A kinematic interpretation of spatial expression gradients from single-snapshot spatial transcriptomics

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Spatial transcriptomics measures gene expression across tissue position, but temporal or mechanistic interpretation of a spatial gradient requires an explicit model. We derive a kinematic interpretation for tissues with a stationary position-conditioned expression field and positive mean cell displacement along an anatomical axis. Under these assumptions, a gene’s gradient sign equals its net-production sign. The measured statistic remains a spatial gradient, and without an independent velocity estimate the framework does not recover absolute rates. We evaluate the framework on a human liver atlas with 16 standard-Visium sections, three matched Visium HD sections and companion single-nucleus RNA-seq; the primary cross-donor analysis uses eight live-donor sections. Gradient direction is reproducible: mean cross-donor correlation is 0.87 on a strict 66-gene panel and 0.67 on a broad 15,192-gene panel. On prespecified top-quartile subsets, cross-platform sign agreement is 14/14 genes for M2 and 13/14 for M6 ( n = 14 per donor); cross-pipeline agreement is 76%. Four diagnostics and a geometric argument show that the gene-gene coupling matrix is not stably identifiable or interpretable as a regulatory Jacobian from one sampled trajectory. In graded steatosis across four donors, GLUL , LYZ and ORM1 show consistent spatial-gradient responses to lipid, but wild-cluster calibration finds cluster-robust significance anticonservative; we report directional observations, not significant discoveries. On the mouse crypt-villus axis, all 15 canonical markers recover their expected directions on an anatomy-derived coordinate. The framework provides a reproducible, splicing-free estimator of spatial expression gradients applicable to imaging-based platforms. Under explicit steady-state and positive-flow assumptions, gradient direction has a kinematic interpretation as net-production direction; cross-sectional data establish gradient reproducibility, not time-resolved dynamics. Separating the observable from its conditional interpretation, and diagnosing the coupling matrix’s identification failure, defines both the method and its inferential boundary.