Trajectory Inference

Monocle uses reversed graph embedding to learn a principal tree structure through high-dimensional gene expression space. It orders cells by projecting them onto the tree and calculating their geodesic distance from a user-defined root state.

• Key innovation: Learns branching trajectories without prior knowledge of marker genes
• Output: A minimum spanning tree on cells with pseudotime assignments
• DDRTree: The core dimensionality reduction algorithm that learns tree-structured manifolds
• Application: Widely used for discovering novel branching points in differentiation cascades

Monocle 3 extends this with UMAP initialization and partition-based graph abstraction for scaling to millions of cells.

Slingshot infers lineage hierarchies by fitting simultaneous principal curves through clusters in a reduced-dimensional space. It identifies the global lineage structure by constructing a minimum spanning tree on cluster centers, then smooths curves through individual cells.

• Key innovation: Simultaneous curve fitting handles multiple lineages without iterative pruning
• Input: Requires prior clustering and dimensionality reduction
• Output: Smooth curves with pseudotime values and lineage assignment weights for each cell
• Flexibility: Agnostic to the dimensionality reduction method used

Slingshot excels at reconstructing topologically simple trajectories with clear branching points, making it a robust default choice for many single-cell studies.

RNA velocity predicts the future transcriptional state of individual cells by modeling the ratio of unspliced to spliced mRNA. This ratio captures the instantaneous rate of gene expression change, providing a directional vector on the transcriptional manifold.

• Key innovation: Infers directionality without requiring a time series or endpoint states
• Mechanism: Unspliced mRNA indicates nascent transcription; spliced mRNA indicates mature transcripts
• Output: A velocity vector field overlaid on embeddings, showing predicted cellular transitions
• Extensions: scVelo generalizes this with a likelihood-based dynamical model

RNA velocity is fundamentally different from pseudotime methods because it predicts future states rather than ordering past observations, enabling the identification of driver genes and transient populations.

PAGA constructs a coarse-grained graph where nodes represent clusters and edge weights quantify connectivity between them. It measures connectivity by comparing the actual number of inter-cluster edges in a k-nearest neighbor graph against a random expectation.

• Key innovation: Provides a statistically interpretable connectivity measure (PAGA connectivity > threshold indicates connected lineages)
• Topology preservation: Resolves complex topologies including cycles and disconnected components
• Integration: Often combined with diffusion pseudotime for ordering within connected components
• Scalability: Designed for atlas-scale datasets with hundreds of cell types

PAGA is particularly valuable for mapping the global topology of complex differentiation landscapes before applying finer-grained trajectory methods.

DPT computes pseudotime as the diffusion distance from a root cell through a random walk on a cell-cell similarity graph. It captures the probabilistic paths a random walker would take, naturally handling noisy data and multiple pathways.

• Key innovation: Robust to noise because it considers all possible paths weighted by probability
• Mechanism: Builds a transition matrix from a k-nearest neighbor graph, then computes distances between diffusion components
• Output: Pseudotime ordering and diffusion components that separate major lineages
• Branch detection: Identifies branching points by analyzing anti-correlated diffusion components

DPT is implemented in Scanpy and is often used alongside PAGA for comprehensive trajectory analysis in single-cell atlases.

Waddington-OT applies optimal transport theory to infer developmental trajectories by finding the most efficient mapping between cell populations at consecutive time points. It minimizes a cost function based on gene expression similarity while respecting growth and death rates.

• Key innovation: Explicitly models temporal couplings and cell proliferation
• Input: Requires time-series single-cell data with known collection times
• Output: Ancestor-descendant relationships with probabilistic couplings
• Temporal resolution: Reconstructs continuous trajectories by interpolating between measured time points

This method is uniquely suited for time-course experiments where cells are sampled at defined intervals, providing a mathematically rigorous framework for inferring cellular flows.

A quantitative measure of a cell's progress through a biological process, such as differentiation. Unlike real time measured in hours, pseudotime is an abstract unit representing the distance along a learned transcriptional manifold. The trajectory's starting point is typically a root cell defined by prior biological knowledge or high expression of stemness markers. The ordering is based on the assumption that cells with similar transcriptomic profiles are at similar stages of a dynamic process.

A computational method that predicts the future state of individual cells by distinguishing between unspliced (nascent) and spliced (mature) mRNA transcripts. The ratio of these transcript types provides a directional vector, or 'velocity,' indicating whether a gene is being activated or repressed. This allows for the inference of directed trajectories without requiring prior knowledge of start or end states, resolving the directionality ambiguity inherent in static transcriptomic snapshots.

A foundational metaphor for trajectory inference where a marble (a cell) rolls down a bifurcating valley. The landscape's ridges and valleys represent stable cell states and differentiation paths. Computational methods aim to reconstruct this manifold from high-dimensional gene expression data. Bifurcation points on the trajectory correspond to cell fate decision points where a progenitor commits to one lineage over another.

A graph-based structure commonly used in early trajectory inference algorithms like Monocle. An MST connects all cells in a reduced-dimensional space with the minimum possible total edge length, creating a skeleton of the differentiation process. The longest path through this tree is often designated as the main trajectory. Modern methods have largely replaced simple MSTs with principal graphs or probabilistic curves to better handle noisy data and complex topologies.

A random-walk-based distance metric that measures the transition probability between cells in a diffusion map embedding. Unlike Euclidean distance, DPT respects the underlying data density and manifold structure, making it robust to noise and dropout events in scRNA-seq data. It calculates the cumulative probability of a random walk transitioning from a root cell to any other cell, providing a smooth, robust ordering that naturally handles branching events.

A mathematical framework for mapping the distribution of cells from one time point to the next by minimizing a transport cost. In trajectory inference, Waddington-OT uses optimal transport to connect cells across consecutive time points in a time-series experiment, reconstructing the most probable ancestral relationships. This approach explicitly models the temporal coupling between snapshots, providing a probabilistic assignment of each cell to its descendants.