[论文解读] TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

Alexander Tong, Jessie Huang+3 more|arXiv (Cornell University)|Feb 9, 2020

Slime Mold and Myxomycetes Research被引用 47

一句话总结

TrajectoryNet 提出了一种带有能量项和生物先验的连续正规化流框架，用于建模随时间点分布的细胞状态之间的动态最优传输，能够从横截面 scRNA-seq 数据获得平滑、非线性的细胞轨迹。

ABSTRACT

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model continuous dynamics and non-linear paths that entities can take in these systems. To address this issue, we establish a link between continuous normalizing flows and dynamic optimal transport, that allows us to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present TrajectoryNet, which controls the continuous paths taken between distributions to produce dynamic optimal transport. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.

研究动机与目标

• Motivate interpolation of time-varying cellular distributions from static snapshots in scRNA-seq data.
• Develop a dynamic OT approach that yields continuous trajectories rather than pairwise-timepoint mappings.
• Leverage continuous normalizing flows within a neural ODE framework to approximate dynamic transport.
• Incorporate priors (growth, manifold density, velocity) to reflect biological constraints and unbalanced transport.
• Demonstrate improved distributional interpolation over static OT baselines on synthetic and real single-cell datasets.

提出的方法

• Formulate dynamic OT via regularized continuous normalizing flows that minimize an energy term modeling path length.
• Use the CNF x'(t)=f_theta(x(t),t) with a loss that includes -log p(x_t) and an energy term lambda_e * integral ||f||^2 plus a Jacobian penalty to discourage curvature.
• Introduce KL divergence penalty to align final distribution with target while allowing a transport path.
• Incorporate biological priors: L_density to follow data manifolds, L_velocity to align local velocity direction (RNA velocity), and L_growth to handle unbalanced transport.
• Extend to multiple timepoints with a single smooth flow rather than pairwise OT between successive timepoints.
• Train with backward adjoint method and a simple feedforward network to parameterize f_theta, using a dynamic OT objective plus priors.

实验结果

研究问题

• RQ1 Can dynamic optimal transport be efficiently approximated in high dimensions using continuous normalizing flows?
• RQ2 Does regularization via energy, Jacobian, and biological priors yield more realistic, manifold-aligned trajectories between timepoints in scRNA-seq data?
• RQ3 How does TrajectoryNet compare to static OT and other interpolation methods for multi-timepoint single-cell datasets in terms of distributional accuracy?
• RQ4 Can the learned dynamics provide interpretable insights into drivers of cellular differentiation and state transitions?

主要发现

• TrajectoryNet outperforms static OT baselines in distribution interpolation (EMD) on synthetic and scRNA-seq datasets.
• Adding density and velocity priors improves alignment to underlying manifold structure and local directionality of dynamics.
• The energy and Jacobian penalties encourage smoother, more direct paths that better approximate the optimal transport flow over time.
• Unbalanced transport via a learned growth term enables mass variation across timepoints, reflecting cellular proliferation or death.
• Applied to mouse cortex and Embryoid body scRNA-seq data, TrajectoryNet yields trajectories that align with known developmental progressions and recovers plausible gene-space trajectories.