  For the vast majority of genes in sequenced genomes, there is limited
understanding of how they are regulated. Without such knowledge, it is not
possible to perform a quantitative theory-experiment dialogue on how such genes
give rise to physiological and evolutionary adaptation. One category of
high-throughput experiments used to understand the sequence-phenotype
relationship of the transcriptome is massively parallel reporter assays
(MPRAs). However, to improve the versatility and scalability of MPRA pipelines,
we need a "theory of the experiment" to help us better understand the impact of
various biological and experimental parameters on the interpretation of
experimental data. To that end, in this paper we create tens of thousands of
synthetic single-cell gene expression outputs using both equilibrium and
out-of-equilibrium models. These models make it possible to imitate the summary
statistics (information footprints and expression shift matrices) used to
characterize the output of MPRAs and from this summary statistic to infer the
underlying regulatory architecture. Specifically, we use a more refined
implementation of the so-called thermodynamic models in which the binding
energies of each sequence variant are derived from energy matrices. Our
simulations reveal important effects of the parameters on MPRA data and we
demonstrate our ability to optimize MPRA experimental designs with the goal of
generating thermodynamic models of the transcriptome with base-pair
specificity. Further, this approach makes it possible to carefully examine the
mapping between mutations in binding sites and their corresponding expression
profiles, a tool useful not only for better designing MPRAs, but also for
exploring regulatory evolution.
