Table 1 A comparative table of mathematical framework for modeling spatiotemporal scRNA-seq data
From: Deciphering cell-fate trajectories using spatiotemporal single-cell transcriptomic data
Mathematical framework | Core goal | Advantages | Limitations |
|---|---|---|---|
Static OT | Map cells across time points. | Provide baseline matching of cell states between two discrete snapshots. | Deliver a static map; no continuous trajectories or temporal dynamics. |
Dynamical OT | Infer velocity along trajectories. | Yield continuous, kinetic-consistent trajectories and a velocity field in gene space. | Assume mass conservation—ignores proliferation, death, and stochasticity. |
GWOT | Align cell-state across conditions. | Match datasets without shared features by preserving intra-condition geometry. | The dynamical form remains unclear; do not generate continuous trajectory |
Dynamical Unbalanced OT | Infer velocity and proliferation. | Add a source-sink term to capture net growth/death while keeping continuous paths. | Treat dynamics as deterministic; stochastic fluctuations remain unmodeled. |
Mean-field Schrödinger bridge | Infer velocity, stochasticity, and interaction. | Introduce both Brownian noise and cell-cell interaction forces within one framework. | Require prior knowledge of cell-cell interaction. |
Regularized unbalanced OT | Infer velocity, proliferation, and stochasticity. | Combine diffusion, creation/destruction, and continuous paths in a single objective. | Neglect cell-cell communication such that cellular interaction effects are absent. |
Unbalanced mean-field Schrödinger bridge | Infer velocity, proliferation, stochasticity, and interaction. | Unified model that simultaneously handles noise, net growth, and interaction forces. | Require prior knowledge of cell-cell interaction. |
Hamilton–Jacobi–Bellman equation | Simplify the difficulty of numerical solution. | Reduce vector-field optimization to learning one scalar field; faster, more stable. | Requires computing second-order spatial derivatives, making numerical solution costly. |
Rigid body transformation invariant OT | Map cells and infers velocity in unpaired spatiotemporal data | Simultaneously infer the rigid spatial transformation and optimal transport mapping for joint alignment of spatial coordinates and gene expression. | Limited to rigid transformations; do not correct nonrigid tissue deformation or local morphogenesis. |
