MINGLE: A Novel Probabilistic Model for Identifying Spatial Gradients and Multi-Neighborhood Membership in Spatial-Omics

Introduction: : Understanding spatial organization of cells within tissues is critical to inform better therapies. Advances in single-cell spatial technologies have enabled high-resolution mapping of cell phenotypes across tissues, revealing complex architectures of interactions across biological scales.
Current approaches in single-cell spatial biology describe hierarchical tissue structures by assigning cells to discrete categories. While many algorithms exist that can be used to define these categories, analysis of spatial organization relies only on classifiers that restrict cells to belong to one category at a time (Fig. 1a). Treating cells and higher-order tissue organizations as discrete states results in a loss of biologically important spatial organization such as gradients and anatomical or categorical “edges”.
To address the limitations of current spatial biology analysis, I created a novel Mixture-based Identification of Neighborhood Gradients with Likelihood Estimates (MINGLE) to probabilistically assign cells to multiple spatial categories simultaneously (Fig. 1b). Applying MINGLE to an annotated human intestine spatial-omics dataset, I quantitatively mapped spatial gradients along the intestine crypt, describing the differentiation from stem cells to epithelial subtypes. I also characterized edge cells at immune follicle light-dark zone transitions and interfaces between stromal and epithelial neighborhoods. Notably, over 12% of several immune, epithelial, and stromal neighborhoods had high membership probability in multiple neighborhoods, reflecting their role in neighborhood-neighborhood interactions and spatial organization. This represents the first quantitative and statistical framework to measure and compare spatial gradients, transition zones, and areas of biological mixing in our tissues, unlocking novel spatial analysis of patterns previously masked by discrete clustering approaches.

Materials and

Methods: : A CODEX human intestine dataset with cell type, neighborhood, community, and tissue unit annotations (Hickey et al. 2023) was used for analysis.
The 10 nearest neighbors and counts of each neighboring cell type were assigned to each cell using a K-nearest neighbors (KNN) function and spatial coordinates (Fig. 1a).
For each annotated neighborhood, the KNN output was filtered for cells in that neighborhood. Then, for each neighboring cell type, the distribution of neighbor counts was computed and served as the ground truth means and spreads for the gaussian mixture model (GMM).
Using these gaussian distributions, each cell’s neighbor composition was compared to the ground truth using a gaussian probability density function (PDF) for each cell type feature. The unnormalized probability of a cell belonging to each neighborhood was calculated as the product of the PDFs across all cell type features and normalized across all possible neighborhoods, producing a probability vector for each cell, quantifying the likelihood of membership in each neighborhood.
The probability associated with each cell’s assigned neighborhood was binned into a range: low (0-0.33), medium (0.34-0.66), and high (0.67-1). For each cell, the 100 nearest neighbors were identified using KNN, and their probability bin labels were counted. To identify gradients of probabilities, K-means clustering of KNN output was applied to group cells into 10 clusters.
A threshold of 0.25 defined positive neighborhood assignment with cells classified as positive for more than one neighborhood considered edge cells. Network graphs were generated to visualize neighborhood pairs above the threshold.

Results, Conclusions, and Discussions:: Applying MINGLE to annotated CODEX data revealed structured spatial probability distributions in human intestine tissue. Cells with low assigned neighborhood probabilities were consistently located at follicle borders and within stromal and epithelial layers, while high probability cells clustered in follicle cores (Fig. 1c-e). These patterns demonstrate that MINGLE effectively captures spatial gradients and edges—features omitted with traditional discrete clustering methods.
To quantify these spatial patterns, cells were grouped into 10 clusters based on the binned neighborhood probabilities of their nearest neighbors (Fig. 2a, b). These clusters formed concentric bands from the follicle center to the periphery, showing a clear gradient of decreasing neighborhood probability (Fig. 2c-i). The smooth transition from inner to outer follicle neighborhoods validated MINGLE’s ability to capture biological transition zones across immune follicle structures (Fig. 2j, k).
Cells with a probability greater than 0.25 (Fig. 3b) in multiple neighborhoods were enriched at follicle boundaries and in epithelial and stromal areas, suggesting a role in neighborhood-neighborhood interactions and structural layering (Fig 3c). Notably, CD4+ T cells, dendritic cells, NK cells, and macrophages showed overlap with multiple neighborhoods (Fig 3d). These patterns align with known broad membership to multiple tissue structures, providing further biological validation for MINGLE’s outputs.
Neighborhood pairs with high overlap, including secretory and transit amplifying zones, reflected lineage relationships within the intestinal crypt but not by region (Fig. 3e, f). Network analysis of most abundant neighborhood pairs in multiply positive cells revealed three core neighborhood units—epithelial, immune, and stromal/vascular—connected though a plasma-cell-enriched node, highlighting higher-order tissue hierarchies and MINGLE’s potential to identify novel spatial interactions (Fig 3g-j).
Overall, MINGLE provides a powerful alternative to discrete clustering by assigning probabilistic spatial identities, uncovering gradients, transition zones, and areas of uncertainty. Its modular, adaptable design makes it applicable across biological scales and spatial modalities including transcriptomics and metabolomics. By quantifying spatial probabilities and uncertainties at single-cell resolution, this framework enables robust, statistical comparisons to understand biology at the interface. MINGLE offers a major advancement for spatial analysis, enabling novel understanding of organization, function, and disease.

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