Quantifying transcript complexity via the condition number of gene-specific random matrix.

Accurate transcript quantification remains a central challenge, as expression levels estimated by different computational tools (e.g. Cufflinks, StringTie, featureCounts, RSEM) often exhibit substantial discrepancies. The observed variability stems from intrinsic transcriptional architectures and is termed transcript complexity. Here we present a theoretical framework to quantify the transcript complexity via the Condition Number (CN) of a gene-specific random matrix, which is based on two key factors: the repertoire of transcripts generated by alternative splicing and the length distribution of reads by RNA-seq. The CN defines a theoretical bound for quantification error and strongly correlates with inter-tool concordance in real data. The CN decreases with increasing read length, thereby explaining the advantages of long-read sequencing. Moreover, hybrid-seq, integrating short- and long-read, is mathematically guaranteed to achieve error rates no worse than either approach alone, with an optimal mixing ratio yielding further improvements. Notably, this optimal ratio can be determined through grid search. These findings establish the CN as a principled standard for assessing transcript complexity, elucidating a fundamental source of quantification uncertainty and guiding sequencing strategies.