The framework, called GRNvelo, was developed by Dongyan Zhang, Jinan Li, Qing Nie, and Xiaoqiang Sun and published in Molecular Systems Biology. It tackles a problem that has frustrated computational biologists for years: single-cell RNA sequencing gives researchers exquisite snapshots of gene expression in thousands of individual cells, but those snapshots are static. Inferring the dynamic trajectories that connect them, and identifying the regulatory genes that steer those trajectories, has remained a major methodological hurdle. Existing tools such as Monocle and TSCAN reconstruct developmental paths by fitting curves through reduced-dimensional data, but they struggle with reversible transitions, branching differentiation, and the nonlinear behavior that characterizes real biological systems.

What sets GRNvelo apart is its multiscale design. At the level of the individual cell, it models gene regulation using nonlinear ordinary differential equations built on Hill functions, the standard mathematical language for describing how transcription factors activate or repress their targets. At the level of the cell population, it employs a partial differential equation that captures how the density of cells in different phenotypic states changes over time, incorporating both proliferation and random phenotypic drift. Through rigorous mathematical analysis, the authors proved that under appropriate conditions the single-cell gene regulatory velocity and the population-level phenotypic transition velocity are formally equivalent, allowing both scales to be unified in a single ODE-PDE system.

To make this ambitious model computationally tractable, the team turned to physics-informed neural networks, or PINNs, a machine learning approach that embeds physical laws directly into the training of neural networks. GRNvelo operates through two cooperating modules. The first, called TC-PINN, jointly infers the gene regulatory velocity of each cell and its latent time, a continuous variable that aligns cells along their developmental course while remaining anchored to the actual experimental time points at which the data were collected. A structured temporal constraint ensures that the inferred latent time stays biologically plausible, mitigating the overfitting that plagues traditional methods when data are sparse. The second module, MP-PINN, refines the velocity estimates within the context of population dynamics, jointly optimizing cell density, velocity, and growth rate so that the reconstructed trajectories respect both the gene regulatory equations and the physical constraints of cell proliferation and competition.

The validation began with synthetic data. The researchers simulated a simple three-gene network with a negative feedback loop and a more complex ten-gene network drawn from the DREAM4 benchmark, generating trajectories with stochastic differential equations. GRNvelo reconstructed cellular velocities, trajectories, growth patterns, and the underlying regulatory networks with striking accuracy. For the three-gene system, the correlation between inferred latent time and true time reached 0.81, and for the ten-gene network it climbed to 0.97. The method also proved robust to noise, maintaining stable performance at noise levels up to 0.06, and it performed comparably on data generated by the Gillespie algorithm, a fundamentally different stochastic simulation framework, suggesting that its success does not depend on any particular modeling assumption.

Benchmarking against state-of-the-art competitors, including TrajectoryNet, MIOFlow, TIGON, and PI-SDE, GRNvelo achieved the best overall velocity reconstruction and temporal accuracy across both synthetic systems. It also outperformed ten dedicated gene regulatory network inference methods, including GENIE3, SINCERITIES, and CellOracle, in reconstructing the true network topology. Remarkably, when tested on simulation data generated under cooperative gene interaction dynamics that the model was never trained on, GRNvelo still correctly identified population-specific growth patterns and the key growth-regulating genes, evidence of genuine generalization capability rather than mere curve fitting.

The real-world tests were equally demanding. Applying GRNvelo to a dataset of 51,274 cells spanning eight time points of human pancreatic beta-cell differentiation, the framework accurately reconstructed all four known differentiation trajectories, and its inferred latent time correlated with experimental time with a Pearson coefficient of 0.627, higher than any competing method. The reconstructed growth dynamics captured the characteristic slowdown of proliferation during endocrine differentiation and its later recovery, matching published biological observations. In a second validation using murine hematopoiesis data with lineage tracing, GRNvelo correctly predicted the bifurcation of progenitors into neutrophil and monocyte fates, and its inferred growth rates correlated strongly with ground-truth clonal measurements.

Perhaps the most striking demonstrations came from perturbation experiments. In CD8 T cells responding to acute viral infection, the team used GRNvelo to simulate the knockout of 39 genes in silico, and the predicted effects correlated with experimental perturbation data at a Pearson coefficient of 0.80. The model predicted that removing KLF2 would redirect differentiating T cells away from the effector fate and toward exhaustion, a prediction that matched experimental observations of accumulating exhausted cell populations. Simulating the combined loss of TCF7 and LEF1 revealed a different phenotype: rather than pushing cells toward exhaustion, the double knockout depleted the memory T cell pool and skewed cells toward a terminal effector state, consistent with the known cooperative role of these transcription factors in memory formation. In drug-resistant lung cancer cells, the framework predicted that adding crizotinib to erlotinib treatment would lock surviving tumor cells in a quiescent, vulnerable drug-tolerant state rather than allowing them to progress to a proliferative resistant phenotype, and that early combination therapy was decisively more effective than delayed administration.

The implications reach well beyond the specific systems studied. By simultaneously outputting cell velocity, latent time, trajectories, growth patterns, and gene regulatory networks within a unified framework, GRNvelo offers biologists a computational laboratory for testing hypotheses before running experiments: predicting responses to multi-gene knockouts, optimizing the timing of drug combinations, and identifying the key regulators of fate transitions. The authors acknowledge limitations, including the method’s reliance on time-series data and its current lack of explicit spatial or cell-cell communication modeling, and they point toward integration with spatial transcriptomics as a future direction. But the vision they articulate is ambitious: a multiscale, physics-informed approach to cellular dynamics that could contribute to the emerging paradigm of AI virtual cells, bringing researchers closer to simulating, and ultimately steering, the fundamental decisions that govern life at the single-cell level.

Subject of Research: A multiscale machine learning framework for inferring gene regulatory network-driven cell fate dynamics from single-cell transcriptomics data

Article Title: Multiscale learning of gene network-driven phenotypic dynamics of single cells

Article References: Zhang, D., Li, J., Nie, Q., & Sun, X. (2026). Multiscale learning of gene network-driven phenotypic dynamics of single cells. Molecular Systems Biology, 22(8), 1333-1359. https://doi.org/10.1038/s44320-026-00220-x

Image Credits: AI Generated

DOI: 10.1038/s44320-026-00220-x

Keywords: GRNvelo, gene regulatory networks, single-cell RNA sequencing, physics-informed neural networks, cell fate, trajectory inference, latent time, cell population dynamics, perturbation prediction, computational biology, pancreatic beta-cell differentiation, drug resistance