MarkovHC

MarkovHC reconstructs multi-scale pseudo-energy landscapes and hierarchical cell-state structures from single-cell omics data to identify cell sub-populations, trajectories, and critical transition points.

Key Features:

• Topological Data Analysis Integration: Integrates cell classification, trajectory reconstruction, and critical point identification within a unified TDA-based theoretical framework.
• Pseudo-Energy Landscape Reconstruction: Models a hypothetical random walk of cells across gene expression states to construct pseudo-energy landscapes that reveal metastability, basins, and critical points.
• Multi-Scale Clustering and Trajectory Tracking: Identifies clusters (basins) and cores (attractors) at multiple scales to track lineage trajectories and state transitions.
• Application to Diverse Single-Cell Omics Data: Applied to RNA-Seq, cytometry, and ATAC-Seq datasets, including human embryonic stem cell-derived progenitor cells and human preimplantation embryos, to recover known and novel cell types and trajectories.
• Rigorous Metastability Theory Foundation: Builds on metastability theory of an exponentially perturbed Markov chain to provide a theoretical basis for hierarchical structure identification.

Scientific Applications:

• Cell type and state identification: Detects cell sub-populations and states, including novel cell types, from high-dimensional single-cell omics data.
• Lineage and trajectory reconstruction: Reconstructs lineage trajectories and identifies critical transition points in differentiation and development.
• Developmental biology (human embryogenesis): Applied to human embryonic stem cell-derived progenitor cells and human preimplantation embryos to map developmental trajectories and transitions.
• Cancer research: Applicable to studies of cellular heterogeneity and state transitions in cancer.

Methodology:

Implements a Markov hierarchical clustering algorithm that models an exponentially perturbed Markov chain and a hypothetical random walk over gene expression states to reconstruct multi-scale pseudo-energy landscapes, identify basins and attractors, and integrate concepts from topological data analysis.