Reconstructing signaling histories of single cells via perturbation screens and transfer learning

Abstract

Manipulating the signaling environment is an effective approach to alter cellular states for broad-ranging applications. Such manipulation requires knowing the signaling states and histories experienced by cells in vivo, for which high-throughput discovery methods are lacking. Here we present an integrated experimental–computational framework that learns transferable signaling response signatures from a high-throughput in vitro perturbation atlas and infers signaling activities and histories in in vivo cell types with high accuracy and temporal resolution. We generated a signaling perturbation atlas on human pluripotent stem cells and used it to train IRIS, a neural-network model. Applying IRIS to mouse embryo single-cell atlases, we uncovered global features of combinatorial signaling code usage, identified biologically meaningful heterogeneity and reconstructed signaling histories along diverse developmental lineages. This framework reveals that diverse cell types share conserved signaling response signatures, and provides a scalable solution for mapping complex signaling interactions in vivo to guide targeted interventions and enable cell fate engineering.

IRIS learns conserved signaling representations from in vitro perturbation data to reconstruct signaling states and histories across diverse in vivo cellular contexts.

Main

Cellular state transitions driven by combinations of external signals are the foundation for building tissues in developing embryos, maintaining physiological homeostasis in adults, and triggering disease onset and progression. Identifying which combinatorial signaling conditions trigger state transitions of the cells in their native contexts is crucial for understanding and engineering the respective biological process. Genetic perturbations and transgenic signaling reporters are the major ways to correlate signaling pathways with cellular state transitions in vivo, but they are difficult to apply to human tissues^1,2. Newer generations of synthetic tools for recording signals have been developed for cells cultured in vitro, but their application in animals remains to be tested^3–5. Importantly, all the above-mentioned approaches are low-throughput and lack temporal precision. In many systems, identifying the combinatorial signaling codes that drive cell state transitions over time remains a challenging goal. The recent rapid growth of single-cell RNA sequencing (scRNA-seq) and spatial transcriptomics data has driven the development of numerous computational algorithms to infer cell–cell communication based on gene expression^6–9. These methods often rely on the presence of ligand–receptor pairs in the tissue, which does not guarantee signaling pathway activation^10–12. Therefore, these methods estimate the signaling potential rather than the signaling state.

Signal activation induces transcriptional responses inside a cell, which is one of the most direct indicators of a cell’s signaling state and compatible with high-throughput measurements. However, given the large number of signaling pathways, the diversity of cell types, and the combinatorial nature of signaling pathway usage, it is impractical to experimentally measure the transcriptional responses of all cell types following stimulation with each defined signal. This raises the question of how many signal perturbation measurements are needed before we can accurately infer signaling states of most cell types in their endogenous contexts. While some signaling pathways use common processing machinery across cell types to produce distinct outcomes, the conservation of transcriptional responses in different cell types remains insufficiently explored¹³. In fact, transcriptional responses to a signaling pathway are often considered unique to each cell type¹⁴. If this is true, one would need to perform signal perturbations on the exact cell type of interest, which is often impractical or not scalable for in vivo cell types. Therefore, we asked if each signaling pathway has its own transcriptional signature that is shared across diverse cell types. If such signatures exist, they offer a new path for mapping cell signaling states and histories in their native contexts.

Here we developed an experimental–computational framework to learn signaling response signatures from high-throughput in vitro perturbations and use these signatures to infer signaling activities across in vivo cell types (Fig. 1a). This framework revealed the existence of response signatures shared across diverse cell types that serve as a distinct ‘fingerprint’ for each signaling pathway. Using these fingerprints, we mapped the signaling states of over 40 defined cell types in mouse embryos, revealing patterns of combinatorial code usage with high temporal resolution and biologically meaningful heterogeneity within each cell type. The framework combines sequential combinatorial signal screens on human embryonic stem (hES) cells with a deep neural-network-based algorithm, which we term Intracellular Response to Infer Signaling State (IRIS). IRIS recovered signaling histories along well-studied cell lineages and made accurate predictions on understudied lineages, such as organ-specific mesenchyme, which was experimentally validated. IRIS greatly reduced the combinatorial signaling space that needs to be experimentally tested to develop hES cell differentiation protocols in vitro. This new framework will enable improved predictive modeling of cell–cell communication that can accelerate discovery in fundamental biology and design of therapeutic interventions.

Fig. 1. IRIS learns response signatures for accurate signaling state inference.

a, Schematic of the proposed workflow for inferring signaling histories and optimizing stem cell differentiation protocols. In vitro high-throughput signal perturbation data sample transcriptional responses to specific signaling pathways, and these response signatures can be learnt by transfer-learning models and used for inferring signaling states among in vivo cell types of interest. The inference can iteratively be used to propose new directed stem cell differentiation protocols. b, Schematic representation of the IRIS model. IRIS uses a CVAE architecture that includes an FNN for classification. This jointly computes a latent space and classifiers for signaling states in the space. c, IRIS improves accuracy of signaling state inference over the response-gene method on an 80/20 train–test split of the mES cell differentiation data.

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Results

Learning generalizable signal response signatures from the ground up using IRIS

Despite the widely held belief in the cell-type specificity of signal responses, a small number of genes have been used to indicate signal activation across cell types, such as Axin2 for the Wnt pathway and Id1 for the bone morphogenic protein (BMP) pathway^15–17. Therefore, we first asked whether these empirically annotated response genes are sufficient for inferring the pathway activation states across diverse cell types¹⁷. We focused on the major developmental signaling pathways, including transforming growth factor beta (TGF-β), fibroblast growth factor (FGF), BMP, Hedgehog (HH), retinoic acid (RA) and WNT. The activation and inhibition of these pathways occur repeatedly throughout development and in adult tissue regeneration, and thus, they are the major pathways extensively used for pluripotent stem cell differentiation^18–20. Using a rare large-scale signal perturbation dataset, in which mouse embryonic stem (mES) cells were stimulated with all possible combinations of these six pathways, we created response scores for each pathway in each cell, inferred signaling states and quantified the inference accuracy²¹ (Supplementary Fig. 1). The response genes had reasonable classification power on RA, WNT and BMP pathways (>0.75 area under the receiver operating curve, AUROC), but performed much worse for TGF-β and FGF. The HH pathway was not included because there were too few stimulated cells to render enough statistical power.

When applied to a gastrulating mouse embryo dataset (embryonic day (E)6.5–E8.5), the response-gene method recovered some ground-truth knowledge, but in general, it was difficult to convert the response scores into a binary classification²² (Supplementary Fig. 2). This is partly because there are no clear cross-cell type heuristics for determining what level of response-gene expression constitutes a responding cell. Gene expression measurements are known to be confounded by batch effects, exacerbating the unreliability of the threshold. The small number of response genes used makes them sensitive to the well-known issue of dropouts for scRNA-seq data²³. Furthermore, these genes were compiled from limited biological contexts that have been extensively studied and may not be generalizable to other cell types. Altogether, these results suggest that shared response signatures might exist across cell types, but such a method based on a small number of genes has limited utility for classifying signaling states.

We hypothesized that this cross-cell type and cross-batch classification problem might be better solved by models of gene expression that are fit to the entire transcriptome as genes do not operate independently of each other²⁴. Models that incorporate the relationship among diverse genes might be more likely to capture the response signatures, be robust to dropouts, and facilitate the choice of thresholds across cell types due to its increased flexibility. Our classification challenge is conceptually similar to the ‘label propagation’ problem in the machine learning field, the goal of which is to learn data features associated with a label and then use those features to annotate unlabeled datasets²⁵. Classic label propagation algorithms have had much success in transferring cell-type labels between different batches of scRNA-seq data. In particular, algorithms based on conditional variational autoencoders (CVAEs), such as scANVI and trVAE, can remove the highly nonlinear batch effects more comprehensively and embed cells with similar gene expression patterns together more robustly than comparatively simpler models^26–28. They also show success in leveraging small annotated datasets, projecting those onto much larger atlases and learning complicated thresholding rules for diverse cell types.

We asked whether we can apply CVAE-based neural networks to learn generalizable signal response signatures from the ground up. Using the mES cell differentiation scRNA-seq dataset as a starting point²¹, we randomly split all the cells into a training set (80%) with signal conditions visible and a test set (20%) with signal conditions hidden. We first applied the CVAE to project all the data across technical batches into a single latent space without awareness of the signal conditions. We then jointly trained the latent space and a classifier network to learn signaling response features, predicted on the test set and compared the prediction with the true signal conditions (Fig. 1b). When we fit the model using the default parameters of scANVI, we observed higher classification accuracy than the aforementioned response-gene method (Fig. 1c). The model learns a probability of signaling activation for each cell from which it derives a binary prediction simultaneously (Supplementary Fig. 3). We named this algorithm IRIS.

Sequential combinatorial signal perturbation screen enables rapid sampling of diverse cell and signaling states

The mES cell dataset produced two main categories of cell states: those resembling primitive streak (PS) cells after 24 h of exit from pluripotency (mP_d1), and cell types derived from anterior PS biased toward endodermal fates (mE_d2)²¹. To test the cross-cell-type and cross-dataset performance of IRIS, we generated three orthogonal signal perturbation datasets based on hES cell differentiation. To maximize cell type/state diversity in the perturbation data, and to produce human cell states that were either related to or distinct from those in the mES cell screen, we designed a sequential combinatorial signal stimulation strategy spanning distinct developmental stages and lineages (Fig. 2a).

Fig. 2. IRIS generalizes across cell types by learning transcriptome-wide signaling response signatures.

a, Design of three sequential combinatorial signaling screens using hES cells. In the last two steps of the hM_d4 screen, signal combinations were represented as points on a 12-dimensional space, with pairwise distances computed using the Hamming distance (HD). Combinations were selected by either a bit-flip strategy (HD = 1 from controls) or a random strategy (HD ≥4 apart) (left). In the hM_d7 screen, four splanchnic mesoderm populations were generated by varying only RA and SHH at steps 2 and 3; these RA–SHH pairs were then carried through step 4, where all 16 possible combinations of TGF-β, WNT, FGF and BMP were applied to each RA–SHH pair. In hE_d8, all conditions originated from a common step 2 population and were stimulated with all 64 possible combinations of six pathways in step 3. hM_d4 and hM_d7, human mesoderm day 4 or 7 respectively; hE_d8, human endoderm day 8; Def. endo., definitive endoderm. b, Diversity of final cell states in each screen, quantified by transcriptome-wide correlation between distinct screens. c, Left: cross-screen generalization of IRIS when holding out one screen at a time; dots show mean F1 scores across data splits. Right: precision–recall (PR) curves show averages across data splits (solid lines) compared with a random baseline (dashed lines). d, Cross-cell-type generalization of IRIS trained on endodermal screens (mE_d2 and hE_d8) and tested on mesodermal screens (hM_d4 and hM_d7). e, Benchmarking against other hyperparameter-optimized machine learning models in a cross-species context. SVM1 and SVM2 are two SVM models that differed in hyperparameters. f, Gene ablation analysis in the cross-validation test by holding out individual screens. Genes were ranked by mutual information and expression levels were progressively randomized by resampling with replacement. IRIS accuracy was computed after each round of randomization. Results for each data split and each pathway were fit to an exponential function and normalized between 0 and 1 for visualization. The number of genes required to reduce accuracy by 50% reflects the transcriptomic information density.

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Two screens captured mesodermal states after four or seven days of differentiation (hM_d4 and hM_d7, respectively), and one captured endodermal cell states (hE_d8). In both mesodermal screens, hES cells were first induced into middle PS cells that are biased toward mesodermal fate (step 1), distinct from the anterior PS in the mES cell screen^17,19. In hM_d4, these cells were exposed to 46 combinations of the six signaling pathways for 1 day (step 2), and each condition was further differentiated by a single or multiple signal combination for 2 days, yielding 96 final states (step 3). The hM_d7 screen contained cells 3 days older, in which cells were first differentiated to four splanchnic mesoderm subtypes (steps 1–3) and then subjected to combinatorial stimulation for 3 days (step 4). In the hE_d8 screen, step 1 combination diverged from the mesoderm screens, generating anterior PS cells similar to the mE_d2 screen. Those cells were then differentiated into definitive endoderm before exposure to 64 combinatorial conditions over 5 days. Each final state was barcoded and pooled within each screen for multiplexed scRNA-seq²⁹.

Sampling of signal combinations was tailored to each screen. In hM_d4, we implemented a two-step sequential combinatorial design. With six signaling pathways acting in two sequential steps, the number of possible combinations is 2¹², which exceeds the current throughput within a single experiment of hES cell differentiation. To maximize informativeness, we represented each step 2–step 3 sequential combination as a 12-digit binary string and spread conditions across the combinatorial space (Fig. 2a). We included 4 published protocols as controls, 38 variants differing by a single ‘bit’ from controls, and 54 random combinations, ensuring a minimum Hamming distance of 4 between any 2 conditions¹⁷. In the hM_d7 screen, BMP, WNT, TGF-β and FGF specify splanchnic mesoderm, whereas RA and SHH influence the organ identity of the emerging splanchnic mesoderm^17,30. Thus, we first generated four splanchnic mesoderm subtypes by varying only RA and SHH, and then applied all 2⁴ combinations of the remaining pathways to each subtype in the final step, yielding 64 distinct final states. For hE_d8, we produced a definitive endoderm progenitor state after 3 days and then sampled the complete 2⁶ combinations in the final step. Across all screens, diverse final states were observed (Extended Data Fig. 1).

Extended Data Fig. 1. Analysis of cell-state diversity in the mES and hES cell screens.

a, Distribution of barcodes recovered after sequencing for each screen. b, Cells activated with the respective signaling pathways in the last step of differentiation are highlighted by the corresponding color. Step 2 or Step 3 (hM_d4), Step 4 (hM_d7), and Step 3 (hE_d8). c, The correlation coefficient averaged across the transcriptome between distinct signal combinations within each screen, highlighting the diversity of final cell states.

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Hierarchical clustering of average cell profiles across screens revealed that human mesodermal datasets (hM_d4 and hM_d7) were more similar to each other than to the human endodermal dataset (hE_d8), while cross-species differences exceeded lineage differences (Fig. 2b). Human and mouse datasets remained distinct, even between corresponding endodermal states (hE_d8 versus mE_d2). Together, these screens generated diverse cell states that form a rich ground-truth basis for model evaluation and training.

IRIS can generalize across batches and cell types

With the new perturbation data, we asked whether IRIS can truly learn response signatures that generalize across cell types. Given the well-known batch effect between datasets that are collected separately, we first optimized IRIS to minimize the batch effect. Taking advantage of the fact that the mES cell data were collected as three independent batches, we performed a hyperparameter search to evaluate how the IRIS architecture affects the cross-batch performance by holding out one batch at a time. Notably, we found that shallow architectures with fewer layers performed the best in this test (Extended Data Fig. 2).

Extended Data Fig. 2. A hyperparameter screen of IRIS reveals optimal architecture for each pathway.

a, Schematic of hyperparameter optimization. The mES cell screen was partitioned into three batches during data collection. In the hyperparameter screen that aims to optimize for cross-batch generalizability, two of the three batches were used for training at a time and the remaining batch was used as a test. Multiple parameters were screened for layers, hidden nodes, and latent variables. b, The performance for each combination of the tested hyperparameters was evaluated based on the AUPRC (Area Under the Precision-Recall Curve) averaged across all three training iterations. c, Averaged cross-batch performance metrics of the ideal hyperparameters. The optimal parameters were chosen from the hyperparameter screen and all pathways showed improvement over the response gene approach. Performance was averaged across all three iterations.

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Using optimized hyperparameters, we performed comprehensive cross-validation by withholding one screen at a time. IRIS showed consistently strong performance across all data splits, demonstrating its ability to generalize effectively to unseen datasets (Fig. 2c and Supplementary Fig. 4). Despite pronounced transcriptomic divergence between training and test populations (Fig. 2b), IRIS was able to generalize across cell types. To further assess cross-cell-type generalization, we trained IRIS exclusively on endodermal lineage cells (mE_d2 and hE_d8) and evaluated it on mesoderm lineages (hM_d4 and hM_d7). As endoderm and mesoderm cells are developmentally distinct, this represents a stringent test of model generalization. Even under this condition, IRIS substantially outperformed random classifiers (Fig. 2d and Supplementary Fig. 5). These results demonstrate that IRIS captures conserved and transferable transcriptional signatures across distinct cell states.

To assess whether IRIS can accurately infer signaling states across species, we trained IRIS exclusively on mouse or human data and tested on the other species. IRIS still successfully captured response signatures generalizable across species (Extended Data Fig. 3a,b). Notably, performance improved markedly when a small portion of labeled in-species data from distinct cell types was included during training (Extended Data Fig. 3c). Furthermore, we found that including out-of-species data also improved in-species predictions (Extended Data Fig. 4). These findings suggest that exposure to diverse cell states, whether within or across species, enhances IRIS’s ability to learn robust, transferable response signatures.

Extended Data Fig. 3. Cross-species generalization test.

a, Mouse-to-human and human-to-mouse generalization tests, in which models were trained exclusively on mouse screens (mP_d1, mE_d2) and evaluated against all human screens (hM_d4, hM_d7, hE_d8), or vice versa. The performance was compared to random baselines. b, Cross-species label randomization test. Comparison between a Null Model and a True Model, both trained exclusively on mouse screens and evaluated for their inference accuracy on one of the human screens (hM_d4) across a range of hyperparameters. The True Model (solid lines) consistently outperforms the Null model (dashed lines), suggesting IRIS is learning meaningful response features in the cross-species context. ECDF, empirical cumulative distribution function. AUROC, area under the receiving operator curve. AUPRC, area under the precision recall curve. c, Evaluating the effect of including in-species (but cross-cell-type) training data on cross-species performance. IRIS was trained either exclusively on the mouse screens or together with 10% of hE_d8, to predict on the unrelated hM_d4 screen.

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Extended Data Fig. 4. Increasing diversity of cell types in training data broadly improves inference accuracy.

a, Including the hM_d4 screen in the training data improved in-sample inference accuracy. IRIS was trained on 80% of the mouse screens with or without 80% of the hM_d4, and tested on the remaining 20% of the mouse screens. b, c, Held-out signal combination test showed consistent improvement of IRIS over the response-gene method and including hM_d4 in training further improved the accuracy of IRIS. Samples with the same combination in Step 1 and Step 2 were held out together or separately. Comparison of IRIS and Response Gene F1 scores for each pathway. Individual points represent the performance of IRIS on each signaling pathway in a given held-out condition (b). The frequency of improvement over the response-gene method for each signaling pathway was calculated and presented as barplot (c).

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We next compared IRIS with simpler machine learning models optimized using the same hyperparameter tuning procedure (Extended Data Fig. 5). IRIS performed comparably or modestly better on the in-sample test using mES cell data and cross-validation using all screens (Extended Data Fig. 5b,c). However, IRIS maintained stronger performance in more challenging, data-limited cross-species settings (Fig. 2e). Because IRIS more consistently outperformed each of the other models across splits of data and signaling pathways, we chose IRIS for the subsequent applications.

Extended Data Fig. 5. Model benchmarking and hyperparameter optimization for white-box machine learning models.

a, PCA was first performed on the data in accordance with Scanpy’s default parameters. The mouse screen was partitioned into three batches during data collection. Individual batches were held out one at a time and the average AUPRC is presented in the heat map for a variety of hyperparameters for each model: SVM (softridge, C = 1, 32, 100), Elastic net (alpha, 10^-n, n = 1, 2, 3, 4, 5, 6), and Random forest (loss=gini, cross entropy, log; number of trees= 10, 100, 1000; max depth=2, 4, 8, 16, None). b, Model benchmaking on the in-sample 80-20 split test with the default parameters of each model (related to Fig. 1c). IRIS outperforms random forests (p < 0.05; one-sided binomial test, n = 5) but there was no statistically significant difference between IRIS and SVM or EN. c, Model benchmarking via a cross-validation test (related to Fig. 2c). IRIS is the most consistently performing model across all signaling pathways and splits (p < 0.05; one-sided binomial test on all possible pairwise comparisons against all other models, n = 100 model-comparisons). The variance was computed by the SEM of 10 replicates of the model runs with different random initializations.

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Finally, we examined the possibility of signal carry-over resulting from prior activation of the same signaling pathway, leveraging the sequential design of hM_d4. Prior stimulation led to an increased false-positive rate (FPR) for BMP, WNT and TGF-β pathways, it decreased the FPR for RA and exerted no significant effect on FGF (Supplementary Fig. 6). Importantly, even in cells with prior exposure, the FPRs remained below 0.3 for most pathways. These observations indicate that, although signal carry-over may contribute to false-positive classifications, its influence is contingent on cell type.

Signaling response signatures reflect transcriptome-wide features

The broad generalizability of IRIS prompted us to investigate what constitutes the signaling response signatures. We first asked whether these signatures rely on a small subset of genes and to what extent the previously annotated response genes contribute (Supplementary Fig. 1a). To quantify the importance of individual genes, we performed a gene ablation test (Fig. 2f). Genes were ranked by mutual information, maximal dispersion or expression level in the cross-validation test. The expression level of each gene was then randomized in the held-out screen to assess its impact on prediction accuracy. Thousands of genes must be randomized before the predictive power falls to random chance, a pattern consistent across all five screens and three ranking metrics (Fig. 2f and Extended Data Fig. 6a). While canonical response genes were ranked highly by mutual information, they explained only a small fraction of the model’s predictive power (Extended Data Fig. 6b). These results, while indirect, suggest that IRIS captures the distributed influence of a broad gene regulatory network, rather than relying on a limited set of ‘context-independent’ response genes.

Extended Data Fig. 6. Gene ablation tests.

a, Gene ablation test on the single screen-heldout cross-validation (related to Fig. 2f). Genes were ranked according to either the highly variable (left column) or highly expressed (right column) gene metrics. The inference accuracy of IRIS was computed after each round of corruption. The result for each data split and each pathway was fit to an exponential function and normalized between 0 and 1 for visualization. AUROC declines gradually over thousands of ranked genes. b, Cross-species gene ablation test. Genes were ranked according to either the highly variable (left column) or mutual information (right column) gene metrics. Dots represent individual groups of genes for visualization. The points which correspond to manually annotated response genes (Supplementary Fig. 1) are highlighted.

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To provide an orthogonal interpretation of the response signatures learnt by IRIS, we combined saliency maps with gene set enrichment analysis (GSEA)³¹. We first examined whether IRIS simply relearned canonical gene sets associated with each signaling pathway. For each pathway, genes were ranked by their contribution to the learned response signature, quantified as the gradient of the output with respect to each gene at different points of training. We then performed GSEA on the weights associated with each predictor and found the classic signaling pathway response-gene sets were enriched or nearly enriched in their respective predictors, suggesting that genes canonically associated with each pathway contribute to the response signature of the corresponding pathway (Extended Data Fig. 7a). However, these contributions are not exclusive and many signaling-related gene sets showed high enrichment across multiple pathways (Extended Data Fig. 7b). Moreover, IRIS response signatures extended broadly across diverse gene sets, including those beyond signaling-associated annotations, supporting that IRIS captures transcriptome-wide features (Extended Data Fig. 7c).

Extended Data Fig. 7. Gene saliency test.

a, To estimate the contribution of each gene to the model performance, gradients of the loss with respect to the input variables (dP/dL) were computed for each pathway during training. Genes were ranked based on the gradient and a GSEA (Gene Set Enrichment Analysis) was performed on each pathway by choosing the gene set annotated as ‘response to’ the corresponding signal (GO number labeled). Two-tailed permutation test (n = 1000). b, GSEA on all signaling-relevant gene sets in the database showed no preferential enrichment of the gene sets annotated to be related to the corresponding pathway. Color lines denote the gene sets assigned to the corresponding signaling pathway by the database. c, GSEA for all gene sets present in the GO Biological Pathways 2021 database showed broad enrichment of many gene sets for each pathway.

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IRIS reconstructs spatiotemporal signaling dynamics of cell fate lineages

Based on the above observations, we trained IRIS on all screens to infer the activities of all five signaling pathways and the 32 possible combinations across ~40 annotated cell-type clusters from gastrulating mouse embryos (E6.5–E8.5)²² (Fig. 3a,b and Supplementary Fig. 7a). This analysis revealed highly dynamic shifts in combinatorial signaling codes during this developmental window. Notably, a global transition occurred around E7.0 when early-stage combinations disappeared and were replaced by new combinations that persisted through E8.5. WNT, FGF and BMP were active across most time points and annotated clusters, but only in subsets of cells in those clusters. By contrast, TGF-β was statistically significantly associated with early time points while RA activity emerged later, consistent with prior findings that TGF-β receptor knockout mice exhibited earlier lethality than RA receptor knockouts^32–34 (Supplementary Fig. 7b).

Fig. 3. IRIS reconstructs spatiotemporal signaling dynamics of cell-fate lineages.

a, Annotated cell populations in gastrulating mouse embryos (E6.5–E8.5)³⁵. endo, endoderm; meso, mesoderm; ecto: ectoderm; neuroecto: neuroectoderm. b, Dynamic transitions of signal combinations across developmental time points. Each combination is color-coded, and cells annotated with that combination are highlighted at each stage. c, Diffusion map of endodermal (n = 11471) and cardiac lineages (n = 18579) (left), and corresponding signal combinations during in vitro differentiation (right). The activation status of TGF-β along the cardiac lineage is unknown. d, IRIS-predicted activation frequency for individual signaling pathways along endodermal (top) and cardiac lineages (bottom). Trends were assessed with a two-tailed Spearman’s correlation test. e,f, IRIS reconstructs the correct temporal order of signal combinations used in differentiation protocols of the endodermal (e) and cardiac (f) lineages. Top: frequency estimates of combinations along each trajectory. Bottom: diffusion maps showing inferred cells with the corresponding combinations (black dots). Pairwise one-tailed Mann–Whitney U tests (alternative: greater) on the correct sequence of combinations were significant for both lineages. g, Schematic of three morphogen gradients that spatially instruct somitic–mesoderm differentiation. Progenitors emerge posteriorly and differentiate as they move anteriorly, coupling spatial position with developmental time. h, Somitic–mesoderm marker gene expression along pseudospace, approximated by diffusion pseudotime. i, Predicted signaling-response probabilities along the inferred pseudospace. Plots show the mean ± s.e.m. in d, h and i, with an asterisk denoting significantly increasing or decreasing trends along temporal or spatial axes, assessed by two-tailed Spearman’s correlation (P < 0.05). See Supplementary Table 1 for P values.

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We next asked whether IRIS could reconstruct signaling histories along diverse cell fate lineages, reflected by sequential usage of signal combinations. The anterior foregut and cardiomyocyte lineages have relatively well annotated signaling histories and are well covered in the mouse gastrulation dataset^34,35 (Fig. 3c and Supplementary Fig. 2). For each lineage, we selected relevant populations, inferred the activity of each pathway independently, and quantified activation probabilities along differentiation trajectories (Fig. 3d and Supplementary Fig. 8a). IRIS correctly recovered known temporal trends, including activation of BMP along the cardiac but not the endodermal lineage, inactivation of Wnt preceding cardiomyocyte differentiation, and the activation of RA in both the later endoderm and cardiac populations that correspond to anterior foregut cells and atrial cardiomyocytes respectively^18,19,36. When comparing inferred signal combinations across pseudotime, their temporal ordering significantly matched expected lineage progression via a permutation test (P < 0.05) (Fig. 3e,f and Supplementary Fig. 8b). For example, the signal combination associated with nascent mesoderm preceded that associated with cardiac specification. These results demonstrate that IRIS can correctly infer signal dynamics and order signal combinations along developmental trajectories.

Unlike other cell–cell communication inference algorithms that use pseudo-bulk analysis, IRIS predicts on individual cells, which allows IRIS to resolve diverse, biologically meaningful cell states within heterogeneous clusters. Within the cardiomyocyte population, IRIS identified enrichment of atrial markers in RA⁺ cells relative to RA⁻ cells (Nr2f2, Kcna5; P < 0.05), consistent with RA’s role in atrial specification³⁶ (Extended Data Fig. 8a,b). In endoderm, FGF⁺WNT⁺BMP⁺ cells were enriched for mid-hindgut markers (Cdx4, Cdx1, Msx1, Msx2 and Lef1; P < 0.05), whereas FGF⁻WNT⁻BMP⁻ cells expressed foregut markers (Sox2 and Tbx1; P < 0.05), consistent with posterior FGF4, BMP2 and WNT ligand activities promoting hindgut and repressing foregut fate in E7.5–E8.5 mouse embryos³⁷ (Extended Data Fig. 8c,d). These results underscore the ability of IRIS to disentangle complex cellular heterogeneity and uncover meaningful biological insights.

Extended Data Fig. 8. Inferred signaling state heterogeneity correlates with biologically meaningful cell-type heterogeneity.

a, Markers associated with different developmental stages of cardiac mesoderm aligned well with the diffusion component position. Both atrial and ventricular markers were expressed in the annotated cardiomyocyte population, revealing the heterogeneity of cell types. b, IRIS revealed heterogeneous states of RA activation within the annotated cardiomyocyte cluster (n = 1206). Cells predicted to be RA+ were enriched for atrial markers (Nr2f2, Kcna5), compared to cells predicted to be RA-. One-tailed Mann-Whitney U-test (alternative: greater). c, IRIS predicted activation of individual signaling pathways in the annotated gut population. d, IRIS identified several main combinatorial signaling states that corresponded to cell fate states within the gut cluster. The gut population (n = 1940) was re-clustered and annotated by the original paper based on cell fate markers (upper left panel)³⁵. Cells inferred to have the denoted combinations are highlighted (upper right panel, black dots). Gut cells associated with different combinatorial signaling states are enriched for different cell-fate markers that correspond to the foregut or mid/hindgut (bottom) (Foregut: Sox2, Tbx1; Mid/Hindgut: Cdx4, Cdx1, Msx1, Msx2, Lef1). One-tailed Mann-Whitney U-test (alternative: greater).

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Next, we asked whether IRIS can identify signaling information associated with cells’ location within a tissue. Somitogenesis is a classic example in which cells become more differentiated along the posterior-to-anterior axis of the tissue. Within this tissue, three morphogens form concentration gradients that provide the positional information to cells, with RA coming from the anterior and WNT/FGF from the posterior³⁸ (Fig. 3g). To test whether IRIS can recover these morphogen gradients, we selected the annotated somitic mesoderm population from the mouse gastrulation dataset and arranged cells along an inferred pseudospatial axis, which accurately recovered anterior–posterior gene expression patterns, with markers for differentiating somites (Mesp2 and Ripply2) decreasing posteriorly and markers for progenitor states (Tbx6) decreasing anteriorly (P < 0.05)^38–40 (Fig. 3h and Supplementary Fig. 9a). Given the spatially graded concentrations of these morphogens, we asked whether IRIS can quantitatively predict signaling strength. Instead of using binary classification, we examined the predicted probability of signaling response, and observed that average predicted probabilities along the spatial axis form gradients analogous to the concentration gradients in the natural tissue (Fig. 3i and Supplementary Fig. 9b). This result suggests that, even though IRIS is trained on binary signaling labels, its predictions may indirectly capture information about signaling strength that is reflected in prediction probability.

We further examined the predicted signal combinations at the single-cell level and asked whether we can use this combinatorial signaling information to correctly map the location of cells within the tissue. While three signaling pathways can theoretically generate eight combinations, five of these eight accounted for the vast majority of IRIS predictions (96%), with cells in the small RA⁻WNT⁺FGF⁻ population (4% of the cells) probably representing FGF or RA false negatives (Supplementary Fig. 9c,d). Placing the other four populations along the anterior–posterior axis based on the three morphogen gradients recovered the spatial patterns of cell-fate gene expression, demonstrating the ability of IRIS to correctly order signal combinations in space in in vivo atlases (Supplementary Fig. 9e).

IRIS performed robustly on in vivo embryonic endoderm and mesoderm cells, prompting us to assess whether its predictive capacity extends to more distantly related cell types. We first applied IRIS to neuroectodermal cells from the same mouse gastrulation dataset, a lineage that was not represented in the training data. The resulting predictions closely mirrored established models of early neural differentiation^41,42 (Extended Data Fig. 9). To further evaluate generalizability, we retrained IRIS to predict on a published dataset of organotypic cultures derived from primary adult human bronchial epithelial cells stimulated with diverse signaling cues, including developmental signals⁴³. These cultures comprised multiple cell types with variable competence to respond. When response competence was approximated by the expression of the corresponding signaling receptors, IRIS-predicted positive responders were significantly enriched among receptor-expressing populations (Supplementary Fig. 10). Together, these findings demonstrate that IRIS generalizes to cell types outside its training domain.

Extended Data Fig. 9. IRIS predictions in early neural differentiation.

a, Diffusion map of cell populations associated with the early neural lineages (top) and a schematic of lineage relationships amongst cell types (bottom). b, Individual probability predictions for each of the five pathways overlaid on the diffusion map. c, Diagram of known spatial gradients during early neural differentiation (top). WNT and FGF are known to posteriorize neural fates while BMP and TGF-β family ligands inhibit neural induction in early development^41,42,56,57. The role of RA has been well characterized for generation of spinal cord⁴¹. NMP (neuromesodermal progenitor)-Spinal cord-Forebrain/Midbrian/Hindbrain cells are aligned along the diffusion pseudospace component, as confirmed by the spatial patterns of marker gene expression (NMP: Cdx4: p = 0.0; Spinal cord: Pax6: p = 1.14e-24; Forebrian/Midbrain/Hindbrain: Otx2: p = 0.0, Sox2: p = 1.48e-209) (middle). The predicted signaling response probabilities across all five pathways show statically significant spatial trends (bottom). The variance was estimated with 1000 bootstrap samples of each of the pseudotime bins. * denotes significantly increasing or decreasing trends along spatial axes (p < 0.05), assessed by two-tailed Spearman’s correlation (n = 8691).

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IRIS helps optimize hES cell differentiation protocol for organ-specific mesenchyme

Finally, we asked whether IRIS can help reveal signaling histories along less-studied cell lineages and inform directed hES cell/human induced pluripotent stem (hiPS) cell differentiation. Organ-specific mesenchymal cells are a family of enigmatic cell types that are essential for organ development, such as instructing the branching morphogenesis in the lung⁴⁴. Their developmental histories are poorly understood and thus, efforts in deriving them from hES cells/hiPS cells to build more realistic organoids have received limited success. Taking advantage of a published dataset on mesenchymal diversity in early mouse organogenesis (E8.5–E9.5), we used IRIS to predict signaling activities during the diversification of organ-specific mesenchyme in the foregut^17,29. We found that WNT and BMP are significantly enriched in respiratory mesenchyme compared to all other mesenchymal fates (Fig. 4a and Supplementary Fig. 11). Although the role of canonical WNT signaling has been studied in the specification of the lung endoderm and differentiation of lung mesenchymal progenitors into various stromal cell types^45–47, its role in the initial specification of the respiratory mesenchymal identity was not reported. To test the prediction made by IRIS, we cultured the E9.0 mouse foregut ex vivo with either a WNT agonist or antagonist for 24 h. WNT activation spatially expanded the expression of key respiratory mesenchymal markers (for example, Tbx4 and Foxf1), whereas WNT inhibition completely eliminated Tbx4 expression (Fig. 4b and Extended Data Fig. 10a). The expansion of these markers was restricted to the anatomical region immediately adjacent to the lung, where the mesenchymal cells probably share common progenitors with the respiratory mesenchyme. This observation suggests that WNT regulates the choice between alternative organ identity of mesenchymal progenitor cells.

Fig. 4. IRIS optimizes hES cell differentiation toward organ-specific mesenchyme.

a, IRIS prediction on early organ-specific mesenchymal cells from E9–E9.5 mouse foregut¹⁷. Cells inferred to have the indicated signaling pathway active are highlighted by the corresponding color. WNT and BMP are significantly enriched in respiratory mesenchyme compared with all other mesenchymal fates. Significance was determined by a one-sided Fisher’s exact test. b, Validation of the IRIS prediction using ex vivo mouse foregut culture. E9.0 mouse foregut tissues were cultured for 24 h with a WNT agonist (CHIR) or an inhibitor (C59), followed by HCR–FISH for respiratory mesenchymal markers in the putative lung region. LE, lung endoderm; A, anterior; P, posterior; D, dorsal; V, ventral; DC, diffusion component. c, Comparison of the original and IRIS-optimized protocols for deriving respiratory mesenchyme from hES cells. The optimized version introduced earlier and extended WNT stimulation while keeping other pathway conditions identical. d, HCR–FISH staining of respiratory mesenchymal markers in hES cell-derived cells at day 7 of differentiation. e, Quantification of d showing significantly increased efficiency of respiratory mesenchyme differentiation by IRIS-optimized protocol. The asterisk denotes significance by one-sided Student’s t-test (P < 0.05). Each experiment was performed with three biological replicates and repeated twice for b and d. See Supplementary Table 1 for P values.

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Extended Data Fig. 10. Validation of IRIS prediction on the role of WNT in respiratory mesenchyme specification.

a, Whole mouse foregut explant images revealed that the expansion of Tbx4+ domain upon WNT stimulation was restricted to the tissues adjacent to the putative lung domain. Zoomed out images of Fig. 4b Activation of WNT by CHIR induces an expansion of the Tbx4+ domain, while treatment of a WNT inhibitor C59 completely ablated the Tbx4+ domain. b, c, Titrating the level of WNT activation in the IRIS-optimized hESC differentiation protocol (WiCells WA01) modulated the expression levels of key respiratory mesenchyme markers. Multiplexed HCR-FISH was performed on Day 7 with representative images shown in (b) and quantification of transcripts per cell in (c). Number of cells for each condition: 6 μM, n = 3228; 4 μM, n = 2986; 3 μM, n = 2990; 2 μM, n = 3040; 1 μM, n = 3417; Original, n = 3913). * denotes significant p value of <0.05 according to one-tailed Student’s T-test with the alternative hypothesis of a greater (TBX4) and less (FOXF1). d, e, IRIS-optimized protocol increased the expression of lung mesenchyme markers at the single-cell level, a result replicated across multiple human pluripotent cell lines. Multiplexed HCR-FISH was performed on Day 7 with representative images shown in (d) and quantification of gene expression levels per cell in (e). Number of cells for each condition: iPSC with IRIS protocol, n = 2421; iPSC with original protocol, n = 3200; WIBR3 with IRIS protocol, n = 1637; WIBR3 with original protocol, n = 2843). One-tailed Student’s T-test with the alternative hypothesis of a greater mean.

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We sought to apply this knowledge to improve hES cell/hiPS cell differentiation protocols for the respiratory mesenchyme, a key step toward building lung organoids with branched structure. The published protocol applied WNT stimulation only during the final 24 h of the 7-day differentiation to promote tracheal fate, a stage that occurs after commitment to respiratory identity³⁰ (Fig. 4c). By contrast, IRIS predicted that WNT signaling functions earlier, during commitment to the respiratory fate itself. We therefore activated WNT earlier and for a longer duration compared with the published protocol, starting from day 4 of in vitro differentiation, which corresponds approximately to the splanchnic mesoderm stage. Earlier WNT activation dramatically increased TBX4 expression in a concentration-dependent manner, and an intermediate WNT activity proved optimal for preserving all key marker genes of respiratory mesenchyme, as high WNT activity reduced FOXF1 expression (Extended Data Fig. 10b,c). The pro-respiratory effect by early WNT activation was reproducible across different hES cell/hiPS cell lines, suggesting that the modified protocol more closely approximates respiratory mesenchymal specification (Extended Data Fig. 10d,e). Modulating WNT alone is unlikely to be sufficient for deriving respiratory mesenchymal cells that are functionally equivalent to their in vivo counterparts, and future efforts to optimize differentiation protocols, by leveraging more comprehensive scRNA-seq atlases of lung development together with the full set of IRIS predictions, will probably further improve differentiation outcomes. Nevertheless, these results demonstrate the utility of IRIS for proposing and optimizing new directed differentiation protocols for stem cells, without having to explore the entire combinatorial space.

Discussion

Mapping cells’ signaling states and histories is crucial for understanding how cells make fate decisions but remains challenging because such experiments in animal models are expensive and low throughput, and comparable tools are lacking for human tissues. We have developed an experimental–computational framework that performs combinatorial signal perturbation screens on a collection of cell types in vitro, and uses signaling response signatures learned from transcriptomic data to infer the activity of the same signaling pathways in vivo. The signaling response signatures serve as accurate classifiers on diverse cell types, including those not represented in the perturbation screens. This cross-cell-type and cross-batch signal classification is enabled by IRIS, a neural network-based transfer learning algorithm. Although our work focused on six recurring developmental pathways that govern many cell fate decisions in early embryos, the same framework can be applied to other signaling pathways, such as NOTCH and YAP pathways in developing embryos, cytokines in the immune system and hormones in regulating physiology.

The transferability of signaling response signatures between unrelated cell types is surprising, because transcriptional responses to signal activation are often considered unique to each cell type^14,48,49. We demonstrated that the response signatures learnt from mES cell and hES cell screens can accurately classify signaling states of cells from mouse embryos at equivalent and later stages. To what extent the response signatures learnt by IRIS generalizes across cells that are far apart in transcriptomic space remains to be determined. The model itself may be improved by integration with recent advances in transformers and foundation models that are able to learn generalizable principles on large, unlabeled datasets^50–53. Increasing cell type diversity in the training data may also enable broader generalization to distant cell types. We envision an iterative cycle of perturbation screens, model training, prediction on new data, and experimental testing, with each round refining the model.

Furthermore, our results support the idea that signaling information can be stored broadly across the transcriptome. Our analysis suggests that many genes carry information about signaling response and classifiers relying on many genes are more robust to cellular contexts and technical noise associated with scRNA-seq data. Across signaling pathways, we observed that response signatures to WNT and RA seem to transfer particularly well across cell types in nearly all tests, whereas FGF often, but not always, underperforms. We suspect that this reflects the extent to which a signaling pathway shares its machineries with other pathways. In particular, FGF shares signal transduction components with many other receptor tyrosine kinase pathways, whose activities may already be present in culture conditions and confound signal inference. In addition, our models were fit to data collected after sequential steps and durations of signal stimulation, which might introduce signaling carry-over from previous stimulation or an artificial delay in the predicted signal activation/inhibition, respectively. How the response signatures evolve over time remains to be rigorously characterized.

Overall, IRIS enables learning signaling states and histories from scRNA-seq data. Reconstruction of signaling histories by IRIS relies on accurate lineage inference, which is an active area of algorithm development. Nevertheless, IRIS can act on imperfect cell clusters that include heterogeneous cell types/states, due to its complete reliance on cell-autonomous information at the single-cell level. As a result, IRIS’ response-centric approach is complementary to other signal inference methods relying on ligand–receptor pairing, such as CellPhoneDB, NicheNet and CellChat^6–8. These two types of approaches can be used jointly to infer potential cell–cell communication, especially in the case of analyzing spatial transcriptomics data. This will expand opportunities in using scRNA-seq and spatial transcriptomics for scientific discoveries and translational applications, such as engineering stem cells and identifying signaling pathways that drive pathological states of the cells.

Methods

Single-cell data processing

Unless otherwise stated, single-cell data were processed using the Scanpy package (v.1.10.0). For visualization, data were log normalized and scaled according to z scores, and nearest-neighbor graphs were constructed from a principal component analysis computed from these scaled expression values. These nearest-neighbor graphs were the basis for the Uniform Manifold Approximation and Projection (UMAP) projections. For developmental lineage visualization, the scanpy.tl.diffmap function was used to visualize developmental trajectories. This function takes data, $X\in R^{n\times d}$, and constructs a pairwise similarity matrix between observations using a Gaussian kernel, $S_{ij}=\exp \left(-\frac{{∣∣{\mathbf{x}}_i-{\mathbf{x}}_j∣∣}^2}{2ϵ}\right)$. Epsilon is used as the bandwidth parameter. This similarity matrix is then converted to a Markov transition matrix using the partition function $P_{\mathit{ij}}=\frac{S_{\mathit{ij}}}{\sum _k{S}_{\mathit{ik}}}$. The eigenvectors are then computed from this transition state matrix and used as the diffusion components. Optimal diffusion components were those which, when used in pairs, correctly placed the lineages in order based on known cell type markers and annotations. Human and mouse gene names were converted between each other using mousipy (v.0.1.5). For consistency in the analysis, when mouse and human data were integrated, human gene names were used.

Signaling state inference with the response-gene method

Response-gene scores were computed by summing the log normalized gene expression values for the response-gene sets for each pathway. For a set of j response genes (G) and expression r,

$$S\left(i\right)=\sum _{i\in G}r\left(j\right).$$

The performance of the inference method was evaluated using the receiver operator characteristic (ROC), precision–recall curve (PRC) and F1 score. The ROC was computed and plotted using sklearn.metrics.roc_curve. Specifically, for each signaling pathway, a variety of arbitrary thresholds for the response gene scores were set to classify the pathway activity. Each cell in the test group was classified to be ON or OFF for the pathway activity based on the corresponding response score. By comparing with the ground-truth label, the true positive rate (TPR) and FPR were calculated for each threshold and plotted against each other to generate the ROC:

$$\mathrm{TPR}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$$

$$\mathrm{FPR}=\frac{\mathrm{FP}}{\mathrm{TP}+\mathrm{FP}}$$

where TP is true positive and FP is false positive. The area under the receiving operating curve (AUROC) was computed using sklearn.metrics.roc_auc_score. The PRC was computed and plotted similarly using sklearn.metrics.prc_curve by setting a variety of arbitrary thresholds for response gene scores. The precision (same as TPR) was plotted against recall at each threshold.

$$\mathrm{Recall}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$$

where FN is false negative. The area under the precision–recall curve (AUPRC) was computed using sklearn.metrics.auc, which computes the integral over these two scores using the trapezoid rule. The F1 score was evaluated using sklearn’s metrics functions (v.1.4.1.post1):

$$\mathrm{F}1=\frac{\mathrm{TP}}{\mathrm{TP}+\frac{1}{2}\left(\mathrm{FP}+\mathrm{FN}\right)}$$

Calculating the F1 score requires a single threshold of response gene scores for each signaling pathway, which was computed by finding the threshold which maximally separates TP and FP according to the ROC curve.

IRIS model and hyperparameter selection

IRIS is a semi-supervised model that was implemented using the scANVI architecture from the scvi-tools package (v.0.20.3)²⁶ and trained on an NVIDIA-A6000 graphics processing unit using the Cuda library (v.11.3). The model architecture is a variant of the CVAE model. It includes an encoder neural network which learns the mapping of the input data X and the conditions S to an n-dimensional latent space Z. A decoder neural network takes as input the conditions S, and latent space encoding in Z. The CVAE model minimizes the evidence lower bound:

$${L_{\mathrm{CVAE}}=E}_{q_{\varphi }\left(\mathbf{Z}\mid \mathbf{X},\mathbf{S}\right)}\left[\log p_{\theta }\left(\mathbf{Z},\mathbf{S}\right)-{\alpha D}_{\mathrm{KL}}\left(q_{\varphi }\left(\mathbf{Z}\mid \mathbf{X},\mathbf{S}\right)\mid p_{\theta }\left(\mathbf{Z}\mid \mathbf{S}\right)\right)\right]$$

where $q_{\varphi }\left(\mathit{Z|X},\mathit{S}\right)$ represents the variational posterior, $p_{\theta }\left(\mathit{X|Z},\mathit{S}\right)$ is the reconstructed distribution from the latent space, and α is a hyperparameter that determines the strength of the Kullback–Leibler regularization term ($D_{\mathrm{KL}}$). For the purposes of this analysis, gene expression counts were assumed to follow a zero-inflated negative binomial distribution (ZINB). The default value of 0.01 was used. Simultaneously, a feedforward neural network (FNN) takes as input Z and S for each data point and minimizes the cross-entropy (CE) loss:

$$\mathrm{CE}=\frac{1}{n}{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{k=1}^K}{Y}_{\mathit{ik}}\log P_{\mathit{ik}}$$

with respect to the target labels Y. Here, k are the individual classes, K is the total number of classes and P is the probability of being assigned either class label. Each node in the neural network uses a rectified linear activation function ReLU = max(0, x). The final layer of the FNN uses a sigmoid function that computes the probability of the two class labels. These are then thresholded with the value 0.5 to binarize the predictions. The two neural networks are trained jointly to minimize the loss L = L_CVAE + CE.

Data were stored in the anndata format with observations as individual cells and variables as gene names. X ∈ R^{n × d} is the input scRNAseq with raw counts as the values. S ∈ R^{n × c} are the conditions from the covariates c (for example batch, cell type and species), with a one-hot encoding. The target labels Y ∈ R^{1 × d} is presented as a vector in the anndata object with binary indicator variables. X was partitioned into training and test data as specified in each trial. Models were fit by minimizing loss on training data and then evaluated on held-out test data by freezing the model weights and evaluating the prediction output. Model performance was evaluated using the ROC, PRC and F1 scores computed on the test data (see above).

Hyperparameter selection was performed by fitting distinct architectures on the training data (layers = 1, 2, 3; hidden nodes = 32, 64, 128, 256, 1,024; latent variables = 10, 20, 30, 50, 60). Their performance was evaluated using AUPRC. The best-performing architectures were then used in subsequent analysis and evaluated via k-fold cross-validation over the batches. Models were trained for 200 epochs because this was found to provide optimal performance across a range of trials.

Setup of the model tests

In-sample tests were performed on random partitions of mES cell screen data or the combined mES cell and hES cell screen data. The data were partitioned using the np.random.choice function to select 20% of the data as test data and the remaining 80% for model fitting. Model performance was evaluated with ROC, PRC and F1. The cross-validation tests were performed by splitting the mES cell screen data into three technical batches (mP_d1, mE_d2 and mixed) and treating the hES cell screen data as three separate technical batches (hM_d4, hM_d7 and hE_d8).

In the first test that performs the hyperparameter screen, the model was fit to two of the three mES cell batches at a time and tested on the third mES cell batch. The test was done iteratively by holding out each batch and averaging the performance metrics across all three held-out batches (Supplementary Figs. 5 and 6).

The second cross-validation test was performed by including all screen data and iterating through all five possible held-out batches (excluding the mixed batch owing to overlap with mP_d1 and mE_d2) (Supplementary Fig. 7).

Three tests of out-of-species generalization were performed. (1) The test with limited data was performed by fitting the model with the complete mES cell screen data and evaluating on the hM_d screen data. F1 scores were computed and compared with simpler ML model benchmarks. (2) The model was fit to the all of the mES cell screen data (mP_d1, mE_d2 and mixed) and evaluated on the hES cell screen data (hM_d4, hM_d7 and hE_d8) and vice versa, and F1 scores were computed and compared with random baselines. (3) To test whether additional target-species data from an unrelated cell type could enable cross-species generalization, the model was fit to mP_d1 plus mE_d2 with or without a random 10% subset of hE_d8 and evaluated on hM_d4. The AUROC and AUPRC scores were compared with and without the subset of hE_d8.

To evaluate whether out-of-species data enhanced in-species prediction, two tests were performed. (1) The model was fit to 80% of the mES cell screens (mP_d1, mE_d2 and mixed) with and without hM_d4 and evaluated on a held-out 20% partition of the mES cell screens. (2) The model was fit to all but a single held-out combination mES cell and hES cell screen data (mP_d1, mE_d2, mixed, with or without hM_d4) and evaluated on that held-out combination. F1 scores were compared with and without hM_d4 in training. To evaluate cross-cell type generalization, the model was fit to the screens representing only endodermal contexts (mE_d2 and hE_d8) and evaluated on either hM_d4 or hM_d7. The performance metrics (F1, AUPRC and AUROC) were compared with random baselines.

Comparison with classic machine learning models

Classic machine learning models such as support vector machines (SVM), random forests (RF) and elastic net (EN) were implemented using the sklearn (v.1.4.1.post1) library and run on the same machine. Hyperparameter selection was performed over multiple orders of magnitude for each of the tunable hyperparameters (Supplementary Fig. 6).

The SVM minimizes the following objective:

$$L\left(\mathbf{w},b\right)=\frac{C}{2}{\mathrm{\parallel }\mathbf{w}\mathrm{\parallel }}_2^2+\frac{1}{n}{\mathbf{1}}^T\left(0,Y\left(Xw+b_1\right)\right)$$

where $w$ is the vector of weights, w ∈ Rⁿ. $N$ is the number of data points, 1 ∈ R^d is a vector of ones, Y ∈ Rⁿ is a vector of the binary labels, b ∈ R is the bias term. The scaling factor, C, was chosen as stated in each analysis.

The RF minimizes the following objective:

$$L_{\mathrm{classification}}=-\frac{1}{n}\sum _{i=1}^n\sum _{k=1}^K{Y}_{ik}\log P_{ik}$$

where $K$ is the number of classes (in this case for binary classification, 1), $n$ is the number of data points, and $P_{\mathit{ik}}$ is the log probability of the correct classification. The classification loss minimizes the cross-entropy loss.

The EN model minimizes the following objective:

$$L\left(\mathit{\beta }\right)=\frac{1}{2n}{\Vert \mathbf{y}-X\mathit{\beta }\Vert }_2^2+\lambda (\alpha {\Vert \mathit{\beta }\Vert }_1+\frac{1-\alpha }{2}{\Vert \mathit{\beta }\Vert }_2^2)$$

where $\beta \in R^{1\times d}$ and are the weights of the model. $N$ is the number of data points ${\Vert \cdot \Vert }_2^2$ is the Euclidean norm, and the ${\Vert \cdot \Vert }_1$ is the regularization penalty, which is set to values as specified in each trial. $\alpha$ is the weighting parameter for L1 and L2 penalties. For all trials, it was set to 0.5.

Computing correlation matrix of transcriptional states and hierarchical clustering

Correlation between cells from two signaling conditions was computed as the averaged gene expression for each gene across both conditions using Pearson’s correlation:

$$R=\frac{\sum _i(x_i-\overline{x})(y_i-\overline{y})}{\surd {(x_i-\overline{x})}^2{{(y}_i-\overline{y})}^2}$$

where $x_i$ and $y_i$ are individual genes in the two conditions $x$ and $y$, respectively. $\underset{¯}{y}$ and $\underset{¯}{x}$ are the average expression over all genes in the respective conditions. Correlation matrices were then generated with scanpy.pl.correlation_matrix. The distance metric used was $1-\mathit{R}$.

All signaling conditions were hierarchically clustered on the dendrogram using Ward’s method. In Ward’s method, two groups are clustered if they result in the smallest increase in total intracluster variance, computed as the error sum of squares:

$$\mathrm{ESS}=\sum _{x\in C_i\cup C_j}{\parallel x-{\mu }_{C_i\cup C_j}\parallel }^2-\left(\sum _{x\in C_i}{\parallel x-{\mu }_{C_i}\parallel }^2+\sum _{x\in C_j}{\parallel x-{\mu }_{C_j}\parallel }^2\right)$$

where $C_i$ and $C_j$ represent clusters that are to be merged, and $\mu$ represents the centroid of a given cluster. This process was continued iteratively until all clusters were merged, representing the root of the dendrogram.

Inferring signaling histories along developmental lineages

IRIS was used to infer signaling histories in the mouse gastrulation dataset, foregut mesenchymal dataset and human airway epithelium^17,35. Cells were first clustered using Leiden clustering in scanpy with default parameters. Cell type annotations were determined using canonical marker genes and annotations provided by each of the datasets. The diffusion components were computed using sc.tl.diffmap and visually inspected for those that placed the cell types and marker gene expression in the expected order consistent with literature. For the cardiac lineage analysis, this included the PS, nascent mesoderm, mixed mesoderm, pharyngeal mesoderm and cardiomyocytes. The endodermal lineage analysis included the PS, APS, definitive endoderm, gut and visceral endoderm. A single diffusion map was made for the endoderm and cardiac lineages. Endodermal cells were subclustered and visualized with a diffusion map. The presomitic mesoderm analysis included only cells from the somitic mesoderm cluster and visualized with a diffusion map. The respiratory mesenchyme lineage analysis included only cells from the dorsal lateral foregut, respiratory mesenchyme, esophageal mesenchyme and pharyngeal mesenchyme, which were projected on a single diffusion map.

To infer the signaling histories, two methods were applied. For the response-gene method, response-gene scores were overlaid on diffusion maps to serve as a relative estimate of the pathway activity. Thresholds were chosen to maximize the separation between true and false positives. For the IRIS method, the model was fit to the raw count matrix using optimized hyperparameters for each pathway. Signaling pathway activities were predicted independently for each pathway and the combinatorial signaling state of a cell was composed by concatenating all of the pathway predictions.

To temporally project inferred signaling states along either the developmental trajectories or spatial axes, selected cell populations were lined up across developmental pseudotime, discretized into 35 bins (or smoothed with a bandwidth of 0.1), which was chosen for better visualization. In the case of somitic mesoderm cells, the pseudotime was used as a proxy for a pseudospatial axis from posterior to anterior of the embryo. To validate the pseudotime/psuedospace trajectories, the expression of key cell fate marker genes were projected and analyzed. Finally, the trends of inferred activities among the five signaling pathways were characterized either separately or as combinations. In the case of individual pathways, the binary classification or predicted response probabilities were projected along the pseudo-axis and trends were quantified via Spearman correlation. The predicted response probabilities are computed by the sigmoid layer of the FNN. In the case of signal combinations, the raw frequency of each inferred combination was plotted across developmental pseudotime, and the temporal ordering of the combinations along these axes were confirmed with Mann–Whitney U tests of the average position along them. We chose to look at trends and order of signaling combinations rather than abundance as not all progenitor cells go on to become a given final cell fate, making direct interpretation difficult.

Feature importance analysis

Feature importance was determined by the reduction of inference accuracy when the expression level of individual genes was sequentially resampled with replacement in the test data. Negative exponential curves of the form ${\mathrm{e}}^{-\alpha t}$ were fit for visualization using curve_fit in the scipy.optimize library. Resampling with replacement was performed using the numpy.choices function on a vector containing all of the original gene expression values. Genes were ranked from high to low either by their dispersion or by mutual information. Dispersion was computed using scanpy.pp.highly_variable_genes: $D=\frac{{\sigma }^2}{\mu }$, where ${\sigma }^2$ is the variance of the expression for a given gene and is the averaged expression for a given gene. Mutual information was calculated for a given gene X and a given signaling state vector Y, which is a vector of 0 and 1 binary values representing signaling stimulation. The entropy (H) and mutual information (I) were approximated using scikit-learn.mutual_info_classif which implements a k-nearest-neighbor estimation of entropy between continuous variables and categorical variables as follows:

$$I\left(X;Y\right)=H\left(X\right)+H\left(Y\right)-H\left(X|Y\right).$$

Gradients–GSEA analysis

Gradients were computed natively by Pytorch (v.2.2.2+cu121). Neural networks were trained via backpropagation and the gradient with respect to the input layer was computed as

$$\frac{\partial L}{\partial \widehat{X}}=\frac{\partial L}{\partial \widehat{y}}\frac{\partial \widehat{y}}{\partial \widehat{X}},$$

where $L$ is the loss function, $y$ is the target vector of signaling labels and $X$ is the input data. Genes were ranked according to the magnitude of the gradient. These rankings were used to perform GSEA using GSEApy (v.1.1.3). The normalized enrichment score S is computed as the maximum value of a running sum according to the following equation:

$$S\left(i\right)=\sum _{j=1}^i\left(\frac{\delta \left(j\right)-{\left|r\left(j\right)\right|}^p}{\sum _{j\in G}{\left|r\left(j\right)\right|}^p}-\frac{1-\delta \left(j\right)}{N-|G|}\right),$$

where the score $S$ is computed for a given gene set of interest $G$, $N$ is the number of genes in the ranked list and $\mathit{|G|}$ is the number of genes in the gene set of interest. The weight parameter p indicates how heavily to weigh each gene’s ranking. $\delta \left(j\right)$ is the indicator function for whether or not a gene jis in the gene set G. $r\left(j\right)$ is the ranking statistic for a given gene. The normalized enrichment score is then computed as $\mathrm{NES}=\frac{\left(S\left(i\right)\right)}{\max \left(S_{\mathrm{null}}\left(i\right)\right)}$. The P value was computed by a permutation test with 1,000 samples. The gene set of interest was considered to be enriched if P < 0.05 and nearly enriched if 0.05 < P < 0.06.

Stem cell maintenance and directed differentiation

Research involving human stem cells was approved by the Whitehead Institute Embryonic Stem Cell Research Oversight Committee in accordance with the guidelines set out by the International Society for Stem Cell Research. hES cells (WiCells WA01), WIBR3 (hES cells) (Whitehead Institute Human Stem Cell Facility) or induced pluripotent stem cells (iPS) cells (WIBR iPSC66) were maintained in mTESR plus (STEMCELL Technologies 100-0276) and StemFlex media (Gibco A3349401), passaged every 4 days at 1:20 using ReLesR (STEMCELL Technologies 100-0483) and checked for the undifferentiated morphology. To differentiate hES cells or iPS cells, cells were dissociated as single cells with accutase (STEMCELL Technologies 07920), counted and plated at a density of 10⁵ cells ml⁻¹ on Matrigel-coated plates (Corning 354277) with 10 μM Rock Inhibitor Y-27632 (STEMCELL Technologies 72308). All differentiation was performed in a basal media that includes Advanced DMEM/F12 (Gibco 12634010), N2 supplement (Gibco 17502048), B27 supplement (Gibco 17504044) and penicillin–streptomycin–glutamine (Gibco 10378016), with the addition of signal agonists and antagonists specified in the following sections.

Sequential combinatorial signal screen with pooled scRNA-seq

For the hM_d4 combinatorial signal screen, hES cells were plated at 5,104 cells per well as single cells into 24-well cell-culture plates. Plates were coated with Matrigel (Corning 354277) at room temperature for 1 h before use. After 24 h of recovery in StemFlex feeder free media, cells were differentiated into the middle PS state with the middle PS induction medium for 1 day (step 1). The middle PS induction medium was supplemented with 6 μM CHIR99021 (Fisher Scientific 44-231-0), 40 ng ml⁻¹ BMP4 (R&D Systems 314-BP-050/CF), 30 ng ml⁻¹ Activin A (R&D Systems 338-AC-010/CF), 20 ng ml⁻¹ FGF2 (R&D Systems 3718-FB-010) and 100 nM PIK90 (EMD Millipore 528117).

The middle PS cells were then used for the sequential combinatorial signal screen that differentiated the cells for 3 more days (step 2 for 1 day + step 3 for 2 days). Among the combinations, three different lateral plate mesoderm (LPM) states (day 2) were induced following published protocols^17,29. Specifically, middle PS was induced into cardiac LPM with 30 ng ml⁻¹ BMP4 (R&D Systems 314-BP-050/CF), 1 μM A83-01 (Fisher Scientific 29-391-0) and 1 μM WNT-C59 (Fisher Scientific 51-481-0). Middle PS was induced into anterior foregut (aFG)-LPM with 30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59, 2 μM RA (Fisher Scientific AC207341000) and 1 μM PMA (Fisher Scientific 50-197-5893). Middle PS was induced into posterior foregut (pFG)-LPM with 30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59 and 2 μM RA. LPM cells were further differentiated into their respective splanchnic mesoderm (SM) fate by cardiac SM induction medium (30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59 and 20 ng ml⁻¹ FGF2), aFG-SM induction medium (30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59, 20 ng ml⁻¹ FGF2, 2 μM RA and 1 μM PMA) or pFG-SM induction medium (30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59, 20 ng ml⁻¹ FGF2 and 2 μM RA) for 2 days. The rest of the sequential combinatorial conditions were chosen either by random combinations of the five signaling pathways (54 combinations) or bit-flip combinations of the five signaling pathways based on the three controls (38 combinations).

Media were changed every day. On day 4, cells were incubated in Rocki for 30 min, dissociated as single cells in accutase and barcoded with multiSeq oligos (Millipore Sigma LMO-001). Each well in the screen received a unique barcode. Multiplexing was performed in accordance with the manufacturer’s protocol²⁸. Cells were resuspended in phosphate-buffered saline + 1% bovine serum albumin (Sigma Aldrich A9418), pooled and sorted for live cells using a 4′,6-diamidino-2-phenylindole (DAPI) stain. Cells were processed using a 10x Chromium flow-cell and sequenced on a Illumina Novaseq sequencer, and 19,155 cells passed quality controls.

For the hM_d7 combinatorial screen, cells were plated as and differentiated to the middle PS state as in hM_d4. Next, they were differentiated into one of four states for 1 day using the LPM condition (30 ng ml⁻¹ BMP4, 1 μM A83-01 and 1 μM WNT-C59) with or without 2 μM RA and 1 μM PMA. For all future steps, the RA and PMA levels were kept constant. Next, they were differentiated to the splanchnic mesoderm-like state for 2 days with (30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59 and 20 ng ml⁻¹ FGF2). Finally, all possible combinations of 30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59 and 20 ng ml⁻¹ FGF2 were then provided to each of the four states for 3 days, totaling 64 conditions. Cells were pooled and sequenced as described in hM_d4. Cells were processed as in hM_d4, and 11,857 cells passed quality controls.

For the hE_d8 combinatorial screen, cells were plated using the same procedure described in hM_d4 with a density of 2 × 10⁻⁵ cells ml⁻¹. They were first differentiated to the anterior PS for 1 day (100 ng ml⁻¹ Activin A and 2 μM CHIR), which was then differentiated into the definitive endoderm for 2 days (100 ng ml⁻¹ Activin A). After this, all combinations of 30 ng ml⁻¹ BMP4, 1 μM A83-01, 1 μM WNT-C59, 20 ng ml⁻¹ FGF2, 2 μM RA and 1 μM PMA were then provided for 5 days to create 64 combinations. Cells were pooled and sequenced as described in hM_d4. Cells were processed as in hM_d4, and 9,921 cells passed quality controls.

Count matrices were generated using CellRanger (v.7.1.0) and aligned to the reference human genome GRCh38. Barcodes were aligned and demultiplexed using the R library deMULTIplex (v.1.0.2)²⁸. Barcodes were visually inspected using tSNEs of cells clustered in barcode space. This was performed in accordance with the criteria specified in deMULTIplex. Once a list of observed barcodes was identified, each barcode was normalized to the number of barcodes observed per cell. Each barcode then had outliers trimmed and its probability density function computed. Lastly, thresholds were identified by defining the local maxima, with the mode for negatives and maximum for positive values. Barcodes were then assigned independently for each cell. Cells with one barcode are designated as singlets, more than one as doublets, and those with none as negatives. The optimal threshold was chosen, which maximized the number of singlets relative to doublets and negatives. A total of 65, 55 and 55 unique barcodes were recovered in the hM_d4, hM_d7 and hE_d8 screens, respectively. Across each of these screens, the maximum number of cells per barcode was 975, 1,255 and 807, respectively.

Directed differentiation into respiratory mesenchyme

hES cells or iPS cells were first differentiated into aFG-SM using the aforementioned media condition. Then, they were induced with either IRIS-optimized media protocol (30 ng ml⁻¹ BMP4, 2 μM RA, 2 μM PMA and 3 μM CHIR) for 3 days, or published protocol (30 ng ml⁻¹ BMP4, 2 μM RA and 2 μM PMA) for 3 days with 2 μM CHIR added only for the last day²⁹. On day 7 of differentiation, samples were fixed in 4% paraformaldehyde for 15 min, then processed for hybridization chain reaction (HCR).

Mouse foregut explant culture

All mouse work was performed in accordance with Massachusetts Institute of Technology’s Division of Comparative Medicine and Committee for Animal Care. To perform the signaling perturbation in explants, E9.0 mouse embryos were collected from wild-type C57BL/6J timed matings. Foreguts were isolated by dissecting the anatomical region between the pharyngeal arches and liver, excluding additional tissues including the somites. Foreguts were cultured in DMEM/F12 (Gibco 10565042) + 5% fetal bovine serum (Takara 631368) + 1% penicillin–streptomycin–glutamate (Gibco 10378016) supplemented with either 3 μM of CHIR or 1 μM C59. After 24 h in culture at 37 °C, samples were fixed in 1% paraformaldehyde overnight at 4 °C and processed for subsequent analysis.

HCR

HCR–fluorescence in situ hybridization (FISH) probes were designed in-house and tested on samples with known expression to validate probe efficiency⁵⁴. Mouse foregut explant or differentiated hES cell samples were dehydrated with 100% methanol and subsequently processed according to the HCR–FISH protocols from Molecular Instruments. In brief, samples were hybridized overnight at 37 °C with 4 μM of probes and amplified overnight at room temperature with B1, B3, B4 and B5 hairpin amplifiers (Molecular Instruments). Afterward, hES cell-derived samples were imaged on a Nikon TI2 widefield fluorescence microscope. Explant samples were imaged on a Zeiss LSM980 Airyscan 2 confocal microscope. Analysis of the hES cell-derived cells was performed by first segmenting in cellpose using the ‘cyto2’ model (parameters: diameter = 35, flow-threshold = 0.7)⁵⁵. Total nuclear fluorescence signal was then measured in each channel with these segmentation masks. Individual fluorescence measurements for each cell were grouped on the basis of the treatment condition, and a Student’s t-test was performed to determine statistical significance using scipy.stats.ttest_ind (v.1.12.0). This test assumes the expression level following a t-distribution, and values are considered significant if P < 0.05. Data were visualized using seaborn.violinplot.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41592-026-03213-8.

Author contributions

N.H. and P.L. conceived the study. P.L. supervised the work. N.H. led the computational and experimental work. C.L. developed the code base. M. Me performed experimental validation in mice. M. Mi assisted with stem cell validation experiments. D.S.F. provided consultation on the work. N.H. and P.L. wrote the paper.

Peer review

Peer review information

Nature Methods thanks Aaron McKenna and Manu Setty for their contribution to the peer review of this work. Primary Handling Editor: Madhura Mukhopadhyay, in collaboration with the Nature Methods team.

Funding

P.L. discloses support for the research of this work from National Institute of Health (grant numbers DP2HD108777 and R00HD087532), Allen Family Philanthropies, Eugene Bell Career Development Professorship, and the Centurion Foundation. N.H. discloses support from the National Science Foundation Graduate Research Fellowship program. M. Me discloses support from MathWorks Graduate Fellowship. D.S.F. discloses support from the Eric and Wendy Schmidt Center fellowship at the Broad Institute. C.L. and M. Mi declare no relevant funding.

Data availability

All data analyzed in this Article are available publicly through online sources. The following data are available at the Gene Expression Omnibus database with their corresponding accession numbers: raw data for hM_d7, hE_d8 (GSE327767) and hM_d4 (GSE289836), the mESC screen (GSE122009), mouse foregut organogenesis dataset (GSE136689) and human airway epithelium (GSE246368). The gastrulation atlas is available on ArrayExpress (E-MTAB-6967). Source data are provided with this paper.

Code availability

Code is available via GitHub at https://github.com/Pulin-Li-Lab/IRIS-signaling-inference.

Competing interests

The authors declare no competing interests.

Extended data

is available for this paper at https://doi.org/10.1038/s41592-026-03213-8.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41592-026-03213-8.