MarkovCellNet: Statistical Inference of Time-Evolving Cell Populations via Compositional Markov Models

Music City Center 

Modeling the temporal dynamics of heterogeneous cellular systems poses significant statistical challenges, particularly in the presence of stochastic transitions and structural heterogeneity inherent in single-cell time-course data. We propose MarkovCellNet, a probabilistic modeling framework that employs distance-aware Markov transition matrices coupled with time-informed dimensionality reduction to infer dynamic cellular trajectories. Cell state distributions are formalized as normalized probability vectors over discrete states and evolved through time via transition matrices which are (1) constructed from biologically informed distance metrics including diffusion, Euclidean, and Manhattan distances and (2) perturbed with Gaussian noise to capture inherent biological variability. The resulting predictive distributions are evaluated under a multinomial sampling model using log-likelihood as a scoring criterion, enabling principled comparison of modeling configurations. We assess the statistical performance of MarkovCellNet on synthetic datasets designed to mimic divergent, periodic, and convergent evolutionary regimes. Our results demonstrate that embeddings derived from PHATE or UMAP, when coupled with diffusion-based transition kernels, yield superior recovery of underlying stochastic dynamics. This framework provides a statistically interpretable and computationally tractable approach for analyzing high-dimensional, time-resolved single-cell data.

Placenta development

Single-cell RNA sequencing

Markov processes

Cell-cell interactions

Dimensionality reduction

Computational models 

Section on Statistical Learning and Data Science