A transformer architecture enables processing of raw mass spectraCasanovo uses a transformer architecture to perform a sequence-to-sequence modeling task, from MS/MS spectrum to the generating peptide (Fig. 1). Transformers are built upon the attention function21, which allows transformer models to contextualize the elements of a sequence; transformer models thus learn the relationships of sequence elements to one another and how their interactions should be interpreted. As such, the transformer architecture has found success in not only natural language processing, but also applications to biological sequences24,25.Fig. 1: Casanovo performs de novo peptide sequencing using a transformer architecture.The peaks from each MS/MS spectrum are contextualized by the transformer encoder. The resulting peak encodings are then fed into the transformer decoder along with the observed precursor mass and charge to iteratively decode the peptide sequence. Casanovo uses a beam search decoding strategy, following the most promising sequence predictions until they terminate or exceed the precursor mass. The highest scoring peptide sequence is returned as the putative peptide that generated the MS/MS spectrum.In Casanovo, each peak in an observed MS/MS spectrum is considered as an element in a variable length sequence. The m/z and intensity values of each peak are encoded using, respectively, a collection of sinusoidal functions and a learned linear layer, and these encodings are summed. The encoded peaks are then input into the transformer encoder, where context is learned between pairs of peaks in the MS/MS spectrum. The contextualized peak encodings are then used as input to the transformer decoder for predicting the peptide sequence.The process of decoding proceeds in an iterative, autoregressive manner. We begin by providing the mass and charge of the observed precursor. The transformer decoder uses the contextualized peak encodings and the precursor information to begin predicting amino acids of the peptide. With the first predicted amino acid, we retain the top k residues, where k is a user-selected value for the number of beams in our beam search. In each subsequent iteration, amino acids are added to the decoded peptide sequence, retaining the top k sequences until the decoded sequences for all of the beams have terminated or exceeded the precursor mass. Finally, the sequence with the highest score is retained as the putative peptide that generated the provided MS/MS spectrum.In generating its predictions, Casanovo will inevitably fail to generate plausible peptides for some MS/MS spectra. For example, some MS/MS spectra contain too few fragment ions to be sequenced reliably, or the true generating peptide may bear a modification that is unknown to Casanovo. We therefore refine the PSMs proposed by Casanovo using a simple precursor mass filter: any PSMs for which the m/z of the peptide falls outside the specified tolerance of the observed precursor, including potential isotopes, is discarded. This filter eliminates many poorly scored peptides from consideration. In our evaluations, PSMs that would normally be removed by this filter were retained and ranked last among all PSMs assigned by Casanovo.Casanovo outperforms state-of-the-art methodsTo evaluate Casanovo, we first used the nine-species benchmark dataset originally created by Tran et al.8 to compare the performance of four de novo peptide sequencing algorithms: Novor, DeepNovo, PointNovo, and Casanovo. For these comparisons, we used the publicly available, pretrained version of Novor to sequence the MS/MS spectra in the benchmark dataset. DeepNovo, PointNovo and Casanovo were trained in a cross-validated fashion, systematically training on eight species and testing on the remaining species. For DeepNovo, we used the models trained and provided by Tran et al.8 for each of the cross-validation splits. For PointNovo, we cross-validated nine models from scratch using the code and settings provided by Qiao et al.17. This benchmark version of Casanovo, Casanovobm, employs a simple greedy decoding algorithm, rather than beam-search decoding. The results (Fig. 2a) revealed that Casanovobm substantially improved peptide-level sequencing performance over Novor, DeepNovo and PointNovo, with an average precision of 0.81 for Casaonovobm compared to 0.58, 0.70 and 0.74 for Novor, DeepNovo and PointNovo, respectively. These results are consistent across all nine species in the benchmark dataset (Supplementary Fig. S1).Fig. 2: Casanovo outperforms PointNovo, DeepNovo, and Novor on a nine-species benchmark.a Casanovo maintains high peptide-level precision (the proportion of correctly predicted peptides) across all values of coverage (the proportion of spectra for which a prediction is made). Each curve is computed by sorting predicted peptides for all nine species according to their peptide-level confidence scores. For Casanovo, all peptides that pass the precursor m/z filter are ranked above peptides that do not pass the filter, and the boundary is indicated by a diamond on each curve. Average precision (AP) corresponds to the area under the precision-coverage curve. b Same as a, but using the revised benchmark and including a version of Casanovo trained on MassIVE-KB. c Casanovo’s amino acid-level precision is greatly improved by the expanded training data provided by MassIVE-KB. The test set is the revised nine-species benchmark, with PSMs only containing modifications considered by both DeepNovo and Casanovo.We hypothesized that Casanovo could achieve even better performance if provided with a larger training set of higher quality PSMs; hence, we turned to the MassIVE-KB spectral library of human MS/MS proteomics data23. MassIVE-KB provided us with a set of 30 million high confidence PSMs, which we previously collected for training our GLEAMS embedding model26. This dataset contains not only a greater diversity of peptides and MS/MS spectra generated from multiple instruments, but also additional types of post-translational modifications. We therefore created a new version of the nine-species benchmark dataset using the same nine PRIDE datasets but including seven different types of variable modifications (methionine oxidation, asparagine deamidation, glutamine deamidation, N-terminal acetylation, N-terminal carbamylation, N-terminal NH3 loss, and the combination of N-terminal carbamylation and NH3 loss). In the process, we also fixed several problems that we uncovered in the previous benchmark, including adding consideration of isotope errors and eliminating peptides that occur in multiple species (see Methods for details). The final, revised benchmark dataset consists of 2.8 million PSMs drawn from 343 RAW files.The results from evaluating with respect to this revised benchmark demonstrate the value of training from a much larger collection of higher quality PSMs (Fig. 2b). When trained on the MassIVE-KB dataset, the average precision of Casanovo increases from 0.83 to 0.95. Furthermore, Casanovo succeeds in making a larger proportion of predictions with m/z values that fall within 30 ppm of the observed precursor (signified by the location of the diamonds in Fig. 2b), increasing from 70% to 97%. Additionally, an analysis of spectrum identifications for all de novo sequencing tools on the nine-species benchmark dataset shows that correct Casanovo PSMs include almost all correct identifications of the competing de novo sequencing methods, as well as approximately 50% more correct PSMs that are unique to Casanovo (Supplementary Fig. S8). This version of Casanovo incorporates beam-search decoding, which improves both average precision and coverage compared to greedy decoding for the same model (Supplementary Fig. S3).In one sense, this comparison is unfair because some of the spectra in the new version of the benchmark contain PTMs that cannot be identified by some of the competing methods. We therefore eliminated these spectra from each test set and then re-computed the precision-coverage curve. The results (Supplementary Fig. S4) are largely unchanged, suggesting that the PTMs contribute little to the observed overall differences in performance.To better understand why the model trained on MassIVE-KB outperforms the one trained on the nine-species benchmark, we performed two follow-up experiments. First, we trained a series of Casanovo models on randomly sampled nested subsets of MassIVE-KB, ranging from 250,000 spectra to the full dataset of 28 million spectra. Each model was then evaluated with respect to the revised nine-species benchmark. The resulting learning curve (Supplementary Fig. S5) shows that the test set performance depends strongly on the size of the training set, though with diminishing returns after a million or so PSMs. Second, we directly compared a Casanovo model trained from a downsampled MassIVE-KB dataset to Casanovobm which averages 9 models cross-validated on the nine-species benchmark, where the training sets contain approximately the same number of peptides (239,697 for Massive-KB and 246,713 for Casanovobm). We then evaluated both models using the revised nine-species benchmark. The results (Supplementary Fig. S6) show that the model trained from MassIVE-KB substantially outperforms Casanovobm, with the average precision increasing from 0.83 to 0.90. Thus, these results suggest that the improved performance of the MassIVE-KB model stems primarily from the improved quality of the data rather than the size of the data set.In addition to evaluating Casanovo’s ability to correctly predict whole peptides, we also evaluated Casanovo’s ability to predict the individual amino acids of each peptide. We did so by ranking amino acids by their associated confidence score and then plotting a precision-coverage curve. We compared two versions of Casanovo (trained from the first benchmark and from MassIVE-KB) with DeepNovo and PointNovo on the revised nine-species benchmark with new modifications eliminated (Fig. 2c). The amino acid-level performance was consistent with the trends we observed in peptide-level performance, with Casanovo outperforming Novor, DeepNovo and PointNovo: Casanovo trained on MassIVE-KB achieves a remarkable average precision of 0.98.Finally, to characterize the improved de novo sequencing performance of Casanovo across generating peptides of different lengths and precursor charge states, we compare all methods on subsets of the revised nine-species benchmark dataset. First, we divide spectra into three groups by charge state where groups contain precursors with 2+, 3+ and 4+ or higher charge states each, and plot peptide precision-coverage curves for each group (Supplementary Fig. S9). As expected, average precision is lower across all methods for groups with higher precursor charge states since those spectra tend to have more complex fragmentation patterns. However, the drop in performance is only 12% for Casanovo in precursors with 4+ or higher charge states versus precursors with 2+ charge states, thanks to the diversity of precursor charge states in its training data where 11% of precursors have 4+ or higher, whereas average precision for all competing methods decreases by more than 60%. Second, we bin spectra according to the length of their generating peptides into groups of short (fewer than 13 amino acids), medium (between 13 and 18 amino acids), and long (greater than 18 amino acids) peptides, and compare de novo sequencing performance in each group (Supplementary Fig. S10). Performance degrades for longer peptides because incorrect amino acid predictions tend to accumulate during decoding, but the observed decrease in average precision for Casanovo is much smaller relative to other methods, highlighting Casanovo’s ability to accurately sequence long peptides as a key contributor to its improved performance.Casanovo unravels the immunopeptidomeOne important application of de novo peptide sequencing is the characterization of the peptides presented by major histocompabilitility complexes (MHCs), which is commonly referred to as the “immunopeptidome.” These antigen peptides are presented on the extracellular surface and serve as targets for immune cell recognition. However, because these antigen peptides are generated through lysosomal or proteasomal degradation, they do not exhibit the characteristic tryptic termini from most proteomics experiments. Consequently, the peptide search space is exponentially larger than considering only tryptic peptides—every peptide subsequence in a protein within a defined peptide length must be considered. Furthermore, mutations in these peptides are of particular interest, because these mutation-containing neoantigens may serve as tumor-specific markers to activate T cells and initiate antitumor immune responses. Unfortunately, expanding the search space to consider all possible mutated peptides is prohibitive both in terms of search speed and statistical power for traditional proteomics search engines.Although immunopeptidomics is a prime application for de novo sequencing, naively applying Casanovo directly to immunopeptidomics data is problematic: the standard Casanovo model is heavily biased to predict tryptic peptides due to their overrepresentation in MassIVE-KB. To demonstrate this effect, we analyzed five mass spectrometry runs generated from MHC class I peptides isolated from MDA-MB-231 breast cancer cells5 in two different ways: first using Casanovo and second by searching against a non-enzymatic digestion of the human proteome (see Methods). Among the peptides accepted at 1% FDR by the database search procedure, we observed a low proportion of “tryptic” peptides, i.e., peptides with C-terminal amino acids of K (1.12%) or R (0.80%). In contrast, among the top-scoring 10% of the Casanovo predictions, we observed a greater than six-fold increase in the rate of tryptic peptide predictions (5.87% K and 6.76% R).We hypothesized that we could reduce this tryptic bias and produce a version of Casanovo that is better suited to immunopeptidomics data by fine tuning our existing model using data that lacks a tryptic bias. To create such a dataset, we combined data from two sources. First, we segregated PSMs from MassIVE-KB according to their C-terminal amino acid and then uniformly sampled up to 50,000 peptides within each group. For most amino acids, MassIVE-KB contained fewer than 50,000 PSMs, so for these we supplemented by randomly extracting additional PSMs from the PROSPECT collection27 (Supplementary Table S1). We then split this new collection of 1 million PSMs into training, validation, and testing sets. We then fine-tuned our existing Casanovo model by training it until convergence on this non-enzymatic training set.The resulting model, Casanovone, performs markedly better than the original Casanovo model at predicting peptides in our held-out, non-enzymatic test set. On the held-out test set of 100,000 non-enzymatic PSMs, Casanovone achieves an average precision of 0.83, compared with 0.60 for the original Casanovo model on the same data (Fig. 3a). The predicted C-terminal amino acid frequencies are also much closer to the true frequencies, with K and R dropping to 1.81% and 1.79%, respectively (Fig. 3b).Fig. 3: Fine-tuning reduces Casanovo’s bias for tryptic peptides.a Fine-tuning Casanovo (Casanovone) improves peptide-level precision on sequencing MS/MS spectra generated by non-tryptic peptides. b Casanovone predicts non-tryptic C-terminal peptides more readily than the standard Casanovo model, improving performance on the non-enzymatic validation set. c Casanovo detects many peptides that are present in the human proteome but are not detected via database search. The dashed dark pink line only includes peptides detected by database search within the 1% FDR threshold, whereas the solid dark pink line includes all peptides from the database search, irrespective of FDR threshold. d The peptides proposed by Casanovo generally have higher predicted binding affinities for the MHC class I receptor, matching the performance of a Tide database search. The vertical bar corresponds to the 500 nM binding affinity below which peptides are predicted to be MHC binders. e Similar to d, but considering only the 1497 peptides that are accepted at 1% FDR by Tide which yielded valid binding affinity predictions from NetMHCpan and a corresponding set of 1497 highest-confidence Casanovo peptides.We next used Casanovone to sequence the immunopeptidome of MDA-MB-231 breast cancer cells5. For each peptide predicted by Casanovo, we investigated whether it (1) occurs anywhere within the human proteome, and (2) occurs within the set of peptides detected using a database search procedure. We first searched the data against a non-enzymatic digestion of the human proteome using the Tide search engine28 followed by Percolator post-processing29, using settings similar to those in the original study5 (see Methods). Out of 26,377 unique peptides predicted by Casanovo, 2459 match to the human proteome, and a majority of these overlap with the 1544 unique peptides identified by Tide at 1% FDR (Supplementary Fig. S11). Notably, these overlapping peptides are predicted with high confidence by Casanovo, almost all within the first 10,000 Casanovo predictions (Fig. 3c). Casanovo predicts an additional 1148 peptides that match to the human proteome but are not identified by Tide at 1% FDR, and further analysis shows that 751 (65.4%) of these peptides correspond to Tide hits that were not accepted at the 1% FDR threshold. To further investigate the plausibility of Casanovo predicted peptides as MHC antigens, we used NetMHCpan-4.130 to predict MHC binding affinity for these peptides. First, we compared peptides that were identified by both Casanovo and database search with peptides that were predicted only by Casanovo and match to the human proteome. These two groups exhibit similar distributions of predicted binding affinity profiles, with 87% of peptides identified by Casanovo alone and 86% of those identified by both methods predicted to be MHC binders at 500 nM (Fig. 3d). In contrast, when we evaluate peptides that are identified by database search but not by Casanovo, the proportion of predicted MHC binders drops substantially to 50%. Overall, these results suggest that Casanovo not only identifies more peptides matching to the human proteome than the standard database search procedure, but the peptides Casanovo predicts are also more likely to bind MHC antigens.We also explored an alternative method for comparing Casanovo and Tide results, which does not rely on mapping Casanovo predictions to the reference proteome. For this analysis, we consider the 1497 peptides identified by Tide at 1% FDR which yielded valid binding affinity predictions from NetMHCpan alongside the top 1497 highest confidence Casanovo predictions. The results (Fig. 3e) agree with those in Fig. 3d: the 960 peptides in common between the two sets of peptides achieve the highest proportion of MHC binders (86%), the Casanovo-only predictions achieve a slightly lower percentage (80%), and the Tide-only predictions have the lowest percentage of MHC binders (70%).Casanovo accurately sequences peptides from complex metaproteomesProteomics applications extend far beyond the analysis of single model organisms or well-characterized biological systems. Indeed, there is growing interest in using mass spectrometry proteomics methods to investigate the dynamics of complex biological ecosystems—whether microbiomes or environmental specimens—for which the identities of its members cannot be known a priori. Due to the unknown complexity of the sample and even the lack of reliable reference proteomes for the likely species in the sample, these metaproteomics experiments are difficult to analyze. One solution to these problems is to search the spectra against a large database, such as one containing all the microbial sequences in public databases for a sample that is likely dominated by unknown microbes. This “big database” approach is widely used but suffers from a significant loss in statistical power due to the implicit multiple hypothesis testing correction that must be made to account for the size of the database. An alternative solution involves first subjecting the sample to genome sequencing, and then using the inferred peptide sequences as the basis for a “metapeptide” database. This approach yields better power to detect peptides31 but requires the availability of a matched DNA sample and the additional cost associated with DNA sequencing.We hypothesized that Casanovo’s improved de novo sequencing capabilities would be useful in both scenarios—either in the presence or absence of a metapeptide database. To test this hypothesis, we applied Casanovo to data from six previously published ocean metaproteomics samples, three from the Bering Strait and three from the Chukchi Sea31. Critically, these samples were also subjected to DNA sequencing; hence, in addition to the non-redundant environmental database, we also have a metapeptide database for each sampling location.We began by measuring the extent to which peptides detected by Casanovo occur within the corresponding metapeptide database or within the larger, non-redundant protein database. Because these samples were digested using trypsin, we used the standard Casanovo model, trained from the tryptic MassIVE-KB dataset. To control the error rate for the matching of Casanovo predictions to these databases, we employed a procedure similar to target-decoy competition used in the false discovery rate estimation for database search (see Methods for details) and only considered as correct Casanovo peptides found in the corresponding database that fall within the 1% random matching threshold. Using this logic, we obtain much better power to detect peptides using Casanovo than using a standard database search procedure against the metapeptide database (Fig. 4a–b). In particular, when we search the data against the metapeptide database using Tide followed by Percolator29, we detect 5623 peptides at 1% FDR in the Bering Strait data and 2460 peptides in the Chukchi Sea data. In contrast, if we run Casanovo and accept as correct only peptides that appear in the metapeptide database (subject to our 1% random matching criterion), then we detect 8277 and 3532 peptides, respectively, in the two datasets, representing increases of 47% and 44%. Casanovo also outperforms database search when we consider the non-redundant protein database rather than the sample-specific metapeptide database. We detect 1364 peptides in the Bering Strait data and 682 peptides in the Chukchi Sea data at 1% FDR by searching the non-redundant environmental database using Tide and Percolator. In comparison, Casanovo predictions, filtered at 1% error rate using the environmental database, detect 3425 and 1612 peptides, respectively, representing increases of 151% and 136%, respectively.Fig. 4: Casanovo improves power to detect peptides from metaproteomics samples.Casanovo assigns more peptides matching the metapeptide database and the non-redundant environment database than Tide and Percolator at 1% FDR in seawater samples from a the Bering Sea and b the Chukchi Sea. Peptides are ranked according to the Casanovo confidence score, assigning each peptide the maximum score across all three runs from each sampling location. Horizontal lines indicate the total number of distinct peptides detected by Tide+Percolator, searching against two different databases. c The PSMs assigned by Casanovo at a 1% error rate and Tide and Percolator at 1% FDR have high cosine similarities to the predicted MS/MS spectra for the respective peptides from Prosit when compared to control PSMs sampled from the Tide search results with > 10% FDR. Each group represents the aggregated results for Bering and Chukchi Sea data, as well as non-redundant environmental and metapeptide databases. d The PSMs assigned by Casanovo at a 1% error rate and Tide and Percolator at 1% FDR closely align with the predicted retention times from Prosit.When using both metapeptide databases or the non-redundant environment database, Casanovo detects most of the peptides identified by Tide database search and Percolator, where it respectively detects 71% and 75% of Tide identifications on metapeptide and non-redundant databases, while also detecting a substantial number of additional unique peptides (Supplementary Fig. S12).To validate the peptides that were detected by Casanovo but not the database search, we used the Prosit machine learning tool32 to predict spectrum peak intensities and retention times for peptide identifications. First, we compared the cosine similarities between the observed and predicted MS/MS spectrum peak intensities across three groups of peptides: peptides only predicted by Casanovo that matched to the database with 1% error, peptides detected both by Casanovo and by Tide and Percolator at 1% FDR, and a control group of peptides detected by Tide and Percolator with >10% FDR. The control group was randomly sampled to be the same size as the Casanovo-only group. The results (Fig. 4c) indicate that the Casanovo-only identifications have a high concentration of high cosine similarity peptides, similar to the overlapping identifications between Casanovo and database search. This stands in contrast with the control group, which exhibits a much broader distribution of cosine similarities.Second, we compared the observed retention times with the predicted retention times from Prosit for the same three groups of peptides. For each group, we calibrated the predicted retentions times to the observed retention times using linear regression (Supplementary Fig. S13). We observed that the peptides detected only by Casanovo and those detected by Casanovo and Tide had a similar slope and resulted in similar residual distributions (Fig. 4d). When compared against the control group, the residual distributions for peptides only detected by Casanovo and those detected by Casanovo and Tide are close to zero.Ultimately, Casanovo does not yet allow us to achieve as much power with the non-redundant database as with the metapeptide database. For example, for the Bering Strait data, the union of the 3425 peptides detected using Casanovo and the 1364 peptides detected using database search is 3750, which is fewer than the 5623 peptides detected using the metapeptide database. (The corresponding numbers for the Chukchi Sea data are 1798 and 2460.) This difference is perhaps not surprising, because the environmental non-redundant database is incomplete: 3715 of the 5623 peptides found by the database search procedure in the Bering Strait metapeptide database are not even present in the environmental database. Thus, a rigorous FDR control procedure for de novo peptide sequencing is needed in order to rescue the many peptides that are correctly detected by Casanovo but cannot be validated by matching to a database.Casanovo shines a light on the dark proteomeThe “dark matter” of mass spectrometry-based proteomics consists of MS/MS spectra that are observed repeatedly across experiments but consistently fail to be identified. In many cases, these MS/MS spectra may have been generated by peptides that are not in the canonical human proteome, because they represent contaminant peptides, result from non-standard enzymatic cleavage, or contain sequence variants. We hypothesized that Casanovo could shed light on some of this dark matter.Accordingly, we applied Casanovo to a collection of MS/MS spectra drawn from a previous analysis26, in which 511 million human spectra from MassIVE were grouped into 60 million clusters, and the clusters were systematically analyzed using targeted open modification searching of representative spectra. The analysis yielded a collection of 39 million unidentified clusters, containing a total of 207 million MS/MS spectra. For our analysis, we selected 3.4 million of these unidentified, clustered MS/MS spectra from eight randomly selected MassIVE datasets. These MS/MS spectra belong to 573,597 distinct clusters. Because we were investigating spectra that had already failed to be identified using a standard, tryptic pipeline, we opted to use the non-enzymatic Casanovo model (Casanovone) to assign a peptide to each selected MS/MS spectrum, eliminating peptides for which the predicted m/z falls outside the associated mass range. This analysis yielded a total of 1.3 million predicted peptides.We sought to ascertain how well Casanovo had assigned peptide sequences to these dark matter clusters by addressing this question in two complementary ways. First, we identified all clusters in which a plurality (and at least two) of the spectra were assigned to the same peptide sequence, and then we mapped those peptides to the human reference proteome, allowing at most one amino acid mismatch. The first step of this procedure assigns peptides to 89,250 (16%) of the clusters, of which 65% could be matched to the human proteome. The clusters identified in this fashion vary in size, ranging from 2 to 542 spectra per cluster, but when we limited the above analysis only to clusters larger than a certain size, we observed that the shares of identified clusters more than doubled (Supplementary Fig. S14). Second, we performed a complementary analysis, first eliminating all predicted peptides that do not occur within the human proteome (again, allowing one mismatch) and then finding clusters with two or more spectra assigned the same sequence and no other spectrum assigned to a different sequence. This procedure assigns peptides to 52,523 clusters, corresponding to 9% of all previously unidentified clusters. The overlap between the two approaches—plurality vote followed by proteome matching or vice versa—is high: 98% of the 52,523 clusters overlapped with the clusters from the previous analysis. Overall, Casanovo is able to assign peptides to 196,724 of the 3.4 million unidentified MS/MS spectra using the combination of these two strategies.One potential reason for an MS/MS spectrum to remain unidentified is the presence in the generating peptide sequence of a genetic variant that does not appear in the reference proteome. To investigate whether Casanovo is identifying such sequences, we looked more closely at the subset of Casanovo cluster assignments that match to the human proteome with a single amino acid mismatch, focusing on the 51,555 assignments that agree between the two methods described above. Two pieces of evidence suggests that these peptides are indeed enriched for genetic variants. First, we observe an enrichment for amino acid substitutions that can be explained by a corresponding single-nucleotide substitution. Among the Casanovo predictions, 83.4% correspond to a potential single-nucleotide substitution, compared with only 38.6% of all possible amino acid substitutions that fit this criterion. Second, we see a strong enrichment for substitutions with positive BLOSUM62 scores33. The BLOSUM score is an integerized log-odds score indicating the empirical substitutability of one amino acid for another. In the BLOSUM62 matrix, only 11% of the 380 non-diagonal entries are positive. However, if we rank the Casanovo-predicted substitutions by frequency, we find that the top five substitutions have BLOSUM scores of 1 or 2 (Supplementary Table S3). This observation strongly suggests that Casanovo is predicting substitutions that are biochemically plausible.
