Pan-tumor spatial transcriptomics reveals conserved properties of tumor organization

Summary

Tumor microenvironments (TMEs) are compositionally and functionally heterogeneous, making it challenging to discover organizing structural principles. Through a study of 262 solid tumors profiled by spatial transcriptomics, we identify a conserved architecture where TMEs are partitioned into discrete, hierarchically organized multicellular sub-regions, which we term “spatial groups” (SGs). As indicated by orthogonal spatial measurements and expert pathologist review, SGs associate with recognizable biological domains spanning global tissue context to local cellular neighborhoods. Comparing tumors through SGs reveals a pan-tumor classification where the dominant axis of variation is spatial heterogeneity of immune biology. In an independent, retrospective cohort of non-small cell lung cancer patients treated with immune checkpoint blockade (ICB; n = 16), pan-tumor spatial biology classification distinguishes clinical response and captures structural and biological hallmarks associated with ICB sensitivity. Together, these findings suggest that SGs may be important organizing domains of the TME that relate spatial structure, biological function, and response to therapy.

Graphical abstract

Highlights

• •Pan-tumor spatial transcriptomics reveals conserved TME organization
• •Spatial groups reflect hierarchically organized spatial biology domains
• •Spatial immune organization is the primary axis distinguishing pan-tumor TME state
• •NSCLC immunotherapy outcomes stratify by immune “spatial group” classification

Behera et al. characterize spatial biology patterns across 262 solid tumors and 18 tumor types, using spatial transcriptomics and multiplexed immunofluorescence. They find pan-tumor, hierarchically organized “spatial groups” that align with coordinated immunological programs and with outcomes after immune checkpoint blockade therapy in a separate cohort of lung cancer patients.

Introduction

The tumor microenvironment (TME) is a complex milieu of interacting cells, proteins, and other biological components that influences critical properties of tumor biology such as growth, metastasis, and response to therapy.^1,2 Biological variation within the TME reflects clinically relevant differences across genetic, pathway, cellular, and tissue-level scales.^3,4 For instance, recent studies have demonstrated prognostic and predictive power of TME biomarkers, such as tumor infiltrating lymphocyte (TIL) score in melanoma and “immunoscore”—the spatial balance of CD3⁺ and CD8⁺ T cell density—in colorectal cancer.^5,6,7,8,9 Such findings have motivated studying the TME with technologies that couple cellular information about RNA or protein levels with cellular spatial locations.¹⁰ Spatial molecular profiling studies in a variety of tumor types have revealed a common theme: substantial intratumoral and intertumoral heterogeneities make elucidating organizing principles of the TME very challenging.¹¹ By extension, the clinical utility of TME spatial profiling has been limited.

Recent efforts have outlined a strategy for learning conserved and translationally relevant aspects of TME spatial biology. These studies have demonstrated recurrent multicellular spatial structures associated with tumor biology and with cancer prognosis.^{12,13,14,15,16,17,18} Obtaining these insights relied on technologies that query tens of proteins to identify phenotypes such as cell type and limited functional states, yet their reliance on limited pre-selected markers may preclude uncovering general principles of TME spatial organization. Spatial transcriptomics (“ST-seq”) enables an unbiased assessment of TME spatial biology. However, the complexity of such data has hindered moving beyond description into elucidating spatial biology principles.^19,20

Advances in statistical inference developed in other fields—protein science, genomics, and microbiome—provide frameworks for addressing this challenge. For instance, studies of amino acid covariation within related proteins have demonstrated protein “sectors”—amino acid groups critical for engineering functional proteins.^21,22,23,24 Similarly, covariation analysis of genomic content across kingdoms of life has revealed collective protein-protein interactions critical for organismal fitness.^25,26,27,28 At the scale of microbiomes, covariation between bacterial taxa across individuals has yielded “ecogroups”—groups of taxa of functional and clinical significance amongst humans.^29,30,31 These studies have established a strategy for studying complex biological systems: first identify an ensemble of systems, and then statistically deduce conserved features across the ensemble critical for system function.

Inspired by such studies, we hypothesized that the analysis of ST-seq data across a diverse ensemble of solid tumors— a “pan-tumor” database—may reveal conserved patterns of TME spatial biology in an unbiased manner. Here, we developed a statistical formalism called TumorSPACE, a method that detects the covariation structure amongst cells or ST-seq “spots” (cell collections) based on measured gene expression. Employing TumorSPACE across 262 solid tumors profiled by ST-seq revealed conserved, hierarchically structured, and transcriptionally covarying TME regions that we term “spatial groups” (SGs). We found SGs to be context-embedded TME spatial domains that enabled comparative spatial transcriptomics (ST-seq) and construction of a pan-tumor model of TME spatial biology. The dominant axis of spatial variation across TMEs was related to immune biology, and classification by our pan-tumor spatial biology model in an independent cohort of non-small cell lung cancer (NSCLC) patients stratified responses to immune checkpoint blockade (ICB) therapy.

Overall, our work motivates describing the TME by hierarchically structured units, SG, thus enabling comparisons of multiscale spatial organization between tumors.

Results

SGs define a conserved architecture of TME spatial biology

To identify general principles of TME organization, we assembled a multimodal database of 262 tumors spanning 18 tumor types (Figure S1A; Table S1). All tumors were profiled by ST-seq (10× Visium platform). Paired hematoxylin and eosin (H&E)-stained images were annotated by a board-certified pathologist at the University of Chicago, using a classification capturing tumor, adjacent normal tissue, and technical features (Figure S1B; Table S2; STAR Methods). These annotations reflected expected biological and technical variation amongst tumor types, such as enrichment for stroma-rich regions amongst pancreatic and endometrial cancers (Figures S1C–S1E).^32,33 For eight tumors, we also performed 51-plex immunofluorescence that enabled higher-resolution characterization of cellular composition and spatial organization (Table S3; STAR Methods). These data were annotated by the same pathologist to define cell types and spatial neighborhoods (Figure S1F; Table S4; STAR Methods). Our goal was to use these data to test whether conserved spatial organizational signatures exist across tumors (Figure 1A).

Figure 1.

A conserved architecture of TME spatial biology

(A) Multimodal database comprising 262 tumors spanning 18 tumor types. All tumors were profiled by spatial transcriptomics (ST-seq) and pathologist annotated; eight tumors were additionally profiled by multiplex immunofluorescence (mIF).

(B) Histogram of correlation values (Pearson’s R) between actual spatial distances for all pairs of spots within a tumor ST-seq dataset and pairwise distances inferred by TumorSPACE. Inset shows inferred spatial distribution of spot locations for the tumor exhibiting the highest Pearson’s R: small cell ovarian cancer sample “P2” (SCOC-P2).

(C) Representation of spatial groups (SGs) in a TumorSPACE map for a specific tumor (SCOC-P2). The TumorSPACE map is a tree structure of spot relationships. Each tree node (colored dots) is a group of spots defined as an SG; colored squares in the bottom are individual spots in the sample. Displayed are examples of non-nested SGs (non-NSGs; left) and nested SGs (NSGs, right); inset displays nesting of the blue SG within its “parent” red SG; scale bars delineate a length of 2 mm.

(D) Comparison of pathologist annotations (left) and SGs (right) aligned in spatial location. Inset (bottom) shows spatial architecture of immune-rich regions (left) and corresponding SGs (right).

(E) Distribution of non-NSGs (gray bars) and NSGs (colored bars) for all tumors in our database. NSGs are partitioned by the degree of nesting (color key). x axis is ordered and labeled by tumor type.

(F) Average degree of nesting grouped by pathologist annotated region (y axis). Error bars: standard error of the mean. ∗Wilcoxon p value < 0.05.

We first asked whether spatial organization within tumors could be inferred from transcriptional data. Prior work has shown that biological processes in the TME can be organized across spatial scales, with some processes embedded within larger domains, while others remain distinct.^17,34 We, therefore, sought a framework that could capture hierarchical spatial organization.^{35,36,37,38,39,40} To this end, we developed TumorSPACE, a method that uses transcriptional covariation to organize spatial transcriptional measurements into a hierarchy (STAR Methods). In this representation, spots with similar gene expression profiles group together into local regions, while broader relationships between spots progressively define larger spatial domains across the tumor. The resulting model is a “TumorSPACE map” (Figure S2A). We applied TumorSPACE to all 262 tumors and then tested whether inferred distances between spots recapitulated their physical distances in the tissue. Across all datasets, inferred organization was significantly more consistent with true spatial distances than expected by chance (q < 0.01) (Figure 1B). Thus, spatial organization in tumors could be recovered from representing transcriptional data as a hierarchy of related regions.

We next examined individual tumors and their TumorSPACE maps. As an example, a small cell ovarian cancer tumor (SCOC-P2) that exhibited strong agreement between inferred and physical spatial relationships showed groups of transcriptionally similar spots corresponding to spatially localized tissue regions (Figure 1B). We call these regions “spatial groups” (SGs) (Figure 1C). Notably, smaller SGs were often physically embedded within larger SGs. We refer to this relationship as spatial nesting, where a “child” region is contained within a broader “parent” region, similar to prior work describing such organizational patterns in specific tumor subsets.^17,41 However, some SGs did not lie within larger domains. We, therefore, distinguished these two organizational patterns as “nested SGs” (NSGs) and “non-nested SGs” (non-NSGs) (Figure 1C) (STAR Methods). To determine whether SGs corresponded to the biological structure, we compared SGs with pathologist-defined spatial domains. As an initial case study, we focused on an NSCLC tumor for which ST-seq and multiplex immunofluorescence (mIF) was performed in serial sections, and spatial coordinates between those experiments could be aligned, allowing SGs to be compared to high-resolution pathologist annotations (Figure S2B; STAR Methods). The largest SGs corresponded to tumor-rich, necrosis-rich, and immune-infiltrated areas (Figure 1D, top), while immune-infiltrated SGs further subdivided into smaller regions recapitulating finer spatial structures, including lymphoid-like follicles, tumor-adjacent CD8⁺ T cell clusters, perivascular niches, and mixed immune infiltrates (Figure 1D, bottom). Together, these results showed, via specific case studies, that SGs recapitulated biologically meaningful hierarchical spatial structures.

For each tumor in our database, we observed that NSGs could be embedded within layers of progressively larger domains. We, therefore, quantified how deeply a given SG resides within this hierarchy (Figure S2C). All tumors contained both non-NSGs and NSGs, with NSGs frequently forming multi-level hierarchies (Figure 1E). We next asked whether hierarchical organization reflected underlying biological features of the tissue. We found that the degree of nesting amongst NSGs was highest in tumor-rich regions and in normal tissues, characterized by highly organized multicellular architecture, and lowest in regions with more homogeneous cellular composition such as inflammation-rich or hemorrhage-rich areas (Figure 1F; Figures S2D–S2F).

Together, these results showed that multiscale organization of pan-tumor spatial biology can be described by hierarchical collections of SGs.

SGs reveal a nested hierarchy of biological domains across tumors

To further interrogate the biological content encoded by SGs, we compared pairs of SGs arising from a common parent by quantifying differences in gene expression, cell type composition, and pathway activity (Figure S3A). Cell type composition within each SG was inferred from ST-seq data, using SpaCET-based deconvolution, and showed broad agreement with pathologist annotations (Figure S3B).⁴² Pathway activity was assessed by applying enrichment analysis to genes that were differentially expressed between SGs (STAR Methods).

As a case study, we analyzed an NSCLC tumor in which matched mIF data revealed clear spatial separation between two well-characterized biological states: tumor proliferation and tumor immune exhaustion (Figure 2A, left).⁹ In the corresponding TumorSPACE map, these regions aligned with two SGs—SG13 and SG18—emerging from a common parent—SG12 (Figure 2A, right). SG13, the proliferative region, was enriched for malignant cells, B cells, and multiple conventional dendritic cell subtypes. In contrast, SG18, the immune-exhausted region, was enriched for endothelial cells, macrophages, plasmacytoid dendritic cells, and cancer-associated fibroblasts (Figure 2B). These cell composition differences were directly observed in mIF data (Figure S3C). At the pathway level, SG13 was enriched for processes associated with proliferation including cell cycle, RNA processing, and membrane trafficking. In contrast, SG18 was enriched for signaling pathways such as RTK, GPCR, and cytokine signaling, as well as innate immune processes, consistent with immune exhaustion (Figure 2C).⁴³

Figure 2.

A model of TME spatial organization linking spatial scale with biological function

(A) Tumor sub-region identification by multiplexed immunofluorescence (left) or the TumorSPACE map (right) for a representative NSCLC tumor. Fluorescence image shows DAPI (blue), proliferative tumor cells (cyan), and immune-exhausted tumor cells (red). TumorSPACE map shows spatial positions of spots colored by SG membership and hierarchical relationship of SG12 with SG13 and SG18. The root of the TumorSPACE map is “SG1.” Scale bars delineate a length of 2 mm.

(B) Differential cell type abundance—log₁₀-transformed ratio of mean abundance (x axis) and log₁₀-transformed p value (y axis) —between SG13 and SG18 based on SpaCET deconvolution. Each point is a cell type.

(C) Number of differentially enriched Reactome pathways between SG13 and SG18 (x axis, color key), grouped by pathway category (y axis).

(D) (Top) Workflow for evaluating if a differentially abundant biological process within a parent SG influences a child SG biological process. (Middle, bottom) Mean odds ratio (y axis, absolute value, log₂ transformed) of parent processes versus physical scale of the parent SG (mm) where the child SG is nested or non-nested (middle), nested only (bottom left), or non-nested only (bottom right). Pearson’s correlation (R) and p values are shown.

(E) TME spatial biology is described by the organization of non-nested and nested spatial groups. Nested spatial groups encode large-scale processes that influence small-scale processes.

As a comparison to SG-based descriptions of spatial heterogeneity, we evaluated Moran’s I, a gene-level statistic that quantifies spatial autocorrelation in gene expression. Unlike TumorSPACE, which identifies spatially heterogeneous domains (i.e., SGs), Moran’s I provides a measure of spatial heterogeneity within user-specified regions but does not identify regions of interest. However, given that both approaches can quantify spatial heterogeneity, we used the example in Figure 2C as a case study to ask whether they yielded consistent interpretations of tumor organization. Computing Moran’s I across genes associated with pathways distinguishing these SGs revealed that SG13 exhibited consistently lower spatial heterogeneity than SG18 (Figure S3D). These results are concordant with the TumorSPACE-derived decomposition: both approaches identified SG13 and SG18 as distinct regions within the parent domain that differ in their spatial organization of gene expression. This comparison also provided insight into the hierarchical structure inferred by TumorSPACE: Moran’s I independently detected that the subregions SG13 and SG18 differed in their spatial heterogeneity within the broader SG12 domain.

We next asked whether SGs capture generalizable patterns of biological organization across tumors. For each SG, we estimated its physical scale based on mean pairwise distances between its constituent spots (STAR Methods). Distinct biological programs were associated with characteristic SG physical scales. Processes associated with large-scale SGs included, for example, CD4⁺ and CD8⁺ T cell abundance. These cell types are excluded from large regions of tumors and were accurately identified as spatially variable, using tools that consider the entire tumor a single domain.^44,45 Processes associated with intermediate-scale SGs—signal transduction, cell-cell communication, and chemokine responses—have been found as spatially variable when dividing tumors into “microregions” of dozens of cells.⁴⁶ Finally, processes associated with the smallest-scale SGs were often related to local tumor-immune interactions and have been detected by tools that focus on the local cell-cell interaction fronts⁴⁷ (Figure S4A). These findings indicated that SGs captured biological organization spanning multiple spatial scales, from tumor-wide structure to localized microenvironmental niches.

Prior work has suggested that some biological programs are organized hierarchically, with large-scale processes influencing more localized phenomena.^17,34,48 To test this, we quantified the dependence between biological programs in parent and child SGs across all tumors (Figure 2D, upper) (STAR Methods). Biological processes associated with larger SGs were predictive of those observed in smaller NSGs, indicating hierarchical organization. In contrast, this relationship was not observed for non-NSGs (Figure 2D, middle and lower).

Together, our findings from Figures 1 and 2 support a model in which the TME is organized as a hierarchy of spatially structured biological processes (Figure 2E). In this model, some spatial domains are embedded within larger ones and reflect biology shaped by their broader context, while others represent spatially independent programs. This hierarchical organization provides a data-driven and conserved link between spatial structure and biological function in tumors, motivating using SGs as a unit of comparison across diverse tumor types.

Classification of TMEs by spatial lability of gene expression

To compare tumors based on their spatial organization, we sought a quantitative representation that preserved spatial heterogeneity. We, therefore, defined gene spatial lability (SLAB), a metric that quantifies the spatial footprint of gene expression differences within a tumor. For each gene, we identified pairs of sibling SGs arising from the same parent SG in which the gene was differentially abundant. To avoid double-counting spatial signal across NSGs, we assigned differential expression to the smaller of the two sibling SGs, corresponding to the most spatially localized change. We then mapped these SGs to their spatial footprint and defined the SLAB score as the fraction of ST-seq spots in which the gene was differentially abundant (Figure 3A) (STAR Methods). Across tumors and genes, SLAB scores were positively correlated with mean expression (Figure S4B). However, SLAB also captured additional modes of variation. As an example, calreticulin (CALR) displayed comparable bulk expression across tumors yet showed large differences in spatial lability (Figure 3A, inset; Figure S4C).

Figure 3.

A spatially aware pan-tumor classification of TMEs

(A) Schematic for the calculation of spatial lability (SLAB) score for a given gene. SGs where the gene is differentially abundant are identified from the TumorSPACE map. The smaller SG is mapped to its corresponding spots. SLAB score is the fraction of ST-seq spots in which the gene is differentially abundant. Inset shows example spatial expression patterns for calreticulin (CALR) across tumors with similar average expression but different SLAB scores. Scale bars delineate a length of 1 mm.

(B) Hierarchical clustering of tumors based on genome-wide SLAB profiles. Each leaf represents a tumor, and spatial class clusters (SC1–SC9) are annotated with the number of tumors from each cancer type.

We next sought to leverage SLAB to compare tumors with one another. To this end, we divided our tumor database into two cohorts: (1) a “pan-tumor cohort” comprising 246 tumor sections across 18 tumor types, and (2) a single-institution retrospective cohort of 16 NSCLC tumors. Unlike the pan-tumor cohort, the NSCLC cohort had paired clinical metadata about disease course and treatment outcomes. We reasoned that this partitioning could test whether a pan-tumor model of SG biology offered insights about clinical outcomes in an out-of-sample collection of tumors. Given that the genome-wide SLAB scores quantitatively represent each tumor, we constructed a matrix where each row corresponded to a tumor within the pan-tumor cohort, each column to a gene, and each entry to the gene-specific SLAB score of a tumor (Figure S4D). Hierarchical clustering of pairwise Euclidean distances between tumors yielded tumor classes based on similarity in genome-wide SLAB profiles. To ensure class robustness, we filtered for groups containing at least five tumors and applied bootstrap resampling to retain only statistically reproducible classes (Figure S4D; STAR Methods).

The resulting classification yielded nine “spatial classes” (SCs): SC1 through SC9, most of which contained tumors spanning diverse anatomical origins (Figure 3B). Only three classes comprised individual tumor types: SC6 and SC7 were composed entirely of gliomas and head and neck squamous cell carcinoma (HNSCC), respectively, while SC8 consisted of gliomas and one sample initially annotated as “normal; peri-tumor” that was later reclassified as glioma upon pathology review. To assess the robustness of SC assignments, we performed several complementary analyses. First, we found that 55% of replicate tumor section pairs were assigned to the same SC despite most pairs originating from non-adjacent tumor sections (Figure S4E). Moreover, using a simulation in which tumors were added incrementally, we found that certain classes (SC1, SC4, and SC9) could be reliably identified with relatively few tumors, whereas others required larger sample sizes (Figure S4F). Finally, we found that across multiple near-optimal TumorSPACE models for individual tumors, SC assignments were highly consistent with nearly all models yielding identical classifications (Figures S4G and S4H).

We next asked the degree to which SC assignments depended on tumor type. To test this, we performed a leave-one-out analysis in which each tumor type was systematically removed. After removal, SCs were recomputed, and held-out tumors were projected into the new classification. Across tumor types, the fraction of tumor types whose class assignment changed ranged from 0% to 14% (Figure S5A). Removal of samples belonging to a tumor type with many samples (e.g., breast cancer) showed larger shifts in SC assignment, whereas tumor types represented by few samples (e.g., melanoma) showed no change (Figures S5B and S5C). Thus, SC designations were not driven by a single tumor type or by sampling bias, but instead reflected structured differences across heterogeneous tumors.

Together, these findings established SCs as robust and largely tumor-type-independent representations of tumor spatial organization. This raised the question of what biological programs underlie these classes.

Biological programs defining SCs

To understand the biology distinguishing SCs, we evaluated differences in SLAB profiles at the branchpoints in our pan-tumor classification (Figure 4A, left) (Table S5). We then applied the overrepresentation analysis (ORA) for pathways to identify biological programs enriched in each branch (Figure 4A, right) (Table S6). Hierarchical clustering of enriched pathways revealed that branchpoints were dominated by few biological axes: adaptive immunity, innate immunity, neurodevelopment, and metabolism (Figure 4B). The three branchpoints highlighting differences in adaptive immunity exhibited the highest differential SLAB in genes related to (1) T cell chromatin remodeling through the NuRD (GATA2DA and MBD2) or SWI/SNF (ARID2) complexes, (2) lymphocyte development (TCF20 and LIF4), or (3) intratumoral T cell function (SNX19 and ZNF671) (Figure 4C, upper left).^{49,50,51,52,53,54,55} The branchpoint corresponding to innate immunity SLAB variation was notable for largely unstudied genes (MAGEB17, ZNF773, and DERPC) and pathways related to either general immune function (GPCR and cytokine signaling) or innate immunity specifically (Figure 4C, upper right).

Figure 4.

Spatial classes reveal biological axes of tumor spatial biology

(A) Workflow for evaluating gene and pathway SLAB differences at all spatial class branchpoints.

(B) Heatmap showing the fraction of differential SLAB pathways (color key) within a pathway category (columns) for each spatial class branchpoint (rows). Heatmap is hierarchically clustered, revealing four biological categories.

(C) Genes and pathways that significantly vary in SLAB for each biological category in (B).

(D) Pan-tumor classification with branchpoints labeled by spatially labile biology categories from (B) (left). Red line distinguishes spatial classes by spatial lability in immune biology: “immune spatially labile” (ISL) versus “immune spatially invariant” (ISI).

Nested within immune function as the primary axis of SLAB variation was a secondary axis: metabolism. The branchpoint that distinguished SC6, a group compose of only gliomas, from SC5 was notable for variation in carbohydrate metabolism, consistent with reports that carbohydrate metabolic reprogramming is directly linked to spatial organization in these tumors (Figure 4C, bottom right).^{17,56,57,58,59} The other metabolism-oriented branchpoint distinguished SC7—purely HNSCC cancers—from SC8/9 and highlighted significant variation in lipid metabolism, a key factor in HNSCC tumor growth and therapeutic resistance.^60,61

The deepest axis of SLAB variation that we identified was in neurodevelopmental biology. This axis was identifiable only in the branchpoint distinguishing SC8 (purely gliomas) from SC9 and was defined by neuron-restricted genes such as TRIM9 and ATCAY (Figure 4C, bottom left).^62,63

Together, our results demonstrated a hierarchy of biological axes that describe variation in tumor spatial organization (Figure 4D, left). Immune function was the dominant axis, consistent with other reports of tumor immune biology having consistent effects on spatial organization across tumor types.²⁰ Based on this result, we defined SC1–SC4 as “immune spatially labile” (ISL) and SC5–SC9 as “immune spatially invariant” (ISI) (Figure 4D, right). We hypothesized that stratifying tumors by these categories might correlate with therapeutic response to ICB. We, therefore, turned to our NSCLC cohort for which we had retrospective clinical data on response to ICB-containing treatment regimens.

Relating our classification of TMEs with therapeutic response to ICB

Despite substantial improvements in overall survival with the use of ICB in the metastatic NSCLC frontline setting, 5-year overall survival remains quite poor, at 19%.⁶⁴ Moreover, the only clinically approved biomarker of response to ICB therapy—PD-L1 immunohistochemistry (IHC)—is weakly predictive of outcomes, prompting ongoing studies on whether gene expression or cell type abundance biomarkers might be more predictive of such outcomes.^4,64,65,66

Patients were selected to be in our NSCLC cohort based on having received frontline ICB immunotherapy with or without chemotherapy (STAR Methods).

For each pre-treatment biopsy sample, we computed genome-wide SLAB profiles and categorized them by their immune spatial lability as per the pan-tumor classification scheme (Figure 4D; STAR Methods). We then compared progression-free survival (PFS) amongst classification by immune spatial lability (ISL versus ISI) or PD-L1 IHC (Figure 5A). In doing so, our strategy evaluated whether the pan-tumor classification could distinguish ICB-related outcomes in the NSCLC cohort. No information from the NSCLC cohort was used to develop the pan-tumor definitions of ISL and ISI. This study was designed as proof of principle that such a biomarker might correspond to outcomes following ICB-containing therapy.⁶⁷ Two possible variables were identified that could confound an association with ICB response: ICB regimen choice and presence of the somatic mutation KRAS G12C, which is targetable in the second line (Figures S6A and S6B). Univariate analysis found that neither variable was associated with PFS in our study (Figure S6C).

Figure 5.

Pan-tumor classification distinguishes responders to immune checkpoint blockade in NSCLC

(A) Workflow for evaluating progression-free survival (PFS) using PD-L1 immunohistochemistry or spatial lability classification in our retrospective cohort of patients with metastatic NSCLC receiving frontline immunotherapy (IO) or IO plus chemotherapy.

(B) Projection of the NSCLC cohort onto pan-tumor “spatial classes.” Each dot is an NSCLC sample, and the size and color describe PFS (color key).

(C and D) Kaplan-Meier survival curves for categorizing the NSCLC cohort by ISL versus ISI (C) or PD-L1 status (D).

(E) Comparison of cell type and cellular neighborhood frequencies determined by pathologist annotation between the ISL and ISI groupings. Features are ordered on the x axis by y axis rank.

(F and G) Representative ISL (F) and ISI (G) NSCLC tumors where biological features are identified by multiplexed immunofluorescence (color key).

(H) Differential SLAB analysis between ISL and ISI in the NSCLC cohort (y axis) versus the pan-tumor cohort (x axis). Overrepresentation analysis (ORA) defines pathways differential in ISL versus ISI categories within the NSCLC cohort (right, top) relative to the pan-tumor cohort (right, bottom).

Scale bars delineate a length of 0.5 mm in (F) and (G).

Of the 16 NSCLC samples, 11 were classified into SCs belonging to the ISL category (SC1, SC2, and SC4), while five samples were classified into SCs belonging to ISI (SC5, SC6, and SC9) (Figure 5B). Strikingly, patients whose tumors fell into the ISL category exhibited significantly longer PFS than those in the ISI category (p = 0.00069) (Figure 5C). In contrast, when patients were stratified using standard PD-L1 IHC thresholds (0%, 1–49%, and greater than or equal to 50%), no significant differences in PFS were observed (p = 0.92), nor were differences detected when applying a binary PD-L1 cutoff of 50% (p = 0.99) (Figure 5D; Figure S6D). Multivariate analysis of ISL/ISI in combination with a second covariate—(1) ICB regimen choice, (2) PDL1 status, (3) the presence of a KRAS G12 mutation, (4) the presence of an STK11 mutation, or (5) the presence of either an EGFR or BRAF mutation—demonstrated in each case that immune spatial lability was significantly predictive of PFS, while the second covariate was not (Figures S6E and S6F). Moreover, eight out of the twelve patients with measurable disease at treatment onset demonstrated shrinkage in tumor volumes shortly after treatment began, suggesting that classification by PFS was detecting differences in treatment response rather than disease prognosis (Figure S6G; STAR Methods).

We next investigated whether ISL/ISI classification might be attributable to sparse biological processes (e.g., CD8⁺ T cell abundance or a T cell exhaustion gene set) identifiable from bulk gene expression data. Using both our pan-tumor and NSCLC cohorts, we created sample-level bulk estimates of (1) SpaCET-deconvoluted cell type abundances and (2) expression of genes found within eight published gene set signatures of ICB response in NSCLC, including T cell effector function, T cell exhaustion, and TGF- β signaling (Table S7: STAR Methods).^{68,69,70,71,72,73,74} As a comparison, we also generated SLAB scores corresponding to each cell type and gene signature. None of these sparse biological processes could stratify ICB response as well as the ISL/ISI classifier. Furthermore, 8 of the top 10 results came from SLAB representation of these processes, rather than bulk estimates (Figure S6H). For example, the most significantly associated process— endothelial cell abundance—was significant only when represented as tumor-wide SLAB scores (p = 0.011) but not when represented as bulk abundance (p = 0.61) (Figures S6I and S6J).

To assess whether ISL and ISI distinctions reflect known features of ICB response, we compared these classifications with high-resolution pathologist annotations derived from mIF data. This analysis was conducted on six NSCLC tumors—two ISI and four ISL. ISL tumors were enriched for spatial features of immune activation, including necrosis and lymphoid follicular inflammation, while ISI tumors were more frequently associated with perivascular inflammation, fibroblast-rich zones, and tumor-stromal interface (Figure 5E). To directly visualize these differences, we examined two representative tumors. The ISL tumor (NSCLC-P6) displayed coherent spatial relationships among tumor regions, lymphoid follicles, and tumor-stroma boundaries, similar to lymphoid aggregate spatial organization in immune-responsive renal cell carcinoma (Figure 5F).⁷⁵ In contrast, the ISI tumor (NSCLC-P16) exhibited fibroblasts interlaced amongst tumor cells, an organization previously linked to T cell exclusion in lung tumors (Figure 5G).⁷⁶ Thus, ISL and ISI designations encompassed known spatial hallmarks of ICB responsiveness in patients.

While the ISL and ISI categories were defined using pan-tumor information, the clinical association with response was derived from our NSCLC cohort. We, therefore, sought to identify whether a subset of pan-tumor immune lability genes might be specifically responsible for the clinical relevance of ISL and ISI distinctions in NSCLC. To do this, we identified the genes with differential SLAB between the pan-tumor ISL/ISI cohorts and then performed a differential SLAB analysis of these genes in NSCLC ISL versus ISI tumors. Top genes distinguishing ISL from ISI in NSCLC were STARD7 and HINT1, implicated in TME immunomodulation across diverse cancers including NSCLC (Figure 5H, left).^77,78 ORA pathway enrichment of genes distinguishing ISL from ISI in NSCLC was notable for (1) the well-studied KEAP1-NFE2L2-axis of tumor immunosuppression in lung tumors and (2) metabolism of linoleic acid, a member of the polyunsaturated fatty acid class that increases ICB sensitivity in NSCLC tumors (Figure 5H, right).^79,80 On the other hand, pathways distinguishing ISL from ISI in the pan-tumor cohort but not our NSCLC cohort were notable for insulin-like growth factor (IGF) signaling. Although IGF1R signaling has been connected to tumor immunomodulation, IGF1R alteration frequency is rare in lung tumors, suggesting why it may not distinguish ISL from ISI tumors in our NSCLC cohort.^81,82,83

Overall, our results illustrated that forward inference about tumor immune spatial biology using our pan-tumor cohort stratified ICB-related outcomes in an out-of-sample NSCLC cohort.

Identifying a panel of mIF markers to approximate the spatial similarity between tumors

Our results illustrated that SGs are spatially, biologically, and clinically relevant organizational units of the TME. However, discovering SGs required genome-wide spatial data, a costly and logistically intensive measurement in clinical settings. Therefore, a natural question is to what degree the spatial similarity between tumors defined by SGs could be measured by lower-throughput assays like mIF that might be more clinically scalable.

Common approaches for extracting information from mIF data on TMEs have included evaluating (1) mean marker abundance, (2) cell type abundance, and (3) cell neighborhood abundance.²⁰ TumorSPACE is an alternate approach for identifying spatial structures in data where biological information is connected to spatial coordinates. By applying TumorSPACE to mIF data, we defined SGs based on marker abundance and computed marker SLAB scores that captured how each marker spatially varied across SGs within a tumor (Figure 6A, left; STAR Methods). This enabled us to ask which representation of mIF data most faithfully recapitulated the spatial similarity between samples defined by genome-wide SLAB profiles.

Figure 6.

Sparse sets of immunofluorescence markers capture spatial similarity between tumors

(A) Workflow for MCMC optimization. Left side shows that mIF data are used to create three representations of tumor spatial biology: marker mean intensity, cell type abundance, and neighborhood abundance. TumorSPACE on mIF data defines SLAB scores for each marker as a fourth representation: marker SLAB. These four representations are evaluated for capturing the spatial similarity between NSCLC tumors, as determined by genome-wide SLAB scores (right) through MCMC simulation (middle). This is an iterative process (blue box): in each step, mIF-based representations of spatial similarity are evaluated against spatial similarity determined by genome-wide SLAB using Pearson’s correlation (y axis in gray box). Simulation (gray box) consists of seed selection, a high-entropy burn-in phase, and a low-entropy phase ending when correlation no longer improves between steps.

(B) (Left) Pearson’s correlation (y axis) between spatial similarity determined by various mIF representations (color key) and spatial similarity determined by genome-wide SLAB versus number of features considered (x axis). (Right) The two top-performing panels used marker SLAB with Pearson’s correlation coefficient of ∼0.9. Each panel has five distinct markers and two shared markers (CD40 and vimentin). Heatmap indicates marker presence (blue) or absence (red) amongst 50 independent MCMC simulations (x axis). For each marker, the right table indicates the top three cell types (x axis) ranked by marker intensity in mIF data (color key).

We leveraged the subset of six NSCLC tumors for which we had aligned ST-seq data and mIF data (Figure S2B; STAR Methods). Each of the four mIF data representations—marker mean intensity, cell type abundance, neighborhood abundance, and marker SLAB—contains a discrete set of features. Given the many-to-many mapping between such features and TME biology (e.g., tumor cells enriched for both E-cadherin and EpCAM, while EpCAM is enriched on both tumor cells and dendritic cells), we sought a data-driven approach for identifying the optimal feature subset. We used Markov Chain Monte Carlo (MCMC) simulations to probabilistically sample feature combinations across each mIF representation. This procedure involves initially selecting a random subset of features (the “seed”) and then performing broad exploratory sampling where features can be easily added or removed from the panel (“high-entropy burn-in”). Once promising combinations are identified, the algorithm fine-tunes the selected features in a “low-entropy convergence” phase. At each step in the MCMC algorithm, the selected feature subset is evaluated using a predefined target function; Pearson’s correlation between the tumor-by-tumor similarity matrix is computed using the mIF feature subset, and the spatial similarity matrix is computed from genome-wide SLAB scores. The simulation terminates once further changes to the feature subset fail to improve this correlation (Figure 6A; STAR Methods).

The MCMC simulation revealed that marker SLAB outperformed all other mIF representations. Notably, correlation using marker SLAB peaked with just seven features (Figure 6B, left). For marker SLAB, there were two optimal marker panels composed of seven markers each (five distinct markers and two overlapping markers, namely CD40 and vimentin) across a collection of 50 independent MCMC simulations (Figure 6B, right). Both panels were enriched for markers specific to similar immune and stromal populations including CD4⁺ T cells, CD8⁺ T cells, macrophages, regulatory T cells (Tregs), and tumor cells (Figure 6B, right). This result indicated that while the two marker panels were compositionally distinct, the cell types encoded by them had similar distributions.

To learn whether these two marker SLAB panels depended on capturing collective information across their constituent markers, we alternatively selected marker SLAB panels, using generalized linear model (GLM) regression. Because GLMs assess individual marker contributions in isolation, we selected the top seven independently performing markers as a GLM-selected marker panel (Figure S6K). The GLM-selected marker panel did not fully overlap with either optimal MCMC marker panel, as several markers in the MCMC marker panels had modest GLM coefficients. While the MCMC marker panels closely recapitulated genome-wide SLAB-based tumor spatial similarity (r = 0.92), the GLM-selected marker panel did not (r = 0.59) (Figures S6L and S6M). These results signified that finding the optimal marker SLAB panel required considering collective information between markers and not only the independent effects.

Together, these findings demonstrated proof of principle that the spatial architecture defined by genome-wide SLAB profiles can be approximated using sparse protein markers from mIF data.

Discussion

Our results establish SGs as TME spatial domains that represent meaningful biological structures. By examining SGs across diverse tumor types, we uncovered a broadly conserved principle of TME spatial biology: SG organization is a nested hierarchy reflecting context-informed biological heterogeneity. Comparing TME architecture defined by SGs across hundreds of tumors revealed that the primary axis of spatial variation was immune biology. This observation led to spatially aware biomarker-stratifying outcomes after ICB therapy in a retrospective cohort of NSCLC patients.

The conserved organization of SGs into nested hierarchies enables a clear direction for the field of high-resolution tumor spatial biology. Currently, our capacity to collect ST-seq data exceeds the rate at which human experts could analyze these data. This necessitates establishing artificial intelligence approaches aligned with principles of tumor spatial biology. Our results demonstrate the integration of biology across spatial scales in the TME, suggesting that a naturally aligned model could be a neural network. Such models contain all-to-all connections between neurons of adjacent layers, yet recent work to constrain these connections has enabled widespread adoption of deep learning models in many fields.^84,85,86 Further work could explore this idea by explicitly modeling SG connections as connected neurons in a manner inspired by “biologically aware” neural networks.⁸⁷

In this work, we developed a unified coordinate system for comparing tumors based on spatial organization. Additionally, using our NSCLC cohort as proof-of-concept, we have shown that new tumors could be embedded into this space to learn about the spatial biology of those tumors, as informed by our pan-tumor cohort. These results suggest that as more datasets are projected into the pan-tumor space, particularly those with linked clinical annotations, the collective reference can sharpen our ability to interpret tumors in clinically meaningful ways. The unified coordinate system we have defined here could ultimately serve immense public utility by enabling decentralized use without moving or exposing patient-level data, while enriching a translational understanding of TME spatial biology.

TME spatial biology encompasses biophysical processes that relate in ways we do not yet understand. As the spatial omics toolbox expands, it will become increasingly important to relate biological learnings from these technologies directly to each other. Our results have demonstrated a complex but definable mapping between spatial modalities—ST-seq and mIF—that made no assumptions about the biological content of each dataset. These results open the door for SG-guided clinical trials whereby genome-wide spatial biology is captured by sparse diagnostic panels. They also suggest that SGs occupy a central place in TME spatial biology that spans RNA and protein abundances and, potentially, additional TME spatial biology axes. Our findings motivate understanding the origins of SGs and the mechanisms by which they are maintained and evolve.

Limitations of the study

Several limitations should be considered when interpreting our results. First, while we defined nine SCs from our pan-tumor cohort, our cohort does not represent all cancer types and patient populations. Our data showed that some tumor types comprise their own SC and that some SCs were only discoverable when studying a large group of tumors. Second, our analysis intersected only two types of spatial information: RNA abundance through transcriptomics, and protein abundance through mIF. Future studies could incorporate other descriptions of spatial biology (e.g., metabolomics) to assess how these complementary data provide additional context to TME spatial biology. Finally, the NSCLC cohort we evaluated was modest in size. While this was sufficient to prove the concept of clinically useful spatial biomarkers, our results motivate pursuing a multi-site prospective trial to test whether SG-based classifications are better than the current standard (PD-L1 IHC) as a predictive clinical biomarker of ICB response.

Resource availability

Lead contact

Requests for further information, resources, and reagents should be directed to and will be fulfilled by the lead contact, Arjun S. Raman (araman@bsd.uchicago.edu).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •All data relevant to our study can be found within supplemental tables. ST-seq data related to the cohort of DLBCL and NSCLC patients are available at https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE292299, with the accession code GEO: GSE292299.
• •All TumorSPACE code, along with documentation and stepwise instructions, are written in the Julia⁸⁸ language and available at https://github.com/aramanlab/TumorSPACE.jl. All processed data and code for producing the figures in this paper are available at https://github.com/aramanlab/Behera_etal_2025.
• •Deposited data in the key resources table: Pathologist-annotated H&E images corresponding to our pan-tumor database are available at https://zenodo.org/records/16856762. Raw and processed (Table S4) mIF data are available at https://zenodo.org/records/16851985 and https://zenodo.org/records/20722579.
• •Any additional information required to reanalyze the data reported in this work paper is available from the lead contact upon request

Acknowledgments

We thank D. Pincus, M. Mani, M. Lingen, D. Zemmour, I. Moskowitz, and R. Ranganathan for helpful discussions. We thank the genomics core and human immunologic monitoring core facilities at the University of Chicago for their aid in sequencing and imaging our ST-seq samples. This work was supported by the Duchossois Family Institute, the Department of Pathology, and the Center for the Physics of Evolving Systems at the University of Chicago. Funding for V.B. was provided by a T32 NIH training grant within the Department of Medicine, Section of Hematology/Oncology at the University of Chicago.

Author contributions

Conceptualization, V.B., J.K., M.C.G., and A.S.R.; methodology, V.B., A.G., H.G., U.-Y.P., B.P., B.A.D., A.H., C.M.B., and A.S.R.; software, V.B. and B.A.D.; investigation, V.B., A.G., H.G., A.D.L., A.P., and A.H.; writing – original draft, V.B. and A.S.R.; writing – review & editing, V.B., A.G., U.-Y.P., C.M.B., J.K., and A.S.R.; supervision, V.B., M.C.G., and A.S.R.; project administration, V.B., H.G., and A.E.; funding acquisition, A.H., M.C.G., and A.S.R.

Declaration of interests

A.S.R. is a founder of Sparsity, Inc.; V.B. is a co-founder of Sparsity, Inc. Patents (63/572,XXX) related to this research have been filed by the University of Chicago, with V.B. and A.S.R. as inventors.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Chemicals, peptides, and recombinant proteins
Xylene	Millipore Sigma	214736
Ethyl Alcohol, 200 Proof	Fisher Scientific	A4094
Eosin Y-solution, Alcoholic	Sigma Aldrich	HT110116
Hematoxylin Solution, Mayer’s	Sigma Aldrich	MHS16
Bluing Reagent, Dako	Agilent	CS702
Glycerol, ultra pure	MP Biochemicals	800688
Hydrochloric Acid Solution, 0.1 N	Fisher Chemical	SA54-1
Nuclease-free Water (not DEPC treated)	Invitrogen	AM9937
Tris (1M, pH7)	Invitrogen	AM9850G
10× PBS	Invitrogen	AM9624
1× PBS	Corning	21-040-CV
10% Tween 20	Bio-Rad	1610781
KAPA SYBR FAST qPCR Master Mix (2×)	KAPA Biosystems	KK4600
SPRIselect Reagent Kit	Beckman Coulter	B23317
8M KOH	Sigma Aldrich	P4494
20× SSC Buffer	Sigma Aldrich	S6639
Qiagen Buffer EB	Qiagen	1014609
Deparaffinization Solution	Qiagen	1064343
Critical commercial assays
Visium CytAssist Slide and Cassettes, 11mm 2rxns	10× Genomics	PN-1000518
Visium FFPE Reagent Kit v2 – Small	10× Genomics	PN-1000436
Visium CytAssist Reagent Accessory Kit	10× Genomics	PN-1000499
Visium CytAssist Spatial Gene Expression for FFPE, Human Transcriptome, 11mm, 2 rxns	10× Genomics	PN-1000522
Visium Human Transcriptome Probe Kit v2 - Small	10× Genomics	PN-1000466
Dual Index Kit TS Set A, 96 rxns	10× Genomics	PN-1000251
RNeasy FFPE Kit	Qiagen	73504
Deposited data
Spatial transcriptomics pre-processed data	This paper	GEO: GSE292299
H&E Pathologist Annotations	This paper	Zenodo: 16856762 https://zenodo.org/records/16856762
MSigDB	https://doi.org/10.1073/pnas.0506580102	https://www.gsea-msigdb.org/gsea/msigdb
Code for making figures and processed data for this paper	This paper	https://github.com/aramanlab/Behera_etal_2025
Raw and processed multiplexed immunofluorescence images	This paper	https://zenodo.org/records/16851985 https://zenodo.org/records/20722579
Software and algorithms
SpaceRanger v2.0.0	10× Genomics	https://www.10xgenomics.com/support/software/space-ranger/latest
QuPath version 0.4.4	https://doi.org/10.1038/s41598-017-17204-5	https://qupath.github.io/
Booster	doi:10.1038/s41586-018-0043-0	https://booster.pasteur.fr/
OpenCV	OpenCV	https://opencv.org/
SpaCET	NA	https://data2intelligence.github.io/SpaCET/articles/visium_BC.html
Enrichr	https://doi.org/10.1186/1471-2105-14-128	https://maayanlab.cloud/Enrichr/
R version 4.1.0 and 4.4.0	R Foundation for Statistical Computing	https://cran.r-project.org/
Julia version 1.9.0	NA	https://julialang.org/
Python version 3.11	Python Software Foundation	https://www.python.org
DeepCell	NA	https://www.deepcell.org/
TumorSPACE	This paper	https://github.com/aramanlab/TumorSPACE.jl
Other
Veriti 96-well Thermal Cycler	Thermo Fisher Scientific	4375786
MasterCycler ×50i	Eppendorf	6301000012
MasterCycler ×50A	Eppendorf	6313000018
High-Capacity Section Dryer	Epredia	A84600051
QuantStudio 6 Pro	Applied Biosystems	A43056
Vectra Polaris Whole Slide Imaging System	Akoya Biosciences	CLS143455
Visium CytAssist	10× Genomics	1000432
Legend Micro 21R Centrifuge	Thermo Fisher Scientific	75002446
Thermomixer C	Eppendorf	5382000023
Heat Block	Thermo Fisher Scientific	88870001
Vortex Mixer	fisherbrand	02-215-414
Mini Centrifuge	fisherbrand	12-006-901

Experiment model and study participant details

Non-small cell lung cancer (NSCLC) patients were treated with immune checkpoint blockade therapy ± chemotherapy at the University of Chicago Medical Center (Chicago, IL). All patients provided written informed consent for the collection and study of pre-treatment diagnostic tumor biopsy samples and for clinical outcomes including treatment regimen, treatment-related toxicities, and disease outcomes, as approved by the University of Chicago Institutional Review Board (IRB 9571 and IRB 24–0063). For the ST-seq analysis, 16 tumor samples were collected prior to therapy initiation, each from a separate patient. Inclusion criteria for these patients included (1) NSCLC stage IV patients either at initial presentation or as progression from previously treated early-stage disease, (2) biopsy of either the primary tumor or a metastatic tumor performed and stored within 6 months prior to treatment in the metastatic setting, (3) subsequent first line treatment with anti-PD1/anti-PD-L1 immune checkpoint blockade (ICB) with or without platinum-based chemotherapy. Exclusion criteria included (1) no prior therapy in the metastatic setting and (2) less than 2 doses of ICB therapy administered. We selected the first 16 patients that met these criteria and that had an available FFPE tumor biopsy block. From the archival block, a fresh 5 μm section was cut and placed on a standard slide for use in ST-seq protocols (see ‘10X Visium spatial transcriptomics (ST-seq)‘). Progression was defined as time from the first dose of ICB until either radiographic or symptom-based evidence of disease progression. ICB regimen, ICB treatment duration, reason for ICB discontinuation, time to progression following ICB start, and time to death following ICB start are listed for all patients (Table S8).

Diffuse large B-cell lymphoma (DLBCL) patients were treated at the University of Chicago Medical Center (Chicago, IL). All patients provided written informed consent for the collection and study of pre-treatment diagnostic tumor biopsy samples and for clinical outcomes including treatment regimen, treatment-related toxicities, and disease outcomes, as approved by the University of Chicago Institutional Review Board (IRB 13–1297). Each biopsy was reviewed by 2 hematopathologists for diagnostic confirmation. Biopsy slides were previously cut from FFPE sections and H&E stained for prior studies.⁸⁹

Demographic information including age, gender, disease stage, and prior treatment is listed for all NSCLC and DLBCL patients (Table S8).

Method details

Download and harmonization of ST-seq data

Previously deposited ST-seq datasets (Table S1) were downloaded for integration from GEO (https://www.ncbi.nlm.nih.gov/geo/) into the pan-tumor ST-seq database as long as they had the following SpaceRanger outputs available: 1) a spot-by-UMI gene count matrix, 2) a spot-by-pixel location matrix, 3) a scalefactors_json.json file containing ‘spot_diameter_fullres’, and 4) the associated H&E image stored either as “tissue_hires_image.png”, “tissue_lowres_image.png”, or a full-resolution image. For analyses including physical distance rather than pixel distance, pixel distance was converted to physical distance by computing a $\frac{pixel}{\mu m}=\frac{’\text{spot}\_\text{diameter}\_\text{fullres}’}{55}$ scaling factor that compares spot diameter in pixels to the known spot diameter of 55 μm.

SpaceRanger processing of ST-seq data

For internally generated ST-seq datasets, reads were aligned and mapped to the hg38 (GRCh38) human genome reference using the SpaceRanger v2.0.0 count pipeline (Table S9). This pipeline generates a raw unique molecular identifier (UMI) gene count matrix in which each row consists of a spot that has X/Y coordinates in pixels that correspond to the aligned H&E image. The SpaceRanger algorithm also identifies spots within or outside of detectable tissue, and for all subsequent analyses only spots within tissue were used.

Pathologist annotation of ST-seq H&E data

Whole-slide H&E images were collected as part of an ST-seq experiment (see ‘10X Visium CytAssist spatial … ‘) or as part of a publicly deposited ST-seq dataset (see ‘Download and harmonization of ST-seq data’). Image data were loaded into QuPath⁹⁰ (version 0.4.4) for visual inspection and manual annotation by a board-certified pathologist. An initial review of all slides revealed a natural hierarchy of histologic features, which was used to develop a structured annotation scheme (Figure S1B; Table S10). Feature categories were defined based on the following criteria: (1) biological relevance, (2) generalizability across tumor types, (3) consistency with a hierarchical annotation scheme, and (4) non-redundancy.

All tissue-containing regions were manually annotated in their entirety. Regions of interest (ROIs) were labeled according to the predefined hierarchical scheme to ensure consistency across the dataset. Ambiguous regions were reviewed in consultation with a second pathologist. In addition, a random subset of 10% slides was re-reviewed by the primary pathologist several months after the initial annotation, with blinded access to prior labels, which confirmed intra-observer reproducibility. Label annotations were identified for ST-seq spot locations by 1) importing ST-seq spot centroid locations into QuPath and 2) identifying the annotated region containing any given spot. These analyses were performed using custom Groovy scripts that have been made available within the figure repository for this paper (see ‘Code availability’).

TumorSPACE: Models and associated analysis

The sub-sections within this section will introduce several variables. Table S15 (‘Definition of TumorSPACE variables in STAR Methods’) contains definitions of all variables in this section.

Overview

Building a TumorSPACE model requires spatial transcriptomic data and two inputs from SpaceRanger: (1) the raw gene UMI count matrix and (2) the spot spatial coordinate matrix. Model building subsequently operates on the gene count matrix to build many models that vary in hyperparameter choice. The spot spatial coordinates are then used for selecting the optimal hyperparameter set that maximizes accurate recovery of spatial spot organization.

Four hyperparameters are tuned during this process: (1) the number of principal components (PCs) of data-variance used for creating a latent space of the transcriptional data, (2) the limit of statistical robustness for spot-spot relatedness in the latent space, (3) the spatial dispersion of the nodes in the latent space hierarchical tree model, and (4) the number of KNN matches used for spot spatial prediction. The following sections will first establish the model latent space and compute statistical robustness and spatial dispersion properties of that latent space. Subsequently, all hyperparameters will be tuned to define the optimal model for mapping transcriptional content from TME spots to TME spatial organization.

Creating a latent space

The first step in building a TumorSPACE model is to create a latent space representation of the gene count data that incorporates statistical bootstrapping. TumorSPACE first embeds ST-seq spots into a latent space by applying singular value decomposition (SVD) to the gene count matrix⁹¹:

$$M=U\mathrm{\Sigma }{V}^T$$ (Equation 1)

M is the SpaceRanger gene count matrix (m spots as rows, n genes as columns), U is the left singular matrix, Σ is the singular value matrix, and V is the right singular matrix. U is defined by cell spots (rows) and left singular vectors (columns), where each entry is the projection of a cell spot onto a left singular vector. Σ is a diagonal matrix where entries are singular values. V^T is defined by genes (rows) and right singular vectors (columns) where each entry is the projection of a gene onto a right singular vector.

First, from 1, a metric termed ‘spectral distance’ (D) between all spots is calculated. This metric was previously developed by our laboratory in the context of analyzing phylogenetic bacterial proteome content.²⁸ As implemented for spatial data in this manuscript, performing SVD on the gene count matrix determines the extent to which each cell spot projects onto each left singular vector. Therefore, a distance considering the transcriptomes of two spots can be computed by measuring the difference in the projections of two spots onto a left singular vector. Note, this definition of distance does not consider any information about spatial spot distribution.

Next, groups of left singular vectors are combined to create ‘spectral groups’. These groups are defined based on the eigenvalues associated with each left singular vector: left singular vectors with similar eigenvalues are grouped together:

$$SG=\{{sg}_1,{sg}_2,\dots \}$$ (Equation 2)

where SG is the total set of spectral groups, sg₁is first set of columns extracted from U, sg₂ is the second set of columns extracted from U, and so on. The concept of spectral groups was also previously developed by our laboratory.⁹² Defining sg_i and sg_i+1 is done by identifying larger than expected decreases in singular values between consecutive left singular vectors. To compute spectral groups, a vector of differences between consecutive singular values is computed for all left singular vectors. We use the upper and lower quartiles of this distribution in combination with a scaling parameter alpha to define the ‘expected difference’ bounds between singular values. Any difference in singular values outside of these bounds deviates from expectation and therefore defines a spectral group (see associated GitHub code for specification of parameters). The spectral distance for a pair of spots within a spectral group is then computed as the Euclidean distance between spot projections onto left singular vectors comprising the spectral group weighted by the eigenvalue associated with each left singular vector. The summation of these distances across all spectral groups is the spectral distance, d_i,j, between spots i and j.

After computing d_i,j for all spots, the resulting construct is a spectral distance matrix D comprised of m rows and m columns where m is the number of spots in the original gene count matrix and each entry in D is the spectral distance between two spots. D is then used as input for hierarchical clustering with complete linkage, resulting in a tree T that relates all spots in a tumor sample to each other. T has m leaves and (m-1) internal vertices (nodes). The leaves are the ST-seq spots and the nodes g∈G represent G hierarchically ordered groupings of these spots. The resulting network is the TumorSPACE latent space of the original gene count matrix.

The number of spectral groups is dependent on how many of the total left singular vectors are considered. An increasing number of left singular vectors being included corresponds directly to the inclusion of deeper principal components when computing the latent space. For TumorSPACE models, the depth of principal components, ‘p’, is a hyperparameter that is tuned for embedding the gene count matrix into a latent space.

Bootstrapping the latent space to evaluate statistical robustness

TumorSPACE does not assume that each node g arises from biological signal. Instead, TumorSPACE bootstraps T using the Booster package’s implementation of transfer bootstrap expectation (TBE), the probability that node g appears in an empirically bootstrapped tree (default settings used for Booster).⁹³ For generating empirically bootstrapped trees, we applied Gaussian multiplicative noise injection to the initial gene count matrix M to create a “bootstrapped” gene count matrix M_B.

$$M_B=M⨀X$$ (Equation 3)

such that ⊙ indicates element-wise multiplication by a normally distributed random variable X ∼ N(μ,σ²)with μ = 1 and σ = 0.2. This matrix was then used as an input to (1) and a tree was created following the steps outlined in ‘Creating a latent space’ to generate a bootstrapped tree T_B. Bootstrapping was done 10 times for a given dataset, followed by input of the original tree T and the bootstrapped trees T_B into Booster for TBE computation. This results in a labeling of the original tree T’s set of nodes G with TBE support values b_G such that b_G∈[0,1].

Calculating physical spatial dispersion in latent space

The final property of T that is computed is the spatial dispersion k for each node comprising T. Spatial dispersion is estimated for each node using Ripley’s reduced second moment function K(r) with border correction.^94,95 Let g_s be the set of ST-seq spots within node g in T. The window of physical tumor space is defined by the spot spatial coordinate matrix such that len_x indicates the x axis window length and len_y indicates the y axis window length. We then compute λ, a normalization factor for spot intensity within a spatial region, and r_max, a factor that incorporates lambda to determine the maximum spatial distance being assessed.

$$\lambda =\frac{\left|{\mathit{g}}_{\mathit{s}}\right|}{{len}_x\ast {len}_y}$$ (Equation 4)

$$r_{\mathit{max}}=\min \text{Error}!\text{Bookmark}\text{not}\text{defined.}$$ (Equation 5)

where min denotes the minimum between a set of values. Let R be the set of spot spatial distances that will be assessed, such that

$$r\in R|R=\left\{0,\frac{r_{\mathit{max}}}{512},\frac{{2\ast r}_{\mathit{max}}}{512},\dots ,r_{\mathit{max}}\right\}$$ (Equation 6)

We define the physical distance δ between any two spots as

$$\delta \left({spot}_i,{spot}_j\right)={\Delta }_{i,j}={\Delta }_{j,i}=\sqrt{{\left(X_{{spot}_i}-X_{{spot}_j}\right)}^2+{\left(Y_{{spot}_i}-Y_{{spot}_j}\right)}^2}$$ (Equation 7)

where (X_spot, Y_spot) denote the physical space coordinates for a given spot. Spatial dispersion K(r) with border correction is then computed for all spots g_s,i, ∈g_s as

$$t_{g_{s,.i}}^r=f\left(g_{s,i},r\right)=\sum _{j=1}^m\mathbf{1}\{0<\delta \left(g_{s,i},{spot}_j\right)<r\}$$ (Equation 8)

$$K\left(r\right)={\sum }_{i=1}^{card\left(G\right)}\left(\frac{\mathbf{1}\left\{b_i\ge r\right\}\ast t_{g_{s,.i}}^r}{\lambda \ast {\sum }_{i=1}^{card\left(G\right)}\mathbf{1}\left\{b_i\ge r\right\}}\right)-\pi r^2$$ (Equation 9)

where t(g_s,i,r) is the number of spots within distance r of a given g_s,i and b_i is the distance from spot g_s,i to the window boundary. The general notation card(S) indicates the number of elements in a set S, and the general notation 1{f(x)} signifies a value of 1 when f(x) is true and a value of 0 when f(x) is false. Finally, spatial dispersion k is computed by summing the absolute value of K(r) over r∈R as follows.

$$k=\sum _{r\in R}abs\left(K\left(r\right)\right)$$ (Equation 10)

This calculation labels all nodes G in tree T with spatial dispersion values k_G such that $k_G{\in }_{\mathbb{R}}\left[0,\infty \right]$.

Hyperparameter optimization to create a TumorSPACE map

TumorSPACE model optimization involves selecting the values of four hyperparameters that maximize model prediction accuracy (described in ‘Prediction Accuracy Calculation’) for a given dataset. These hyperparameters tune three properties of tree T – principal component depth p (from ‘Creating a latent space’), node TBE support b (from ‘Bootstrapping the latent space to evaluate statistical robustness’), node spatial dispersion k (from ‘Calculating physical spatial dispersion in latent space’) – as well as one property of accuracy computation, the number of spot KNN matches κ. We perform hyperparameter tuning as a nested grid search by tuning p as an outer layer and then optimizing [b, k, κ] for a given value of p.

First, a set of PC depth values (n_p where default is set to 10) is randomly selected to create a set $P=\left\{p_1,p_2,\dots ,p_{n_p}\right\}$. The PCs termed p_i are chosen on a logarithmic interval between a minimum and maximum PC depth, which is the rank of the gene count matrix M. Next, a matrix of three hyperparameter values, $H=\{h_{1\dots n_H}^{\left(1\right)},h_{1\dots n_H}^{\left(2\right)},h_{1\dots n_H}^{\left(3\right)}$}, are created where the vectors h⁽¹⁾, h⁽²⁾, and h⁽³⁾ are independently sampled from distributions as follows.

$${h^{\left(1\right)}\in }_{\mathbb{R}}{10}^{X\ast \mathit{log}10\left(\frac{b_{\mathit{max}}+1}{b_{\mathit{min}}+1}\right)+\mathit{log}10\left(b_{\mathit{min}}+1\right)}-1$$ (Equation 11)

$$h^{\left(2\right)}{\in }_{\mathbb{R}}{10}^{X\ast \mathit{log}10\left(\frac{k_{\mathit{max}}+1}{k_{\mathit{min}}+1}\right)+\mathit{log}10\left(k_{\mathit{min}}+1\right)}$$ (Equation 12)

$$h^{\left(3\right)}{\in }_{\mathbb{Z}}round\left({10}^{X\ast \mathit{log}10\left(\frac{{\kappa }_{\mathit{max}}+1}{{\kappa }_{\mathit{min}}+1}\right)+\mathit{log}10\left({\kappa }_{\mathit{min}}+1\right)}\right)$$ (Equation 13)

In (11–13), X is a random variable drawn from Uniform([0,1]). Default values for hyperparameter bounds are b_min = 0, b_max = 0.5, k_min = 0, k_max = 1 κ_min = 5, κ_max = 300. A minimum of n_H = 100 sets of {h⁽¹⁾,h⁽²⁾,h⁽³⁾} are initially sampled, after which additional sets are sampled until prediction accuracy optimization has converged. Prediction accuracy convergence is reached when the difference in prediction accuracy (defined below in ‘Prediction Accuracy Calculation’) for the top 2 scoring hyperparameter sets is less than 0.05. For a given hyperparameter set h_i, the TumorSPACE tree T is filtered for the set of nodes G_filt such that each node in G_filt satisfies

$$b\ge h_i^{\left(1\right)}ANDk\ge h_i^{\left(2\right)}$$ (Equation 14)

The final filtered tree, T_filt, comprises the set of nodes G_filt’, which consists of G_filt as well as the complete set of parent nodes from which G_filt descend even if those parent nodes do not meet the criteria in (14), along with all ST-seq spots. We found that optimal hyperparameter values varied widely amongst datasets, underscoring the importance of fitting these parameters for each individual dataset (Figure S7A).

Prediction accuracy calculation

To identify the TumorSPACE model properties that were optimized for predicting spot spatial locations from transcriptomic data, we masked the physical location of each ST-seq spot and identified its k nearest neighbors in the TumorSPACE latent space by minimizing spectral distance.

For any masked spot i amongst all spots I, we can define its κ nearest neighbors NN_i,κ as

$${NN}_{i,\kappa }={\mathit{argmin}}_{j\in J}^{\kappa }\left(d\left({spot}_i,{spot}_j\right)\right)$$ (Equation 15)

where i∈I, κ∈h⁽³⁾ as defined in (13), J is the set of all spots other than spot i, and argmin^κ selects the set of κ spots with the smallest spectral distance relative to spot i. To prevent overfitting, we identified for each spot_i,z∈NN_i,κ a randomly chosen ${spot}_{i,z}^{\prime }$ that belongs to the internal node g^i,z within T_filt immediately ancestral to spot_i,z.

We then estimated the location of masked spot i based on the x and y locations of the corresponding ${spot}_{i,z}^{\prime }$ spots.

$${\hat{X}}_{{spot}_i}=\frac{1}{\kappa }\sum _{z=1}^{\kappa }{X}_{{spot}_{i,z}^{\prime }}and{\hat{Y}}_{{spot}_i}=\frac{1}{\kappa }\sum _{z=1}^{\kappa }{Y}_{{spot}_{i,z}^{\prime }}$$ (Equation 16)

Finally, we computed the Pearson Correlation ρ between the vectorized matrix Δ_actual of pairwise actual spot-spot physical distances and the vectorized matrix Δ_predicted of pairwise predicted spot-spot physical distances.

$${\Delta }_{actual}\left[i,j\right]=\sqrt{{\left(X_{{spot}_i}-X_{{spot}_j}\right)}^2+{\left(Y_{{spot}_i}-Y_{{spot}_j}\right)}^2}$$ (Equation 17)

$${\Delta }_{predicted}\left[i,j\right]=\sqrt{{\left({\hat{X}}_{{spot}_i}-{\hat{X}}_{{spot}_j}\right)}^2+{\left({\hat{Y}}_{{spot}_i}-{\hat{Y}}_{{spot}_j}\right)}^2}$$ (Equation 18)

$$\rho =corr\left(vec\left({\Delta }_{actual}\right),vec\left({\Delta }_{predicted}\right)\right)$$ (Equation 19)

where vec() indicates matrix vectorization to a single column and corr() indicates Pearson Correlation. To compute a null distribution for ρ using empirical bootstrapping of actual versus predicted spot locations in a given dataset, we shuffled the vector ${\hat{S}}_{{spot}_i}=\left({\hat{X}}_{{spot}_i},{\hat{Y}}_{{spot}_i}\right)$ without replacement and then re-computed (17–18) using this shuffled vector ${\hat{S}}_{{spot}_i}^{shuffled}$ of predicted spot locations.

$${\hat{S}}_{spot}^{shuffled}=\{K\subseteq {\hat{S}}_{{spot}_i}|card\left(K\right)=card\left(I\right)\}=\left({\hat{X}}_{spot}^{shuffled},{\hat{Y}}_{spot}^{shuffled}\right)$$ (Equation 20)

$${\Delta }_{predicted}^{shuffled}\left[i,j\right]=\sqrt{{\left({\hat{X}}_{{spot}_i}^{shuffled}-{\hat{X}}_{{spot}_j}^{shuffled}\right)}^2+{\left({\hat{Y}}_{{spot}_i}^{shuffled}-{\hat{Y}}_{{spot}_j}^{shuffled}\right)}^2}$$ (Equation 21)

$${\rho }^{shuffled}=corr\left(vec\left({\Delta }_{actual}\right),vec\left({\Delta }_{predicted}^{shuffled}\right)\right)$$ (Equation 22)

For Figure 1B, ρ^shuffled is computed for 100 shuffles and the maximum ρ is taken as the ‘null’ prediction value. The null distribution is plotted in the gray distribution in Figure 1B.

Finally, the optimal TumorSPACE model $T_{filt}^{opt}$ is found that maximizes ρ across hyperparameter sets P and H.

$$T_{filt}^{opt}={\mathit{argmax}}_{p\in P,h\in H}^1\left({\rho }_{p,h}\right)$$ (Equation 23)

TumorSPACE model outputs

For a given input tumor ST-seq dataset, the output from TumorSPACE includes: (1) the TumorSPACE model $T_{filt}^{opt}$, (2) the Pearson Correlation estimate ρ, and (3) the set of predicted spot locations $\left({\hat{X}}_{{spot}_i},{\hat{Y}}_{{spot}_i}\right)$ for all ST-seq spots. The final set of internal nodes within $T_{filt}^{opt}$ are termed Spatial Groups (SGs).

Nested spatial group (NSG) depth

We computed NSG depth as a measurable quantity that describes how a given NSG relates to the other parts within a TumorSPACE model. As such, we define ‘NSG depth’ as a property of all NSGs within a TumorSPACE model.

To first define NSG depth, we compute the complete ancestral node path for any internal node g_i within $T_{filt}^{opt}$ as

$$A_{g_i}^{path}=\left\{a_{g_i}^0,a_{g_i}^1,a_{g_i}^2,\dots ,a_{g_i}^n\right\}$$ (Equation 24)

such that

$$a_{g_i}^0=g_i$$ (Equation 25)

$$a_{g_i}^{k+1}=A\left(a_{g_i}^k\right)fork\in \left[1,n-1\right]$$ (Equation 26)

$$a_{g_i}^n\in G$$ (Equation 27)

$a_{g_i}^k$ indicates the k^th ancestral node of node g_i, A(node) denotes the immediate ancestral nodeof a given node in $T_{filt}^{opt}$, and G is the set of internal nodes in $T_{filt}^{opt}$. By definition, $a_{g_i}^n$ will be the root node of $T_{filt}^{opt}$. We next define the spatial domain size ${\sigma }_{{node}_g}$ for a given node g as the mean spot-spot physical distance between all spots within g.

$${\sigma }_{{node}_g}=\frac{\sum _{i=1}^I\sum _{j=1}^J\delta \left({spot}_i,{spot}_j\right)}{I\ast J}whereI=J=card\left(g_s\right)$$ (Equation 28)

Finally, we identify the subset of nodes $A_{g_i}^{nested}$ within $A_{g_i}^{path}$ that satisfy the condition whereby the (k+1)^th node is equal to or larger in spatial domain size than the k^th node in that path.

$$A_{g_i}^{nested}\in A_{g_i}^{path}|\{\begin{array}{c}{A}_{g_i}^{path}=\left\{a_{g_i}^0,a_{g_i}^1,a_{g_i}^2,\dots ,a_{g_i}^n\right\}\\ A_{g_i}^{nested}=\left\{a_{g_i}^0,a_{g_i}^1,a_{g_i}^2,\dots ,a_{g_i}^k\right\}\\ {\sigma }_{a_{g_i}^{l+1}}\ge {\sigma }_{a_{g_i}^l}\end{array}$$ (Equation 29)

where k ≤ n and 0 ≤ l ≤ k. The NSG depth, ${\lambda }_{{node}_g}$, for a given internal node g_i is defined to be the number of ancestral generations that satisfy this condition of spatial domain nesting.

$${\lambda }_{{node}_g}=card\left(A_{g_i}^{nested}\right)-1$$ (Equation 30)

SG-based differential abundance

Differential abundance calculation requires two inputs: (1) an optimized TumorSPACE model $T_{filt}^{opt}$ and (2) a spot-by-feature matrix F. We computed differential abundance using three types of biological processes: genes, pathways, and deconvoluted cell type proportions. Computation of gene count, pathway usage, and cell type proportion matrices are described in the ‘SpaceRanger’, ‘Pathway over-representation analysis’, and ‘SpaCET’ Methods sections, respectively. The gene count matrix is normalized by the spot-wise total UMI count.

First, we identified a subset of SGs G_DA∈G at which DA will be computed. We set a minimum of 10 spots that must be present in both a given SG g_DA∈G_DA and in its sibling node $g_{DA}^{\prime }$ (e.g., A and A′ in Figure 3A) for inclusion within G_DA.

$$G_{DA}=\left[g_{DA}\in G_{filt}^{\prime }|card\left(C\left(g_{DA}\right)\right)\ge 10\&card\left(C\left(g_{DA}^{\prime }\right)\right)\ge 10\right]$$ (Equation 31)

where C(n) indicates the row indices within matrix F of the spots descending from SG g_DA. Subsequently, for each node g_DA and process f, the spot-wise process values between g_DA and $g_{DA}^{\prime }$ are compared using a two-sided Wilcoxon Rank-Sum Test, where the test p-value is given by W(a,b).

$$p_{g_{DA},f}=W\left(F_{C\left(g_{DA}\right),f},F_{C\left(g_{DA}^{\prime }\right),f}\right)$$ (Equation 32)

To facilitate empirical correction for multiple hypothesis testing, we perform 20 shuffles of the process values between g_DA and $g_{DA}^{\prime }$, followed by computation of the Wilcoxon p-value between these shuffles. Let $C_{n_{total}}$ be the concatenation of spot indices C(g_DA) and $C\left(g_{DA}^{\prime }\right)$.

$$C_{g_{total}}=C\left(g_{DA}\right)+C\left(g_{DA}^{\prime }\right)$$ (Equation 33)

$$C_{g_{total}}^{shuffled}=\{K\subseteq C_{g_{total}}|card\left(K\right)=card\left(C_{g_{total}}\right)\}=C_{g_{DA}}^{shuffled}+C_{g_{DA}^{\prime }}^{shuffled}$$ (Equation 34)

$$C_{g_{DA}}^{shuffled}=C_{g_{total}}^{shuffled}\left[1:card\left(C\left(g_{DA}\right)\right)\right]$$ (Equation 35)

$$C_{g_{DA}^{\prime }}^{shuffled}=C_{g_{total}}^{shuffled}\left[\left(card\left(C\left(g_{DA}\right)\right)+1\right):\left(card\left(C\left(g_{DA}\right)\right)+card\left(C\left(g_{DA}^{\prime }\right)\right)\right)\right]$$ (Equation 36)

$$p_{g_{DA},f}^{shuffled}=W\left(F_{C_{g_{DA}}^{shuffled},f},F_{C_{g_{DA}^{\prime }}^{shuffled},f}\right)$$ (Equation 37)

Let $P_{g_{DA},j}^{shuffled}=\left\{p_{g_{DA},j,1}^{shuffled},p_{g_{DA},j,2}^{shuffled},\dots ,p_{g_{DA},j,n}^{shuffled}\right\}$ be the set of n DA probabilities for node g_DA and shuffle j, where n is the number of processes in F. Then, a given process is found to be differentially abundant at a given node if its unadjusted p-value, $p_{g_{DA},f}$, is less than the minimum of all shuffled probabilities for that node. To assign the direction of process abundance change for nodes with significant abundance changes, given that our test examines relative changes in expression between g_DA and in its sibling node $g_{DA}^{\prime }$, we defined the larger of the two nodes as having a “baseline expression profile” for that shared local transcriptional and spatial context. Conversely, the smaller of the two nodes was defined as having either increased or decreased abundance relative to the larger node.

Contextual dependence of processes based on architecture of SGs

To determine whether differentially abundant processes within child SGs were impacted by the differentially abundant processes of their parent SGs, we computed the odds ratio test for independence as follows. Let f_i∈F and f_j∈F denote two biological processes drawn from the set of all pathways and cell types identified (see ‘Pathway over-representation analysis’ and ‘SpaCET’ sections). Across all TumorSPACE models, we identified the set of child-parent SG pairs – denoted by (N_i,P_j) – such that $N_i^{+}$ and $N_i^{-}$ indicate the subset of child SGs where process i was increased or decreased in abundance, respectively, and $P_i^{+}$ and $P_i^{-}$ indicate the subset of parent SGs where process j was increased or decreased in abundance, respectively. Then, the odds ratio of independence OR_i,j was defined as,

$${OR}_{i,j}=\frac{\left(\raisebox{1ex}{$card\left(N_i^{+},P_i^{+}\right)$}\!\left/ \!\raisebox{-1ex}{$card\left(N_i^{-},P_i^{+}\right)$}\right.\right)}{\left(\raisebox{1ex}{$card\left(N_i^{+},P_i^{-}\right)$}\!\left/ \!\raisebox{-1ex}{$card\left(N_i^{-},P_i^{-}\right)$}\right.\right)}$$ (Equation 38)

Standard definitions were used for calculation of odds ratio standard error and p-values.⁹⁶

SG-based spatial lability (SLAB) score

Given a single TumorSPACE model $T_{filt}^{opt}$ and a process f_i for which differential abundance has been computed in $T_{filt}^{opt}$, we define the SLAB score as follows. Let $G^{f_i}$ be the set of SGs in $T_{filt}^{opt}$ in which the process f_i is differentially abundant (q < 0.05). For each node $g_k^{f_i}\in G^{f_i}$, this means that process f_i is differentially abundant between $g_k^{f_i}$ and its sister node ${g_k^{f_i}}^{\prime }$ in $T_{filt}^{opt}$. First, we identify which of the nodes, either $g_k^{f_i}$ or ${g_k^{f_i}}^{\prime }$, contains the fewer number of spots. This node is defined as the node with either increased or decreased abundance of process f_i, while the node with the greater number of spots is considered to be the ‘baseline’ abundance state for process f_i in that subset of the tumor biopsy. $DA\left(T_{filt}^{opt},f_i,g_k^{f_i}\right)$ describes the set of spots with differential abundance in process f_i for TumorSPACE model $T_{filt}^{opt}$ at node $g_k^{f_i}$:

$$DA\left(T_{filt}^{opt},f_i,g_k^{f_i}\right)=\left\{\min \left(\left[C\left(g_k^{f_i}\right),C\left(g_k^{{f_i}^{\prime }}\right)\right]\right)|g_k^{f_i}\in G^{f_i}\right\}$$ (Equation 39)

Next, we compute the union of those differentially abundant spots and compute the fraction that these spots constitute compared to the total set of spots I in the biopsy as a whole.

$$SLAB\left(T_{filt}^{opt},f_i\right)=\frac{card\left(U\left\{DA\left(T_{filt}^{opt},f_i,g_k^{f_i}\right)|g_k^{f_i}\in G^{f_i}\right\}\right)}{card\left(I\right)}$$ (Equation 40)

SLAB score correlation with bulk expression

For correlation of genome-wide SLAB scores with bulk gene expression, as in Figure S4B, we did the following. First, we identified the set of all dataset-gene pairs for which the gene had greater than 0 UMIs detected per spot and a non-zero SLAB score in that dataset. Next, to enable computing correlation statistics, we identified genes with greater than 10 dataset entries in the filtered dataset-gene pair list. For these genes, we computed the Pearson Correlation estimate and p-value between SLAB score and mean spot UMI count across datasets. Correction for multiple hypothesis testing was done using the Benjamini-Hochberg method with a corrected q-value threshold of 0.05.⁹⁷

Spatial lability pan-tumor classification

Given the set of genome-wide SLAB scores that were computed for all datasets within the pan-tumor ST-seq database (see ‘Download and harmonization of ST-seq data’ and ‘SpaceRanger processing of ST-seq data’), we aligned these score vectors into a matrix $M_{SLAB}^{Pan}$ such that each dataset was a row and each gene was a column. For any instances where a gene had mapped reads in one dataset but not another – thus resulting in blank cells in this matrix – the score within this matrix was set to zero. Next, Euclidean distance was computed between each pair of rows, resulting in a distance matrix that compared all datasets to each other. Finally, the Unweighted Pair Group Method with Arithmetic mean (UPGMA) algorithm was used for constructing a hierarchical tree relating datasets to each other (Figure S4D).⁹⁸

Spatial Classes were identified from this hierarchical tree by filtering the tree branchpoints in two steps. First, only branchpoints with at least five datasets in each child branch were retained. Second, empirical bootstrapping using transfer bootstrap expectation (TBE) was applied to identify statistically robust branchpoints.⁹³ For this, the SLAB matrix was re-sampled 100 times so that columns (genes) were randomly selected with replacement. From these re-sampled matrices, the same hierarchical tree algorithm was applied, resulting in 100 bootstrapped trees. The original tree was then compared to these re-sampled trees to infer TBE support values ranging from 0 (no reproducibility) to 1 (perfectly reproducible) for each branchpoint in the tree. Branchpoints with TBE ≥ 0.95 were retained at this step. The resulting terminal leaves of these branches were defined as ‘Spatial Classes’.

In order to simulate defining a pan-tumor classification of tumors based on SLAB scores using variably sized training cohorts consisting of randomly selected tumors (see Figure S4F), we did the following. Our pan-tumor cohort consisted of 202 unique tumors amongst the 246 ST-seq datasets. We simulated 100 random orderings in which these 202 tumors would be added to the training data corpus one at a time. As a tumor is added to the training corpus, it is given the same Spatial Class designation as from training a pan-tumor model with all data, as in Figure 3B, which are considered the ‘ground truth’ Spatial Classes for these tumors. The addition of a single tumor, along with all of its replicate datasets, constitutes one ‘epoch’ in a simulation. Following each epoch, the entire ‘testing’ set of 246 datasets is compared in their SLAB scores to each dataset within the training corpus using Euclidean distance between SLAB vectors. For any Spatial Classes represented by a non-zero number of datasets in the training corpus, the mean Euclidean distances are calculated to the testing datasets, and testing data are assigned to the Spatial Class that minimizes distance. Finally, these ‘simulated’ Spatial Class assignments are compared to the ground-truth Spatial Class assignments. Each Spatial Class is evaluated at each Epoch using an F1 statistic – the harmonic mean of precision and recall, bounded from 0 to 1.

Differential SLAB score analysis

At each high-confidence branchpoint identified in ‘Spatial lability pan-tumor classification’, we compared the datasets within the child branches for differential SLAB scores at all genes. Let the dataset groups with these branches be named A and A'.

To compare gene-level SLAB scores, we first compose the matrix L^A of SLAB scores where L^A has a+a′ rows corresponding to tumors a∈A and a′∈A′ and F columns where f∈F constitutes the full set of genes. Next, for each gene f, we compare the tumors in A and A′ where C(X) indicates the row indices within matrix L^A that correspond to tumors in either group. Comparison is performed using a Mann-Whitney U Test, where the test p-value is given by MW(a,b).

$$p_{A,f}=MW\left(L_{C\left(A\right),f}^A,L_{C\left(A^{\prime }\right),f}^A\right)$$ (Equation 41)

To facilitate empirical correction for multiple hypothesis testing, we perform 1000 shuffles of the SLAB counts between A and A′, followed by computation of the MW p-value between these shuffles. Let $C_{A_{total}}$ be the concatenation of row indices C(A) and C(A′).

$$C_{A_{total}}=C\left(A\right)+C\left(A^{\prime }\right)$$ (Equation 42)

$$C_{A_{total}}^{shuffled}=\{J\subseteq C_{A_{total}}|card\left(J\right)=card\left(C_{A_{total}}\right)\}=C_A^{shuffled}+C_{A^{\prime }}^{shuffled}$$ (Equation 43)

$$C_A^{shuffled}=C_{A_{total}}^{shuffled}\left[1:card\left(C\left(A\right)\right)\right]$$ (Equation 44)

$$C_{A^{\prime }}^{shuffled}=C_{A_{total}}^{shuffled}\left[\left(card\left(C\left(A\right)\right)+1\right):\left(card\left(C\left(A\right)\right)+card\left(C\left(A^{\prime }\right)\right)\right)\right]$$ (Equation 45)

$$p_{A,f}^{shuffled}=MW\left(L_{C_A^{shuffled},f}^A,L_{C_{A^{\prime }}^{shuffled},f}^A\right)$$ (Equation 46)

Let $P_{A,j}^{shuffled}=\left\{p_{A,j,1}^{shuffled},p_{A,j,2}^{shuffled},\dots ,p_{A,j,n}^{shuffled}\right\}$ be the set of n probabilities for group A and shuffle j, where n is the number of genes in F. Then, a given gene is found to have a differential SLAB score between a given grouping A vs. A′ if its unadjusted p-value, p_A,f, is less than the 5^th percentile (q = 0.05) of all shuffled probabilities.

Classification of NSCLC datasets by pan-tumor spatial lability

For comparison of out-of-sample NSCLC tumors to the pan-tumor Spatial Classes lability groups shown in Figure 3B, we first computed SLAB scores for all genes and aligned the score vectors to match the columns (genes) of the pan-tumor SLAB score matrix $M_{SLAB}^{Pan}$. Any genes with no detectable reads for a given sample had their SLAB score set to zero. We called this new matrix $M_{SLAB}^{NSCLC}$. For every pair of rows $\left(r_{p_i}^{Pan},r_{n_j}^{NSCLC}\right)$, where $r_{p_i}^{Pan}$ indicates the score vector for sample p_i∈P in the pan-tumor database and $r_{n_j}^{NSCLC}$ indicates the score vector for sample n_j∈N in the NSCLC out-of-sample dataset, we computed the Euclidean distance $D_{p_i,n_j}^{SLAB}$ that describes the similarity between these two samples with respect to their SLAB scores. We then computed the mean of $D_{p_i,n_j}^{SLAB}$ for the subset of the P datasets corresponding to each Spatial Class (SC1-9). Each NSCLC sample was assigned to the Spatial Class that minimized this mean distance.

Classification of NSCLC datasets using bulk expression and published gene sets

To determine whether classification of tumor datasets by either (1) bulk expression versus SLAB score, (2) previously published gene sets for NSCLC IO response, or (3) SpaCET-inferred cell type abundance was predictive of PFS in our NSCLC cohort, we performed the following analysis.

First, we computed aligned matrices as described in ‘Spatial lability pan-tumor classification’ for both the pan-tumor datasets and the NSCLC datasets where matrices contained either SpaCET-inferred cell type abundance, bulk expression data or SLAB score data. For bulk expression, we computed the mean spot-wise UMI count for any given gene. Second, we filtered the aligned matrices for subset of columns (genes) described by a particular gene set or used all columns for the ‘all genes’ analysis. Third, we computed the [16 x 246]-dimension distance matrix between the 16 rows (samples) in the NSCLC matrix and the 246 rows (samples) in the pan-tumor matrix. Fourth, K-means clustering with K = 2 was performed row-wise on this matrix to divide the NSCLC datasets into 2 groups based on their distance vectors to the pan-tumor datasets. K-means clustering was performed 100 times for each condition using different random seeds each time. Finally, the two classes of NSCLC datasets were applied to survival analysis (described below in ‘Survival analysis’) to determine if they were predictive of NSCLC ICB outcomes.

Alignment of ST-seq and mIF data

Coordinates were aligned between CODEX mIF data and ST-seq data generated from serial tissue sections as follows. First, the DAPI channel of the CODEX data and the H&E image of the ST-seq data were identified for alignment. The alignment process employed the Scale-Invariant Feature Transform (SIFT) algorithm, which identified key points in images and matched the feature descriptors of key points to identify corresponding pairs of points from different images.⁹⁹ Based on the matched points, an affine transformation was performed to map the coordinate system of the ST-seq data to that of the mIF data. We first converted the H&E images into grayscale and adjusted their contrast using Contrast Limited Adaptive Histogram Equalization (CLAHE; implemented in OpenCV¹⁰⁰). The SIFT algorithm was then applied to detect features in both the H&E and DAPI images. Feature matching was performed based on the SIFT descriptors, with manual adjustments to the feature matching ratio depending on the similarity of the images. A transformation matrix was estimated using the Random Sample Consensus (RANSAC) algorithm, allowing for rotation, translation, and scaling transformations. The RANSAC inlier threshold was also manually adjusted to accommodate varying degrees of distortion between images. Two of the eight tissues in which alignment was attempted could not be aligned because the SIFT algorithm could not identify sufficient matching features between the images (>7 matching features).

SpaCET

SpaCET estimates deconvoluted cell type proportions within spots of an ST-seq experiment.⁴² It requires the user to supply (1) the SpaceRanger gene count matrix as input and (2) a value for the ‘cancerType’ parameter to define the SpaCET library scRNA-seq datasets used for cell type definition. The ‘cancerType’ values chosen for each ST-seq dataset are listed in Table S11. Otherwise, default parameters and commands were used as per the repository instructions (https://data2intelligence.github.io/SpaCET/articles/visium_BC.html).

Pathway over-representation analysis (ORA)

For genes identified as differential between SGs (see Figure 2) or between Spatial Classes (see Figure 4), we conducted over-representation pathway analysis (ORA) for the set of Reactome pathways within the MSigDB database^101,102 (Table S12). ORA was performed using Enrichr with default parameters, which uses a Fisher exact test to compute enrichment of a gene list for a given pathway.¹⁰³ The background gene set used was the set of all genes with mapped reads in any sample. Correction for multiple hypothesis testing was implemented by using a false discovery rate threshold of <0.1.

Survival analysis

For survival analysis we used the R ‘survival’ package to model progression-free survival (PFS) as a function of possible confounder variables (Treatment regimen, PD-L1 status, somatic mutation status) or classification variables (PD-L1 multi-class, PD-L1 binary, ISL/ISI, bulk expression- and SLAB score-gene sets). For confounder analysis, outcomes were modeled using Cox’s univariate or multivariate proportional hazards model. For Kaplan-Meier survival curves stratified by classification variables, survival was estimated using the Kaplan-Meier method and reported p-values were calculated using the log rank statistical test. For censored data labeling, 1 indicates that PFS was observed while 0 indicates the patient was censored for PFS.

Pathologist annotation of CODEX mIF data

Nuclear segmentation and cell boundary definition

Following image acquisition and pre-processing (see ‘Experimental method details: CODEX multiplexed immunofluorescence’), we applied the neural network-based cell segmentation tool, DeepCell, on the DAPI channel for nuclei identification.¹⁰⁴ Next, these nuclei segmentation masks were used to estimate whole cell segmentation boundaries using the ‘skimage.morphology.binary_dilation’ function in the Python scikit-image package.¹⁰⁵ This function dilates nuclear segmentation boundaries by stochastically flipping pixels into the mask boundary with a probability equal to the fraction of positive neighboring pixels for 9 cycles. We then computed mean expression for each antibody across pixels within each whole cell segmentation boundary, which we define as the signal intensity ${Signal}_i^t$ for cell i and target t.

Cell-level quality control

Since there is technical variation in CODEX staining and imaging quality, we applied multiple quality control filters to eliminate cells with atypical quality characteristics. First, we defined for cell i the signal sum Σ_i, mean μ_i, standard deviation σ_i, and coefficient of variation CoV_i across the set of targets T, composed of DAPI + all antibodies in Table S3.

$${\mathrm{\Sigma }}_i=\sum _t{Signal}_i^{t}fort\in T$$ (Equation 47)

$${\mathrm{\mu }}_i=\frac{{\mathrm{\Sigma }}_i}{card\left(T\right)}$$ (Equation 48)

$${\mathrm{\sigma }}_i=\sqrt{\frac{\sum _t{\left({Signal}_i^t-{\mathrm{\mu }}_i\right)}^2}{card\left(T\right)}}$$ (Equation 49)

$${\text{CoV}}_i=\frac{{\mathrm{\sigma }}_i}{{\mathrm{\mu }}_i}$$ (Equation 50)

We then filtered cells for analysis by removing outliers for Σ_i, CoV_i, and ${Signal}_i^{DAPI}$ using manual thresholding of outlier thresholds and representative visual inspection to confirm low quality cells.

Annotation of cell types

Unsupervised clustering was performed by computing nearest neighbor distances (n_neighbors = 30) and Leiden clustering (resolution = 1) using the Python scanpy package.^106,107 Clustering was done simultaneously using all NSCLC mIF datasets. Clusters were annotated by a board-certified pathologist based on mean marker expression and manual inspection of raw mIF data. Following this, lymphocytes, macrophages, and indeterminate/mixed populations were subjected to sub-clustering and fine-level annotation. Finally, the initial annotations and fine annotations were merged to create a unified annotation of cell types across NSCLC mIF datasets (Table S4).

Annotation of neighborhood types

Unsupervised identification of neighborhood clusters was performed by 1) defining local regions consisting of the 25 nearest cells in physical space and 2) clustering these regions into classes based on the frequencies of cell annotations they contain. This was done by defining the number of classes to be either 10 (‘neighborhoods’) or 30 (‘sub-neighborhoods’). Finally, classes were annotated by a board-certified pathologist based on the mean frequencies of their member cell annotations and by manual inspection of raw mIF data (Table S4).

Markov Chain Monte Carlo (MCMC) simulation

CODEX mIF intensity normalization

Prior to using CODEX mIF intensities as an input to MCMC, we normalized signal intensities for (1) variation in local background and (2) variation in signal distribution between samples.

To correct for variation in local background, we divided each sample into 100 equally sized bins and used multi-Gaussian modeling for each target t∈T to identify the upper limits of that marker’s local null distribution. Let i and j represent the bin numbers in the x and y directions respectively. Then we denote cells_i,j as the set of cells in a given sample bin (i,j) and ${Signal}_{i,j}^t$ as the set of signal intensities for marker t for cells_i,j. We used the ‘mclust’ R package to fit 2 Gaussians to ${Signal}_{i,j}^t$ for all values of i, j, and t. Then we defined the upper bound ${Background}_{i,j}^t$ of the null distribution as the 95% percentile of that distribution for a given bin and marker. Finally, we subtracted ${Background}_{i,j}^t$ from ${Signal}_{i,j}^t$ as a correction for local background signal variation.

$$i,j{\in }_{\mathbb{Z}}\left\{1,2,3,...,10\right\}$$ (Equation 51)

$${Signal}_{i,j}^t\sim N\left({\mu }_1,{\sigma }_1^2\right)+N\left({\mu }_2,{\sigma }_2^2\right)where{\mu }_1<{\mu }_2$$ (Equation 52)

$${Background}_{i,j}^t={\mu }_1+1.645\ast \frac{{\sigma }_1}{\sqrt{card\left({cells}_{i.j}\right)}}$$ (Equation 53)

$${Norm}_{i,j}^t={Signal}_{i,j}^t-{Background}_{i,j}^t$$ (Equation 54)

Cell-level normalized marker intensity data is contained within Table S4.

MCMC data inputs

As depicted in Figure 6A, there were four representations of the mIF data that were used as inputs to the MCMC simulation: 1) mean marker intensity, 2) cell type abundance, 3) neighborhood abundance, and marker SLAB. For each representation, mIF data coordinates were aligned to ST-seq spot coordinates (see ‘Alignment of ST-seq and mIF data’), and only the intensity data and annotations corresponding to cells located within ST-seq spot boundaries were considered. We found that amongst the six datasets with aligned ST-seq and mIF data, the mean number of mIF cell segmentations per ST-seq by dataset ranged from 15.2 cells/spot to 23.3 cells/spot (Figure S7B).

For mean marker intensity, we computed the mean intensity for each marker across all cells within a dataset. For cell type and neighborhood abundance, we computed the frequency of each cell type or neighborhood type annotation across all cells within a dataset. For marker SLAB, we first computed the sum of marker intensities for all cells in a spot. This resulted in a matrix of summed marker intensities where each spot in a dataset is arranged in rows and each mIF marker is arranged in columns. This matrix and the ST-seq spot coordinate matrix were used as inputs for TumorSPACE to compute SGs, differential marker abundance across SGs, and marker-wide SLAB scores as described in ‘TumorSPACE: models and associated analysis’. With each representation, the final matrix used as input to MCMC had dimensions of 6 samples x f features, where f is the number of features for that data representation.

MCMC algorithm

To perform empirical feature selection so that tumor spatial similarity defined by genome-wide SLAB could be compared to the four mIF data representations as described in Figure 6, we applied a Markov Chain Monte Carlo (MCMC) approach. This was useful given the following properties of this task. First, this is a cardinality-contained optimization problem and therefore is NP-hard due to the discrete nature of feature selection. This requires solving the problem ‘in-shell’ for each cardinality ranging from one to the total number of features corresponding to a particular mIF representation. Furthermore, due to the lack of an analytical model that relates genome-wide SLAB to the mIF feature space, we set our objective ($\mathcal{L}$) as the correlations between SLAB properties (D^SLAB) and equivalent properties produced by our feature set (D^mIF). This correlation objective function is non-convex, meaning the search space possibly contains multiple local optima, thus rendering standard gradient-based optimization algorithms infeasible.

To address this, we created a Markov Chain Monte Carlo (MCMC) simulation framework as follows. For any cardinality ‘k’, the procedure begins by selecting a random subset of k features (S) referred to as ‘the seed’ out all possible k-membered subsets (S_k) of total mIF-feature space F_mIF. From there, the MCMC algorithm enters a ‘high-entropy burn-in’ phase of broad exploratory sampling for 10,000 steps during which it probabilistically accepts steps in order to allow the system to escape local optima and survey a wide range of feature selection possibilities with a bias toward ones that increase the objective. Following this period, the algorithm transitions to a more focused ‘low-entropy convergence’ phase of 15,000 steps by starting with the optimized configuration from the burn-in phase and fine-tuning the feature selection by only accepting small changes that increase the objective.

Let S_k be the set of all k-membered subsets of mIF Features (F_mIF), $\mathcal{L}$ denote the correlation objective to be maximized, S∗ denote the element of S_k that maximizes this objective, and D^mIF (S) be the SLAB distances produced by a an element S of S_k.

$$\mathcal{L}=Correlation\left({\mathit{D}}^{\mathit{m}\mathit{I}\mathit{F}}\left(S\right),{\mathit{D}}^{\mathit{S}\mathit{L}\mathit{A}\mathit{B}}\right)with{S}^{\ast }=\underset{S\in S_k}{\mathit{argmax}}\mathcal{L}$$ (Equation 55)

10× Visium CytAssist spatial transcriptomics (ST-seq)

Tissue quality was determined by isolation of RNA from FFPE using the Qiagen RNeasy FFPE kit. Samples were then analyzed for tissue extraction quality using the Agilent 2100 bio-analyzer and Agilent RNA-6000 pico kit. For each sample, a DV200 score – the fraction of RNA fragments >200 nucleotides in length – was calculated. Tissue quality for all samples was tested on unstained sections adjacent to the section used for ST-seq.

DLBCL samples were previously H&E stained. Imaging and coverslip removal were completed as described by 10× Protocol CG000518-Rev A and decrosslinking was performed according to 10× Protocol CG000520-Rev A.^108,109 NSCLC samples underwent deparaffinization, H&E staining, imaging, and decrosslinking according to CG000520-Rev B.¹⁰⁹ Sample imaging for all samples was performed using the Akoya Biosciences Vectra Polaris at 20× magnification.

We next performed the following steps as per either 10× Protocol CG000495-Rev A for the DLBCL samples or 10× Protocol CG000495-Rev E for the NSCLC samples.¹¹⁰ First, samples underwent probe hybridization with Visium Human Transcriptome Probe Set v2.0, followed by probe ligation, and associated washes (Table S13). Two native tissue slides and one Visium CytAssist 11 × 11 mm slide were then placed within the Visium CytAssist to enable RNA digestion, tissue removal, and transfer of ligated products onto the two fiducial frames of the Visium Slide. Next, we performed probe extension and elution off the Visium Slide, followed by pre-amplification and SPRIselect cleanup. For SPRIselect cleanup, DLBCL samples placed in only the ‘High’ position of the 10× magnetic separator, while NSCLC samples were placed in both ‘High’ and ‘Low’ positions according to CG000495-Rev E. To identify the optimal number of cycles for library amplification, we performed qPCR using Applied Biosciences QuantStudio 6 Pro as per CG000495-Rev E (Table S9). For this step, we included 0.5 μL of carboxy-X-rhodamine (ROX) with the DLBCL samples and not with the NSCLC samples. Sample Index PCR was run using the sample-specific optimal number of cycles, followed by: cleanup, Agilent TapeStation QC, sequencing, and demultiplexing using Bcl2fastq. Sample sequencing was performed on a NovaSeq 6000 for DLBCL samples and a NovaSeqX for NSCLC samples. Sample-specific parameters and QC are listed in Table S9. For DLBCL experiments, we used the Applied Biosystems Veriti 96 well thermocycler, while for NSCLC samples we used the Eppendorf Mastercycler ×50a and ×50I.

CODEX multiplexed immunofluorescence

Slide preparation

NSCLC samples were obtained as unstained slides mounted with 5 μm thickness formaldehyde-fixed, paraffin-embedded (FFPE) sections from the same patient biopsies as described in ‘Patient samples‘. Coverslips were coated with 0.1% poly-L-lysine solution prior to mounting tissue sections to enhance adherence. The prepared coverslips were washed and stored according to guidelines from the CODEX user manual.¹¹¹

Antibody preparation

Custom conjugated antibodies were conjugated using the CODEX conjugation kit as per the CODEX user manual (Table S3). Briefly, the antibody is (1) partially reduced to expose thiol ends of the antibody heavy chains, (2) conjugated with a CODEX barcode, (3) purified, and (4) added to Antibody Storage Solution for long-term stabilization. Subsequently, antibody conjugation is verified using sodium dodecyl sulfate-polyacrylamide gel electrophoresis and with QC staining.

Staining and data acquisition

Sample slides are stained following protocols in the CODEX User Manual. Briefly, samples are pretreated by heating at 60°C overnight, followed by deparaffinization, rehydration using ethanol washes, and antigen retrieval via immersion in Tris-EDTA pH 9.0 for 20 min. Samples are then blocked in staining buffer and incubated with the antibody cocktail for 3 h at room temperature. After incubation, samples are washed and fixed following the CODEX User Manual. Data acquisition was performed using the PhenoCycler-Fusion 2.0 with a 20× objective, resulting in a resolution of 0.5 μm/pixel.

Patient tumor PD-L1 IHC

FFPE biopsy samples were probed for PD-L1 expression using a qualitative immunohistochemical assay with the Dako 22C3 antibody (Pharm Dx kit). PD-L1 expression was classified using the Tumor Proportion Score (TPS), which represents the percentage of viable tumor cells that show partial or complete membrane staining. Normal background histiocytes served as internal controls to ensure quality of the PD-L1 staining. Quantification was performed by a board-certified pathologist as part of routine clinical care.

Patient somatic mutation testing

The molecular profiles of the tumor biopsies were analyzed using Oncoplus or Oncoscreen, two Next Generation Sequencing (NGS) assays.¹¹² A description of patient mutation status can be found in Table S8. Since the list of targeted genomic regions varied by the year in which testing was performed, a list of Oncoplus/Oncoscreen versions used for each patient as well as a list of the targeted genomic regions for each version can be found in Tables S8 and S14, respectively.

For the Oncoplus analysis, DNA was isolated from the samples using the QIAamp DNA Blood Mini Kit (Qiagen), fragmented, and prepared into a sequencing library with patient-specific indexes (HTP Library Preparation Kit, Kapa Biosystems). Targeted genomic regions were enriched using a panel of biotinylated oligonucleotides (SeqCap EZ, Roche Nimblegen) supplemented with additional oligonucleotides (xGen Lockdown Probes, IDT). The enriched libraries were then sequenced on an Illumina HiSeq 2500 system, and the data was analyzed via bioinformatics pipelines against the hg19 (GRCh37) human genome reference sequence.

For Oncoscreen, DNA was isolated from formalin-fixed paraffin-embedded (FFPE) tumor tissue using the QIAamp DNA FFPE Tissue Kit (Qiagen). DNA was quantified using the Qubit fluorometric assay (Thermo Fisher Scientific) and a quantitative PCR assay (hgDNA Quantitation and QC kit, KAPA Biosystems). Targeted genomic regions were amplified using multiplex PCR (Thermo Fisher Scientific); PCR products were used to prepare NGS libraries with patient-specific adapter index sequences (HTP Library Preparation Kit, KAPA Biosystems). The enriched libraries were then sequenced on an Illumina MiSeq system, and the data was analyzed via bioinformatics pipelines against the hg19 (GRCh37) human genome reference sequence.

Patient tumor volume measurements

For measurement of tumor volume changes over time, computed tomography (CT) imaging reports were obtained for patients in the NSCLC as permitted by the IRBs referenced in ‘Patient samples’. For patients with measurable disease at the time of treatment start (denoted as month zero), the largest lesion was identified and labeled the ‘index lesion’. Changes in index lesions were collected when described in serial reports by a board-certified radiologist as part of routine clinical care.

Quantification and statistical analysis

TumorSPACE was implemented in Julia (v1.9.0) using SpectralInference (v0.4.1), PhyloNetworks (v1.0.0), HypothesisTests (v0.11.3), NewickTree (v0.3.1), and BOOSTER (v0.4.2) for transfer bootstrap expectation support. Additional spatial transcriptomic and cell-type analyses were performed in R (v4.1.0) using Seurat (v4.4.0), spatstat (v3.0.8), SpaCET (v1.3.0), ape (v5.8.1), phangorn (v2.12.1), phytools (v2.5.2), castor (v1.8.5), mclust (v6.0.1), GSEABase (v1.56.0), and the Behera2025paper R package (aramanlab/Behera_et al._2025). Gene set analyses were performed in Python (v3.11.5) using gseapy (v1.1.10), numpy (v1.24.4), pandas (v1.5.3), scipy (v1.10.1), and statsmodels (v0.14.0). Visualizations were generated using ggplot2 (v3.5.1) in R.

Statistical analyses were conducted in R, Python, and Julia. Spatial Group (SG) inference was performed using TumorSPACE, which applies singular value decomposition (SVD) to spot-by-gene count matrices to construct spectral distance matrices, followed by hierarchical clustering to delineate SG domains; branch support was estimated by Transfer Bootstrap Expectation (TBE) using BOOSTER with multiplicative Gaussian noise injection (n = 10 replicates per SVD run). Pathway enrichment was assessed by gene set over-representation analysis and GSEA (gseapy; 20,000 permutations). For CODEX multiplex immunofluorescence data, local background intensity was corrected using Gaussian mixture modeling (mclust; G = 2); CODEX panel selection used a custom MCMC approach (25,000 iterations; n = 50 independent random seeds) with Pearson correlation as the energy function. Spatial clustering of SG domains was assessed using Ripley’s K with border correction (spatstat). The Wilcoxon rank-sum test was used to compare features between SG nodes and sibling subtrees, with empirical p-values estimated from 1,000 permutations; multiple comparisons were adjusted using the Benjamini-Hochberg method. Contextual concordance of SG biology across nested tree nodes was evaluated using the chi-square test with odds ratios and 95% confidence intervals. A p-value <0.05 was considered statistically significant.¹¹³ Exact values of n and precision measures for plotting are provided in the figure legends.

Published: August 28, 2026