  Transcription is a complex phenomenon that permits the conversion of genetic
information into phenotype by means of an enzyme called RNA polymerase, which
erratically moves along and scans the DNA template. We perform Bayesian
inference over a paradigmatic mechanistic model of non-equilibrium statistical
physics, i.e., the asymmetric exclusion processes in the hydrodynamic limit,
assuming a Gaussian process prior for the polymerase progression rate as a
latent variable. Our framework allows us to infer the speed of polymerases
during transcription given their spatial distribution, whilst avoiding the
explicit inversion of the system's dynamics. The results, which show processing
rates strongly varying with genomic position and minor role of traffic-like
congestion, may have strong implications for the understanding of gene
expression.
