  Genes with similar transcriptional activation kinetics can display very
different temporal mRNA profiles due to differences in transcription time,
degradation rate and RNA processing kinetics. Recent studies have shown that a
splicing-associated RNA production delay can be significant. We introduce a
joint model of transcriptional activation and mRNA accumulation which can be
used for inference of transcription rate, RNA production delay and degradation
rate given genome-wide data from high-throughput sequencing time course
experiments. We combine a mechanistic differential equation model with a
non-parametric statistical modelling approach allowing us to capture a broad
range of activation kinetics, and use Bayesian parameter estimation to quantify
the uncertainty in the estimates of the kinetic parameters. We apply the model
to data from estrogen receptor (ER-{\alpha}) activation in the MCF-7 breast
cancer cell line. We use RNA polymerase II (pol-II) ChIP-Seq time course data
to characterise transcriptional activation and mRNA-Seq time course data to
quantify mature transcripts. We find that 11% of genes with a good signal in
the data display a delay of more than 20 minutes between completing
transcription and mature mRNA production. The genes displaying these long
delays are significantly more likely to be short. We also find a statistical
association between high delay and late intron retention in pre-mRNA data,
indicating significant splicing-associated production delays in many genes.
