[Paper Review] Reconstructing probabilistic trees of cellular differentiation from single-cell RNA-seq data

Miriam Shiffman, William Stephenson+5 more|arXiv (Cornell University)|Nov 28, 2018

Single-cell and spatial transcriptomicsBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This paper proposes a Bayesian nonparametric generative model that reconstructs probabilistic trees of cellular differentiation from single-cell RNA-seq data by extending the Dirichlet diffusion tree to model continuous pseudotime along latent bifurcating trajectories. It introduces a novel MCMC sampler combining Metropolis-Hastings and message passing for efficient inference, demonstrating accurate recovery of latent cell trajectories and branch uncertainty in simulated data.

ABSTRACT

Until recently, transcriptomics was limited to bulk RNA sequencing, obscuring the underlying expression patterns of individual cells in favor of a global average. Thanks to technological advances, we can now profile gene expression across thousands or millions of individual cells in parallel. This new type of data has led to the intriguing discovery that individual cell profiles can reflect the imprint of time or dynamic processes. However, synthesizing this information to reconstruct dynamic biological phenomena from data that are noisy, heterogenous, and sparse---and from processes that may unfold asynchronously---poses a complex computational and statistical challenge. Here, we develop a full generative model for probabilistically reconstructing trees of cellular differentiation from single-cell RNA-seq data. Specifically, we extend the framework of the classical Dirichlet diffusion tree to simultaneously infer branch topology and latent cell states along continuous trajectories over the full tree. In tandem, we construct a novel Markov chain Monte Carlo sampler that interleaves Metropolis-Hastings and message passing to leverage model structure for efficient inference. Finally, we demonstrate that these techniques can recover latent trajectories from simulated single-cell transcriptomes. While this work is motivated by cellular differentiation, we derive a tractable model that provides flexible densities for any data (coupled with an appropriate noise model) that arise from continuous evolution along a latent nonparametric tree.

Motivation & Objective

• To develop a generative model that infers latent cellular differentiation trajectories from noisy, sparse, and zero-inflated single-cell RNA-seq data.
• To extend the Dirichlet diffusion tree framework to model continuous pseudotime along nonparametric trees, rather than restricting data to discrete nodes or leaves.
• To enable joint inference of tree topology, latent cell states, and differentially expressed genes while quantifying uncertainty in cell branch assignments.
• To design an efficient MCMC inference algorithm that leverages model structure through message passing and variable augmentation for scalable posterior computation.
• To validate the method on simulated data and demonstrate recovery of ground-truth trajectories and topology using a novel triplet metric.

Proposed method

• Extends the classical Dirichlet diffusion tree to model gene expression as evolving continuously along a latent binary tree, with pseudotime parameterized as a continuous latent variable from root to leaves.
• Uses a generative model for scRNA-seq count data that incorporates a negative binomial noise model to account for zero-inflation and overdispersion.
• Applies Pólya Gamma augmentation to enable exact Gaussian belief propagation on the tree structure, facilitating efficient message passing for latent state inference.
• Develops a novel MCMC sampler that interleaves Metropolis-Hastings updates for tree structure with message-passing steps for latent states, exploiting conditional independence in the tree.
• Incorporates variable augmentation to improve mixing and convergence of the MCMC chain, particularly in high-dimensional gene expression spaces.
• Employs a triplet metric to quantitatively compare inferred and ground-truth cell topologies by assessing consistency in pairwise cell distances and outlier assignments across trees.

Experimental results

Research questions

• RQ1 Can a probabilistic, continuous-time model accurately reconstruct the latent trajectory of cellular differentiation from static, noisy single-cell RNA-seq snapshots?
• RQ2 How can uncertainty in cell lineage assignment be quantified and visualized across different branches of a differentiation tree?
• RQ3 To what extent can a Bayesian nonparametric model infer both tree topology and differentially expressed genes without requiring pre-processing such as dimensionality reduction?
• RQ4 How does the inclusion of continuous pseudotime improve the fidelity of trajectory reconstruction compared to discrete-node models?
• RQ5 Can the model detect and represent subtle topological differences in cell fate decisions, especially near bifurcation points with overlapping or closely spaced branches?

Key findings

• The triplet metric showed a significant improvement in topology recovery, increasing from 0.520 in the initial tree to 0.828 in the maximum a posteriori (MAP) tree, compared to 0.409 for a random tree.
• Cells exhibited higher confidence in branch assignment near terminal leaves, especially when branches diverged early and were well-separated in latent space.
• Cells near overlapping or closely spaced internal branches showed the highest uncertainty in lineage assignment, reflecting the model’s ability to capture ambiguity in cell fate.
• The MCMC sampler successfully converged toward the true topology, as evidenced by the increasing triplet metric and stable posterior estimates across iterations.
• The model successfully recovered latent trajectories from simulated single-cell transcriptomes, demonstrating robustness to noise and sparsity.
• The probabilistic framework enabled coherent quantification of uncertainty in cell state and lineage, moving beyond point estimates to provide interpretable confidence in branch assignments.