Trajectory Uncertainty Framework (TUF): A Modular Framework for Identifying Transitional and Branch-Point Cell States in Single-Cell Trajectory Analysis

Single-cell trajectory inference methods assign pseudotime coordinates but provide limited information on assignment uncertainty, especially at transitional states and branch points. We introduce the Trajectory Uncertainty Framework (TUF), a modular, downstream approach that defines a 2D uncertainty coordinate system for single-cell data. TUF decomposes local uncertainty into the Temporal Entropy Score (TES; temporal heterogeneity) and the Trajectory Divergence Score (TDS; directional divergence).

Synthetic benchmarks demonstrate that the joint interpretation of TES and TDS helps distinguish true fate bifurcations. Applied to pancreatic endocrinogenesis, intestinal epithelium, glioblastoma, and breast cancer datasets, the TUF coordinate system identifies known transitional populations. To isolate the transcriptional drivers of uncertainty beyond baseline tumor biology, we employed a fractional logit residual analysis. This reveals that TES and TDS are associated with context-specific transitional programs: in glioblastoma, residual TES is enriched for inflammatory remodeling while TDS marks proliferative and metabolic stress, whereas in breast cancer, residual TES is enriched for EMT-associated and extracellular matrix remodeling programs, and TDS marks distinct lineage-associated programs. These axes show minimal gene overlap (Jaccard 0.079 in glioblastoma; 0.028 in breast cancer) and remain robust across independent Julia and Python implementations.

SiCell.jl provides an efficient, open-source implementation of TUF and is available under the MIT license via the Julia General Registry and GitHub.