CytoSignal detects locations and dynamics of ligand–receptor signaling at cellular resolution from spatial transcriptomic data

Abstract

Cells communicate through ligand–receptor (LR) signaling interactions, but identifying when and where these interactions are active remains challenging. We developed CytoSignal to infer the locations and dynamics of cell–cell communication at cellular resolution from spatial transcriptomic data. Here we show that our cellular resolution, spatially resolved signaling scores enable several important analyses—identifying spatial gradients in signaling strength, quantifying the locations of contact-dependent and diffusible interactions, detecting signaling-associated genes and identifying differential signaling across multisample data. Additionally, we can predict the temporal dynamics of a signaling interaction at each spatial location. We experimentally validate our results in situ by proximity ligation assay, confirming that CytoSignal predicts the locations of LR interactions more accurately than previous approaches. This study addresses the field’s current need for a robust and scalable tool to detect cell–cell signaling interactions and their dynamics at cellular resolution from spatial transcriptomic data.

CytoSignal models ligand–receptor interactions at cellular resolution using spatial transcriptomic data, inferring interaction scores at each spatial position and predicting temporal dynamics by incorporating RNA velocity.

Main

Intercellular signaling occurs through many mechanisms, such as secreted ligands binding to transmembrane receptors or membrane-bound proteins dimerizing on adjacent cells. Cell signaling influences differentiation and fate specification during normal development¹, and intercellular communication coordinates immune response, growth and physiological tissue function² in the developed organism. However, identifying which signaling interactions operate between which cells under particular conditions remains challenging. Single-cell RNA-sequencing (scRNA-seq)³ datasets allowed some progress by revealing which ligands and receptors are expressed by each cell type within a heterogeneous tissue⁴. Numerous methods have been developed to infer cell–cell communication from scRNA-seq data^5–9; however, these scRNA-seq methods have the following two key limitations: (1) they do not incorporate information about the spatial proximity of cells and (2) they infer signaling among groups of cells rather than at single-cell resolution.

Spatial transcriptomic protocols measure both gene expression profiles and spatial coordinates within a tissue, providing crucial information about the spatial proximity of cells expressing ligands and receptors. Methods have been developed to detect cell signaling from spatial transcriptomic data^10–14; however, these approaches identify interactions among large predefined groups of cells (cell types). Other methods have been published to detect cell signaling at the cellular level from spatial transcriptomic data^15,16, but they do not make predictions for each ligand–receptor (LR) pair individually. Some recent methods can predict activity for individual LR pairs at individual tissue positions^17–21. However, these methods model contact-dependent and diffusible interactions in the same manner. Contact-dependent interactions require cells to be immediately adjacent within the tissue^22–24, while interactions between diffusible ligands and transmembrane receptors require cells to be close but not necessarily touching. Furthermore, most existing approaches infer only the state of cell signaling at the time of measurement and not the changes in their interactions over time.

To address these limitations, we developed CytoSignal, which uses spatially resolved gene expression data to estimate static and dynamic signaling among single cells at specific spatial positions. CytoSignal calculates a simple, principled score to identify which cells and locations within a tissue have significant activity for a particular signaling interaction. CytoSignal distinguishes between contact-dependent and diffusion-dependent signaling mechanisms, identifies signaling-associated genes and finds signaling interactions with significant activity changes across multisample spatial transcriptomic datasets. Additionally, our approach can predict the rate of change of a signaling interaction at each tissue location. Furthermore, we designed an in situ validation analysis through proximity ligation assay (PLA)^25–27 to verify the tissue locations where these interactions occur in the developing mouse embryo. This analysis allows us to confirm the physical locations where a ligand binds to its receptor, providing ground-truth data to support CytoSignal predictions and to benchmark against previous methods.

Results

CytoSignal and VeloCytoSignal identify locations and dynamics of signaling interactions at cellular resolution

A key insight behind the CytoSignal method is that LR signaling is driven by protein–protein interactions that happen at specific tissue positions. Following this assumption, we construct a score to measure the signaling interaction strength at each position within a tissue (Fig. 1a). The LR interaction score (LRscore) is the product of ligand (L) and receptor (R) expression in the spatial neighborhood of the cell. Calculating a signaling score for each spatial position also allows us to separately quantify the locations at which interactions based on diffusible versus contact-dependent factors occur (Fig. 1a).

Fig. 1. CytoSignal and VeloCytoSignal model the spatiotemporal dynamics of LR signaling interactions at cellular resolution.

a, Diagram of CytoSignal approach. CytoSignal models the signaling strength (LRscore S = L × R) for each interaction in each cell while considering both the spatial neighbors of each cell and the diffusion-dependent or contact-dependent nature of the interaction. Expression of individual components within interactions involving multiple subunits is also considered. Cytosignal then identifies which cells have significant activity for a particular signaling interaction by spatial permutation. CytoSignal can also detect differential signaling interactions from multisample data, spatial gradients in signaling and signaling-associated genes. Mouse brain coronal images in a are from NIAID NIH BIOART (https://bioart.niaid.nih.gov/). b, Diagram of VeloCytoSignal approach. VeloCytoSignal predicts the temporal dynamics of a signaling interaction at each spatial location by combining RNA velocity from the ligand and receptor genes to calculate the time derivative (dS/dt) of the CytoSignal test statistic (S). The direction of the arrows indicates whether the signaling activity is increasing (pointing upward, colored in red) or decreasing (pointing downward, colored in blue) in each spatial neighborhood, and the lengths of the arrows indicate the rate of change. Sub., subunit; FC, fold change.

Intuitively, the LRscore quantifies the amount of signal received by each cell, which is related to the amount of protein–protein interaction between ligand and receptor occurring at that position. Additionally, the simple form of the score allows inference of signal-sending cells for each signal-receiving cell. To determine which cells show the most significant evidence for a signaling interaction, CytoSignal constructs a null distribution by permuting the spatial locations of cells and performing spatial false discovery rate (FDR) correction (Fig. 1a). CytoSignal can also identify spatial gradients in signaling strength (Fig. 1a). Because we calculate a score for each signaling interaction at each position in the tissue, we can look for signaling-associated genes in an unbiased manner. In contrast, previous methods that investigate expression of downstream signaling genes often rely on annotations of signaling pathways^6–8, which can be unreliable and incomplete. To identify differentially expressed genes associated with each signaling interaction, we perform a sparse regression analysis using the LRscore from CytoSignal as the response variable. This also allows us to control for cell type as a confounder when identifying signaling-associated genes. These signaling-associated genes can subsequently be used to identify Gene Ontology (GO) terms or transcription factors (TFs) associated with the signaling interaction.

We also developed a method for inferring temporal changes in signaling strength at each position in a tissue (Fig. 1b). Intuitively, our key insight is that signaling interaction strength changes when either ligand or receptor expression changes. Previous work has shown that spliced and unspliced counts can be used to estimate the time derivative of a gene’s expression, a concept called RNA velocity^28–30. We realized that these velocity estimates of the rate of change in ligand and receptor expression can then be used to predict whether a particular signaling interaction will increase or decrease in strength over time. We refer to our approach for calculating the rate of change of signaling interactions as VeloCytoSignal, as it merges velocity analysis with signaling analysis (see Supplementary Note 1 for a more detailed description of the intuition and motivation behind CytoSignal and VeloCytoSignal).

CytoSignal detects spatially resolved signaling interactions, spatial gradients and signaling-associated genes in Slide-seq and Slide-tag data

We first applied CytoSignal to Slide-seq (v2; ref. ³¹) and Slide-tags³² spatial transcriptomic data from embryonic mouse brains. Both protocols enable transcriptome-wide detection of RNAs and achieve single-cell (or near single-cell) resolution. We then performed several analyses that are now possible with cellular resolution, spatially resolved signaling inference (Fig. 2). In particular, we identified spatial gradients in cell signaling, determined signaling-associated genes and mapped spatial differences in the extent of contact-dependent versus diffusion-dependent signaling. We demonstrate these analyses and visualizations using several of the top-ranked significant signaling interactions inferred by CytoSignal (adjusted P < 0.05).

Fig. 2. CytoSignal identifies spatial gradients in signaling strength and signaling-associated genes in mouse cortical development.

a, Ligand (Sema3a) and receptor (PlexinA4 complex1) expression data, Sema3a–PlexinA4 signaling interaction scores (LRscores), and inferred locations with significant signaling activity. Each dot is a Slide-seq bead; the x and y coordinates are spatial position, and color indicates expression level, LRscore or cell type. b, Inferred signal-sending and signal-receiving cell interactions for Sema3a–PlexinA4. Top layer, locations with significant signaling activity inferred by CytoSignal (signal-receiving cells). Bottom layer, signal-sending cells. c, Circos plot showing cluster-level summaries of signaling activities between tissue locations across all diffusion-dependent interactions. Line thickness indicates the number of significant diffusion-dependent interactions between cells in the corresponding clusters. Clusters with ‘s-’ and ‘r-’ prefixes represent clusters serving as the signal-sending cluster or signal-receiving cluster. d, Spatial gradient of LRscores for the Sema3a–PlexinA4 interaction along cortical layers. Each dot represents a bead in the Slide-seq dataset; the x axis is the cortical depth in µm and the y axis is the LRscore. Colors indicate cluster assignments. e, Efnb4 (ligand) and Epha4 (receptor) expression, Efnb1–Epha4 signaling interaction scores (LRscores), and inferred locations with significant signaling activity. Each dot is a Slide-seq bead; the x and y coordinates are spatial position, and color indicates expression level, LRscore or cell type. f, Inferred signal-sending and signal-receiving cell interactions for the Efnb1–Epha4 interaction in the Slide-seq cortex data. g, Circos plot across all contact-dependent interactions in the Slide-seq cortex data. h, Wnt5a and Epha7 expression, Wnt5a–Epha7 LRscores, and inferred locations with significant signaling activity. i, Inferred signal-sending and signal-receiving cell interactions for the Wnt5a–Epha7 interaction in the Slide-tags brain data. j, Total number of significant diffusion-dependent interactions per spatial location in the Slide-tags brain data. k, Heatmap representation of genes and GO terms associated with the Wnt5a–Epha7 interaction. The color of each grid square represents the regression weight for each gene (positive weight means a positive association with Wnt5a–Epha7 signaling). White indicates that this gene is not annotated with the corresponding GO terms in the column. l, Efnb1 and Epha7 expression, Efnb1–Epha7 LRscores and inferred locations with significant signaling activity. m, Inferred signal-sending and signal-receiving cell interactions for the Efnb1–Epha7 interaction in the Slide-tags brain data. n, Genes associated with the Efnb1–Epha7 interaction and their related GO terms. o, Total number of significant contact-dependent interactions per spatial location in the Slide-tags brain data. p, Efnb1–Epha7 interaction strength as a function of distance from the centroid of the brain. SVZ, subventricular zone; IZ, intermediate zone; CP, cortical plate; sig., significant; NS, not significant; CR, Cajal–Retzius cells; VZ, ventricular zone; L5/6, cortical layers 5 and 6; CHP, choroid plexus; END, endothelial; FBR, fibroblast; RDG, radial glia; WBC, white blood cells; N_1–N_16, neuronal clusters/subtypes.

The output of CytoSignal is a score for each signaling interaction at each individual spatial location. Thus, we can visualize a single signaling interaction using a spatial plot in which each point represents a tissue position with measured gene expression (bead, spot or cell), and is colored by the inferred signaling activity (Fig. 2a,h,e,l). We also developed a three-dimensional visualization method (Methods), depicting signal-sending cells (Fig. 2b,i,f,m, bottom layer) and signal-receiving cells (Fig. 2b,i,f,m, top layer). Each cell is colored by its cluster assignment, and the edges between cells represent inferred signaling interactions. To provide a cluster-level perspective, we used Circos plots to show the total number of significant edges sent and received by each cluster across all diffusion-dependent and contact-dependent interactions separately (Fig. 2c,g).

The top interactions inferred by CytoSignal are known to be well established in embryonic neural development. CytoSignal revealed an interaction mediated by a diffusible ligand Semaphorin 3A, encoded by the gene symbol Sema3a, and the PlexinA4-Neurophilin1 coreceptor complex, encoded by Plxna4 and Nrp1 (ref. ³³; ranked fourth by the number of significant positions). It has a well-described role in neuronal axon guidance³⁴ and neural migration³⁵ (Fig. 2a). In the Slide-tags data, CytoSignal identified another diffusible ligand-dependent interaction related to the WNT signaling pathway, Wnt5a-Ephrin type-A receptor 7, encoded by the gene Epha7, which is potentially involved in the patterning decisions in the embryonic cortical areas^36,37 (Fig. 2h). The contact-dependent interaction between Efnb1 and Epha4 (ranked first in spatial variability) was identified in both datasets and is known to be involved in axon guidance and nerve regeneration³⁸ (Fig. 2e,l).

By inferring a signal strength at each spatial position, CytoSignal can identify continuous spatial gradients of signal strength. To demonstrate this capability, we calculated the LRscore of the interaction between Sema3a and Plexina4-Nrp1 complex in each bead as a function of its cortical depth (Methods; Fig. 2d). The LRscore of this signaling interaction shows a unique spatial gradient that transiently increases, reaches its highest level in the SVZ layer and finally decreases. We then performed a similar analysis in the Slide-tags data by plotting the LRscore of the interaction between ephrin-B1 and ephrin type-A receptor 4, encoded by the genes Efnb1 and Epha4, respectively, in each nucleus against its distance from the tissue centroid (Fig. 2p). This signaling interaction also shows a spatial gradient of LRscores that remains low for neurons near the centroid but increases rapidly with distance from the centroid (Fig. 2p).

We next asked which differentially expressed genes are associated with these signaling interactions using regularized linear regression (Methods). For each interaction, we fit an elastic net regression model to predict the LRscore from gene expression and cluster labels, then selected the features with nonzero coefficients that are most predictive for the LRscore (Fig. 1a). We plot the regression weights of the selected genes as a heatmap along with their enriched GO terms (Fig. 2k,n). For the diffusion-dependent interaction Wnt5a–Epha7, interaction-related genes selected by the model are strongly enriched for Wnt signaling terms, including ‘regulation of Wnt signaling pathway’ and ‘canonical Wnt signaling pathway’ (Fig. 2k). For the contact-dependent interaction Efnb1–Epha4, interaction-related genes are strongly enriched for GO terms associated with nervous system development, including ‘positive regulation of neuron differentiation’ and ‘neural tube development’ (Fig. 2n).

CytoSignal can also identify spatial regions that are enriched for contact-dependent or diffusion-dependent interactions. To demonstrate this, we summarized the total number of significant contact-dependent and diffusible interactions per spatial location (Fig. 2j,o). Across the tissue, spatial locations near fibroblasts and their adjacent cells show the largest number of significant diffusible interactions (Fig. 2j and Supplementary Fig. 1). This is consistent with biological knowledge that central nervous system (CNS) fibroblasts are involved in a variety of diffusible signaling pathways, including transforming growth factor β, platelet-derived growth factor receptor β and interferon-γ signaling, all encoded by TGFβ, PDGFRβ and IFNγ, respectively³⁹. Furthermore, CytoSignal highlights that spatial locations, including radial glia and their surrounding neurons, have the largest number of significant contact-dependent interactions compared with other locations in the tissue (Fig. 2o and Supplementary Fig. 1). These findings align with previously reported roles for fibroblasts and radial glia^39–41.

CytoSignal reveals locations and signaling-associated genes for contact-dependent and diffusible signaling interactions in mouse embryo Stereo-seq data

We next applied CytoSignal to Stereo-seq data from whole-mouse embryos (E9.5–E16.5)⁴². Stereo-seq uses DNA nanoball-patterned arrays to measure transcriptome-wide expression at subcellular resolution. By quantifying signaling interactions at individual tissue locations, CytoSignal identified signaling-associated genes and differences in the locations of diffusible versus contact-dependent signaling interactions.

CytoSignal was able to detect spatially significant and biologically meaningful interactions from the Stereo-seq data, such as Dll1–Notch1 in the E12.5 E1S2 slice (Fig. 3a,b). The Notch-Delta signaling system has a vital role in the development of the CNS^43,44, and sustained expression of Notch1 triggers choroid plexus tumor development in mice^45,46. Accordingly, we observe an enrichment of Dll1–Notch1 in the right half of the choroid plexus cluster and the intersection area between the Brain cluster and the left half of the choroid plexus cluster (Fig. 3a). Using the LRscores at individual tissue positions, we identified signaling-associated genes that were strongly enriched for GO terms correlated with CNS development including ‘central nervous system development’ and ‘neuron fate commitment’ (Fig. 3c). Activated Notch1 promotes progenitor cell identity in the mouse embryonic forebrain⁴⁷, consistent with the GO terms we observed, including ‘positive regulation of neuron differentiation’ and ‘neural precursor cell proliferation’.

Fig. 3. CytoSignal reveals spatiotemporal variation between diffusion and contact-dependent interactions at cellular resolution.

a, Ligand (Dll1) and receptor (Notch1) expression data, Dll1–Notch1 signaling interaction scores (LRscores) and inferred locations with significant signaling activity. b, Inferred signal-sending and signal-receiving cell interactions for the Dll1–Notch1 interaction. c, REVIGO plot of GO terms enriched among genes associated with Dll1–Notch1 interaction. d, Circos plot of total contact-dependent interactions between tissue locations for all clusters. e, Total number of significant LR interactions per location focusing on the brain region across five time points from E12.5 to E16.5. Dotted rectangles highlight the regions that best reflect differences in spatial enrichment between diffusion-dependent and contact-dependent interactions. f, Ligand (Fgf8) and receptor (Fgfr1) expression data, Fgf8–Fgfr1 signaling interaction scores (LRscores) and inferred locations with significant signaling activity. Each dot is a tissue position; the x and y coordinates are spatial positions and color indicates expression level, LRscore or cell type. g, Inferred signal-sending and signal-receiving cell interactions for the Fgf8–Fgfr1 interaction. h, REVIGO plot of GO terms enriched among genes associated with Fgf8–Fgfr1 interaction. i, Circos plot of total diffusion-dependent interactions between tissue locations for all clusters. BR, brain; CRP, cartilage primordium; LP, lung primordium; MSN, mesentery; LV, liver; MN, meninges, CP, choroid plexus; CR, connective tissue; ME, mucosal epithelium; OE, Olfactory epithelium; MST, mesothelium; MSC, muscle; EP, epidermis; JAT, jaw and tooth; DRG, dorsal root ganglion; GT, GI tract; HR, heart; IE, inner ear; UR, urogenital ridge; BV, blood vessel; OV, ovary; KN, kidney; SN, spinal cord; PAN, pancreas.

The diffusion-dependent interaction Fgf8–Fgfr1 showed interesting spatial signaling activity patterns in the E12.5 E1S1 slice (Fig. 3f). Fibroblast growth factor (FGF) signaling mediated by FGF ligands, including Fgf8 and their receptors FGF receptors (FGFRs), including Fgfr1, has been well described for patterning and neurogenesis. Both LRscore and permutation tests indicated strong activity of the Fgf8–Fgfr1 interaction near the choroid plexus, which is located at the border between the meninges and brain (Fig. 3f). Using LRscores at individual tissue positions, we identified signaling-associated genes that were strongly enriched for GO terms associated with neural development (Fig. 3h). These terms are consistent with previously reported roles of FGF signaling in neural development^48–54.

Separately inferring contact-dependent and diffusion-dependent interactions at each position in a tissue allows us to identify differences in the dominant mode of signaling across different developmental structures and stages (Fig. 3e). For example, the choroid plexus region shows a time-dependent change in contact-dependent signaling from E12.5 to E16.5, with the highest number of contact-dependent interactions observed at E14.5 (Fig. 3e). In contrast, the cells with the highest number of significant diffusion-dependent signaling interactions are not concentrated in the choroid plexus (Supplementary Fig. 2). This difference is not driven solely by differences in the total amount of diffusible versus contact-dependent interactions; the total number of significant contact-dependent interactions within the inset region in Fig. 3e is similar to the total number of diffusion-dependent interactions. Furthermore, cells receive signals not only from nearby locations but also from more distant locations within adjacent clusters (Fig. 3g, bottom layer). As a comparison, the edge plot for contact-dependent interaction Dll1–Notch1 reveals almost straight edges, indicating that cells primarily communicate with directly neighboring cells (Fig. 3b, bottom layer). We also summarized the total number of significant edges sent and received by each cluster across all 209 significant diffusion-dependent and 49 significant contact-dependent interactions separately (Fig. 3d and Fig. 3i). We identified spatial locations near the cartilage primordium and jaw and tooth regions to be the top active signal-sending and signal-receiving region (Fig. 3i). This aligns with known regulatory mechanisms of bone development that rely heavily on well-characterized signaling pathways mediated by diffusible molecules, including as sonic hedgehog, bone morphogenetic protein, FGF and WNT signaling pathways, encoded by the SHH, BMP, FGF and WNT gene families, respectively^55–58.

Spatially adjacent PLA and high-resolution spatial transcriptomic profiling confirm locations of LR protein–protein interactions predicted by CytoSignal

A key challenge in computational analysis of LR signaling is the lack of ground truth for evaluating predictions and the difficulty of direct validation. Many previous methods rely primarily on computational validation, which is insufficient to demonstrate robustness and applicability. However, the simple and direct nature of the LRscores calculated by CytoSignal allows validation in tissue. Specifically, the detection of protein–protein interactions in situ can be accomplished using the PLA (Fig. 4a).

Fig. 4. Paired PLA and spatial transcriptomic profiling allows systematic benchmarking of cellular-resolution cell signaling analysis.

a, Diagram of PLA. PLA detects proteins in close spatial proximity using two primary antibodies that specifically bind to each protein, followed by PLA probes. The PLA probes bind and create a fluorescent signal only when the ligand and receptor proteins are within 40 nm of each other. b, Diagram of paired PLA and spatial transcriptomic experiment. Visium HD and PLA were performed on spatially adjacent sections from mouse embryos. We performed two separate Visium HD experiments and profiled five sections using PLA. Early mouse embryo images in b from Servier Medical Art (https://smart.servier.com) licensed under CC BY 3.0. c, Signaling activity for Dll1–Notch1 as predicted by five computational methods using the Visium HD data. d, Benchmarking cell signaling analysis using paired PLA and spatial transcriptomic data. Each row represents predictions from CytoSignal and the corresponding measured PLA signals for a specific LR interaction. PLA column, microscope image, fluorescence PLA signal. PLA (binarized), fluorescence classifier trained to predict binary PLA values from the signaling score output by each cell signaling method. The classifiers are trained with fivefold cross-validation; each dot in the box plot represents the AUC from a single fold. Box plots display the median (central line), the 25th and 75th percentiles (box bounds) and whiskers extending to 1.5× the interquartile range; points beyond the whiskers are shown as outliers. e, Unsupervised cluster annotation of Visium HD datasets. Each number represents a cluster. The locations of the fields of view from d are indicated with numbered rectangles. f, Systematic benchmarking of cell signaling analysis in each of the clusters for interaction Dll1–Notch1. AUCs are calculated separately for each cluster. Max. maximum; GI, gastrointestinal; ST, spatial transcriptomic; Ab, antibody.

We first sought to use PLA to assess our results from previously published mouse embryo Stereo-seq data. This experiment suggests that spatial positions with high CytoSignal scores indeed correspond to the locations of LR interactions in situ, while previous cluster-level methods show many false-positive and false-negative predictions (Supplementary Note 3 and Extended Data Figs. 1 and 2).

Extended Data Fig. 1. Proximity ligation assay confirms in situ ligand–receptor protein–protein interaction locations recovered by CytoSignal.

a, Quantitative summary of CytoSignal benchmarking with previous methods using PLA validated signaling activities. Each grid square represents the connectivity ratio of each interaction inferred by CytoSignal or previous methods in a pair of clusters. Scores range from 0 (gray) to 1 (blue). b, Fields of view used for PLA imaging and comparison with CytoSignal predictions. Numbers colored in black correspond to the numbers colored in white at the upper right corner of c. c, PLA imaging results and CytoSignal predictions. Each row represents the predictions of CytoSignal and PLA signals for one ligand–receptor interaction. The ‘LRscore’ column shows CytoSignal predictions, and the columns ‘PLA’ and ‘Control’ represent PLA signals in the experimental and negative control samples, respectively. The number in white indicates the FOV; numbers correspond to b. Inset images are high-magnification (×63) views. Scale bar: 200 µm. Scale bar for Ostp-Cd44: 100 µm. Scale bar for inset images: 5 µm.

Extended Data Fig. 2. Benchmarking the physical distances between significant signal-sending and signal-receiving locations inferred by CytoSignal and previous methods.

a, Probability density of significant signaling location pairs as a function of physical distance identified by CytoSignal. The x-axis is the physical distance in µm and the y-axis is the density of the number of signaling cells. Please note that the x-axis is truncated between 750 µm and 8,000 µm because the density is 0 within this range. b, Probability density of signaling location pairs identified by CellChat Spatial as a function of their physical distances. c, Probability density of signaling location pairs identified by CellChat as a function of their physical distances. d, Probability density of signaling location pairs identified by CellPhoneDB as a function of their physical distances.

To position CytoSignal among previously published cell–cell communication methods, we performed a comprehensive literature review of more than 100 cell–cell communication methods⁵⁹. We grouped the methods into eight categories based on the following three properties: (1) use of directly measured (not inferred) spatial transcriptomic data, (2) single-spot predictions and (3) predictions for each LR pair separately (Table 1). We subsequently benchmarked CytoSignal against all methods that have all three properties^17–21 (Table 1, category 1).

Table 1.

Literature review of cell–cell communication methods

Method category	Use directly measured (not inferred) spatial transcriptomic data	Make predictions at the single-spot level	Infer activity for each LR pair	Cell–cell communication methods
Category 1	✓	✓	✓	CytoSignal, stLearn, spatialDM, COMMOT, LIANA+, NICHES
Category 2	✓	✖	✓	spaCI, GCNG, CellPhoneDB (v3 and v4), Squidpy, MISTy, HoloNet, stMLnet, BATCOM, SpaCeNet, GraphComm, NCEM, STcomm, SpaCET, SpaTalk, Renoir, Giotto
Category 3	✓	✓	✖	CLARIFY, DeepLinc
Category 4	✖	✓	✓	cell2cell, SpaOTsc, Scriabin
Category 5	✖	✓	✖	DeepCOLOR
Category 6	✓	✖	✖	CCPLS, MESSI, CellNeighborEX, SVCA
Category 7	✖	✖	✖	Neighbor-seq, topic modeling, MESSI, CellNeighborEX, scMultisim
Category 8	✖	✖	✓	BulkSignalR, CCCExplorer, InterCellDB, SingleCellSignalR, CCInx, FlyPhoneDB, PlantPhoneDB, DiSiR, CellChat (v1 and v1.6), CellPhoneDB (v1 and v2), ICELLNET, Domino, FunRes, SEARCHIN, NicheNet, LRLoop, scSeqComm, CytoTalk, exFINDER, SoptSC, CellCall, CellComm, NeuronChat, scConnect, MEBOCOST, CellAgentChat, InterCellar, MultiNicheNet, scITD, TALKIEN, Cellinker, CellComNet, CellEnBoost, REMI, calligraphy, DeepCCI, HiVAE, LR Hunting, scTensor, LIANA, ESICCC, CINS, Differential NicheNet, Connectome, iTALK, DIALOGUE, MOFAcell, Tensor-cell2cell, TraSig, TImeTalk, CellTalker, CellCommuNet, PyMINEr, LIRICS, NATMI, CrossTalkeR, COMUNET, CommPath, RobustCCC, scDiffCom, scLR, scTenifoldXct, SPROUT, RNA-Magnet, RaCinG, SPRUCE

We next performed an experiment to obtain position-matched PLA and spatial transcriptomic data, providing ground-truth data that allows us to evaluate the accuracy of LR interactions inferred from spatial transcriptomics (Fig. 4b). We profiled two distinct sections with Visium HD and assayed a total of five LR pairs (Igf2–Igf2r, Spp1–Cd44, Fgf8–Fgfr1, Efna3–Epha5 and Dll1–Notch1). We profiled three LR pairs adjacent to the first Visium HD slide and two adjacent to the second Visium HD slide. We then used computational image registration to align the PLA data to the Visium HD data. For each tissue location, we quantified corresponding PLA fluorescence signals and labeled each spot as either positive or negative for the interaction (Methods). Thus, this experiment yielded PLA signals and high-resolution spatial transcriptomic profiles at each location in the mouse embryo, enabling systematic benchmarking of how well existing computational tools can infer signaling activity at cellular resolution.

All methods showed low correlation between predicted and measured PLA when compared across the whole embryo. Visual inspection of the data indicated that there is indeed high correspondence between PLA and predicted signal from spatial transcriptomics in certain regions of the embryo (Fig. 4c and Extended Data Fig. 3). Thus, we evaluated the methods by training a classifier for each region to predict positive or negative PLA signal, then calculating the area under the curve (AUC) per method per region (Supplementary Note 3). We found AUC values substantially higher than random expectation in many regions. CytoSignal demonstrated strong predictive performance, consistent with the qualitative similarity between LRscore and PLA signal (Fig. 4d).

Extended Data Fig. 3. Comparison of signaling predictions between competing methods.

Predictions of interaction signaling by different computational methods on selected regions of interest of all four interactions. Scale bar: 200 µm.

To ensure that the comparison was not biased by manually selected regions, we repeated this analysis using spatial domains through unsupervised clustering (Fig. 4e). We again found many regions in which the CytoSignal and other approaches could predict the PLA signal with high AUC, notably above random expectation (Fig. 4f). Furthermore, in nearly every region, CytoSignal consistently achieved robust performance, often showing improved AUC values compared with other methods (Fig. 4f and Extended Data Fig. 4). We also repeated our benchmarking analysis using the area under the precision-recall curve alongside the AUC metric (Extended Data Fig. 5) and observed the same improved performance. Further analyses suggest that this improved performance arises from the spatial smoothing steps performed by CytoSignal (Supplementary Note 3 and Extended Data Figs. 6 and 7). CytoSignal also shows markedly improved time and memory efficiency compared with previous cell-level and cluster-level methods (Supplementary Fig. 3).

Extended Data Fig. 4. Systematic benchmarking of predicted signals by five computational methods in each of the clusters for all five signaling interactions using AUC.

AUCs are calculated in each of the clusters separately.

Extended Data Fig. 5. Systematic benchmarking of predicted signals by five computational methods in each of the clusters for all five signaling interactions using AUPRC.

AUPRCs are calculated in each of the clusters separately. LIANA+: using the bivariate function ‘cosine’ as suggested in the tutorial. AUPRC, area under the precision-recall curve.

Extended Data Fig. 6. Benchmarking of CytoSignal predictions using different imputation strategies.

a, AUC difference between all radii used compared to the default 200 µm. A negative ∆AUC means the default version using a 200 µm radius is better. R-300, R-400, R-500, R-600, R-800 and R-1000: LRscores calculated using radii of 300, 400, 500, 600, 800 and 1,000 µm. Sample sizes: n = 33 clusters per boxplot for FGF8-FGFR1 and n = 28 clusters per boxplot for IGF2-MPRI and OSTP-CD44 (3 interactions × 6 methods); total n = 534. b, AUC difference between all strategies. imp_receptor: imputing receptor only; no_imputation: no imputation on ligands and receptors. Sample sizes: n = 33 clusters per boxplot for A1 sample interactions (DLL1-NOTC1, FGF8-FGFR1) and n = 28 clusters per boxplot for D1 sample interactions (EFNA3-EPHA5, IGF2-MPRI, OSTP-CD44); 5 interactions × 2 methods; total n = 300 (n = 150 per method). c, AUC difference between the modified version and the default version of CytoSignal. sum_ligand: modified CytoSignal that ligand imputation is just the average ligand expression within a circle of fixed radius. Sample sizes: n = 33 clusters for A1 sample interactions (DLL1-NOTC1, FGF8-FGFR1) and n = 28 clusters for D1 sample interactions (EFNA3-EPHA5, IGF2-MPRI, OSTP-CD44); total n = 150. Individual cluster values are overlaid as jittered points. All box plots display the median (central line), the 25th and 75th percentiles (box bounds), and whiskers extending to 1.5× the interquartile range; points beyond the whiskers are shown as outliers.

Extended Data Fig. 7. Systematic benchmarking of predicted signals by five computational methods in each of the clusters for all five signaling interactions using additional parameter settings.

AUCs are calculated in each of the clusters separately. CytoSignal_no_smooth: default CytoSignal with the final step of LRscore smoothing removed. LIANA+: using the bivariate function ‘cosine’ as suggested in the tutorial. LIANA+_pd: using bivariate function ‘product’. ‘LIANA+_norm_pd’: using bivariate function ‘norm_product’.

CytoSignal identifies differential signaling interactions from multisample spatial transcriptomic data

Identifying LR interactions that vary across spatial transcriptomic datasets could reveal signaling changes associated with disease status, age, developmental stage, genotype or other important covariates. Thus, we extended CytoSignal to perform differential signaling analysis of multisample spatial transcriptomic data using negative binomial regression (Methods). We can incorporate sample-level and spot-level covariates, including cell type or spatial region annotations, case–control status, replicate structure, sequencing depth, age and sex.

To simulate multisample spatial transcriptomic data with changes across conditions, we used scDesign3 (ref. ⁶⁰), a widely used single-cell and spatial data simulator. We used mouse Stereo-seq data to initialize the parameters for the scDesign simulation, then changed the expression of ligand and/or receptor genes across simulated conditions (Fig. 5a). To investigate how sensitivity and specificity are affected by the nature of the signaling change, we varied the degree of expression change per spot and the number of affected spots. We used negative binomial regression to identify LR combinations showing significant changes across conditions (Supplementary Fig. 4). CytoSignal maintains a low false-positive rate and low false-negative rate across a range of parameter values (Fig. 5b,c).

Fig. 5. CytoSignal identifies differential signaling interactions in real and simulated spatial transcriptomic data.

a, Simulation of spatial transcriptomic data under normal and perturbed conditions using scDesign3. b, CytoSignal maintains a low false-positive rate in real and simulated data. Real, false-positive rates inferred from multiple replicates from real Stereo-seq data; simulated, false-positive rates inferred from simulated multisample spatial transcriptomic data using scDesign3 under normal conditions. c, CytoSignal maintains a low false-negative rate in simulated data across a range of parameter settings. Perturb_1–45k, false-negative rates inferred from simulated multisample spatial transcriptomic data with perturbations in 1k, 5k, 10k, 15k, 20k, 25k, 30k, 35k, 40k and 45k cells; Perturb_1k, false-negative rates inferred from simulated multisample spatial transcriptomic data with perturbations in 1,000 cells repeated ten times. d, Differential signaling interactions identified between the brains of young and old mice. Each dot represents a signaling interaction, color-coded for significance. Red, interactions with an absolute log₂(fold change) > 0.1; green, interactions with an absolute log₂(fold change) > 0.1 and a FDR-corrected P > 0.05; gray, interactions with neither absolute log₂(fold change) > 0.1 nor FDR-corrected P > 0.05. The P values are computed by Nebula using Wald chi-square tests and the FDR is then controlled using the Benjamini–Hochberg method. e, Spatial heatmap of LRscores of differential signaling interactions. A total of five brains from old mice and four brains from young mice are shown for each interaction. Each dot represents a spot and is colored by the LRscore inferred by CytoSignal. f, Spatial distribution of microglia cells in the brains of young and old mice. Each dot represents a spot colored by its cell type. Red, microglia cells; gray, other cells. g, Differential signaling interactions for cell type and age. Each dot represents an interaction. For each interaction (dot), the color indicates the associated covariate (such as cell types or age), while the size reflects the −log(P_FDR) of its significance. Larger dots indicate greater significance. Each column corresponds to a covariate and all the dots in a column share the same color. The y axis represents the log of fold changes. Astro 1–2, astrocyte subtypes; DG, dentate gyrus; Dopa SN, dopaminergic neurons of the substantia nigra; Dopa VTA, dopaminergic neurons of the ventral tegmental area; Ex CA1 and Ex CA3, excitatory neurons of hippocampal Cornu Ammonis regions CA1 and CA3; Ex L1–L6, excitatory neurons of cortical layers 1–6; Ex MB, excitatory neurons in the midbrain; In Adarb2⁺, Adarb2-expressing inhibitory neurons; In MB, inhibitory neurons in the midbrain; In Pvalb⁺ and In Sst⁺, parvalbumin-expressing and somatostatin-expressing inhibitory neurons, respectively; Oligo, oligodendrocytes; OPC, oligodendrocyte precursor cells.

We also assessed the false-positive rate of our multisample test using real Stereo-seq data from biological replicates. Thus, we consider any signaling interactions reported by our test as showing significant differences across replicates to be false positives. Encouragingly, this analysis showed a low false-positive rate (median = 0; Fig. 5b). There is no corresponding way to estimate the false-negative rate using real data because the true differential interactions are unknown. However, the false-positive rate estimated from simulated data closely matches the false-positive rate we found in our real data analysis, suggesting that the simulations accurately reflect the characteristics of real spatial transcriptomic data. We performed further simulations to confirm that a negative binomial model accurately fits the LRscore distribution across a range of ligand and receptor expression levels (Supplementary Figs. 5–9).

We next used CytoSignal to identify age-associated LR signaling changes in a mouse model of Parkinson’s disease⁶¹. The four young and five aged mice harbor a genetic knockout that results in age-related pathology similar to Parkinson’s disease in humans. CytoSignal identified 42 diffusion-dependent and 3 contact-dependent interactions with significant activity changes (FDR < 5%) between young and old mice (Fig. 5d). Interestingly, many of the changes involved immune-related signaling interactions and showed increased signaling in the old mice, including Spp1–Cd44 and the Sema6d/Plexin complex (Fig. 5e). This observation of increased signaling activity in the old mice is consistent with the finding reported in the original study⁶¹, in which the old mouse brains showed a marked increase in microglial cell counts (Fig. 5f). Finally, because CytoSignal can incorporate multiple covariates, we also identified a number of signaling interactions linked to specific cell types (Fig. 5g).

VeloCytoSignal identifies spatiotemporal dynamics of signaling activity during mouse embryonic development

Elucidating spatiotemporal changes in cell signaling activity is crucial for understanding the role of cell–cell communication in cell fate specification and tissue homeostasis. To address this challenge, we developed an approach, VeloCytoSignal, for predicting the instantaneous rate of change of a signaling interaction at a specific position within a tissue by combining RNA velocity from the ligand and receptor genes to calculate the time derivative $\left(\frac{\mathit{dS}}{\mathit{dt}}\right)$ of the CytoSignal LRscore (S). One output of VeloCytoSignal is a three-dimensional velocity plot, in which the directions of the arrows indicate whether signaling activity is currently increasing (pointing upward) or decreasing (pointing downward) at each spatial position (Fig. 6a,c).

Fig. 6. VeloCytoSignal resolves the spatiotemporal dynamics of upregulated signaling activities across multiple embryonic stages.

a, Signaling velocity (LRvelo) scores for the Alb–FcRn interaction across four time points (E10.5–E13.5). Each point is a spot and the color indicates cell type. Three-dimensional arrows overlaid on the spatial coordinates indicate the signaling velocity for a spatial bin; arrow direction and color indicate the sign of the velocity (red and up indicate increasing signaling; blue and down indicate decreasing signaling). Arrow length indicates velocity magnitude. Black rectangles highlight the liver. b, RNA velocity estimates for ligand Alb and receptor FcRn (calculated by VeloVAE) used as input to VeloCytoSignal and corresponding interaction velocity estimates (LRvelo). Each dot is a Stereo-seq position, the x axis is the inferred latent time and the y axis is the spliced expression level for RNA velocity and LRscore for interaction velocity. Arrow direction and length indicate the velocity of each cell. Please note that cells are subsampled to avoid overplotting. c, LRvelo scores for the Wnt5a–Antxr1 interaction plotted as in a. Black rectangles highlight the jaw and tooth regions. d, RNA velocity estimates for the corresponding ligand gene Wnt5a and receptor gene Antxr1 and interaction velocity (LRvelo). e, Mean of spatially resolved scores calculated by CytoSignal as a function of time. Dots and lines are colored by cell types.

To validate the predicted temporal trends in signaling activity, we applied VeloCytoSignal to Stereo-seq data from four consecutive time points (E10.5, E11.5, E12.5 and E13.5). We used each time point separately to predict the temporal trend in signaling activity, thereby blinding VeloCytoSignal to the true time-point information and then compared the predicted trend with the observed signaling activity at the next time point (Fig. 6b,d). Gene velocity, predicted spliced counts and latent time in each spot were inferred using our previously published method VeloVAE⁶², and signaling velocity (LRvelo) values were calculated using VeloCytoSignal.

We investigated the following two liver-specific interactions in detail: Alb–FcRn and Lgals9–Cd47. Our 3D velocity plots across four time points showed a sharp increasing trend in Alb–FcRn interaction uniquely in the liver (Fig. 6a). Velocity estimates for the ligand Alb along with the receptor components B2m and Fcgrt displayed a consistent trend, with the rate of increase becoming higher at each time point (Fig. 6b). We validated that this predicted temporal trend is correct by plotting the average LRscore of the real data across consecutive embryonic time points, which confirmed the trend predicted by VeloCytoSignal (Fig. 6e). The temporal trend of Lgals9–Cd47 signaling also closely matched the true temporal trend observed across the four consecutive time points (Supplementary Fig. 10).

We also found a signaling interaction with a clear temporal trend in the developing jaw region of the mouse embryo. The signaling activity of the Wnt5a–Antxr1 interaction is largely static across the embryo, except in the jaw and tooth region, which shows significant signaling velocity (adjusted P < 0.05; Fig. 6c). This trend is supported by the velocities of both ligand and receptor genes (Fig. 6d) and matches closely with what is observed in the real data from consecutive time points. Interestingly, the signaling activity of this interaction dramatically increases from E11.5 to E12.5 (Fig. 6e), aligning with a transient pulse of Wnt signaling during tooth development⁶³. Additional details about these VeloCyto analyses can be found in Supplementary Note 4.

Discussion

Cell–cell communication mediated by LR interactions plays a crucial role in cell differentiation, tissue homeostasis, immune response and disease, but has been difficult to study in an unbiased manner. CytoSignal infers the activity and dynamics of signaling interactions at each spatial position within a tissue using spatial transcriptomic data. By taking this cell-level approach, we can perform several new types of analyses—identifying spatial gradients in signaling, finding signaling-associated genes, locating contact-dependent versus diffusion-dependent interactions and identifying signaling interactions with significant changes across multisample datasets. Our model identified interactions in the developing mouse embryo, neurogenesis in the adult mouse brain and a mouse model of neurodegeneration. Additionally, we confirmed that the interaction scores predicted by CytoSignal correspond to the locations of LR protein–protein interactions in situ.

CytoSignal is applicable to most spatial transcriptomic techniques, requiring only a cell-by-gene matrix and a cell-by-spatial-position matrix. VeloCytoSignal requires additional information about RNA processing, such as spliced and unspliced transcripts. We hope that our methods help address the current need for analyzing rapidly increasing spatial transcriptomic datasets. As technologies for in situ molecular measurement continue to advance, we aim to continue expanding the applicability of these approaches across data modalities.

We anticipate that our approach can be used to unveil signaling networks across a variety of physiological and pathological contexts. For instance, in the tumor microenvironment, CytoSignal could reveal interactions among malignant cells, healthy cells and immune cells. Additionally, VeloCytoSignal could provide unique insights into how the dynamics of spatially resolved signaling pathways affect tissue repair over time when applied to time-series data from damaged tissue. We hope that our methods enable similar analyses across a range of tissue contexts.

Methods

Mouse fetal sample collection

C57BL/6J (JAX000664) mice were acquired from The Jackson Laboratory. The strain used was C57BL/6 with the substrain C57BL/6J, and the genetic background was pure wild-type C57BL/6J. All mice were housed in the animal facility accredited by the Association for Assessment and Accreditation of Laboratory Animal Care, located in the Behavioral and Biological Sciences Building at the University of Texas Health Science Center at Houston. Animal rooms were climate-controlled and maintained at 21 ± 1 °C and 30–65% humidity on a 12-h light/12-h dark cycle (lights on at 0600 Central Standard Time). Mice were housed in individually ventilated cages (Tecniplast) under specific pathogen-free conditions. We have complied with the ARRIVE 2.0 guidelines. Access to water and food (irradiated LabDiet 5053) was ad libitum. All procedures complied with the Guide for the Care and Use of Laboratory Animals and were approved by the University of Texas Health Science Center at Houston’s Animal Welfare Committee (protocol AWC-21-0070). For prenatal experiments, male C57BL/6 mice were mated with female C57BL/6 mice and the vaginal plug was checked in the morning and determined as 0.5 dpf. Pregnant mice were sacrificed at embryonic day (E)12.5. Fetuses at E12.5 were used for analysis; sex was not determined due to the embryonic stage. A total of three pregnant female mice and 14 fetuses were used for the experiments. Mice were euthanized by overdosage of inhalation anesthesia in a drop jar (Fluriso, isoflurane USP; VetOne) followed by decapitation.

Estimating spot-level signaling activity with LRscores

The spatially resolved interaction score for each interaction in each location is defined as the coexpression of ligand and receptor genes within close spatial proximity. The computation can be divided into the following four main steps: (1) defining spatial neighbors for each location, (2) calculating the amount of ligand (L) and receptor (R) each location can receive from its spatial neighbors, (3) calculating LR coexpression within each spatial neighborhood and (4) spatial smoothing.

CytoSignal defines spatial neighborhoods for diffusion-dependent and contact-dependent interactions differently. For diffusion-dependent interactions, for each location i, we define its spatial neighbors as all locations j within a circle centered at i with a predefined radius r (200 µm by default). To estimate the amount of receptors present at each location (R), we use normalized gene expression directly, without smoothing, since receptors are located on cell membranes and are not diffusible. We next calculate the amount of ligand L that location i receives using all other locations j weighted by the physical distances between them and transformed by a Gaussian kernel.

Each cell or spatial position i has two kinds of neighborhoods as follows:

$${\mathcal{N}}_i^{\mathrm{DT}}\left(\mathrm{Delaunay}\mathrm{triangulation}\mathrm{neighbours}\right)\mathrm{and}{\mathcal{N}}_i^{\epsilon }(\epsilon -\mathrm{ball}\mathrm{neighbours}).$$

Please note that in both cases, the index cell i is included in the neighborhood. For every LR pair (l, r), we first compute the total ligand signal L_i and receptor signal R_i at cell i.

First, for diffusion-dependent interactions, to determine the LRscore of the interaction between ligand l and receptor r, we compute L_i and R_i, which represent the total amounts of ligands and receptors gathered at cell i as:

$$L_i=\sum _{k\in {\mathcal{N}}_i^{\epsilon }}{l}_k{\tilde{w}}_{\mathrm{G}}\left(k,\mathrm{i}\right),R_i=r_i.$$

where l_k represents the gene expression of ligand l at cell k, r_i represents the gene expression of receptor r at cell i, and $\tilde{w}$ is the weight of cell k based on its distance from cell i (see section ‘Determining the optimal parameters of the Gaussian kernel for diffusible ligands’ for details).

We use a Gaussian kernel to determine how much weight we should give to cell k (sending cell) when estimating the ligand received by cell i. The unnormalized Gaussian weight sent from a neighbor k to receiver i is given by:

$$w_G\left(k,i\right)=\frac{\exp \left[-{\left(d\left(k,i\right)\right)}^2/\left(2{\sigma }^2\right)\right]}{\sigma \sqrt{2\pi }}$$

where dₖ,ᵢ is the Euclidean distance between the two cell centroids. The derivation of the Gaussian kernel is presented below in the section ‘Determining the optimal parameters of the Gaussian kernel for diffusible ligands’.

Next, we normalize within the ligand sender’s own ε-ball neighborhood. This accounts for differences in the cell density around each ligand-sending cell (so that ligand-sending cells in areas of higher cell density are weighted less than ligand-sending cells in areas of lower cell density).

$${\tilde{w}}_G\left(k,i\right)=\frac{w_{\mathrm{G}}\left(k,i\right)}{{\sum }_{m\in {\mathcal{N}}_k^{\epsilon }}{w}_G\left(k,m\right)}.$$

We also define $d\left(k,k\right)\approx {10}^{-9}\mathrm{\mu }\mathrm{m}$, to prevent division by zero and give the sender a nonzero self-weight.

The final LRscore is defined as the product of L and R. Thus, putting the above formulas together, we obtain:

$${\mathrm{LRscore}}_i=L_i{R}_i=\sum _{k\in {\mathcal{N}}_i^{\epsilon }}{l}_k{\tilde{w}}_G\left(k,i\right)r_i$$

Similarly, for contact-dependent interactions, we define L_i and R_i as follows:

$$L_i=\sum _{k\in {\mathcal{N}}_i^{\mathrm{DT}}}{l}_k{w}_{\mathrm{DT}}\left(k,i\right),R_i=r_i.$$

Here the weight sent from k to i is uniform over the Delaunay triangulation neighbors of k. We also define the weight of the receiving cell i as 1:

$$w_{\mathrm{DT}}\left(k,i\right)=\left\{\begin{array}{cc}1,& k=\mathrm{i}\\ \frac{1}{\left|{\mathcal{N}}_k^{\mathrm{DT}}\right|-1},& k\ne \mathrm{i}\end{array}\right)$$

The LRscore for a contact-dependent interaction is thus—

$${\mathrm{LRscore}}_i=L_i{R}_i=\sum _{k\in {\mathcal{N}}_i^{\mathrm{DT}}}{l}_k{w}_{\mathrm{DT}}\left(k,i\right)r_i$$

Finally, for both diffusion-dependent and contact-dependent interactions, we take the arithmetic mean of the LRscore for each cell across its directly connected neighborhood within ${\mathcal{N}}_i^{\mathrm{DT}}$—

$${\mathrm{LRscore}}_i=\frac{1}{\left|{\mathcal{N}}_i^{\mathrm{DT}}\right|}\sum _{k\in {\mathcal{N}}_i^{\mathrm{DT}}}{\mathrm{LRscore}}_k.$$

Next, for both diffusion-dependent and contact-dependent interactions, we performed spatial smoothing of the inferred LRscores by calculating a weighted sum across all neighbors within a 200 µm radius of each cell. The weights were determined based on the physical distances between the index cell and its neighbors and were transformed using a Gaussian kernel as specified above.

We then performed spatial permutation tests to obtain the statistical power of the inferred LR signaling interactions. We assumed that the locations of cells are independently distributed. By default, we set the permutation size to 100,000. Given n cells in the dataset, we permuted the whole dataset 100,000/n times to generate a dummy dataset. We then followed the standard CytoSignal procedure of inferring spatial neighbors, calculating LRscores and applying spatial smoothing to obtain a null distribution of LRscores for each LR interaction. Finally, for each LR interaction, we calculated a P value by comparing the observed LRscore to the generated null distribution and performed spatial FDR correction⁶⁴.

Additionally, we used SPARK-X⁶⁵, a scalable nonparametric test, to identify interactions with spatially variable LRscores. As we have an LRscore for each interaction in each cell, we can directly apply SPARK-X to the LRscore matrix as if it were a gene expression matrix. SPARK-X outputs a P value for each interaction, representing its level of spatial variability. We then ranked the interactions based on these P values. By default, CytoSignal also ranks all interactions by the total number of cells exhibiting significant signaling based on the spatial permutation tests. CytoSignal uses the CellPhoneDB (v2.0) database to identify LR interactions. However, users can provide a database of their choice after it is formatted according to CytoSignal’s requirements.

Determining the optimal parameters of the Gaussian kernel for diffusible ligands

For determining the kernel parameters, we assume that a ligand diffuses across a two-dimensional tissue space and that its concentration follows a Gaussian distribution, with overall concentration summing to unity. In other words, consider a two-dimensional Gaussian centered at the origin—

$$f\left(x,y\right)=\frac{1}{2\pi {\sigma }^2}\exp \left(-\frac{x^2+y^2}{2{\sigma }^2}\right)$$

We want to determine a bandwidth parameter σ such that the total density beyond a predefined radius t is less than a trivial value ε. In other words—

$${\iint }_{S}f\left(x,y\right)dxdy\le \epsilon$$

where $S=\left\{\left(x,\mathrm{y}\right)|r=\sqrt{x^2+y^2}\ge t\right\}$ is the region outside the predefined radius t.

We can then convert the Cartesian coordinates to polar coordinates using radius r and angle θ—

$$\begin{array}{c}{\iint }_{S}f\left(x,y\right)dxdy={\iint }_{S}f\left(r\cos \theta ,r\sin \theta \right)rdrd\theta =\hfill \\ {\int }_0^{2\pi }d\theta {\int }_t^{\infty }\frac{r}{2\pi {\sigma }^2}\exp \left(-\frac{r^2}{2{\sigma }^2}\right)dr={\int }_t^{\infty }\frac{r}{{\sigma }^2}\exp \left(-\frac{r^2}{2{\sigma }^2}\right)dr\hfill \end{array}$$

If we make the substitution $u=\frac{r^2}{2{\sigma }^2}\Rightarrow du=\frac{r}{{\sigma }^2}dr$, then the left-hand side of the inequality becomes—

$${\iint }_{S}f\left(x,y\right)dxdy={\int }_{u=\frac{t^2}{2{\sigma }^2}}^{\infty }{e}^{-u}du=\exp \left(-\frac{t^2}{2{\sigma }^2}\right)$$

Our goal is to have $\exp (-\frac{t^2}{2{\sigma }^2})\le \epsilon$. We can now solve the inequality for σ (recall that t is a predefined radius (by default 200 µm), and ε is a small value, such as 10⁻⁹):

$$\sigma \le \frac{t}{\sqrt{-2\log \epsilon }}$$

Identifying signaling-associated genes

For Stereo-seq data, we first subset the genes to 1,272 TFs using a publicly available 1,374 TFs⁶⁶. An elastic net with identity link function was then fitted using glmnet 4.1-8 in R, with all selected TFs as well as all cluster labels. We tuned the model using six mixing parameters (0.5, 0.6, 0.7, 0.8, 0.9 and 1) by cross-validation. The best model was used to identify the most interaction score predictive TFs for each interaction.

For Slide-seq and Visium data, we filter out genes expressed in fewer than 50 cells as well as ligand and receptor genes. We iteratively apply one-sided Wilcoxon tests between permutation-significant and insignificant groups within every cluster, with an alternative hypothesis that the permutation-significant groups have higher expression levels. For each cluster, the top 50 significant genes (Benjamini–Hochberg correction applied, FDR < 0.05) from the Wilcoxon test are selected as predictors for downstream analysis. For high-quality data with lower sparsity, we use all available TFs from a publicly available TF list⁶⁶ as predictors. We do not apply any filtering steps to TFs as they are usually well described and relatively few in number. Cluster annotations are also considered as covariates and are added to all regression models.

The output of the regression is a set of predictive TFs or genes as well as their coefficients, which are then passed to downstream analyses such as GO enrichment analysis. The GO analysis using GOrilla can be performed with the following settings: (1) organism, ‘Mus musculus’; (2) running mode, ‘Two unranked lists of genes’, with model-selected TFs as the target set and the other TFs in the 1,272 TFs as the background for the Stereo-seq. For Slide-tag and Visium, we used model-selected genes as the target set and other genes in the dataset as the background. (3) Ontology, ‘Process’ and (4) check the box ‘Show output also in REVIGO’. For the ‘P-value threshold’, we used 0.001.

For visualizing signaling-associated genes and their enriched GO terms using a heatmap, we manually selected significant GO terms (P = 0.001) based on their functional relevance. All elastic net-selected genes are ranked by their regression weights and at most the top 20 genes are shown in the heatmap.

VeloCytoSignal: calculating signaling velocity (LRvelo)

In VeloCytoSignal, estimation of LR interaction velocity requires RNA velocity information, which is based on mRNA splicing dynamics. We used VeloVAE to infer RNA velocity from Stereo-seq data. VeloVAE is a deep generative model that recovers the temporal order of cells and gene splicing dynamics in terms of the transcription, mRNA splicing and degradation rates using a pair of neural networks. The model consists of an encoder, which performs variational inference of latent cell time and state, and a decoder, which predicts unspliced and spliced counts using an ordinary differential equation model.

All datasets were preprocessed using the scVelo preprocessing pipeline. Specifically, we selected the top 2,000 highly variable genes while keeping all genes involved in a predetermined list of cell–cell interactions. We then trained VeloVAE using the default hyperparameters, except for the latent dimension and batch size. We used a latent dimension of 5 for Stereo-seq E9.5 and 10 for all other datasets. As for batch size, we set it to the default (128) for Stereo-seq 9.5, increased it to 256 for Stereo-seq E12.5, further increased it to 512 for Stereo-seq E10.5, E11.5, E13.5, E14.5 and E15.5, and set it to 2,048 for Stereo-seq E16.5. In general, the batch size was scaled proportionally to the number of cells. After training, we extracted the inferred parameters and computed RNA velocity analytically using the predicted (u) and (s) values as follows: $v_u=\alpha -\beta u$, $v_s=\beta u-\gamma s$.

Next, we feed RNA velocity from VeloVAE to VeloCytoSignal to compute the LRvelo. Because gene expression is defined as the sum of spliced and unspliced counts, we can rewrite the CytoSignal test statistic as follows:

$$S=(L_s+L_u)\times (R_{\mathit{u}}+R_s)$$

Because the statistics L and R are smoothed across spatial neighbors, we also applied spatial smoothing to the RNA velocity estimates inferred by VeloVAE, following the exact strategy. Next, it is straightforward to calculate the time derivative of S at each location following the product rule of differential calculus:

$$\frac{\mathit{dS}}{\mathit{dt}}=(L_s+L_u)\times \frac{d(R_u+R_s)}{\mathit{dt}}+(R_u+R_s)\times \frac{d(L_s+L_u)}{\mathit{dt}}$$

After calculating LRvelo estimates at each location, we averaged the values across each location’s Delaunay triangulation neighbors to obtain LRvelo estimates for each spatial neighborhood.

Benchmarking CytoSignal and previous methods

For quantifying whether the results of CytoSignal and previous methods align with PLA results, we adopted the concept of signal-sending and signal-receiving cluster pairs from earlier methods and defined a connectivity ratio (r) as the ratio between the number of significant edges (s) and the total number of all possible edges (t) between a signal-sending cluster and a signal-receiving cluster. An edge represents an interaction between two nearby cells that are either directly connected or within 200 μm of one another. Significant edges (s) denote the edges that end in locations within the receiving cluster that were identified as statistically significant by spatial permutation.

We then compared the physical distances between signal-sending and signal-receiving cells, as identified by CytoSignal and previous methods, at the cluster level. This analysis included all 332 interactions in the intersection of CellChatDB and CellphoneDB (v2) and was applied to a whole-mouse embryo dataset (E12.5 E1S2; 46,982 cells and 20 clusters). We ran four workflows with default parameters—CytoSignal, CellChat (v2.1.0), CellChat spatial and CellphoneDB (v2.1.7). Because CytoSignal directly outputs signal-receiving cells and their corresponding signal-sending cells, we directly calculated their physical distances. In contrast, previous methods report P values for each interaction across signal-sending and signal-receiving cluster pairs. To obtain the physical distances between each signal-sending and signal-receiving cell pair from cluster-level inferences, we randomly sampled 1,000 cells from the sending and receiving clusters individually and matched them into 1,000 pairs. This was done for each significant interaction identification and each cluster pair. We calculated the spatial distance between each cell pair and finally formed the distribution.

We benchmarked the time and memory usage of CytoSignal and eight previous methods, including CellChat (v2.1.2), CellChat with spatial information, CellPhoneDB (v2.1.7), Commot (v0.0.3), LIANA+ (v1.5.0), NICHES (v1.1.0), SpatialDM (v0.2.0) and stLearn (v0.4.12). We applied all nine methods to the eight Stereo-seq whole-mouse embryo datasets and conducted a total of 72 runs. Each run was performed on a Fedora Linux operating system platform with a single Intel Xeon Gold 6154 CPU (3.00 GHz). Besides, we limited the maximum time to 1 h and the maximum memory usage to 128 GiB, which is commonly available to researchers in a practical analysis setting. For a fair comparison, we used a customized database input containing 50 interactions from the intersection of CellChatDB and CellPhoneDB (v2). The 50 entries contain 16 contact-dependent interactions, 17 diffusion-dependent interactions with single-molecule receptors and 17 diffusion-dependent interactions with complex receptors, each of which was randomly selected from the corresponding category.

To ensure a fair comparison of cell–cell communication inference using different methods, we followed the tutorial and adopted the parameters provided by the authors. For CytoSignal, we analyzed according to the default workflow, which consists of (1) imputing ligands and receptors, (2) calculating LRscores and (3) performing permutation tests. We used the functions findNN, imputeLR and inferIntrScore. For both CellChat methods, we computed communication probabilities and aggregated the inferred network using the functions computeCommunProb, filterCommunication and aggregateNet. For CellPhoneDB, we applied its statistical analysis method with the terminal command ‘cellphonedb method statistical_analysis’. For COMMOT, we performed their spatial communication inference with the spatial_communication function. For LIANA+, we identified spatial neighbors using the spatial_neighbors function and computed bivariate scores using the bivariate function. For NICHES, we conducted cell-to-cell spatial inference. We called the RunNICHES function specifically with only the CellToCellSpatial mode on. For SpatialDM, we computed the neighbor-weight graph, identified globally significant LR pairs and selected locally significant LR pairs. We used the functions from SpatialDM, including weight_matrix, extract_lr, spatialdm_global, sig_pairs, spatialdm_local and sig_spots. For stLearn, we performed the LR analysis and obtained the adjusted P values using the run and adj_pvals functions from its cci submodule, respectively. The nine methods use different programming languages— CytoSignal, CellChat and NICHES are built with R, while the others rely on Python. Accordingly, we recorded the wall-time usage of the benchmarking tests above using the R package microbenchmark (v1.5.0) and Python time module. Peak memory usage was all recorded with cmdbench (v0.1.22). Of note, CellPhoneDB was presented as a command-line interface tool and its time usage was also taken from the cmdbench report.

Multisample analysis across spatial transcriptomic datasets

We conducted extensive fitting tests on both simulation and real datasets to assess whether the negative binomial distribution effectively fits spatial transcriptomics data (Supplementary Figs. 5, 6, 7, 8 and 9). Next, to apply the CytoSignal multisample extension, we reran the preprocessing steps without normalization and scaling. Subsequently, we imputed the unnormalized data and calculated LRscores following the standard CytoSignal pipeline. Because imputation results in decimal values, we rounded the LRscores to the floor integers. We then fitted the negative binomial mixture model, adapted from nebula⁶⁷, on nine mouse brains using LRscores as the response variable and age (young/old), phenotype (WT/OVX) and cell types as categorical predictors. By default, we applied two thresholds—the minimum number of cells with nonzero counts for each gene (mincp = 5) and the minimum counts per cell for each gene (cpc = 0.001), to filter out low-expressed interactions. We also used the library size of each sample as the ‘offset’ variable to account for differences in sequencing depth across samples. We then applied FDR correction across all interactions and calculated the log₂ fold change by comparing the expected means between experiment and control. We considered only interactions with FDR < 0.05 and an absolute value of log₂(fold change) > 0.1 to be significantly differential.

Statistics and reproducibility

No statistical method was used to predetermine sample size. No data were excluded from the analyses. The experiments were not randomized and the investigators were not blinded to group allocation during experiments and outcome assessment.

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 10.1038/s41588-026-02624-9.

Author contributions

J.L. and J.D.W conceived the idea, implemented the method, performed data analyses and wrote the manuscript. H.M., S.O. and N.O. generated the PLA data. H.M., P.M. and V.N.L. generated the Visium HD data. W.Q. and Y.W. contributed to implementing the method. J.G., A.K.Y.C., G.G., Y.G. and Y.S. contributed to data analysis.

Peer review

Peer review information

Nature Genetics thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Data availability

Our Visium HD data are available on GEO (GSE291088). Slide-seqV2 data, Slide-tags data and STARmap PLUS data are available at Broad Institute Single Cell Portal (https://singlecell.broadinstitute.org/single_cell/) with ID SCP815, SCP2170 and SCP1375. Stereo-seq datasets from all time points are available at https://db.cngb.org/stomics/mosta. The 10x Visium dataset is available at https://www.10xgenomics.com/datasets/visium-cytassist-mouse-embryo-11-mm-capture-area-ffpe-2-standard. The MERFISH dataset is available at https://info.vizgen.com/mouse-brain-data. Processed data in the format of CytoSignal objects are available at 10.5281/zenodo.14941008 (ref. ⁶⁸) and 10.5281/zenodo.14934588 (ref. ⁶⁹). Raw images from the PLA are available at 10.5281/zenodo.18625864 (ref. ⁷⁰).

Code availability

CytoSignal and VeloCytoSignal are implemented in R. The package is available on GitHub at https://github.com/welch-lab/CytoSignal (ref. ⁷¹). Notebooks for reproducing the main figures are available on GitHub at https://github.com/welch-lab/cytosignal-figure (ref. ⁷²).

Competing interests

All authors declare no competing interests.

Extended data

is available for this paper at 10.1038/s41588-026-02624-9.

Supplementary information

The online version contains supplementary material available at 10.1038/s41588-026-02624-9.