligands.Source: Figure S10 · p. 58
• Additional conditional designs included luciferin in a hybrid helix–sheet topology and a substituted naphthalene diimide in a helix bundle.These examples cover natural and non-natural ligands.Source: Figure S25 · p. 69

B.1 Materials and instrumentation

• Commercial chemicals and literature-prepared racemic standards 1b, 2b, and 4b were used with M9-N buffer and chromatographic, spectrometric, and GC instrumentation.The methods included HPLC–MS, chiral HPLC–UV, and GC–FID/GC–MS analyses.Source: §B.1 · pp. 72–73

B.2 Cloning and transformation in 96-well plates

• Genes were assembled into pET22b(+) between NdeI and XhoI sites, expressed with C-terminal His-tags, and verified at approximately 95% sequence accuracy.Variants were organized in 96-well plates with TmTrpB as negative control and evolved protoglobin as positive control.Source: §B.2 · p. 73

B.3 Protein expression and reaction screening in plates

• Plate reactions used induced BL21 cultures supplemented with ALA, anaerobic M9-N buffer, 10 mM substrate, 15 mM EDA, and 5% MeCN before overnight incubation.Products 1b, 3b, and 4b were analyzed by reversed-phase HPLC–MS, whereas 2b used GC–MS extraction and analysis.Source: §B.3 · pp. 73–74, Table S5 · p. 74

B.4 Protein expression and whole-cell validation reactions

• Promising variants were re-expressed in flasks, sequence-confirmed by Sanger sequencing, normalized to OD600 = 30, and tested in triplicate under anaerobic whole-cell conditions.Reactions used 10 mM substrate, 15 mM EDA, 5% MeCN, and overnight incubation at room temperature.Source: §B.4 · pp. 74–75

B.4.1 Analysis by GC-FID (compounds 1b - 4b)

• Whole-cell products 1b–4b were extracted with internal standard and quantified by GC-FID using integrated product peaks and calibration curves.The analysis used an Agilent J&W HP-5 column with a 10-minute oven program.Source: §B.4.1 · p. 75

B.4.2 Analysis by LC–MS (compound 4b for directed evolution)

• Compound 4b samples for directed-evolution analysis were quantified by reversed-phase HPLC–MS using papaverine hydrochloride as an internal standard and simultaneously prepared calibration curves.Samples were clarified after MeCN addition, and integrated product and internal-standard peaks were quantified with Agilent software.Source: §B.4.2 · p. 75, Table S8 · p. 75

B.4.3 Analysis of enantioselectivity

• Products 1b–3b were analyzed by chiral HPLC–UV, whereas 4b was analyzed by chiral GC–FID after organic extraction and concentration.The procedures specify product-specific columns, solvent conditions, flow rates, temperatures, runtimes, and UV detection at 235 nm for 1b–3b.Source: §B.4.3 · p. 76

B.5 Hemochrome assay

• Protein concentration was determined from oxidized and dithionite-reduced hemochrome UV–Vis spectra of cell lysates using an extinction coefficient and dilution factor.Lysates were produced by sonication on wet ice and clarified by centrifugation.Source: §B.5 · p. 76

B.6 Selectivity results

• Selectivity validation reported enantiomeric ratios of 61:39 for dCT-H11 in 1b cyclopropanation, 63:37 for dCT-F9 in 2b B–H insertion, and 40:60 for dCT-H11 in 3b C–H insertion.For 1b, the corresponding trans:cis diastereomeric ratio was 99:1.Source: Figure S29 · p. 77, Figure S30 · p. 77, Figure S31 · p. 78

B.7 Directed evolution

• Directed evolution screened eight epPCR plates by HPLC–MS, sequenced variants, and validated the highest performers in triplicate with enantioselectivity measurements.The workflow included parent and sterile controls, Gibson assembly, and LevSeq sequence verification.Source: §B.7 · p. 79, Table S9 · p. 79, Table S10 · p. 79
• Selected evolution variants changed spirocyclopropanation enantiomeric ratios from 68:32 for parent dCT-H11 to 75:25 for dCT-r1-E12 and 25:75 for dCT-r1-F1.These validation results are shown for reaction 4b.Source: Figure S33 · p. 80

B.8 DNA sequences of the best designs

• The supplementary information lists DNA sequences for the best designs, including dCT-H11, dCT-H10, dCT-F9, dCT-G9, and dCT-G1.These sequences are presented as nucleotide strings for the corresponding designs.Source: §B.8 · pp. 81–82

B.9 Calibration curves for GC-FID analysis; B.9.1 Calibration curves for 1b; B.9.2 Calibration curves for 2b; B.9.3 Calibration curves for 3b; B.9.4 Calibration curves for 4b

• GC–FID calibration curves used analyte-to-internal-standard ratios with achiral analysis: 1,2-diphenylethane served as internal standard for 1b and 3b, while 1,2,3-trimethoxystyrene served for 2b.For 2b, the calibration-curve slope was used to calculate enzymatic product yield.Source: §B.9 · p. 83, Figure S34 · p. 84, Figure S35 · p. 84

B.10 Calibration curves for LC-MS analysis

• LC–MS calibration used tert-butyl-3-methyleneazetidine-1-carboxylate (4a) standards spanning 10–300 µM with papaverine hydrochloride as internal standard.Stocks were prepared in acetonitrile and analyzed from 300 µL aliquots combined with 50 µL internal-standard solution.Source: §B.10 · p. 87

B.11 Synthesis of product standard 3b

• Product standard 3b was synthesized through copper-catalyzed N-arylation followed by esterification, and its NMR data agreed with the literature.The reported characterization includes 1H NMR and 13C NMR data in CDCl3.Source: §B.11 · pp. 87–88

B.12 HPLC–UV chromatograms for enantioselectivity determination

• HPLC–UV chromatograms show authentic standards and dCT-B9 reaction samples for compounds 1b, 3b, and 2b, providing chromatographic references for these compounds.Source: Figure S43 · p. 90, Figure S44 · p. 90, Figure S54 · p. 95

B.13 Chiral GC–FID traces for enantioselectivity determination

• Chiral GC–FID traces compare racemic and enantiopure 4b standards with reactions from dCT-H11 and six evolved dCT-r1 variants.The documented evolved variants are dCT-r1-B7, dCT-r1-E3, dCT-r1-E12, dCT-r1-F1, and dCT-r1-D1.Source: Figure S75 · p. 106, Figure S76 · p. 106, Figure S77 · p. 106
• The B.13 trace set includes chiral GC–FID measurements for 4b produced by the evolved variant dCT-r1-F1.This trace complements the other evolved-variant measurements in the enantioselectivity dataset.Source: Figure S81 · p. 107
• The B.13 trace set also includes chiral GC–FID measurement for 4b produced by evolved variant dCT-r1-D1.This provides the final listed evolved-variant trace in the supplied series.Source: Figure S82 · p. 107