HMCVelo: A Deterministic Model for Hydroxymethylation Velocity in Single Cells

I present hydroxymethylation velocity (HMCVelo), the first velocity framework for DNA methylation dynamics. HMCVelo is a deterministic ordinary differential equation (ODE) model that computes the time derivative of hydroxymethylation state for individual cells and genes. The model exploits a recent advance in single-cell epigenomics--Joint single-nucleus hydroxymethylcytosine and methylcytosine sequencing (Joint-snhmC-seq)--which enables subtraction-free quantification of 5-hydroxymethylcytosine (5hmC) and 5-methylcytosine (5mC) at single-cell resolution, resolving temporal methylation dynamics from static molecular snapshots. HM-CVelo models the methylation-demethylation cycle as three coupled processes--methylation, hydroxymethylation, and demethylation--governed by gene-specific rate parameters estimated at steady state via constrained least-squares regression. Scale invariance reduces the parameter space from three to two free parameters per gene. Applied to murine cortical cells (n = 519 and n = 545), HMCVelo infers cellular trajectories with velocity confidence scores exceeding 0.89 across all cell types, compared to confidence scores below 0.45 when RNA velocity is repurposed on the same data. I further prove that in any closed biochemical system with a conservation law, the complement variable cannot resolve trajectory bifurcations--a result with implications for embedding basis selection in all future velocity frameworks applied to cyclic biochemical systems. This work provides a foundation for multi-omic trajectory inference integrating epigenetic and transcriptomic measurements.