Multi-omic trajectory on CITE-Seq data

Question

[firestar]

I have 10x single-cell multiomic CITE-Seq data with RNA gene expression and cell surface markers. I used Seurat to create a WNN UMAP that combines RNA and surface marker data. Now, I would like to create a trajectory on this UMAP.

Actually, I am able to create a trajectory on this UMAP using Slingshot for example, but the trajectory is only based on RNA. The WNN UMAP is quite different from the RNA only UMAP and I think the RNA trajectory doesn't do justice.

Does anyone know of any tools/methods that can create a joint trajectory using both omics?

[ATpoint]

The UMAP must be based on something, typically a PCA or something like this. So why not running slingshot on either that PCA-like dimred, or the UMAP itself? After all, trajectory is a fancy term for finding a path through a lot of points.

[firestar]

Is it? Is the trajectory purely created from the dimensionality reduction? I assumed the RNA expression matrix was used somewhere? I mean on a KNN graph rather than the DR?

[ATpoint]

No, not to my knowledge. At least I always run slingshot on reduced dimensions, and I cannot recall ever hearing anything else. Graphs in single-cell are (to me knowledge) always built from reduced dimensions. Like PCA, or any of these integration methods, like fastMNN, harmony etc.