Phenotype Interactions

Phenotype Interactions computes spatial association statistics for all phenotype pairs:

1. Input — Cell positions (from coded image centroids) and cell type labels (from phenotyping).
2. Distance computation — For each pair of cells (of different types), compute the Euclidean distance between them.
3. Observed frequency — Count how many cross-type cell pairs fall within each distance threshold. For example: how many CD8+ T cells are within 30 µm of a CK+ tumor cell?
4. Expected frequency — Compute the expected count under a null model (typically, random relabeling of cell types while preserving positions). This controls for overall cell density.
5. Significance test — Compare observed to expected using a statistical test. Significantly more than expected → attraction (co-location). Significantly fewer → repulsion (exclusion). Not significantly different → spatial independence.

Spatial point processes (MIT Statistical Models): A collection of typed cell positions is a marked spatial point process. The fundamental question is whether the marks (cell types) are spatially independent of each other — does knowing a cell's position tell you anything about what type it is? The Poisson null model assumes positions and marks are independent. Phenotype Interactions tests this null hypothesis using observed cross-type pair counts versus expected counts under the null.

The K-function framework (Ripley): Ripley's K-function K(r) counts the expected number of points within distance r of a typical point, normalized by overall density. When K(r) exceeds the Poisson expectation (πr²), points are clustered at scale r. When K(r) is less, points are dispersed. The cross-type variant K_ij(r) measures the spatial association between types i and j. Phenotype Interactions implements variants of this framework to quantify pairwise spatial associations.

Statistical significance testing (Dilbilir): Simply observing that two cell types are near each other doesn't prove interaction — it could be chance. Statistical methods compare the observed spatial pattern to a null distribution generated by Monte Carlo simulation (randomly permuting cell type labels many times). The observed interaction is significant only if it falls outside the central 95% of the null distribution. This controls for confounding factors like uneven cell density and non-uniform tissue geometry.

Biological interpretation: Attraction between CD8+ T cells and tumor cells suggests active immune recognition and effector function. Repulsion might indicate immune exclusion mechanisms (PD-L1 expression, physical barriers, immunosuppressive cytokines). These spatial patterns carry prognostic and predictive information — immunotherapy works better in immune-inflamed tumors (attraction) than immune-excluded tumors (repulsion).

Characterizing tumor-immune spatial relationships in a melanoma cohort:

1. 5 phenotypes: Melanoma (SOX10+), CD8+ T cell, CD4+ T cell, Macrophage (CD68+), Treg (FOXP3+)
2. Phenotype Interactions at 20, 50, 100 µm distance thresholds
3. Results:
   • CD8+ ↔ Melanoma: Attraction at 20 µm (p < 0.01) — active engagement
   • Treg ↔ Melanoma: Attraction at 50 µm (p < 0.01) — immunosuppressive niche
   • CD8+ ↔ Treg: Attraction at 20 µm (p < 0.05) — Tregs suppress CD8+ cells in proximity
   • CD4+ ↔ Melanoma: Repulsion at 20 µm (p < 0.05) — excluded from direct contact

The interaction matrix reveals the spatial social network: CD8+ T cells engage tumor cells directly, but regulatory T cells cluster nearby — potentially suppressing the anti-tumor response.