Trajectory Inference

Assigns each cell a pseudotime value representing its position along a biological continuum rather than real clock time. Cells are ordered from least differentiated (stem-like) to most differentiated (terminal) states. The root of the trajectory is typically defined by the user based on prior biological knowledge, such as the expression of known progenitor markers. Monocle 3 and Slingshot are widely used implementations that construct minimum spanning trees or principal curves through the high-dimensional expression space.

Cells are represented as nodes in a nearest-neighbor graph where edges connect transcriptionally similar cells. Trajectory inference algorithms then learn a principal graph that passes through the densest regions of the data manifold. Methods like PAGA (Partition-based Graph Abstraction) generate coarse-grained topologies that preserve both continuous and disconnected structures, enabling the reconstruction of complex topologies including bifurcations, multifurcations, and convergent differentiation paths.

Extends static trajectory inference by incorporating splicing dynamics to predict the future transcriptional state of each cell. By distinguishing between unspliced (nascent) and spliced (mature) mRNA reads, RNA velocity computes a vector field that indicates the direction and speed of transcriptional change. Tools like scVelo and velocyto model these dynamics using differential equations, resolving directional ambiguity in trajectories where static pseudotime alone cannot distinguish between differentiation and dedifferentiation.

Identifies genes whose expression changes as a function of pseudotime using generalized additive models or tradeSeq's negative binomial regression. This analysis reveals the transcriptional cascades driving lineage commitment. Key outputs include:

Determines the global structure of the differentiation landscape, including the number of lineages, branch points, and terminal fates. Slingshot identifies lineages as smooth curves through clusters, while Monocle learns a principal tree. CellRank combines RNA velocity with Markov state modeling to compute fate probabilities for each cell, quantifying the likelihood of reaching each terminal state. This enables probabilistic fate mapping rather than deterministic assignment.

Trajectory inference provides a computational realization of Waddington's epigenetic landscape, where cells are visualized as marbles rolling downhill through valleys representing developmental paths. Branch points correspond to bifurcations where cells commit to distinct lineages. Modern methods like STREAM and Monocle project cells into low-dimensional spaces that recapitulate this landscape, enabling intuitive visualization of lineage hierarchies and cell fate decisions.

A quantitative measure of a cell's progression along a continuous biological process, such as differentiation or cell cycle, inferred from transcriptomic similarity rather than real clock time. Pseudotime assigns each cell a scalar value representing its position along a trajectory, with the root typically set to the earliest progenitor state. Unlike real time, pseudotime is a latent dimension reconstructed computationally and has no inherent units. It enables the ordering of cells along a continuum, revealing gene expression cascades that drive lineage commitment.

A computational method that predicts the future transcriptional state of individual cells by distinguishing between unspliced (nascent) and spliced (mature) mRNA reads. The ratio of unspliced to spliced transcripts for each gene provides a directional vector indicating whether that gene is being up- or down-regulated. When aggregated across the transcriptome, these vectors form a velocity field that predicts cellular transitions, enabling the inference of directed trajectories without requiring assumptions about start or end states.

A trajectory inference algorithm that computes pseudotime by modeling cellular transitions as a diffusion process on a nearest-neighbor graph. DPT calculates the probability of a random walk reaching each cell from a user-defined root, producing a robust distance metric that captures branching lineages. Unlike linear ordering methods, DPT naturally accommodates complex topologies including bifurcations and multifurcations, making it well-suited for developmental systems with multiple terminal fates.

A graph-theoretic structure that connects all cells in a reduced-dimensional space using the minimum possible total edge weight, forming a skeleton of the differentiation landscape. In trajectory inference, MST is often constructed on cluster centroids to identify lineage relationships and branching points. While computationally efficient, MST-based methods can oversimplify complex topologies and are sensitive to noise, leading modern tools to prefer probabilistic or principal graph approaches.

A conceptual metaphor for cellular differentiation in which a marble (cell) rolls down a branching valley, with bifurcations representing lineage commitment decisions. In computational terms, Waddington's landscape is modeled as a potential function where stable cell states occupy valleys (attractors) and transitions traverse ridges. Modern trajectory inference tools aim to reconstruct this epigenetic landscape from transcriptomic data, quantifying the stability of intermediate states and the barriers between lineages.

A method that constructs a coarse-grained graph representation of single-cell data by estimating connectivity between clusters rather than individual cells. PAGA preserves both continuous transitions and discrete clustering structure, generating a topology-preserving map of the data manifold. It is particularly effective for resolving complex differentiation hierarchies with multiple branch points and for visualizing high-level lineage relationships while maintaining statistical robustness against noise.