An information theoretic treatment of sequence-to-expression modeling

Abstract

Studying a gene's regulatory mechanisms is a tedious process that involves identification of candidate regulators by transcription factor (TF) knockout or over-expression experiments, delineation of enhancers by reporter assays, and demonstration of direct TF influence by site mutagenesis, among other approaches. Such experiments are often chosen based on the biologist's intuition, from several testable hypotheses. We pursue the goal of making this process systematic by using ideas from information theory to reason about experiments in gene regulation, in the hope of ultimately enabling rigorous experiment design strategies. For this, we make use of a state-of-the-art mathematical model of gene expression, which provides a way to formalize our current knowledge of cis-as well as trans-regulatory mechanisms of a gene. Ambiguities in such knowledge can be expressed as uncertainties in the model, which we capture formally by building an ensemble of plausible models that fit the existing data and defining a probability distribution over the ensemble. We then characterize the impact of a new experiment on our understanding of the gene's regulation based on how the ensemble of plausible models and its probability distribution changes when challenged with results from that experiment. This allows us to assess the 'value' of the experiment retroactively as the reduction in entropy of the distribution (information gain) resulting from the experiment's results. We fully formalize this novel approach to reasoning about gene regulation experiments and use it to evaluate a variety of perturbation experiments on two developmental genes of D. melanogaster. We also provide objective and 'biologist-friendly' descriptions of the information gained from each such experiment. The rigorously defined information theoretic approaches presented here can be used in the future to formulate systematic strategies for experiment design pertaining to studies of gene regulatory mechanisms.In-depth studies of gene regulatory mechanisms employ a variety of experimental approaches such as identifying a gene's enhancer(s) and testing its variants through reporter assays, followed by transcription factor mis-expression or knockouts, site mutagenesis, etc. The biologist is often faced with the challenging problem of selecting the ideal next experiment to perform so that its results provide novel mechanistic insights, and has to rely on their intuition about what is currently known on the topic and which experiments may add to that knowledge. We seek to make this intuition-based process more systematic, by borrowing ideas from the mature statistical field of experiment design. Towards this goal, we use the language of mathematical models to formally describe what is known about a gene's regulatory mechanisms, and how an experiment's results enhance that knowledge. We use information theoretic ideas to assign a 'value' to an experiment as well as explain objectively what is learned from that experiment. We demonstrate use of this novel approach on two...

Deciphering enhancer sequence using thermodynamics-based models and convolutional neural networks

“…When testing three different modes of repression, we were surprised to note that a “direct repression” mechanism, where a bound repressor’s regulatory contribution does not depend on how far its binding site is from an activator’s site, has the same predictive ability as the two “short-range repression” mechanisms tested. In light of literature evidence for short-range repression (55, 56), this finding suggests that discerning true mechanisms from modeling of experimental results ex post facto may not be adequately powered, and that active learning approaches (57, 58) that suggest the most informative future experiments may be called for.…”

Global shape of Toll activation is determined bywntDenhancer properties

“…The model relies upon predetermined binding motifs (position weight matrices) of the TFs to identify and quantify binding site strengths in the enhancer. Here, we used an ensemble of models, trained on an enhancer of the gene intermediate neuroblasts defective (ind) in our previous work (9), and applied it to the wntD enhancer. Binding motifs for Dorsal, Zld, and Cic were obtained from FlyFactorSurvey (21).…”

“…We constructed a probability distribution over these models following the procedure in ref. 9 and computed the predicted effect of each singlenucleotide mutation in the enhancer as the average, over this distribution of the RMSE between predicted DV expression profiles with and without the mutation. An "A" to a "C" mutation at position −358 in the 500-bp enhancer, which targets a high-specificity position in a Cic-binding site and had among the largest predicted effects of any single mutation, was chosen for further study.…”

“…To examine whether changing the activation threshold of wntD will modify the global Toll signaling profile, it was necessary to define which sequences in the wntD enhancer regulate its activation threshold. We used the thermodynamics-based model generator GEMSTAT (8,9) to quantitatively describe the combinatorial logic of transcription factor (TF) binding sites within the wntD enhancer. The GEMSTAT models identify binding sites for one or more TFs in the enhancer and use the strengths of these sites, as well as cellular concentrations of the TFs, to predict the expression level driven by that enhancer.…”