BRCA1/2 and efficacy prediction for PARP inhibitors. We trained and evaluated predictive models for loss-of-function (LOF) of 145 individual DNA damage response genes based on genome-wide mutational patterns, including structural variants, indels, and base-substitution signatures. We identified 24 genes whose deficiency could be predicted with good accuracy, including expected mutational patterns for BRCA1/2, MSH3/6, TP53, and CDK12 LOF variants. CDK12 is associated with tandem duplications, and we here demonstrate that this association can accurately predict gene deficiency in prostate cancers (area under the receiver operator characteristic curve = 0.97). Our novel associations include mono- or biallelic LOF variants of ATRX, IDH1, HERC2, CDKN2A, PTEN, and SMARCA4, and our systematic approach yielded a catalogue of predictive models, which may provide targets for further research and development of treatment, and potentially help guide therapy.DNA repair deficiencies in cancers may result in characteristic mutational patterns, as exemplified by deficiency of  Many different aspects of the environment – such as ultraviolet radiation, carcinogens in food and drink, and the ageing process itself – damage the DNA in human cells. Normally, cells can repair these sites by activating a mechanism known as the DNA damage response. However, the hundreds of genes that orchestrate this response are also themselves often lost or damaged, allowing the unrepaired sites to turn into permanent mutations that accumulate across the genome of the cancer cell.BRCA1 or BRCA2 gene, both of which are part of the DNA damage response. However, it remained unclear how many other genes involved in the DNA damage response also lead to detectable mutational signatures when lost.By studying the DNA of cancer cells, it has been possible to identify characteristic patterns of mutations, called mutational signatures, that appear in different types of cancer. One specific pattern has been linked to the loss of either the BRCA1/BRCA2 and their known mutational signature. However, it also found 23 other associations between DNA damage response genes that had been lost or damaged and particular patterns of mutations in a variety of cancers. These findings suggest that mutational signatures could be used more widely to predict which DNA damage response genes are no longer functioning in the genome of cancer cells.To investigate, Sørensen et al. computationally analysed data from over six thousand cancer patients. They looked for associations between over 700 DNA damage response genes and 80 different mutational signatures. As expected, the analysis revealed a strong connection between the loss of BRAC1/BRAC2 has been shown to make patients more responsive to a certain type of chemotherapy. Further experiments are needed to determine whether the connections identified by Sørensen et al. could also provide information on which treatment would benefit a cancer patient the most. In the future, this might help medical practitioners provide more personalized treatment.The mutational signature caused by the loss of  BRCA1/2 deficiency renders cancers susceptible to treatment with PARP inhibitors (CDK12-mutated cancers have a suggested sensitivity to CHK1 inhibitors (The DNA damage response (DDR) and repair pathways are central to the genetic integrity of cells, and deficiencies may cause mutational patterns genome-wide . Some DNhibitors , mismatchibitors  but resihibitors , and CDKhibitors . Becausehibitors . HoweverBRCA1/2 deficiencies (-d), which can be successfully predicted by measuring the accumulation of small deletions with neighbouring microhomologous sequences  caused by equences , such asequences . Likewisequences . Mutatioications  and CDK1ications . The scoications .To achieve this, mutations observed genome-wide may be condensed into mutational summary statistics for predictive modelling, including statistics based on single base subsitutions (SBSs), indels, and different types of structural variants (SVs). The SBSs are statistically assigned to so-called SBS signatures that are catalogued and enumerated within the COSMIC database . Some ofHere, we performed a systematic screen for DDR gene deficiencies that can be predicted through their association with genome-wide mutational patterns. We developed a generic approach to train predictive statistical models that identify associations with individual mutational summary statistics that capture the mutational patterns, including SBS signatures, indels, and large SVs. We applied it to 736 DDR gene deficiencies, considering both mono- and biallelic loss-of-function (LOF), identified across 32 cancer types, in a combined set of whole cancer genomes from 6065 patients  in prostate cancer. Furthermore, we present unexpected predictive models of several DDR deficiencies; ATRX and IDH1 deficiency in cancers of the central nervous systems (CNSs), HERC2 and CDKN2A deficiency in skin, PTEN deficiency in cancers of the CNS and uterus, and SMARCA4 deficiency in cancers of unknown primary.Our analysis revealed 24 DDR genes where deficiencies are associated with specific mutational summary statistics in individual cancer types across 48 predictive models. These results recapitulated the expected associations between mutational patterns and deficiencies of We compiled and analysed 2568 whole-genome sequences (WGS) from The Pan-Cancer Analysis of Whole Genomes (PCAWG)  and 3497For each genome, we evaluated 736 known DDR genes for both germline and somatic LOF events . We annon = 1702), or LOH events combined with a single pathogenic germline (n = 3562) or somatic (n = 3078) variant  with pathogenic potential (TP53 deficiency (TP53-d) was the most frequent LOF event  or more than 10 monoallelic LOF events (n = 341) (BRCA2-d in the set of HMF breast cancer tumours (n = 645) as an example, we observed biallelic LOF events in 17  tumours and monoallelic LOF events in 7  tumours (BRCA2 wild-type (WT) tumours  were used as a background set for training the predictive models  . Using B tumours . We furte models . The higBRCA2-d, we observed a strong association with the number of deletions at sites of microhomology  regression model and evaluated the ability to discriminate between deficient and WT tumours (Methods). For homology , with a findings . The LASfindings  and havefindings .Notably, some models include features with negative coefficients. The biological interpretation would be that tumours with a certain gene deficiency have fewer mutations attributed to a particular mutation pattern. Negative features were excluded in the development of the HRDetect algorithm , but we For each model, we evaluated the predictive performance using the area-under-the-receiver-operating-curve (AUROC) score as well as the precision-recall area-under-the-curve (PR-AUC) score. The PR-AUC score is a more robust measure for unbalanced data sets ; howeverFor the downstream analysis, we included (shortlisted) models with PR-AUC-E that was substantial  and significant  .BRCA1/2, TP53, CDK12, PTEN, ARID1A, and IDH1A. Each case is described in the respective part of the results.Additionally, we calculated the PR-AUC-E of each model when applied to the same cohort in the opposite data set . Due to BRCA2-d in breast cancers of the HMF data set, our model achieved an AUROC of 0.93 and a PR-AUC-E of 0.29   . The mod × 10−4) . NotablyBRCAness . HoweverBRCAness .BRCA2, each model is specified by a set of predictive features representing mutational patterns associated with DDR gene LOF. We divided the models into four groups based on aetiology and origin: models of BRCA1/2-d  and BRCA2 LOF mutations in non-metastatic ovary cancers . In contrast, BRCA2 LOF mutations in primary breast cancers were associated with decreased survival   in survival for l cancer . The assctations . Interes< 0.004)  and 3. Tpatients . The sener types . For mosBRCA2 in cancers of the ovary, prostate, pancreas, and breast. In addition, three models predicted BRCA2 monoallelic loss in cancers of the pancreas, breast, and prostate. Finally, we derived a single model of biallelic BRCA1 loss in ovarian cancer  and had PR-AUC-E above 0.2  in the other data set, suggesting that the model works independently of the metastatic capacity of the tumour  in the other data set, suggesting that the predictive performance generalises independent of metastatic tumour state (We detected 11 predictive models (four based on PCAWG and seven on HMF) of monoallelic  the CNS . These p the CNS . In line the CNS , TP53-d ur state .MSH3, SMC2, SMC6, BMPR2, CLASP2, SRCAP, UBR5, and UVRAG) of monoallelic LOF with PR-AUC-E ranging from 0.21 (CLASP2) to 0.62 (MSH3)  harbour 22% (5.9-fold enrichment) of all the DDR LOF events across the HMF colorectal cancer samples (n = 475).We suggest that the high number of models of monoallelic deficiencies may arise from spurious LOF events in DDR genes in a subset of colorectal cancers that are hypermutated. In line with this, the hypermutated samples  to 33% (BMPR2) of the mutated tumours (MSH3-d) might be the consequence of the hypermutator phenotype. In other words, the causality may be reversed in these cases, and the mutational process driven by MSH3-d may have caused the majority of their LOF events. This notion is supported by investigating the features of the models. All eight models are characterised by a single, primary predictive feature: Insertions , deletions in repetitive DNA (MSH3 and SRCAP), or deletions not flanked by repetitive or microhomologous DNA (CLASP2)  . Each ofR system . Notablyic state .MSH6, a gene implicated in MMR and microsatellite stability  by an enrichment of deletions in repetitive DNA . Indeed, the loss of CDK12 has been demonstrated to sensitise cancer cells to CHK1—  to 22 .The shortlisted predictive LOF models further include biallelic LOF of  Figure 6. The numATRX-d  and that both ATRX and IDH1 were predominantly hit by somatic mutations .We found that IDH1 and ATRX is well described in gliomas  that could be predicted with relatively high accuracy  was almost equivalent to SBS signature 27. Signature 4 is associated with smoking across several cancer types  and head and neck (p = 4.8 × 10−7), but we could not evaluate this in lung cancers, as the signature is not among its set of cohort-specific signatures.We discovered eight tumours (HMF) out of 77 with cancers of unknown primary with er types ; interessarcomas  and strosarcomas . Its gensarcomas  and metasarcomas . We eval primary . We alsoSMARCA4-d .Twelve cancers had a high posterior probability of MARCA4-d  despite SMARCA4 among the cancers of unknown primary and identified a significantly lower expression of SMARCA4 in tumours with biallelic LOF mutations compared to WT . Further studies are thus needed to clarify if the observed associations can be explained through such an ascertainment bias rather than causatively by SMARCA4-d.Given that cancers of unknown primary have disparate origins, this raises the possibility that the patients with high posterior probability of CDKN2A are known to predispose for melanoma . Its predictive features are enrichment of deletions at sites of microhomology, non-clustered inv. (100 kb to 1 Mb), and SBS signature 7, in order of predictive importance . Tumours that are co-mutated in TP53  and HERC2  showed a significantly higher number of deletions compared to tumours with LOF in either gene alone  and cancers that are WT for both genes (p < 7.2 × 10−7) (y of P53 . We obse × 10−7) .PTEN is a tumour suppressor gene found in various cancer types   . In contocations .ARID1A LOF  by depletion of SBS signature 8 mutations in metastatic prostate cancer , which expectedly increased when comparing with BRCA1/2-deficient patients  primarily by a decreased number of SBS signature 7 mutations, UV induced  (MEN1 is a regulator of gene transcription and germline deficiencies are causatively associated with developing Multiple Endocrine Neoplasia Type 1 (MEN1), which is a rare, hereditary tumour condition  . MEN1 isondition . Howeverondition . Studiested MEN1 .RB1 biallelic LOF among the metastatic urinary tract cancers by an increase of mutations attributable to UV-related SBS signature 7  (We could predict  = 0.84) . SBS sig = 0.84) . However = 0.84) . AlthougThe cancer-specific, incomplete repair of endogenous and exogenous DNA lesions leave specific genome-wide mutational patterns. Their detection provides potentially powerful information on the fidelity of individual DNA repair pathways and response to chemo- and immunotherapies. Taking advantage of a large pan-cancer data set, our analysis shows that mutational patterns are associated with DNA repair defects across a wide range of cancers and repair mechanisms. In this study, we have contributed concrete initial predictive algorithms for mutational patterns of several DDR gene deficiencies, with potential use for clinical intervention.CDK12 deficiency (CDK12-d), which has previously been associated with a tandem duplication phenotype– with power similar to that of HRD detection. This suggests a clinical benefit of clinical application of predictive algorithms to test for CDK12-d, specifically when considering the application of CHK1 inhibitors in prostate, ovary, and breast cancer treatment , as more common variants are likely benign. Given the high number of variants evaluated overall, false-positive germline LOF calls are expected. However, they are unlikely to associate with specific mutational patterns and thus are unlikely to contribute significant, shortlisted false-positive predictive models of DDR deficiency. Likewise, in cancers with hypermutator phenotypes, somatic LOF events may be caused by and associated with specific mutational patterns. This leads to predictive models that in effect detect instances of reverse causality, as discussed for the monoallelic models found in colorectal cancer. We investigated whether reverse causality was a likely explanation for an association captured by a predictive model by evaluating whether the annotated LOF events matched the predictive mutational features . In geneOur conservative LOF curation, and a lack of expression or protein-level data, is expected to cause some LOF events to be missed. This may explain a high posterior probability of a particular gene LOF in some tumours, but no evidence of genetic disruption . The data came from two independent data sets: the PCAWG   and the https://dcc.icgc.org/pcawg), and for patients with more than one sample, we always selected the earliest, whitelisted sample available. We discarded six PCAWG samples of bone/soft tissue, as these were discarded in prior publications based on the PCAWG data set  of all samples for variants between the Ensembl (GRCH37/hg19) start and end position of each DDR gene  in order to separate likely pathogenic variants from likely benign variants . All varWe also used the copy number profiles of each sample to discover genes with bi- or monoallelic losses of parts of genes. Any overlap between a gene and a copy number loss was indicated as an LOF event, under the assumption that losing any part of the protein-coding DNA is detrimental to the complete protein product. We considered events in which the minor allele copy number was below 0.2 to be an LOH, whereas we considered events with a total tumour copy number below 0.3  as deep deletions. This cutoff is adapted from the work of n = 25,399). In cases where the monoallelic hit is accompanied by an LOH, we considered the event a biallelic loss . Finally, genes that were completely depleted in a sample were considered biallelic lost (n = 66). We did not consider a single LOH event as a monoallelic loss due to the broad impact and high frequency of such events, with ~25 times higher rates of LOH than deep deletions . Regions with at least 10 breakpoints having at least 10 times smaller inter-rearrangement distance than the average across the genome of that cancer were considered clusters . SVs wern = 194). Likewise, we selected all cases with more than 10 tumours with monoallelic variants (n = 341)  within the gene. For modelling of cancers with biallelic variants in a gene, we selected all DDR gene-cohort combinations where more than five tumours had biallelic variants in the same gene (n = 341) . This seFor each model, we calculated per-sample weights to counter the imbalance in the data, so that the weight of each sample was one minus the proportion of tumours with this mutational status (either pathogenic or non-pathogenic/WT). We then used logistic regression model with LASSO regularisation (henceforth LASSO regression), with the alpha parameter at 1, from the R-package ‘glmnet’ (v4.0)  to seleck cross-fold validation sets , we ran an LASSO regression with a nested fivefold cross-validation and the assigned weights , to produce a set of lambda values. From the LASSO regression, we selected the lambda value corresponding to the binomial deviance which is one standard deviation away from the observed minimal binomial deviance of the regression, in order to avoid overfitting   . In a fek-fold cross-validation.Finally, we generated a model by including the entire data set. This was done to train the best possible model in terms of selected features and coefficients, and this is the model reported in the main figures, whereas the performance measures shown in the main figures are derived from the k-fold cross-validation to get a measure of the predictive performance of each model. Due to the strong imbalance in the data, we use the PR-AUC enrichment from the true-positive rate (PR-AUC-E) as our statistic of performance, while also reporting traditional AUROC scores. The true-positive rate is the baseline that would be expected for a non-informed model. By subtracting the true-positive rate from the PR-AUC of each model, we can compare the performance between models despite different sample sizes.We used n) for each of the 535 models, storing the PR-AUC-E for each permutation. For models where the number (r) of permutations leading to PR-AUC-E values as or more extreme than the original model was smaller than five, we ran an additional 10,000 permutations, up to a maximum of 30,000 permutations. A p value q values) smaller than 0.05 were shortlisted  based on both their PR-AUC-E performance (effect size) and their significance. Across the 535 initial models, we observed a mean PR-AUC-E of 0.04 with a standard deviation of 0.099 (90%-quantile = 0.18) . The PR-ch model . The Benrtlisted . In concFor each model, we evaluated the ability to predict mutations in the opposite data set, as a way to evaluate if the model is restricted to metastatic/primary tumours or not. To do this, we identified the set of mutated and WT samples in the opposite data set and used the model on each sample to acquire a posterior probability. Based on these, we calculated the PR-AUC-E of each model in the opposite data set . We permhttps://dcc.icgc.org/api/v1/download?fn=/PCAWG/clinical_and_histology/pcawg_donor_clinical_August2016_v9.xlsx). For samples with no registered survival time, we used the feature ‘donor_interval_of_last_followup’.For the 48 shortlisted models, we performed a survival analysis of the underlying data . For eacFor the HMF data, we acquired metadata as part of the DR-282 data package. These data included biopsy date, date of death (when applicable) and treatment end date. For deceased patients, we measured the survival time from biopsy date to date of death; for the remaining patients we measured the survival time from biopsy date to treatment end date.n = 77), we also analysed the SMARCA4 expression patterns. RNAseq FASTQ files were obtained from the HMF (DR-282) for 58 of the tumours. Reads were pseudoaligned to GRCh37 transcripts from Gencode (V37lift37) and quantified using Kallisto version 0.48.0 (SMARCA4 transcripts (ENST00000644737.1) and calculated an overall gene-level TPM score as the sum of the transcript-level TPM scores.For the metastatic cancers of unknown primary  feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and W Kimryn Rathmell as the Senior Editor. The reviewers have opted to remain anonymous.Thank you for submitting your article "Pan-cancer association of DNA repair deficiencies with whole-genome mutational patterns" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Below you will find several suggestions for text changes that will improve the clarity of the manuscript. We encourage you to consider these suggestions and ask that you provide a response indicating how you have addressed those that you agree have merit in the text.Reviewer #1 (Recommendations for the authors):Some open questions and comments follow.The authors mention that they excluded age-related signature 1 from the modeling as a potential confounder. Given this issue, I wondered why the clocklike signature SBS5 was not excluded for the same reason.Monte Carlo simulation to test the performance of the lasso is mentioned twice in the main text but appears not to be described in the methods.Regarding spurious LOFs potentially driving models in some colorectal subsets, I question why hypermutated samples were not screened ahead of modeling or further QC of variant calls from HMF and PCAWG performed.At various points in the manuscript, the authors emphasise which models are predictive across primary and metastatic samples. This is interesting. It would have been useful to see these points consolidated in a single section of the text or a figure to allow readers to consider which deficiency models are generalizable across tumours of different metastatic potentials. Do the authors have a hypothesis as to why this might be? Where models are not generalizable is this down to insufficient power or because there is an alteration in the mode of damage associated with that deficiency in mets?Re SMARCA4-d in tumours of unknown primary with SMARCA4 WT, is it established that there is no epigenetic silencing event in these cases?Reviewer #2 (Recommendations for the authors):A well-motivated paper using various computational analyses and a pan-cancer data set to decipher DDR genes that may be used for clinical intervention afterextensive validation.There are a few questions that need to be addressed, as outlined below:Despite the association between BRCA genes and mutation signature 3, previous studies have suggested that lesions in PALB2 and RAD51-related genes might contribute to mutational signature 3 activity. It would be interesting to figure out why these genes were not detected by the model.How does the damage in DDR genes differ between patients?I would recommend that the authors perform univariate and multivariate Cox proportional hazard models to explore associations of biomarkers (24 genes) with PFS, DSS, or OS. Reviewer #1 (Recommendations for the authors):Some open questions and comments follow.The authors mention that they excluded age-related signature 1 from the modeling as a potential confounder. Given this issue, I wondered why the clocklike signature SBS5 was not excluded for the same reason.We thank the reviewer for noting the recent updates to the COSMIC annotation of the mutational signature 5, which is now listed as potentially associated with time/age. Previously, signature five was not associated clearly with time/age, and has been suggested to be associated with other DNA damage response processes including the hormone receptor positive subtype of breast cancers. We have clarified this in the manuscript, Materials and methods subsection: “Mutational patterns of single base substitutions, indels and structural variants”:“We did not exclude signature 5 although it has suggested association with age, because it also has suggested associations to the hormone receptor positive subtype of breast cancers”Monte Carlo simulation to test the performance of the lasso is mentioned twice in the main text but appears not to be described in the methods.This was a textual error on our part and we thank the reviewer for making us aware the structure was unclear. The Monte Carlo simulations are described in the Materials and methods subsection: “Model selection”. To make this clear, we have retitled the subsection to: “Model selection using Monte Carlo simulations”, and updated the text to make it more evident to the reader.Regarding spurious LOFs potentially driving models in some colorectal subsets, I question why hypermutated samples were not screened ahead of modeling or further QC of variant calls from HMF and PCAWG performed.We agree with the reviewer that hypermutated cancers present a challenge for an automated and generic modeling procedure. In particular, they may harbor large numbers of LOF events, many of which may be inconsequential for cancer evolution. , which helps illustrate this.) We decided to include hypermutated tumours to ensure a uniform application and evaluation of our generic procedure, and since genetic hypermutator phenotypes are well described among colorectal cancers. Given that our procedure separates samples by cancer type, hypermutated colorectal cancers samples would not affect models trained for other cancer types.Inspired by the comment from the reviewer, we evaluated the enrichment of LOF mutations among the subset of hypermutated tumors and now include a paragraph on this in the subsection: “Colorectal cancer models derived from hypermutated mismatch repair deficient tumours”:“The high number of models of monoallelic deficiencies may arise from spurious LOF events in DDR genes in a subset of colorectal cancers that are hypermutated. In line with this, the hypermutated samples  harbour 22% (5.9 fold enrichment) of all the DDR LOF events across the HMF colorectal cancer samples (n=475).”MSH3-d model or any of the other models among the colorectal cancer samples. We did not include these results in the manuscript.We further reran our predictive modeling pipeline with exclusion of these hypermutated colorectal tumor samples. However, no DDR genes then had LOF sets sufficiently large to fulfill our modeling criteria . We would thus be unable to detect the In terms of the risk of false variant calls, our setup relies on the extensive quality control performed by the PCAWG and the Hartwig Medical Foundation and thus on the tradeoff between sensitivity and specificity chosen for their variant calling. This tradeoff relies on access to BAM files and extensive experimentation, which was not the focus of our study and thus out of scope. Importantly, mutational signatures are generally robust towards false mutation calls as long as they are not systematic; this has been extensively considered for the HMF and PCAWG data specifically ; HMF: ).At various points in the manuscript, the authors emphasise which models are predictive across primary and metastatic samples. This is interesting. It would have been useful to see these points consolidated in a single section of the text or a figure to allow readers to consider which deficiency models are generalizable across tumours of different metastatic potentials. Do the authors have a hypothesis as to why this might be? Where models are not generalizable is this down to insufficient power or because there is an alteration in the mode of damage associated with that deficiency in mets?We agree with the reviewer that it may be of general interest to include an overview of the performance of each model across metastatic and primary tumours. We have expanded our analysis to include a unified overview of the predictive power in the opposite data set. These results are now provided in Supplementary File 1h and summarized in Figure 3—figure supplement 1. We provide introduce this analysis and the models that have significant predictive power in the opposite data in a short separate Results’ subsection: “Testing models in the opposite data set” (and include a corresponding Methods’ subsection):“Additionally, we calculated the PR-AUC-E of each model when applied to the same cohort in the opposite data set . Due to the difference in biology between the two sets, and low numbers of LOF mutated samples, we did not use this as a model performance criteria but have included the PR-AUC-E values and p-values from the tests (Supplementary File 1h). We identified significant predictive power, across both metastatic and primary cancers, for deficiency models of BRCA1/2, TP53, CDK12, PTEN, ARID1A, and IDH1A. Each case is described in the respective part of the results.”Notably, the currently available data sets are not well suited to pinpoint systematic differences between metastatic and primary tumours due to varying cohort sizes of different cancer types within and between the two data sets. Many models cannot be evaluated in other cancer types or the opposite data set due to lack of samples with mutations in a given DDR gene. Thus, we cannot exclude that more models may have predictive power between both metastatic and primary cancers than what we can currently identify.Re SMARCA4-d in tumours of unknown primary with SMARCA4 WT, is it established that there is no epigenetic silencing event in these cases?We do not have access to epigenetic data from the tumours of unknown primary, but were able to access expression data for a subset of them (58 of 77). Expression analysis did not indicate that epigenetic silencing was taking place, which we now show in Figure 6k and state in the subsection: “Predictive model for SMARCA4-d in cancer of unknown primary”:-2; Figure 6k). For the 12 tumours with high signature 27 exposure but no biallelic LOF mutations, we did not observe a similar decrease in expression , suggesting that SMARCA4 was not epigenetically silenced or otherwise transcriptionally inactivated in these cases.”“We evaluated the expression of SMARCA4 among the cancers of unknown primary and identified a significantly lower expression of SMARCA4 in tumours with biallelic LOF mutations compared to wild type (p=0.54x10Reviewer #2 (Recommendations for the authors):A well-motivated paper using various computational analyses and a pan-cancer data set to decipher DDR genes that may be used for clinical intervention afterextensive validation.There are a few questions that need to be addressed, as outlined below:Despite the association between BRCA genes and mutation signature 3, previous studies have suggested that lesions in PALB2 and RAD51-related genes might contribute to mutational signature 3 activity. It would be interesting to figure out why these genes were not detected by the model.PALB2 and RAD51 and signature 3. However, we did not have sufficient data to evaluate this as we only identified a single patient with a LOF mutation in RAD51 and a single in PALB2 across all breast cancer samples of both data sets.We agree with the reviewer that it is reasonable to expect associations between How does the damage in DDR genes differ between patients?We have included Supplementary File 1g, which summarizes the types of DDR gene damages across the samples included for the training of each predictive model. Additionally, we now include Figure 1—figure supplement 1, which shows the rate of LOF events in DDR genes at a per-tumour level. To preserve patient privacy and the data agreements, we cannot present DDR gene damages at an individual sample level. We now detail this in the Materials and methods section, subsection: “Annotating biallelic and monoallelic gene hits”:“We have summarised the causes of LOF annotation at a per-model basis (Supplementary File 1g), including an annotation of the number of tumours with events hotspot locations, microhomologous DNA, and repetitive DNA. We do not disclose this information at a per-sample level in order to maintain patient privacy and data safety.“I would recommend that the authors perform univariate and multivariate Cox proportional hazard models to explore associations of biomarkers (24 genes) with PFS, DSS, or OS.We agree that it is of general interest to understand the association between DDR deficiencies and survival, though we have low numbers of LOF mutated samples in most cases as well as missing survival data in some cases, and thus limited statistical power for detecting significant hazard associations.We have now included Kaplan-Meier plots and the results of fitting univariate Cox-regression models to overall survival statistics (the only type we have available). The results are reported in the Results’ subsection “Survival analysis” with a full summary given in Figure 3—figure supplement 1 and individual Kaplan-Meier plots shown in Figure 3—figure supplement 2:29. Interestingly, several models of BRCA1/2 LOF mutations associated with improved survival, including BRCA1 LOF mutations in metastatic ovary cancers  and BRCA2 LOF mutations in non-metastatic ovary cancers . In contrast, BRCA2 LOF mutations in primary breast cancers were associated with decreased survival . This may potentially reflect differences in both molecular diagnostic practices and treatment regiments across these cancer types. For instance, platin-based treatment irrespective of BRCA1/2 status has been standard for groups of the ovarian and pancreatic cancer patients, while traditionally not for the breast cancer patients30,31. The sensitising effect of BRCA1/2 deficiency might thus explain the associated survival differences among cancer types32. For most models the differences in survival were insignificant, though this may be related to the generally small set of LOF mutated samples.”“For each of the shortlisted models, we evaluated the difference in overall survival between samples carrying LOF mutations and those that did not. We observed nominally significant differences  in survival for BRCA2 and TP53 in multiple cancer types as well as for UVRAG in colorectal cancer . The association of TP53 monoallelic LOF with decreased survival is in line with expectationsWe have not extended this analysis further given the general small number of LOF mutated samples and resulting issues with lack of power.


However, technical artifacts, either introduced during library preparation and/or data analysis, can influence the detected RNA expression levels. A critical step, especially in large and low input datasets or studies, is data normalization, which aims at eliminating the variability in data that is not related to biology. Many normalization methods have been developed, each of them relying on different assumptions, making the selection of the appropriate normalization strategy key to preserve biological information. To address this, we developed NormSeq, a free web-server tool to systematically assess the performance of normalization methods in a given dataset. A key feature of NormSeq is the implementation of information gain to guide the selection of the best normalization method, which is crucial to eliminate or at least reduce non-biological variability. Altogether, NormSeq provides an easy-to-use platform to explore different aspects of gene expression data with a special focus on data normalization to help researchers, even without bioinformatics expertise, to obtain reliable biological inference from their data. NormSeq is freely available at:   The continuous improvement of RNA sequencing (RNA-seq) methodologies , togetheAlthough high-throughput RNA sequencing offers valuable insights into disease biology, it can also be subjected to various non-biological technical biases, which can result in differences in sequencing depth ,6, or GCInitially, intra-sample ‘normalization by library size’ methods ,9, like et al.  genes will increase. Key assumptions for distribution-based methods are that only a few DE genes exist and technical artefacts affect DE and non-DE genes in the same way . Over thet al. ), which et al. . HoweverTo this end, we developed NormSeq, a freely accessible webserver tool that is dedicated to the evaluation and direct comparison of the most commonly used data normalization methods for any user-supplied RNA-seq expression dataset. The goal of NormSeq is to systematically compare normalization approaches and guide the user towards the best normalization method, i.e. the one that correctly recovers biological signal. We implemented the use of the information gain metric to guide the selection of the most appropriate normalization method and RLE plots for a visual inspection of the normalization results. Moreover, NormSeq includes the possibility of performing batch-effect correction, as well as multiple downstream analyses, such as consensus differential gene expression, multiple visualizations and the download of all the information available on the webserver.https://arn.ugr.es/normSeq.NormSeq is available at: Different experimental conditions and designs call for different normalization methods . NormSeqtxt, csv, tsv or xls formats or by providing a URL link to the file in one of those formats. A matched annotation file is mandatory to initiate the normalization analysis on the webserver, and users have the possibility to provide an additional batch-effect annotation file. Several parameters can be adjusted to personalize the normalization analysis. This includes the selection of a minimum read coverage, the choice for computational batch effect correction, and differential expression analysis related parameters. A separate job will be created for each normalization analysis with a URL that will remain active for 15 days.The normalization analysis starts with user-provided datasets that are required to be presented as raw count tables. Users can supply the count matrix by directly uploading a file in A unique feature of NormSeq is the possibility to select the most optimal normalization method for a given dataset by means of the information gain , an information theory method  Figure . In esseThe challenge in computing information gain in RNA-seq datasets resides mainly in the fact that the underlying probability distribution of the data is not known, and the continuous normalized data needs to be transformed from a continuous scale to a discrete probability distribution. Different methods exists to do this transformation. Among them, we selected the ‘Nearest Neighbour’ transformation that has been described as optimal for this type of experimental design ,18.NormSeq offers the information gain distribution for all chosen normalization methods in two formats: for each pair-wise group comparison and for each individual group. For pair-wise group comparisons Figure , a normaBesides the information gain analysis, the RNA expression distribution is shown Figure . This isFinally, NormSeq offers RLE plot visualization, which is included to assess and estimate the unwanted variation removal of each method. All together, these tools assist users in the selection of the most optimal normalization method for downstream analysis of their particular dataset.NormSeq offers a multitude of visualization options that can be personalized and downloaded. The visualization section of the NormSeq webserver is divided into three sections. Hierarchical clustering analyses are incorporated for side-by-side visualization of similarities between samples for each chosen normalization method Figure . PrincipBatch effect correction using the ComBat-Seq tool  is offert-test. We provide a summary with under-, and over-expressed RNAs for each DE protocol. The consensus differential expression between all methods is calculated and can be visualized with Upset plots  analysis is one of the most commonly used applications of RNA-seq data analysis . NormSeqs Figure . Additios Figure .r: 0.75; Figure r: 0.21; Figure To illustrate the usefulness of our normalization tool, we analyzed a publicly available tRNA sequencing dataset, accession number GSE141436 from the NCBI Gene Expression Omnibus (GEO) repository . In thisTaken together, the panel of tools provided by NormSeq to evaluate normalization methods clearly indicated that each normalization method perform differently for every dataset. As the performance of each normalization method heavily depends on the sequencing protocol, the design of the study, as well as the biological circumstances, the NormSeq application can guide the user in effortlessly selecting the most appropriate normalization method to better capture meaningful expression profiles of RNAs of interest.mutual_info_classif function from Scikit-learn python package (MinMax function from the same package. The plotly package (NormSeq website was implemented using a Django framework, together with Bootstrap and Javascript. Information gain is calculated by means of  package . PCA plo package , and the package  were useIn this manuscript we introduce NormSeq, a web server that provides users a guided normalization selection for high-dimensional and complex RNA-seq datasets. The main goal of NormSeq was to create an analytic and user-friendly platform that simplifies RNA-seq data normalization and differential expression analysis. To the best of our knowledge, NormSeq is the first web server that offers logical and stepwise navigation through seven different options for data normalization, four differential expression analysis protocols, information gain calculation and optional batch effect correction for the analysis of high-throughput RNA-seq data.Future improvements will include incorporation of additional normalization methods and visualization options, as well as the inclusion of an optional stand-alone version of the NormSeq tool. Finally, we also plan to extend our NormSeq webserver towards the application of data generated with different high-throughput profiling platforms such as single cell RNA-sequencing.https://arn.ugr.es/normSeq/ and the source code is available at https://github.com/cris12gm/normSeq.NormSeq is freely available for all users at: gkad429_Supplemental_FileClick here for additional data file.


Variational autoencoders (VAEs) have rapidly increased in popularity in biological applications and have already successfully been used on many omic datasets. Their latent space provides a low-dimensional representation of input data, and VAEs have been applied, e.g. for clustering of single-cell transcriptomic data. However, due to their non-linear nature, the patterns that VAEs learn in the latent space remain obscure. Hence, the lower-dimensional data embedding cannot directly be related to input features.To shed light on the inner workings of VAE and enable direct interpretability of the model through its structure, we designed a novel VAE, OntoVAE (Ontology guided VAE) that can incorporate any ontology in its latent space and decoder part and, thus, provide pathway or phenotype activities for the ontology terms. In this work, we demonstrate that OntoVAE can be applied in the context of predictive modeling and show its ability to predict the effects of genetic or drug-induced perturbations using different ontologies and both, bulk and single-cell transcriptomic datasets. Finally, we provide a flexible framework, which can be easily adapted to any ontology and dataset.https://github.com/hdsu-bioquant/onto-vae.OntoVAE is available as a python package under  In recent years, deep learning (DL) has been widely used to analyze high-dimensional biological omics data, especially single-cell RNA sequencing (RNA-seq). In contrast to linear methods, such as principal component analysis (PCA), non-linear models can capture more complex patterns in the data , which cDifferent approaches have already been used to tackle the problem of limited interpretability. Tybalt tries to extract a biologically meaningful latent space by examining how different latent vectors separate covariates and then investigating the associated gene weights of the latent vectors of interest in the one-layer decoder . Other min silico and then monitoring how these changes propagate through the network, OntoVAE can simulate the effects of drug treatment or genetic alterations. The investigation of subsequent alterations in the activation of hidden nodes representing processes or phenotypes allows to uncover complex genotype–phenotype relationships. Thus, we consider OntoVAE a powerful tool for in silico screening approaches.Here, we introduce OntoVAE (Ontology guided VAE), a novel flexible VAE architecture with a multi-layer, sparse decoder that allows for the incorporation of any kind of hierarchical biological information encoded as an ontology. OntoVAE provides direct interpretability in its latent space and decoder, as the activities of the neurons now correspond to activities of biological processes or phenotypes. Its efficient implementation allows users to consider thousands of terms and monitor their activity changes, without the need to preselect-specific processes. Importantly, OntoVAE can be used for predictive modeling. By modulating the values of input features x the input data and z the latent space. The decoder part, or generative model, yields a likelihood distribution The VAE is a probabilistic DL model consisting of two coupled, but independently parameterized neural networks: an encoder, which learns a probability distribution over a compressed representation of the high-dimensional input data, which we refer to as latent space, and a decoder, which tries to reconstruct the original input from this latent space representation after sampling from the learnt distribution . More fo network . During The first part of solution . The repsolution .OntoVAE is a modified VAE whose latent space and decoder are implemented so that they can incorporate any DAG, such as a biological ontology . For thiThe decoder of OntoVAE is linear, multi-layered and sparse, as it only models connections between parent and child terms of the ontology as well as between terms and annotated genes. In contrast to a standard VAE where connections are only present between neighboring layers, OntoVAE also has to model connections between non-neighboring layers as well as between any layer and the reconstruction layer, as terms in each depth level have genes annotated to them. This is achieved by a successive layer concatenation process similar to the skip connections in DenseNet .The preprocessed ontologies and datasets used in the manuscript are provided under geneontology.org  together with the GAF annotation file  .Ontology was downloaded from ion 2.1) , ending hpo.jax.org  together with an annotation file (genes_to_phenotype.txt) containing the mapping of HPO IDs to genes (The ontology was downloaded from Genotype Tissue Expression (GTEx) bulk RNA-seq data from human tissues was retrieved through the R package recount3 (v 1.1.8), which is communicating with recount3, a database of uniformly reprocessed RNA-seq datasets (Bulk RNA-seq data sequenced from muscle samples of limb-girdle muscular dystrophy (LGMD) patients and healthy individuals were downloaded from Gene Expression Omnibus (accession number: GSE202745) (https://github.com/LucasESBS/vega-reproducibility) (The preprocessed single-cell RNA-seq dataset of interferon (IFN)-ß treated peripheral blood mononuclear cells (PBMCs) was downloaded through the github repository of VEGA (https://figshare.com/projects/OntoVAE_Ontology_guided_VAE_manuscript/146727: (i) GO with Ensembl IDs trained on GTEx bulk RNA-seq data downloaded through recount3, (ii) HPO with Gene Symbols trained on GTEx bulk RNA-seq data downloaded through recount3, and (iii) GO with Gene Symbols trained on unstimulated cells from the PBMC dataset. The exact layer compositions of the three models are given in The OntoVAE framework is written in pytorch. All OntoVAE models in this manuscript have been trained with a batch size of 128, a dropout of 0.2 in the hidden layer of the encoder, a dropout of 0.5 on the latent space layer, and a weighting coefficient of 1e-4 on the KL loss. Model training was performed on 80% of the samples, while the remaining 20% were used for validation. Models were usually trained over 300 epochs, and the model with the best validation loss was used. AdamW was used as the optimizer together with a learning rate of 1e-4. The dimensions of latent space and decoder are always defined by the used ontology. Three neurons were used per ontology term. The following pretrained models are provided under P-value cutoff of .05 at each node in the decoder.We retrieve the activities at each node when running samples through a pretrained model by attaching pytorch hooks to each layer. To compare pathway activities between groups of samples, we performed two-tailed Wilcoxon tests using the stats.ranksums function from the scipy package (v 1.5.2) with a For each GO term and each tissue, we trained a 1-vs-all naive Bayes classifier with 10-fold cross-validation and computed the median area-under-the-curve (AUC) from the ten folds. Subnetworks of the GO graph that are represented in P-value ⩽ .05). We then counted the number of hits per tissue and used this as a measure to rank all tissues for one term, with the tissue with most hits receiving Rank 1 for this term, the tissue with second most hits receiving Rank 2 and so on. For a given tissue, the terms were then sorted again based on their rank, the number of hits, and the median of the Wilcoxon test statistic. We then took the top 100 terms of the tissue and clustered them based on their Wang semantic similarities (http://ontovaemodelexplorer.pythonanywhere.com/). The rankings of the GO terms for all tissues can be found in the For the creation of tissue-specific GO networks for the GTEx dataset , we perfFor all possible pairs of GO terms, we compared their sets of descendant genes. We use the term “descendant genes” to specify the set of genes that is either directly annotated to a given term or to one of its descendant terms. js was calculated by dividing the number of elements in the intersection of the two sets by the number of elements in their union. We then defined three intervals , and 1000 random term pairs were sampled from each class to produce the boxplots in the right panel of in silico gene knockouts have been performed by setting the input value for a gene to zero before running data through the trained model and retrieving pathway activities. For the study of drug-induced perturbations, in silico stimulation of genes was performed by increasing their input value prior to running data through the trained model.All simulations in this study were carried out in a single-gene context, meaning that we only perturbed the expression of one gene at a time. For the study of genetic perturbations, Knockout of Duchenne muscular dystrophy (DMD), COX5A, and SFSWAP was performed in the 881 muscle samples.Systematic knockout of all 4774 genes annotated to HPO was performed in the 881 muscle samples.Systematic stimulation of all 5472 genes annotated to GO and expressed in the unstimulated cells of the PBMC dataset was performed by setting their input value to 8, as 6.8 was the maximum expression value found in the unstimulated cells.For analysis of perturbation consequences, one-tailed paired Wilcoxon tests were performed between the same set of samples pre- and post-perturbation using the function stats.wilcoxon from the scipy package (v 1.5.2).Tests were performed at each node in latent space and decoder to identify terms significantly downregulated upon knockout  was performed between IFN stimulated and unstimulated cells for each cell type separately. Only genes were included that could also be mapped to GO. We performed two-tailed Wilcoxon tests using the stats.ranksums function from the scipy python package (v 1.5.2) and corrected for multiple testing with the function stats.multitest.fdrcorrection from the python package statsmodels (v 0.12.0). For each cell type, we then selected genes significantly upregulated upon IFN treatment, using an FDR threshold of 0.1. Gene set upregulated in CD4T cells was termed CD4T_IFN-ß_stim_up.n = 42) and controls (n = 33) using the R package DESeq2 (v 1.26.0). Eight patient samples and one control sample had been excluded as outliers prior to analysis after PCA inspection of the dataset. We used a significance threshold of 0.1 for the adjusted P-value and kept only genes that could be mapped to HPO. Genes upregulated in LGMD muscles compared to control were termed LGMD_up, genes downregulated in LGMD muscles compared to control were termed LGMD_dn.DGEA was performed between muscle samples of patients  was performed with the R package clusterProfiler (v 3.14.3).Overrepresentation analysis (ORA) was performed with the R package clusterProfiler (v 3.14.3).To compare gene expression, OntoVAE + GO, OntoVAE + Reactome, VEGA + Reactome, and expiMap + Reactome, cells were clustered using Leiden clustering (scanpy v1.9.3) with the resolution hyperparameter set to 0.2, 0.2, 0.4, 0.3, and 1.2, respectively. Adjusted rand index (ARI) was then computed with the adjusted_rand_score function from scikit-learn (v1.0.2).To make the latent space and decoder part of a VAE model biologically interpretable, we created a novel architecture that we named OntoVAE where we implemented the latent space and decoder in a way that any biological ontology, such as GO or HPO, can be incorporated . Thus, eFollowing the lines of previous research .Because a high AUC does not necessarily correspond to a high pathway activity, we took a different approach in extracting the top GO terms for a given tissue. We performed Wilcoxon tests between all possible pairings of tissues at each node, and then assigned a rank to each term for each tissue (see Section 2), allowing us to further group the terms that were most relevant for a given tissue into a network based on their Wang semantic similarities. All results can be found in the In order for the previous results to be biologically meaningful, we should obtain similar results every time we train the same model with the same hyperparameters. To confirm this, we trained the model 10 times using the same hyperparameters, and using either one, two or three neurons per term, resulting in 30 trained models. For each GO term, we then calculated the Pearson correlation with itself when retrieving its pathway activities from two different models and found that the majority of correlations was higher than 0.95, thus ensuring the reproducibility of OntoVAE .In the context of these investigations, we also wanted to explore how the model would perform if the ontology information was integrated in the encoder. Thus, we performed the same experiment with a GO-encoder model and found the results to be less reproducible  and the We additionally investigated the influence of using different trimming thresholds with the same approach of correlating pathway activities between two models, and found that thresholds of 1000/30 (top/bottom) and 1200/10 showed a good agreement, while 800/50 showed worse correlations with the other thresholds . We hypoWe also investigated the validation loss of our model and how it changes in dependence of the number of neurons per term  and the in silico knockout of the DMD gene in the GTEx muscle samples. The DMD gene encodes for the protein dystrophin, which is located primarily in muscles and attaches the cytoskeleton to the extracellular matrix. Depletion of functional dystrophin protein due to a mutation in the DMD gene causes DMD, a genetic disease leading to muscle weakness and muscle degradation   , the othLGMD_dn) .n = 16) and healthy individuals (n = 15)  . For bot(n = 15) , confirm(n = 15) . We foun(n = 15) . The rem(n = 15) . This anet al., in which PBMCs from lupus patients were treated with IFN-ß (a type I IFN) and single-cell RNA-seq was performed . To investigate which genes had the highest influence on the node in the GO-decoder corresponding to type I IFN signaling pathway, we computed a paired Wilcoxon test between the activations at this node before and after stimulation for each gene in the CD4T cells  CD4T cells. For this purpose, we retrieved OntoVAE pathway activities for CD4T control, in silico perturbed CD4T, and IFN-stimulated CD4T cells, computed a UMAP over the control and ground truth cells, and then projected the in silico cells onto that UMAP space. With increasing stimulation of the 717 leading edge genes, the in silico perturbed cells are approaching the ground truth cells in the UMAP space  for VEGA and https://scarches.readthedocs.io/en/latest/expimap_surgery_pipeline_basic.html (as of February 2023) for expiMap. For comparison, we also trained OntoVAE as a single-layer model with Reactome pathways in the latent space. We then performed Leiden clustering on the four alternative methods, and directly on the gene expression data, and computed the ARI to assess the quality of the clustering  as well as on a single-cell RNA-seq dataset (PBMC). Using GTEx and GO, we demonstrated that the model generates reproducible results and outputs meaningful pathway activities in latent space and decoder. Furthermore, we applied OntoVAE in two scenarios of predictive modeling: genetic alterations and drug treatments. Again using GTEx and GO, we showed that we obtain meaningful terms in the decoder and reconstruction layer when simulating gene knockouts. Using GTEx and HPO, we showed how to systematically perform an One limitation of our model is that we only model one type of relationship between terms, namely the “is a” relationship, as there is no straightforward way to model different kinds of connections. By enabling more complex and diverse relationships between nodes, our current model could incorporate knowledge-graphs as a decoder in a similar fashion as we did for ontologies as an alternative to graph-neural networks that are commonly used (In summary, OntoVAE can be adapted to any ontology and dataset and used to compute pathway activities and to predict disease or treatment induced changes in gene expression. Our model fully exploits the conceptual complexity of the hierarchical structure of the ontology and can highlight difference between samples at different levels of the ontology. In future work, it will be interesting to also investigate the effect of multiple perturbations at a time, and see if synergistic effects can be recovered by OntoVAE. We envision that our method will be a useful first step in identifying sets of target genes or pathways, which can then be further validated experimentally.btad387_Supplementary_DataClick here for additional data file.


Single cell RNA‐seq (scRNA‐seq) profiles conceal temporal and spatial tissue developmental information. De novo reconstruction of single cell temporal trajectory has been fairly addressed, but reverse engineering single cell 3D spatial tissue organization is hitherto landmark based, and de novo spatial reconstruction is a compelling computational open problem. Here it is shown that a proposed algorithm for de novo coalescent embedding (D‐CE) of oligo/single cell transcriptomic networks can help to address this problem. Relying on the spatial information encoded in the expression patterns of genes, it is found that D‐CE of cell–cell association transcriptomic networks, by preserving mesoscale network organization, captures spatial domains, identifies spatially expressed genes, reconstructs cell samples’ 3D spatial distribution, and uncovers spatial domains and markers necessary for understanding the design principles on spatial organization and pattern formation. Comparison to the novoSpaRC and CSOmap  on 14 datasets and 497 reconstructions, reveals a significantly superior performance of D‐CE. The authors develop a novel de novo oligo and single cells spatial reconstruction method, developmental coalescent embedding (D‐CE). DC‐E can further optimize the reconstruction result by adding a template or markers. Under the evaluation of three indexes, ordering index, angular separation index, and PSImcc, DC‐E shows superior reconstruction performance compared with novoSpaRC, CSOmap, and other three methods. Various computational tools based on this assumption have been established to model the developmental time trajectories. For instance, Monocle reduces the data dimensionality and uses the minimum spanning tree to model the developmental paths. Diffusion pseudotime, which is based on diffusion‐like random walk distances, is used to map developmental branching decisions. Spatial distribution and patterning of cells are not only essential for development but also for disease diagnosis and prognosis. Patterning and morphogenesis during development, injury or regeneration are processes of cell movements and organizations guided by three major forces: small or macromolecule morphogen gradient, bioelectric voltage gradient and mechanical force gradient, forming local environment or spatial domains, and program or reprogram the cells at the epigenome and transcriptome levels. Thus, transcriptomic‐based computational reverse engineering of 3D tissue distribution in a “pseudospace” could be potentially achieved. A benchmark cell population timer/clock has been proposed to test the performance of pseudotime algorithms to approximate the real developmental time of each single cell. Similarly, a benchmark microdissection‐based 3D transcriptome, termed Geo‐seq, can be used to evaluate algorithms to approximately map single cells onto in vivo positions. While technologies to generate spatially resolved transcriptomes are still evolving and not yet achieving single cell resolution or in 3D space, the vast majority of the millions perhaps billions of scRNA‐seq can benefit from de novo single cell level 3D reconstruction. Currently, there exist only two algorithms (novoSpaRC and CSOmap) to do so computationally, that is to de novo reconstruct the spatial cell distributions and spatial transcriptomes, with encouraging yet highly variable results. Thus, de novo spatial reconstruction is still a compelling computational open problem. Some landmark‐based computational approaches, such as Seurat and Halpern et al.’s method, have been proposed to reconstruct spatial distribution of single cell transcriptomes in zebra fish embryos and mouse liver based on preselected or verified spatially expressed landmark genes. But, these approaches are not de novo reconstruction methods because the landmark genes are ad hoc expressed in certain specific 3D spatial positions of the considered in vivo tissue, and act as surrogate labels for the positions when revealed and input to the algorithms. So far, effective, universally (tissue‐wide) applicable, completely de novo approaches have yet to be developed, and only recently the first template structure constrained approach named novoSpaRC was proposed by Nitzan et al. with encouraging yet variable results highly dependent on the input template. CSOmap based on ligand–receptor interactions is another de novo method recently developed, but performs no better than novoSpaRC. To address the de novo reconstruction of oligo and single cell 3D spatial tissue ordering and localization, we design a novel algorithm termed De Novo Coalescent Embedding (D‐CE) according to the network‐based conceptual framework of Coalescent Embedding (CE), which is a model‐free unsupervised machine intelligence methodology for network geometry embedding. However, D‐CE is remarkably different from previous CE algorithms, which were designed for hyperbolic embedding. Although it shares with them the rationale to exploit the phenomenon of network coalescence, D‐CE is innovative because it introduces for the first time a de novo network‐based strategy in spatial pattern reconstruction of oligo and single cells  that simultaneously profile thousands and more single cells—have becoming powerful tools to capture such continuous spatiotemporal changes during development.1 Base22.1 For instance, CE showed to boost the detection of community structural organization in social networks and to reliably capture the original geometry of macroscale structural brain connectomes. The name coalescent embedding derives from “angular coalescence,” which is a term proposed to indicate that, as a result of this methodology of embedding, the individual network nodes geometrically aggregate together  forming a pattern that is progressively ordered along the geometrical angular coordinates. In CE algorithms, the node angular coordinates are ordered according to latent relations of topological homophily (similarity) between the network nodes, instead the node radial coordinates according to latent relations of topological hierarchy between the network nodes  decomposition of the centered shortest‐path kernel obtained from the transcriptome‐similarity network. The result of this network embedding procedure is the angular coalescence that is an angular similarity pattern which preserves the mesoscale network structure of cell‐assemblies (which are network communities: cohort of cells with higher intrasimilarity in respect to the rest of the network) and the relationships among cell‐assemblies, and these relationships map the relative locations of the cell‐assemblies and entities within.The network embedding step, is designed according to topological machine learning theory,18 and in this study, we first use this dataset to establish our 3D reconstruction D‐CE method  as marker genes. The expression patterns of these self‐nominated marker genes, when used, can further enhance the accuracy of spatial template‐fitting. This is no longer a mere de novo reconstruction, but rather a self‐generated (because the makers are self‐generated by D‐CE and not indicated by previous knowledge in scientific literature) marker‐based reconstruction Figure . The int19 , which are then fairly compared by considering the best of these settings. In order to appraise the extent to which different normalization methods and distance metrics would affect the performance of D‐CE, we considered Geo‐seq samples whose 3D domain labels are known and can be used as gold standards to evaluate the reliability of a de novo 3D reconstruction algorithm. Each Geo‐seq sample is not a single cell but a portion of tissue constituted by a cohort of ≈10–20 single cells, however this genome‐wide 3D labeled dataset is an ideal dataset to design and to test D‐CE performance. We considered the sample–sample transcriptome distance matrix (weighted network) using each of 12 normalization methods (Table  (1‐Spearman rank coefficient (RCC)), Pearson distance (PD) (1‐Pearson correlation coefficient (PCC)), Euclidean distance (ED), and PCC and RCC filtered by connectivity specificity index (CSI), named PCC‐CSI and RCC‐CSI  is used to test how well the four groups are separated according to angular coordinates in the embedding space. Projection separability index‐Matthews correlation coefficient  is used to evaluate the group separability and relative orientation in geometrical space. Ordering Index  to evaluate the accuracy of ordering the layers from distal to proximal . To evaluate the accuracy of the reconstruction, we grouped the Geo‐seq samples into four groups: 1–2) proximal anterior and distal anterior (pA and dA); 3–4) proximal posterior and distal posterior (pP and dP) Figure . Angular15 , while other methods, in particular PCA and UMAP mostly separate samples based on germ layers rather than spatial domains Figure . The fac22 theSimilarly, for the mouse brain parietal region scRNA‐seq data, for which both the brain domain labels and the cell type labels are known, only D‐CE can well separate and reconstruct spatial positions of single cells from the same cell type (lineage), while other methods, in particular PCA and t‐SNE mostly separate samples based on cell types rather than spatial domains Figure . These b2.3Next, we investigated whether D‐CE is also applicable to other spatial transcriptomic data with gold standard position labels in a template for each sample, either at oligo cell or single cell resolutions. on which was novoSpaRC developed and optimized. As only the expression data of 84 Drosophila embryo development regulating TFs are measured (no ligand and receptor genes), CSOmap, which only accepts human or mouse data and using ligand and receptor genes for reconstruction, is not applicable on this dataset. All the 84 genes were used for D‐CE reconstruction. We found that, instead of PD (as before), its local‐threshold‐variation named PCC‐CSI  performs the best for spatial reconstruction among all 5 distance options  as the reconstructed locations for each sample, we visualized its spatial reconstructions based on 0, top 1 or top 2 marker genes used. Consistent with the visual appearances, judged by the quantitative parameters of OI, ASI, and PSImcc, the de novo reconstruction by D‐CE is much closer to the annotated original gold standard structure than that by NovoSpaRC  identified by D‐CE allows D‐CE‐t fully reconstruct the sample distribution on all 3 dimensions , the pattern is not as good as dorsal/ventral pattern. For zebrafish embryo blastoderm cap, D‐CE well reconstructed the dome shape of the blastoderm cap, while NovoSpaRC only captured the top outline . Compared with novoSpaRC, D‐CE reconstructed gene expression patterns have significantly higher OI to the FISH images . Again, as CSOmap accepts only human or mouse data as input, is not applicable to datasets of other species.To further test whether D‐CE can reconstruct spatial gene expression patterns of different cells directly using scRNA‐seq data, we applied it to a Drosophila embryo scRNA‐seq dataset10  and a high reconstruction accuracy (cancerous prostate) dataset, despite at different rate of increase  . Then we match them to the positions in the original structures. Consistent with the best reconstruction by D‐CE when directly compared to domain labels , these indexes confirm that of 3D model built by D‐CE after template fitting to 2D can accurately reconstruct 2D distributions of the samples , which is a procedure developed under the assumption and in the context of computational systems biology networks, therefore we cannot guarantee is valid for network reconstruction of any type of data in general. In fact, D‐CE performance is far different from routine dimensionality reduction methods such as PCA, t‐SNE, and UMAP, which we have tested and compared to and showed that do not work for spatial reconstruction as D‐CE does. D‐CE is based on biologically valid assumptions that we described above. However, when the transcriptome does not respond to local environment or form spatial domain, such as a partial transcriptome biased for cell type marker genes, the escaping cancer cells or highly mobile or shuttling cells, might defy such an assumption, and thus their locations will be hard to reconstruct. For example, MERFISH is another method generating spatial transcriptomes, however due to the limited throughput, only cell type specific marker genes were profiled, thus biasing reconstructions by all 3 spatial reconstruction methods to cell type classification, therefore we did not include the MERFISH data in the overall comparison of the 3 methods although even under this circumstances, D‐CE still performs the best  but also to determine and remove local background level links using CSI, because this will allow to cell assemblies’ connectivity to standout in the network structure. Indeed, we find that filtering PCC using CSI performs better than directly using PD network for large datasets (more than 150 nodes/samples) as indicated by gradient down‐sampling of the BDTNP dataset  from the original fully connected association network. A widely used strategy is to apply a rigid threshold which cuts off the links lower than a certain strength in the association network, however this strategy does not adapt the thresholding to the local neighborhood information imprinted in the association network. CSI is a strategy developed to address this issue by adapting the thresholding to the local links’ strengths (association) pattern.32 TheMachine learning can be model‐based or model‐free. Methods that are model‐based require an accurate knowledge of the processes behind the 3D morphogenesis and an appropriate formalization of these processes in a mathematical model whose parameters can be learned from the data. For instance, Bayesian approaches’ parameters can be learned by maximum likelihood estimation. To the best of our knowledge, there is not yet any method for single cell 3D spatial reconstruction that is model‐based because due to the complexity of the process it is difficult to write down an accurate mathematical model whose parameters can be learned from the few and heterogeneous data currently available. In this scenario, model‐based methods would offer poor results because of the missing knowledge for modeling and poor data for learning. For this reason, current approaches for single cell 3D spatial reconstruction, such as de novo reconstruction methods novoSpaRC and CSOmap, and landmark‐based reconstruction methods, such as Satija et al.’s method 2, are data‐driven. This means that they do not exploit an explicit mathematical model of the process behind the data to predict their reconstruction, but they derive an implicit  representation of the data directly from the data according to the assumption of the latent manifold of the data. That is, such data are the geometrical representation of the mathematical relation between the data samples, and can be learned by approximating the multidimensional similarity (or dissimilarity) relation of the data samples. Based on this assumption, a solution is to approximate the manifold similarity relations by means of a network connectivity.18Just as spatial transcriptome can provide a blueprint for spatially mapping a gene expression, and identify spatial marker genes and spatial transcription domains, a precise in silico de novo spatial reconstruction algorithm like D‐CE/D‐CE‐t can serve the same propose—provide the spatial domain organizations and markers, without the need of expensive spatial sample preparation, and can generate the spatial information for scRNA‐seq data which lacks spatial information.Currently all methods for 3D spatial reconstruction of single cell data including novoSpaRC and CSOmap are unsupervised for a concrete reason. A constraint to build supervised approaches is to have 3D genome‐wide single cell ground‐truth datasets on which we can implement the training phase of the supervised algorithms. The “crude” reality is that at the moment we do not have such data and therefore we cannot build supervised approaches. We hope that future efforts and improvements in ground‐truth data production could help to set an initiative such as a competition in single cell 3D spatial reconstruction similar to the effort performed in the DREAM challenge.334https://www.github.com/rajewsky‐lab/novoSpaRC.186 Geo‐seq samples with known positions in mouse embryo E6.5, E7.0, and E7.5 and 69 scRNA‐seq datasets (GSE120963) in E7.0 mouse embryo with A and P spatial labels were used to develop the 3D reconstruction method. For better comparison with novoSpaRC, the same expression matrix as novoSpaRC is used, which is downloaded from ovoSpaRC.10 which are genes with GO terms containing keywords of “differentiation,” “development,” and “morphogenesis,” 2302 transcription factors obtained from the AnimalTFs and RIKEN databases, and 4895 signaling genes obtained from the previous curation. All samples are first subjected to batch effect correction by ComBat. Then the batch effect corrected RPKMs (Reads Per Kilobase of exon model per Million mapped reads) are used for further analysis. All expressed genes are defined as RPKM>1 in at least 2 samples. Among them, there are 3795 developmental genes, 1646 transcription factors, and 3470 signaling genes for downstream analysis. The union, intersection, and difference of each pair of datasets or among the 3 datasets, all expressed genes and all expressed genes minus the developmental genes were used to generate a total of 19 gene lists for spatial reconstruction, gene expression levels are transformed by log 10(FPKM + 1). For each dataset, 12 different normalization methods were applied to each gene set  homophily (similarity) on the angular coordinates and ii) hierarchy on the radial coordinates. In this study, the main hypothesis is that, according to CE rationale, the embedding of a developmental network of transcriptomic topological similarity between cells (an association network derived from their gene expression) should produce an angular coalescent cell ordering that recapitulates the original single cell samples’ 3D spatial tissue distribution. While the cell hierarchy on the radial coordinates is obtained via a measure of node centrality in the network topology. The details of how to implement angular and radial inference is in the network embedding sub‐section below. Indeed, any CE algorithm such as D‐CE consists of two steps  the pairwise distance matrix between samples is generated by using Spearman distance:22 the PCC similarity network according to this formulai and j are two samples (nodes in the correlation network). The same formula can be used to compute RCC_CSIi,j.In addition, a second strategy that is designed to apply a soft‐threshold that penalizes nontopological‐specific low correlations and rewards local connectivity similarities that are associated to high correlations, is also considered. This second strategy can be applied only to adjust correlation networks, hence it will be applied only to RCC and PCC. The first step is based on computing the Connectivity Specificity Index (CSI).23 Forx+) of this similarity matrix are “reversed” to obtain a distance matrix according to this reverse functionThe result of this first step is a similarity matrix where a zero element indicates that the similarity between two samples is negligible according to CSI. Then, the nonzero elements ( Euclidean distance (ED), PCC‐CSI distance, and RCC‐CSI distance.In summary, 5 different distance matrices are prposed which represent 5 different network construction options for D‐CE: Pearson distance (PD), Spearman distance,22 EucStep 2: Network EmbeddingAfter getting the sample–sample distance matrix (network) according to one of the 5 different options described above, the network embedding step of the D‐CE algorithm consists of two routines.n‐by‐n distance matrix doubly‐centering operation given by the formulan‐by‐n matrix of all 1's.(2.1) The first routine is associated with inferring the 3D angular coordinates of the samples and consists of two subroutines. The first subroutine is the  They rely on the concept of kernel trick, initially introduced by Aizerman et al. As a matter of fact, D‐CE  is a nonlinear kernel‐based machine, in D‐CE the inference of the kernel is network‐topology‐driven because the distances between the points are inferred by means of the CSI filtered association network, where CSI is tailored for biological networks such as the ones here considered. This implies that D‐CE is able to perform nonlinear network‐driven dimension reduction, which makes this approach very different from any linear technique such as PCA. In standard kernel‐based machines, data should be centered in the feature space, by shifting the origin to the centroid of the data. Hence, D‐CE distance matrix (kernel) is also centered. From an algorithmic point of view, centering is performed easily with matrix algebra, by a subsequent column and row centering of the kernel matrix, according to the formula above.Kernel‐based machines provide a framework to generalize linear pattern recognition methods to the nonlinear domain.39 The that is a solution that is not considered in this study because it is still under debate and in the previous study on coalescent embedding did not provide any major increment in performance.However, recent studies are also advocating the option to not center the kernel,39 thaS is an n‐by‐n diagonal matrix with singular values of X¯ on its diagonal and sqrt is the square root operation. U and V are two unitary matrices, the columns of which are singular vectors of X¯. V' is the Hermitian transpose (the complex conjugate of the transpose) of V. Since X¯ is symmetric in this particular care U = V. Dn,3 is the score matrix where each row is a node of the network and each column is a different dimension of embedding that can be used to assign to each network node respectively the x, y, z coordinate of the 3D embedding. Then, the coordinates are transformed into polar coordinates and the angular coordinates are kept.The second subroutine is the spectral decomposition of the doubly‐centered distance matrix by means of the SVD therefore it is high in the topological hierarchy. Indeed, being similar to many nodes means that many nodes consider you at the center of the connectivity structure. Hence, according to the CE methodology, nodes with higher strength should be located toward the center of the embedding and therefore have lower radial coordinates; whereas nodes with lower strength should be located toward the periphery of the embedding and therefore have higher radial coordinates. On the basis of this rationale, a procedure is designed to infer the radial coordinates that is described step by step below. For a certain node i, its similarity is defined assi,j is the similarity metric between node i and j, and N denotes all nodes connected to i. For Spearman, Pearson, and Euclidean distance network, si,j=1−di,j/maxi,jdi,j, where di,j is the distance between node i and j, and for CSI network, si,j = CSIi,j .(2.2) The second routine is associated with inferring the radial coordinates as a function of the node strength, which is the sum of the edge similarities incident on a node. A node with high strength is very similar to many other nodes in the network,15 theith node is determined by the following formula that is termed heterogeneity‐adaptive radius (HAr) and is specifically designed for D‐CE embedding in order to capture the node hierarchy and according to the rationale that is clarified belowio is the ranking value of ith node, and the logarithm adjustment ln (io) of the ranking value is introduced to mitigate the growth of the denominator when the strength of a node is low and, possibly, many nodes with similarly low strength are arbitrarily ordered in the high value zone of the ranking. The adjustment coefficient β=RSD1+RSD, where RSD=std(S)mean(S)is the relative standard deviation of the strength among all nodes, is a measure of heterogeneity of the node strength distribution.Nodes are first sorted in descending order by strength with nodes with highest strength ranked first. Then, the radial coordinate of the iHAr is confined to the interval]0,10,1[. In contrast, if the network hierarchical organization is lower than the previous case, for example, it is assumed that β  =  1/2, then the node with the highest strength (for which io =  1) takes ir =  1/2, and the radial coordinates space available for the representation will be squeezed to the radial interval [0.5,1[. In conclusion, the proposed formula to infer radial node coordinates in D‐CE will visually represent networked systems with very high hierarchical organization as a 3D distribution of points occupying all the radial space from the periphery to the center of the radial coordinates. Instead, in case of networked systems with very low hierarchical organization, all the nodes will be compressed and equally distributed toward the periphery of the polar coordinate representation, and occupy only a reduced and peripheral portion of the radial space.Note that some networked systems might have a hierarchical organization that changes across the angular coordinates with a certain pattern. In this case, the 3D embedding might result in not spherical and assume other shapes, for instance an ellipsoidal shape.The time complexity of the method is O(N^2) where N is the number of cells, because it is constrained by the SVD, as explained in the previous study on coalescent embedding.15k‐nearest‐neighbor graph of the Euclidean distance matrix of samples and template is first computed, and the shortest distance between samples and positions(sC and tC) are calculated by Dijkstra algorithm, and the cost matrix C is calculated by: C  = Cs  · (p × q) · Ct, if marker genes are provided, the cost of gene Cg is defined as the Euclidean distance divided by the maximum Euclidean distance between samples and templates, and the total cost is calculated by the weighted sum of C and Cg and the optimal transportation is done using function “sinkhorn” in python package “POT” similar to that in novoSpaRC, so mask and marker information could be included. Then to make sure on sample is mapped to only one position, the position‐cell pair is first selected that have maximum weight in the optimal transport matrix, and map the cell to the position, then the node‐cell pair is removed, and the same mapping is repeat until each the cell is mapped to a position in the template.To enable template and marker gene expression information to be used, a template containing each sample positions (not labels) is first constructed, and then optimal transportation is used to get the transport matrix between samples and positions, assuming that the sample and position weight follow a uniform distribution (p and q). D‐CE coordinates are used to calculate the Euclidean distance between each pair of cells. For the cost distance, a sitionsCs and Ct To facilitate single cell resolution mapping, as an additional option of D‐CE‐t package (“‐scmap”), after reconstruction, single cell samples can be also mapped to the spatial location with maximum probability.The 3D coordinates of each sample from each of the 60 possible strategies of D‐CE  were obtained to evaluate the performance of each of them in spatial reconstruction as follows. 2) The projection separability index—Matthews correlation coefficient (PSImcc) is calculated by the mean value of Matthews correlation coefficient between the order of cells from each pair of clusters (groups) and the order that well separate the 2 clusters when all the cells from those 2 clusters are projected to the line that link the median of the 2 clusters. For each pair of clusters cluster 1 and cluster 2, which have n1 samples in cluster 1 and n2 samples in cluster 2, labels: L: {nl|n ∈ 1: (n1 + n2),nl ∈ {0, 1}} where 0 present cluster 1 and 1 present cluster 2, the samples are first projected to the line that link the center of the 2 clusters, then, the samples can be divided into 2 clusters according to the projected positions of the samples, label n1 samples in one side to be cluster 1’ and n2 samples in the other side to be cluster 2’ then labels L2: {nl|n ∈ 1: (n1 + n2),nl ∈ {0, 1}} then, the comfusion matrix is calculated and Matthews correlation coefficient is calculated by mcc=TP∗TN−FP∗FN(TP+FP)∗(TP+FN)∗(TN+FP)∗(TN+FN), where TP is “True Positives,” FNis “False Negatives,” FP is “False Positives,” and TP is “True Positives,” then, since the position of the 2 clusters are unknown, a comparison of the mcc is taken when label the samples in each of the 2 side as cluster 1, and take the maximum to be PSImcc. 3) The ordering index (OI) is used to compare the order of samples to the known order of samples. The OI of A, P, L, or R samples was calculated in each reconstruction between their original proximal to distal orders and their orders in reconstructed coordinates. The original order is determined by the labels of samples, and the rank/order of samples in the reconstructed spatial structures are determined bya)First OI calculated for the Geo‐seq samples in each spatial domain, A, P, L, or R, separately. For each domain, the reconstructed spatial positions of samples from each layer were obtained, if there are more than one sample in the same layer, the geometric center of all the samples in this layer is used as the spatial position;b)The center of the first layer samples is designated as the reconstructed position of the first layer, then rank the sequential layers by the shortest spatial distance to the last layer.c)The RCC of the original and reconstructed ranks are calculated as OI.d)The minimal OI in A, P, L, and R is taken as the overall OI of the reconstruction.For spatial reconstruction, the anterior and posterior samples are further divided into 4 groups according the spatial locations: dA, dP, pA, and pP, which means the distal/proximal part of anterior/posterior, the four groups are colored with red, green purple and yellow, respectively, in Figure 15 2) x and z coordinates in original locations, then the angular coordinates are used to calculate ASI and PSImcc as described above. Same as the mouse embryo, the fly embryo is bilaterally symmetric along y axis, therefore only half of the embryo is used as novoSpaRC did. As the order of cells on y axis was not considered by novoSpaRC, the reconstructed spatial order is also evaluated in x and z axes using the ASI and PSImcc of the 4 groups according to x and z axes. For OI, the x, y, or z coordinate is sorted from high to low and divided into 10 groups, the original order of other groups is determined by the ascending order of coordinate, the geometric center of each groups in the reconstructed structure is calculated as the spatial location of this group. The group with lowest mean coordinate is designated as the first group, then the rest are calculated as described above for Geo‐seq data.For the BDTNP dataset, the embryo is cut into 4 groups according to the ovoSpaRC,10 theBesides D‐CE, 5 other dimensionality reduction methods, PCA, t‐SNE, and UMAP are also tested for spatial reconstruction in Cartesian coordinates, and then they are compared with D‐CE using ASI, PSImcc, and OI. The 3 indexes of all the results using D‐CE, PCA, t‐SNE, and UMAP are ranked in descending order, and the maximum ranks are calculated as described above.For CSOmap, the TPM of all LR genes were used for spatial reconstruction. Only human and mouse LR interaction were provided.As novoSpaRC method is developed specifically for Berkeley Drosophila Transcription Network Project (BDTNP) dataset, which only contains the expression level of 84 TFs. For comparison to novoSpaRC, the D‐CE of the BDTNP data used all 84 TFs’ profiles with the same normalization method and distance metric as for to the 3D reconstruction of the Geo‐seq data.T+m×nbetween m samples and n locations is calculated using novoSpaRC, then the dot product T+m×n·Ln×3, where Ln × 3 is the original 3D coordinates of the locations, is used to determine the reconstructed sample locations. Specifically, Ti,j is the probability of sample i mapping to location j, and as the distribution of ∑jTi,j follow a uniform distribution, the weighted sum coordinates of all the locations for sample i is is used to as novoSpaRC reconstructed location  of sample i, where is the coordinate of the location j.To determine the coordinates of samples reconstructed by novoSpaRC, the probabilistic coupling matrix Putative domains are obtained by K means clustering of the samples according to the coordinates in the reconstructed structure based on the elbow method  and cut into 10 layers according to the x and z axis. Then the RCC between FISH order and each rotated reconstructed structure layer order were calculated. The orientation with max RCC is defined as the optimal orientation, whose OI is used as the final OI.Log2 transformed FPKM (Fragments Per Kilobase of exon model per Million mapped fragments) was used for D‐CE and novoSpaRC. TPM (Transcripts Per Kilobase of exon model per Million mapped reads) was used for CSOmap reconstruction as required. The spatial order of the samples is reconstructed using D‐CE, novoSpaRC and when applicable CSOmap (only applicable to human and mouse LR‐including gene sets). To evaluate the reconstructed spatial gene expression patterns for the Drosophila and zebra fish embryo scRNA‐seq datasets, as there is no specific label for each sample, the coarse‐grain domains were obtained on the matching FISH image by first converting it to gray scale, and then cut into 10 layers along either anterior‐posterior or dorsal‐ventral axis. The gray‐scale density of each layer was used as the gold standard expression level in each layer. The direction of the reconstructed structure is corrected by rotating around x and y coordinates and used as gold standards to compute OI, ASI, and PSImcc after the embedding of the samples.For 8 transcriptome data with spatial coordinates, such as barcoded microarray‐based spatially resolved transcriptome, LCM‐seq, seqFISH, and MERFISH data, the spatial order or coordinates in a template as gold standard is used to evaluate the reconstructed structure of each method. The log2 transformed gene expression values were used for reconstruction. For each experiment, samples are labeled by their The reconstructed coordinates are rotated 30 times along the XY and XZ planes respectively (12 degrees each time) to calculate the RCC between the gene expression level and the rotated coordinate X, arriving at a 30 by 30 matrix of RCC. Then the 30 by 30 RCC matrix is converted into a vector of 900 values, and clustered into 2 and 3 clusters by K‐means for 2D and 3D templates, respectively. The top EOC gene in the large and small clusters are the selected as the top 1 and 2 spatial marker genes for D‐CE‐t as default. NovoSpaRC randomly selected 1 or 2 markers for marker‐based template fitting, but it was done 100 times to select the best one for a favorable result for novoSpaRC.Top 5% EOC genes in each dataset were used for GO and KEGG GSEA analysis with genes’ EOC as the rank and genesets with each GO and KEGG term as signatures. The function “GSEA” in R package “clusterProfiler” was used with “pvalueCutoff = 0.05, pAdjustMethod = fdr, maxGSSize = 500 ”, and default settings for other parameters.Mid‐gastrulaton stage  embryos were collected from C57BL/6 mice, and embryos images were taken for recording and confirmation of developmental staging. Animal procedures conducted in this study were approved by the Institutional Animal Care and Use Committee of Guangzhou Institutes of Biomedicine and Health, Chinese Academy of Sciences .The authors declare no conflict of interest.Y.Z. and S.Z. contributed equally to this work. J.D.J.H. conceived the project. J.D.J.H. designed, with C.V.C.’s help, the project and analyses. J.D.J.H. and C.V.C invented the network construction, J.D.J.H. and Y.Z. invented de novo marker identification and one‐to‐one template fitting part of D‐CE. C.V.C. invented the network embedding part of D‐CE and designed the algorithm. Y.Z. and S.Z. wrote, verified, and tested the codes with occasional help from C.V.C. J.D.J.H., C.V.C., Y.Z., and S.Z. wrote the paper. J.X. did in situ hybridization supervised by G.P., Y.Y. prepared embyos.Supporting InformationClick here for additional data file.