Deriving Ranges of Optimal Estimated Transcript Expression Due to Non-identifiability

Abstract

Current expression quantification methods suffer from a fundamental but under-characterized type of error: the most likely estimates for transcript abundances are not unique. Current quantification methods rely on probabilistic models, and the scenario where it admits multiple optimal solutions is called nonidentifiability. This means multiple estimates of transcript abundances generate the observed RNA-seq reads equally likely, and the underlying true expression cannot be determined. The non-identifiability problem is further exacerbated when incompleteness of reference transcriptome and existence of unannotated transcripts are taken into consideration. State-of-the-art quantification methods usually output a single inferred set of abundances, and the accuracy of the single expression set is unknown compared to other equally optimal solutions. Obtaining the set of equally optimal solutions is necessary for evaluating and extending downstream analyses to take non-identifiability into account. We propose methods to compute the range of equally optimal estimates for the expression of each transcript, accounting for non-identifiability of the quantification model using several novel graph theoretical approaches. It works under two scenarios, one assuming the reference transcriptome is complete, another assuming incomplete reference and allowing for expression of unannotated transcripts. Our methods calculate a "confidence" range for each transcript, representing its possible abundance across equally optimal estimates. This range can be used for evaluating the reliability of detected differentially expressed (DE) transcripts, as a large overlap of confidence range between DE conditions indicates the prediction may be unreliable due to uncertainty. We observe that 5 out of 257 DE predictions are unreliable on an MCF10 cell line and 19 out of 3152 are unreliable on a CD8 T cell dataset. The source code can be found at https://github.com/Kingsford-Group/subgraphquant.

Jumper Enables Discontinuous Transcript Assembly in Coronaviruses

“…Fifth, there are possibly multiple optimal solutions to the DTA problem that present equally likely viral transcripts with different relative abundances in the sample. A useful direction of future work is to explore the space of optimal solutions similar to the work done in [18]. Finally, the approach presented in this paper can extended to the general transcript assembly problem, where a topological ordering of the nodes in the splice graph will serve the same function as the unique Hamiltonian path of the segment graph did in the DTA problem.…”

“…Here, a path π is a subset of edges E that can be ordered ( v 1 , w 1 ), … , ( v | π | , w | π | ) such that w i = v i +1 for all i ∈ [| π | − 1] = {1, … , | π | − 1}. While splice graphs are DAGs and typically have a unique source and sink node as well, they do not necessarily contain a Hamiltonian path [9, 16–18].…”

“…We follow the generative model which has been extensively used for transcription quantification [19–21]. The notations used in this paper best resemble the formulation described in [18]. Let be composed of reads be { r 1 , … , r n } and the set of transcripts be with lengths L 1 , … , L k and abundances c = [ c 1 , … , c k ].…”

“…(1) defines the probability in terms of the observed reads r and their induced paths π ( r ) ⊆ E ( G ) in the segment graph G . The authors in [18] use this characterization of reads as paths in a general splice graph to account for ambiguity in the transcript of origin for the reads. For a general splice graph, such a characterization is required to capture all the possible observed reads.…”

Accounting for fragments of unexpected origin improves transcript quantification in RNA-seq simulations focused on increased realism

“…However, the results presented in (1,2,7) and in this manuscript suggest that one important aspect of accurate quantification will be properly determining when sequenced fragments, despite exhibiting sequence similarity to annotated transcripts, are most likely to have arisen from a transcribed sequence that differs from the annotation. In addition to the improvements introduced by Srivastava et al (1), and in lieu of full transcript assembly, both transcript quantification over splicing graphs (12) and determination of optimal abundance ranges implied by non-identifiability in the underlying inference problem (13) are promising directions to pursue.…”