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Spatial velocity

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tagsrna-velocity, spatial, migration, gnn, physical-units

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Spatial velocity

中文導讀

Spatial velocity 指兩件相關的事:(1) 把 transcription rate 寫成「細胞自己 + 空間鄰居」的函數 (spatially coupled,用 GNN),(2) 推出 cell 在組織裡的 migration velocity——空間位置對時間的 變化率,有物理單位(μm/hour)。代表作 TopoVelo。對 physical-time grounding 的意義很特別:空間 尺度是真的(μm 量得到),所以 migration velocity 可以對 live-cell imaging 驗證;但時間尺度還是 得借假設(例如 gene cycle = 20h)才湊得出 μm/hour。也就是 space 有 anchor、time 沒有——這正好凸顯 physical-time 問題的核心是 時間 那一軸。

Two ideas under one name

  1. Spatially coupled transcription. Make a gene’s transcription rate a function of a cell’s own state and its spatial neighbors’ states, via a graph neural network over a tissue graph. This is the spatial counterpart of GRN coupling (grn-informed-velocity): context = neighbors instead of regulators. Captures ligand–receptor signaling, gap junctions, diffusible morphogens.
  2. Cell (migration) velocity. The rate of change of a cell’s spatial position over time — distinct from RNA (expression) velocity. In real spatial-transcriptomic units this is a physical migration speed (μm/hour).

Why it matters for physical time

Spatial velocity splits the grounding problem cleanly:

  • The spatial scale is measured (μm cell–cell distances), so migration velocity can be validated against an external physical measurement — TopoVelo’s ~10 μm/h cortical estimate matches live-cell-imaging neuron migration rates.
  • The temporal scale is not measured — to express velocity per hour, TopoVelo imports the convention that a gene’s induction/repression cycle takes 20 hours. The absolute time still rests on an assumption, exactly the splicing-kinetics-ode scale degeneracy.

So spatial coupling gives a real anchor on space but not on time — sharpening that the open problem in physical-time-grounding is specifically the temporal axis. This is directly relevant to FlowVelo: a spatial or transport prior may anchor geometry/space, but metric time still needs its own signal.

Other spatial-velocity methods

TopoVelo is the case study here; the family is growing — spVelo (Genome Biology 2025) targets multi-batch spatial data, and TopoVelo’s benchmarks also cite STT, Spateo, Cell2fate and GASTON. Most have not yet been read through the physical-time lens (see their TODO notes).

TopoVelo · spVelo · grn-informed-velocity · splicing-kinetics-ode · physical-time-grounding · metabolic-labeling · latent-time · RNA velocity · FlowVelo · optimal-transport

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