300 simulated cells sit on a shared "ground-truth" differentiation manifold (a stem state branching into two committed fates). Each modality — RNA, ATAC and protein (CITE-seq) — observes that same underlying state through its own noise and technical rotation, plus a batch-specific offset, mimicking real assay-to-assay and lab-to-lab variation.
The joint embedding is a per-cell weighted nearest-neighbour (WNN)-style fusion: modality coordinates are averaged using the slider weights, then a batch-correction term is subtracted with strength α, similar to anchor-based integration (Seurat/Harmony).
joint_i = (w_R·RNA_i + w_A·ATAC_i + w_P·Prot_i) / (w_R+w_A+w_P)
corrected_i = joint_i − α · (w_R·B_R + w_A·B_A + w_P·B_P)/(w_R+w_A+w_P)
pseudotime(i) = shortest-path distance to root along the
minimum spanning tree of {corrected_i}
- RNA / ATAC / protein weights — set how much each omics layer contributes to the fused 3D position (WNN-style).
- Batch integration α — 0 = raw uncorrected batches (two clouds visibly split apart), 1 = full correction.
- Cell type / Pseudotime — recolours cells by ground-truth branch or by computed pseudotime.
- Pause probe — freezes the moving marker that traces the inferred trajectory (minimum-spanning-tree diameter path).
This mirrors real trajectory-inference pipelines (Monocle, PAGA, Slingshot) used to study lineage commitment, cancer evolution and immune cell differentiation from multi-omic single-cell atlases.