Thermodynamic State Ensemble Models of cis-Regulation

A major goal in computational biology is to develop models that accurately predict a gene's expression from its surrounding regulatory DNA. Here we present one class of such models, thermodynamic state ensemble models. We describe the biochemical derivation of the thermodynamic framework in simple terms, and lay out the mathematical components that comprise each model. These components include (1) the possible states of a promoter, where a state is defined as a particular arrangement of transcription factors bound to a DNA promoter, (2) the binding constants that describe the affinity of the protein–protein and protein–DNA interactions that occur in each state, and (3) whether each state is capable of transcribing. Using these components, we demonstrate how to compute a cis-regulatory function that encodes the probability of a promoter being active. Our intention is to provide enough detail so that readers with little background in thermodynamics can compose their own cis-regulatory functions. To facilitate this goal, we also describe a matrix form of the model that can be easily coded in any programming language. This formalism has great flexibility, which we show by illustrating how phenomena such as competition between transcription factors and cooperativity are readily incorporated into these models. Using this framework, we also demonstrate that Michaelis-like functions, another class of cis-regulatory models, are a subset of the thermodynamic framework with specific assumptions. By recasting Michaelis-like functions as thermodynamic functions, we emphasize the relationship between these models and delineate the specific circumstances representable by each approach. Application of thermodynamic state ensemble models is likely to be an important tool in unraveling the physical basis of combinatorial cis-regulation and in generating formalisms that accurately predict gene expression from DNA sequence

Thermodynamics-Based Models of Transcriptional Regulation by Enhancers: The Roles of Synergistic Activation, Cooperative Binding and Short-Range Repression

Quantitative models of cis-regulatory activity have the potential to improve our mechanistic understanding of transcriptional regulation. However, the few models available today have been based on simplistic assumptions about the sequences being modeled, or heuristic approximations of the underlying regulatory mechanisms. We have developed a thermodynamics-based model to predict gene expression driven by any DNA sequence, as a function of transcription factor concentrations and their DNA-binding specificities. It uses statistical thermodynamics theory to model not only protein-DNA interaction, but also the effect of DNA-bound activators and repressors on gene expression. In addition, the model incorporates mechanistic features such as synergistic effect of multiple activators, short range repression, and cooperativity in transcription factor-DNA binding, allowing us to systematically evaluate the significance of these features in the context of available expression data. Using this model on segmentation-related enhancers in Drosophila, we find that transcriptional synergy due to simultaneous action of multiple activators helps explain the data beyond what can be explained by cooperative DNA-binding alone. We find clear support for the phenomenon of short-range repression, where repressors do not directly interact with the basal transcriptional machinery. We also find that the binding sites contributing to an enhancer's function may not be conserved during evolution, and a noticeable fraction of these undergo lineage-specific changes. Our implementation of the model, called GEMSTAT, is the first publicly available program for simultaneously modeling the regulatory activities of a given set of sequences

A Conserved Developmental Patterning Network Produces Quantitatively Different Output in Multiple Species of Drosophila

Differences in the level, timing, or location of gene expression can contribute to alternative phenotypes at the molecular and organismal level. Understanding the origins of expression differences is complicated by the fact that organismal morphology and gene regulatory networks could potentially vary even between closely related species. To assess the scope of such changes, we used high-resolution imaging methods to measure mRNA expression in blastoderm embryos of Drosophila yakuba and Drosophila pseudoobscura and assembled these data into cellular resolution atlases, where expression levels for 13 genes in the segmentation network are averaged into species-specific, cellular resolution morphological frameworks. We demonstrate that the blastoderm embryos of these species differ in their morphology in terms of size, shape, and number of nuclei. We present an approach to compare cellular gene expression patterns between species, while accounting for varying embryo morphology, and apply it to our data and an equivalent dataset for Drosophila melanogaster. Our analysis reveals that all individual genes differ quantitatively in their spatio-temporal expression patterns between these species, primarily in terms of their relative position and dynamics. Despite many small quantitative differences, cellular gene expression profiles for the whole set of genes examined are largely similar. This suggests that cell types at this stage of development are conserved, though they can differ in their relative position by up to 3–4 cell widths and in their relative proportion between species by as much as 5-fold. Quantitative differences in the dynamics and relative level of a subset of genes between corresponding cell types may reflect altered regulatory functions between species. Our results emphasize that transcriptional networks can diverge over short evolutionary timescales and that even small changes can lead to distinct output in terms of the placement and number of equivalent cells

Quantitative Models of the Mechanisms That Control Genome-Wide Patterns of Transcription Factor Binding during Early Drosophila Development

Transcription factors that drive complex patterns of gene expression during animal development bind to thousands of genomic regions, with quantitative differences in binding across bound regions mediating their activity. While we now have tools to characterize the DNA affinities of these proteins and to precisely measure their genome-wide distribution in vivo, our understanding of the forces that determine where, when, and to what extent they bind remains primitive. Here we use a thermodynamic model of transcription factor binding to evaluate the contribution of different biophysical forces to the binding of five regulators of early embryonic anterior-posterior patterning in Drosophila melanogaster. Predictions based on DNA sequence and in vitro protein-DNA affinities alone achieve a correlation of ∼0.4 with experimental measurements of in vivo binding. Incorporating cooperativity and competition among the five factors, and accounting for spatial patterning by modeling binding in every nucleus independently, had little effect on prediction accuracy. A major source of error was the prediction of binding events that do not occur in vivo, which we hypothesized reflected reduced accessibility of chromatin. To test this, we incorporated experimental measurements of genome-wide DNA accessibility into our model, effectively restricting predicted binding to regions of open chromatin. This dramatically improved our predictions to a correlation of 0.6–0.9 for various factors across known target genes. Finally, we used our model to quantify the roles of DNA sequence, accessibility, and binding competition and cooperativity. Our results show that, in regions of open chromatin, binding can be predicted almost exclusively by the sequence specificity of individual factors, with a minimal role for protein interactions. We suggest that a combination of experimentally determined chromatin accessibility data and simple computational models of transcription factor binding may be used to predict the binding landscape of any animal transcription factor with significant precision

Optimization of reporter gene architecture for quantitative measurements of gene expression in the Drosophila embryo

Quantitative assessment of gene regulation is critical for mathematical modeling of transcriptional systems for systems biology efforts. Enhancers, also termed cis-regulatory modules (CRMs), are the primary mediators of transcriptional regulation in higher eukaryotes; transcription factors binding to CRMs dictate the likelihood and frequency of promoter activation. To provide a suitable platform for in-depth CRM analysis, we adapted a targeted integration vector to compare action of basal promoters with diverse combination of TATA, Inr and DPE motifs, as well as a set of 3′-UTRs representative of those used in different reporter vectors. This “Honda” series of reporter gene vectors was activated by a regulatory element binding Dorsal and Twist activators suitable for transcription in the early Drosophila embryo. The diverse promoters functioned in a similar manner with minor quantitative differences, consistent with a lack of enhancer-promoter specificity. Constructs bearing SV40 3′-UTR sequences appeared to produce somewhat higher levels of mRNA. Confocal laser scanning microscopy revealed that the mRNA distribution produced by these constructs was punctate; this pattern appears to be dependent on 5′-UTR sequences, as an optimized vector including an alternate 5′-UTR produced a more even distribution, which may be preferable for quantitative imaging. This set of Honda vectors contains convenient sites for modification of basal promoter, 3′ UTR, and enhancer, and will be useful for analysis of CRMs and quantitative studies of gene expression

Versatility of Cooperative Transcriptional Activation: A Thermodynamical Modeling Analysis for Greater-Than-Additive and Less-Than-Additive Effects

We derive a statistical model of transcriptional activation using equilibrium thermodynamics of chemical reactions. We examine to what extent this statistical model predicts synergy effects of cooperative activation of gene expression. We determine parameter domains in which greater-than-additive and less-than-additive effects are predicted for cooperative regulation by two activators. We show that the statistical approach can be used to identify different causes of synergistic greater-than-additive effects: nonlinearities of the thermostatistical transcriptional machinery and three-body interactions between RNA polymerase and two activators. In particular, our model-based analysis suggests that at low transcription factor concentrations cooperative activation cannot yield synergistic greater-than-additive effects, i.e., DNA transcription can only exhibit less-than-additive effects. Accordingly, transcriptional activity turns from synergistic greater-than-additive responses at relatively high transcription factor concentrations into less-than-additive responses at relatively low concentrations. In addition, two types of re-entrant phenomena are predicted. First, our analysis predicts that under particular circumstances transcriptional activity will feature a sequence of less-than-additive, greater-than-additive, and eventually less-than-additive effects when for fixed activator concentrations the regulatory impact of activators on the binding of RNA polymerase to the promoter increases from weak, to moderate, to strong. Second, for appropriate promoter conditions when activator concentrations are increased then the aforementioned re-entrant sequence of less-than-additive, greater-than-additive, and less-than-additive effects is predicted as well. Finally, our model-based analysis suggests that even for weak activators that individually induce only negligible increases in promoter activity, promoter activity can exhibit greater-than-additive responses when transcription factors and RNA polymerase interact by means of three-body interactions. Overall, we show that versatility of transcriptional activation is brought about by nonlinearities of transcriptional response functions and interactions between transcription factors, RNA polymerase and DNA.SFIDeposited by bulk impor