contrastTrailExpr: Differential trail expression analysis
In CellTrails: Reconstruction, visualization and analysis of branching trajectories

Description Usage Arguments Details Value Author(s) References See Also Examples

Comparison of feature expression dynamic between two trails.

contrastTrailExpr(
  sce,
  feature_names = featureNames(sce),
  trail_names,
  score = "rmsd"
)

`sce`	A `SingleCellExperiment` object
`feature_names`	Name of feature; can be multiple names
`trail_names`	Name of trails
`score`	Score type; one of {"rmsd", "tad", "abc", "cor"}

Genes have non-uniform expression rates and each trail has a distinct set of upregulated genes, but also contains unequal numbers of cells. Because pseudotime is based on transcriptional change, its axis may be distorted, leading to stretched or compressed sections of longitudinal expression data that make comparison of trails challenging. To align different trails, despite these differences, CellTrails employs a dynamic programming based algorithm that has long been known in speech recognition, called dynamic time warping (Sakoe and Chiba, 1978). RNA expression rates are modeled analogous to speaking rates (Aach and Church, 2001); the latter accounts for innate non-linear variation in the length of individual phonemes (i.e., states) resulting in stretching and shrinking of word (i.e., trail) segments. This allows the computation of inter-trail alignment warps of individual expression time series that are similar but locally out of phase.

Univariate pairwise alignments are computed resulting in one warp per feature and per trail set. Similar to a (global) pairwise protein sequence alignment, monotonicity (i.e., no time loops) and continuity (i.e., no time leaps) constraints have to be imposed on the warping function to preserve temporal sequence ordering. To find the optimal warp, a recursion rule is applied which selects the local minimum of three moves through a dynamic programming matrix: suppose that query snapshot g and reference snapshot h have already been aligned, then the alignment of h+1 with g+1 is a (unit slope) diagonal move, h with g+1 denotes an expansion by repetition of h, and h+2 with g+1 contracts the query by dropping h+1.

The overall dissimilarity between two aligned expression time series x and y of length n is estimated by either the root-mean-square deviation RMSD(x, y) = √(∑(x - y)^2/n), the total aboslute deviation TAD(x, y) = ∑(|x-y|), the area between the aligned dynamic curves (ABC), or Pearson's correlation coefficient (cor) over all aligned elements.

Numeric value

Daniel C. Ellwanger

Sakoe, H., and Chiba, S. (1978). Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech, and Signaling Processing 26, 43-49.

Aach, J., and Church, G.M. (2001). Aligning gene expression time series with time warping algorithms. Bioinformatics 17, 495-508.

dtw

# Example data
data(exSCE)

# Differential expression between trails
contrastTrailExpr(exSCE, feature_name=c("feature_1", "feature_10"),
                 trail_names=c("Tr1", "Tr2"), score="rmsd")