SCTree

SCTree assesses statistical tree-like structures in high-dimensional single-cell gene expression data to test and validate cell fate determination trajectories.

Key Features:

• Statistical framework: An adaptive statistical framework tailored for high-dimensional single-cell datasets to test and validate structured continuous trees (SCTrees) representing cellular progression during differentiation.
• Mathematical foundations: Leverages concepts from metric geometry and random matrix theory as the theoretical basis for structure detection.
• Gromov-Farris transform and semicircular law: Extends the Gromov-Farris transform and applies the semicircular law to translate tree-detection into a matrix-based inference problem.
• Signal matrix detection: Converts detection of tree structures into a signal matrix detection challenge enabling statistical testing under sufficient signal-to-noise ratio.
• Detection capabilities: Identifies linear progressions and both single and multiple branching events in single-cell gene expression data.
• Validation and unified assessment: Provides a unified statistical assessment of hidden structures with validation reported from simulations and real scRNA-seq datasets.

Scientific Applications:

• Developmental biology: Testing and validating differentiation trajectories to characterize cell fate decisions during development.
• Regenerative medicine: Assessing lineage progression and branching relevant to cell replacement and regenerative strategies.
• Single-cell transcriptomics analysis: Statistically evaluating tree-like structures inferred from scRNA-seq gene expression profiles.

Methodology:

Extends the Gromov-Farris transform and applies the semicircular law from random matrix theory, framing tree detection as a signal matrix detection problem using metric-geometry-based transforms and statistical testing when the signal-to-noise ratio is sufficiently high.