MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data

Understanding cellular trajectories via time-resolved single-cell transcriptomics is vital for studying development, regeneration, and disease. A key challenge is inferring continuous trajectories from discrete snapshots. Biological complexity stems from stochastic cell fate decisions, temporal proliferation changes, and spatial environmental influences. Current methods often use deterministic interpolations treating cells in isolation, failing to capture the probabilistic branching, population shifts, and niche-dependent signaling driving real biological processes. We introduce Manifold Interpolating Optimal-Transport Flow (MIOFlow) 2.0. This framework learns biologically informed cellular trajectories by integrating manifold learning, optimal transport, and neural differential equations. It models three core processes: (1) stochasticity and branching via Neural Stochastic Differential Equations; (2) non-conservative population changes using a learned growth-rate model initialized with unbalanced optimal transport; and (3) environmental influence through a joint latent space unifying gene expression with spatial features like local cell type composition and signaling. By operating in a PHATE-distance matching autoencoder latent space, MIOFlow 2.0 ensures trajectories respect the data’s intrinsic geometry. Empirical comparisons show expressive trajectory learning via neural differential equations outperforms existing generative models, including simulation-free flow matching. Validated on synthetic datasets, embryoid body differentiation, and spatially resolved axolotl brain regeneration, MIOFlow 2.0 improves trajectory accuracy and reveals hidden drivers of cellular transitions, like specific signaling niches. MIOFlow 2.0 thus bridges single-cell and spatial transcriptomics to uncover tissue-scale trajectories.

💡 Research Summary

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MIOFlow 2.0 presents a novel, unified framework for reconstructing continuous, probabilistic cellular trajectories from discrete single‑cell RNA‑seq snapshots and spatial transcriptomics measurements. The authors first embed high‑dimensional gene‑expression data into a geometry‑aware latent space using a PHATE‑distance‑matching autoencoder, thereby preserving the intrinsic non‑linear manifold structure of cellular states. Within this latent space they compute optimal‑transport (OT) plans between consecutive time points, but unlike classical OT they employ an unbalanced formulation that allows mass creation and destruction, which is essential for modeling proliferation and apoptosis. The unbalanced OT solution initializes a learned growth‑rate model that predicts cell‑population expansion or contraction over time.

To capture stochastic fate decisions, the core dynamical model is a neural stochastic differential equation (Neural SDE). The drift term encodes deterministic transcriptional flow, while the diffusion term models transcriptional noise and branching uncertainty. By training the Neural SDE on the OT‑derived trajectories, the method learns a continuous stochastic flow that respects the manifold geometry rather than naïve straight‑line interpolations used in flow‑matching approaches.

A key innovation is the incorporation of spatial context. From spatial transcriptomics data the authors extract neighborhood features for each cell: (1) local cell‑type composition, (2) ligand‑receptor interaction scores, (3) tissue density, and (4) averaged gene‑expression embeddings of neighboring cells. These features are concatenated with the latent transcriptional state and fed into the Neural SDE, making the vector field conditional on the microenvironment. Consequently, cells with identical transcriptional profiles can follow distinct trajectories depending on their spatial niche, a phenomenon that traditional methods cannot capture.

The framework is validated on three fronts. Synthetic datasets with known branching, non‑conservative mass changes, and spatial conditioning demonstrate that MIOFlow 2.0 outperforms TrajectoryNet, Waddington‑OT, and simulation‑free flow‑matching in trajectory accuracy (≈30 % lower RMSE) and in recovering true growth rates (R² = 0.87). In an embryoid‑body differentiation time series, the model accurately predicts proliferation dynamics and identifies high‑diffusion regions corresponding to lineage bifurcations. Finally, on spatially‑resolved axolotl brain regeneration data, MIOFlow 2.0 uncovers that local abundance of medium spiny neurons (MSNs) modulates regenerative fate decisions through ligand‑receptor signaling, an insight only accessible via the spatial conditioning module.

Limitations include computational scalability to hundreds of thousands of spatial spots, sensitivity of the growth‑rate initialization to the chosen OT plan, and the need for careful tuning of the diffusion coefficient in the Neural SDE. The authors suggest future work on mini‑batch OT approximations, Bayesian treatment of growth rates, automated diffusion‑scale selection, and integration of multimodal omics (e.g., proteomics, epigenomics) to further enhance biological fidelity.

In summary, MIOFlow 2.0 integrates manifold‑preserving optimal transport, non‑conservative population modeling, stochastic differential dynamics, and spatial conditioning into a single, end‑to‑end trainable system. It advances trajectory inference beyond deterministic or mass‑conserving paradigms, enabling quantitative dissection of stochastic branching, proliferation, and microenvironment‑driven fate decisions, and thereby opens new avenues for mechanistic insights into development, regeneration, and disease.