Emergence of activation or repression in transcriptional control under a fixed molecular context.

For decades, studies have noted that transcription factors (TFs) can behave as either activators or repressors of different target genes. More recently, evidence suggests TFs can act on transcription simultaneously in positive and negative ways. Here we use biophysical models of gene regulation to define, conceptualize and explore these two aspects of TF action: "duality", where TFs can be overall both activators and repressors at the level of the transcriptional response, and "coherent and incoherent" modes of regulation, where TFs act mechanistically on a given target gene either as an activator or a repressor (coherent) or as both (incoherent). For incoherent TFs, the overall response depends on three kinds of features: the TF's mechanistic effects, the dynamics and effects of additional regulatory molecules or the transcriptional machinery, and the occupancy of the TF on DNA. Therefore, activation or repression can be tuned by just the TF-DNA binding affinity, or the number of TF binding sites, given an otherwise fixed molecular context. Moreover, incoherent TFs can cause non-monotonic transcriptional responses, increasing over a certain concentration range and decreasing outside the range, and we clarify the relationship between non-monotonicity and common assumptions of gene regulation models. Using the mammalian SP1 as a case study and well controlled, synthetically designed target sequences, we find experimental evidence for incoherent action and activation, repression or non-monotonicity tuned by affinity. Our work highlights the importance of moving from a TF-centric view to a systems view when reasoning about transcriptional control.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses.

The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses.

The Hill functions, ℋh(x)=xh/1+xh, have been widely used in biology for over a century but, with the exception of ℋ1, they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, co-regulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalises most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ωm⊂ℝ+2, for any equilibrium model with m input binding sites. Ωm exhibits a cusp which approaches, but never exceeds, the sharpness of ℋm but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ωm, whose structure may be of mathematical interest, and suggest the importance of characterising Hopfield barriers for other forms of cellular information processing.

Transcriptional activators in the early Drosophila embryo perform different kinetic roles.

Combinatorial regulation of gene expression by transcription factors (TFs) may in part arise from kinetic synergy-wherein TFs regulate different steps in the transcription cycle. Kinetic synergy requires that TFs play distinguishable kinetic roles. Here, we used live imaging to determine the kinetic roles of three TFs that activate transcription in the Drosophila embryo-Zelda, Bicoid, and Stat92E-by introducing their binding sites into the even-skipped stripe 2 enhancer. These TFs influence different sets of kinetic parameters, and their influence can change over time. All three TFs increased the fraction of transcriptionally active nuclei; Zelda also shortened the first-passage time into transcription and regulated the interval between transcription events. Stat92E also increased the lifetimes of active transcription. Different TFs can therefore play distinct kinetic roles in activating the transcription. This has consequences for understanding the composition and flexibility of regulatory DNA sequences and the biochemical function of TFs. A record of this paper's transparent peer review process is included in the supplemental information.

Transcriptional kinetic synergy: A complex landscape revealed by integrating modeling and synthetic biology.

Transcription factors (TFs) control gene expression, often acting synergistically. Classical thermodynamic models offer a biophysical explanation for synergy based on binding cooperativity and regulated recruitment of RNA polymerase. Because transcription requires polymerase to transition through multiple states, recent work suggests that "kinetic synergy" can arise through TFs acting on distinct steps of the transcription cycle. These types of synergy are not mutually exclusive and are difficult to disentangle conceptually and experimentally. Here, we model and build a synthetic circuit in which TFs bind to a single shared site on DNA, such that TFs cannot synergize by simultaneous binding. We model mRNA production as a function of both TF binding and regulation of the transcription cycle, revealing a complex landscape dependent on TF concentration, DNA binding affinity, and regulatory activity. We use synthetic TFs to confirm that the transcription cycle must be integrated with recruitment for a quantitative understanding of gene regulation.

Leadership.

We asked group leaders how they foster mutually reinforcing research productivity and psychological safety in their teams.

A Mutation in the Drosophila melanogaster eve Stripe 2 Minimal Enhancer Is Buffered by Flanking Sequences.

Enhancers are DNA sequences composed of transcription factor binding sites that drive complex patterns of gene expression in space and time. Until recently, studying enhancers in their genomic context was technically challenging. Therefore, minimal enhancers, the shortest pieces of DNA that can drive an expression pattern that resembles a gene's endogenous pattern, are often used to study features of enhancer function. However, evidence suggests that some enhancers require sequences outside the minimal enhancer to maintain function under environmental perturbations. We hypothesized that these additional sequences also prevent misexpression caused by a transcription factor binding site mutation within a minimal enhancer. Using the Drosophila melanogastereven-skipped stripe 2 enhancer as a case study, we tested the effect of a Giant binding site mutation (gt-2) on the expression patterns driven by minimal and extended enhancer reporter constructs. We found that, in contrast to the misexpression caused by the gt-2 binding site deletion in the minimal enhancer, the same gt-2 binding site deletion in the extended enhancer did not have an effect on expression. The buffering of expression levels, but not expression pattern, is partially explained by an additional Giant binding site outside the minimal enhancer. Deleting the gt-2 binding site in the endogenous locus had no significant effect on stripe 2 expression. Our results indicate that rules derived from mutating enhancer reporter constructs may not represent what occurs in the endogenous context.

Dissecting the sharp response of a canonical developmental enhancer reveals multiple sources of cooperativity.

Developmental enhancers integrate graded concentrations of transcription factors (TFs) to create sharp gene expression boundaries. Here we examine the hunchback P2 (HbP2) enhancer which drives a sharp expression pattern in the Drosophila blastoderm embryo in response to the transcriptional activator Bicoid (Bcd). We systematically interrogate cis and trans factors that influence the shape and position of expression driven by HbP2, and find that the prevailing model, based on pairwise cooperative binding of Bcd to HbP2 is not adequate. We demonstrate that other proteins, such as pioneer factors, Mediator and histone modifiers influence the shape and position of the HbP2 expression pattern. Comparing our results to theory reveals how higher-order cooperativity and energy expenditure impact boundary location and sharpness. Our results emphasize that the bacterial view of transcription regulation, where pairwise interactions between regulatory proteins dominate, must be reexamined in animals, where multiple molecular mechanisms collaborate to shape the gene regulatory function.

Quantitative Comparison of the Anterior-Posterior Patterning System in the Embryos of Five Drosophila Species.

Complex spatiotemporal gene expression patterns direct the development of the fertilized egg into an adult animal. Comparisons across species show that, in spite of changes in the underlying regulatory DNA sequence, developmental programs can be maintained across millions of years of evolution. Reciprocally, changes in gene expression can be used to generate morphological novelty. Distinguishing between changes in regulatory DNA that lead to changes in gene expression and those that do not is therefore a central goal of evolutionary developmental biology. Quantitative, spatially-resolved measurements of developmental gene expression patterns play a crucial role in this goal, enabling the detection of subtle phenotypic differences between species and the development of computations models that link the sequence of regulatory DNA to expression patterns. Here we report the generation of two atlases of cellular resolution gene expression measurements for the primary anterior-posterior patterning genes in Drosophila simulans and Drosophila virilis By combining these data sets with existing atlases for three other Drosophila species, we detect subtle differences in the gene expression patterns and dynamics driving the highly conserved axis patterning system and delineate inter-species differences in the embryonic morphology. These data sets will be a resource for future modeling studies of the evolution of developmental gene regulatory networks.

Signal Integration by Shadow Enhancers and Enhancer Duplications Varies across the Drosophila Embryo.

Transcription of developmental genes is controlled by multiple enhancers. Frequently, more than one enhancer can activate transcription from the same promoter in the same cells. How is regulatory information from multiple enhancers combined to determine the overall expression output? We measure nascent transcription driven by a pair of shadow enhancers, each enhancer of the pair separately, and each duplicated, using live imaging in Drosophila embryos. This set of constructs allows us to quantify the input-output function describing signal integration by two enhancers. We show that signal integration performed by these shadow enhancers and duplications varies across the expression pattern, implying that how their activities are combined depends on the transcriptional regulators bound to the enhancers in different parts of the embryo. Characterizing signal integration by multiple enhancers is a critical step in developing conceptual and computational models of gene expression at the locus level, where multiple enhancers control transcription together.

Hunchback is counter-repressed to regulate even-skipped stripe 2 expression in Drosophila embryos.

Hunchback is a bifunctional transcription factor that can activate and repress gene expression in Drosophila development. We investigated the regulatory DNA sequence features that control Hunchback function by perturbing enhancers for one of its target genes, even-skipped (eve). While Hunchback directly represses the eve stripe 3+7 enhancer, we found that in the eve stripe 2+7 enhancer, Hunchback repression is prevented by nearby sequences-this phenomenon is called counter-repression. We also found evidence that Caudal binding sites are responsible for counter-repression, and that this interaction may be a conserved feature of eve stripe 2 enhancers. Our results alter the textbook view of eve stripe 2 regulation wherein Hb is described as a direct activator. Instead, to generate stripe 2, Hunchback repression must be counteracted. We discuss how counter-repression may influence eve stripe 2 regulation and evolution.

Analysis of Genetic Variation Indicates DNA Shape Involvement in Purifying Selection.

Noncoding DNA sequences, which play various roles in gene expression and regulation, are under evolutionary pressure. Gene regulation requires specific protein-DNA binding events, and our previous studies showed that both DNA sequence and shape readout are employed by transcription factors (TFs) to achieve DNA binding specificity. By investigating the shape-disrupting properties of single nucleotide polymorphisms (SNPs) in human regulatory regions, we established a link between disruptive local DNA shape changes and loss of specific TF binding. Furthermore, we described cases where disease-associated SNPs may alter TF binding through DNA shape changes. This link led us to hypothesize that local DNA shape within and around TF binding sites is under selection pressure. To verify this hypothesis, we analyzed SNP data derived from 216 natural strains of Drosophila melanogaster. Comparing SNPs located in functional and nonfunctional regions within experimentally validated cis-regulatory modules (CRMs) from D. melanogaster that are active in the blastoderm stage of development, we found that SNPs within functional regions tended to cause smaller DNA shape variations. Furthermore, SNPs with higher minor allele frequency were more likely to result in smaller DNA shape variations. The same analysis based on a large number of SNPs in putative CRMs of the D. melanogaster genome derived from DNase I accessibility data confirmed these observations. Taken together, our results indicate that common SNPs in functional regions tend to maintain DNA shape, whereas shape-disrupting SNPs are more likely to be eliminated through purifying selection.

Transcriptional precision and accuracy in development: from measurements to models and mechanisms.

During development, genes are transcribed at specific times, locations and levels. In recent years, the emergence of quantitative tools has significantly advanced our ability to measure transcription with high spatiotemporal resolution in vivo Here, we highlight recent studies that have used these tools to characterize transcription during development, and discuss the mechanisms that contribute to the precision and accuracy of the timing, location and level of transcription. We attempt to disentangle the discrepancies in how physicists and biologists use the term 'precision' to facilitate interactions using a common language. We also highlight selected examples in which the coupling of mathematical modeling with experimental approaches has provided important mechanistic insights, and call for a more expansive use of mathematical modeling to exploit the wealth of quantitative data and advance our understanding of animal transcription.

Quantitative Measurement and Thermodynamic Modeling of Fused Enhancers Support a Two-Tiered Mechanism for Interpreting Regulatory DNA.

Computational models of enhancer function generally assume that transcription factors (TFs) exert their regulatory effects independently, modeling an enhancer as a "bag of sites." These models fail on endogenous loci that harbor multiple enhancers, and a "two-tier" model appears better suited: in each enhancer TFs work independently, and the total expression is a weighted sum of their expression readouts. Here, we test these two opposing views on how cis-regulatory information is integrated. We fused two Drosophila blastoderm enhancers, measured their readouts, and applied the above two models to these data. The two-tier mechanism better fits these readouts, suggesting that these fused enhancers comprise multiple independent modules, despite having sequence characteristics typical of single enhancers. We show that short-range TF-TF interactions are not sufficient to designate such modules, suggesting unknown underlying mechanisms. Our results underscore that mechanisms of how modules are defined and how their outputs are combined remain to be elucidated.

Combinatorial Gene Regulation through Kinetic Control of the Transcription Cycle.

Cells decide when, where, and to what level to express their genes by "computing" information from transcription factors (TFs) binding to regulatory DNA. How is the information contained in multiple TF-binding sites integrated to dictate the rate of transcription? The dominant conceptual and quantitative model is that TFs combinatorially recruit one another and RNA polymerase to the promoter by direct physical interactions. Here, we develop a quantitative framework to explore kinetic control, an alternative model in which combinatorial gene regulation can result from TFs working on different kinetic steps of the transcription cycle. Kinetic control can generate a wide range of analog and Boolean computations without requiring the input TFs to be simultaneously bound to regulatory DNA. We propose experiments that will illuminate the role of kinetic control in transcription and discuss implications for deciphering the cis-regulatory "code."

Information Integration and Energy Expenditure in Gene Regulation.

The quantitative concepts used to reason about gene regulation largely derive from bacterial studies. We show that this bacterial paradigm cannot explain the sharp expression of a canonical developmental gene in response to a regulating transcription factor (TF). In the absence of energy expenditure, with regulatory DNA at thermodynamic equilibrium, information integration across multiple TF binding sites can generate the required sharpness, but with strong constraints on the resultant "higher-order cooperativities." Even with such integration, there is a "Hopfield barrier" to sharpness; for n TF binding sites, this barrier is represented by the Hill function with the Hill coefficient n. If, however, energy is expended to maintain regulatory DNA away from thermodynamic equilibrium, as in kinetic proofreading, this barrier can be breached and greater sharpness achieved. Our approach is grounded in fundamental physics, leads to testable experimental predictions, and suggests how a quantitative paradigm for eukaryotic gene regulation can be formulated.

SiteOut: An Online Tool to Design Binding Site-Free DNA Sequences.

DNA-binding proteins control many fundamental biological processes such as transcription, recombination and replication. A major goal is to decipher the role that DNA sequence plays in orchestrating the binding and activity of such regulatory proteins. To address this goal, it is useful to rationally design DNA sequences with desired numbers, affinities and arrangements of protein binding sites. However, removing binding sites from DNA is computationally non-trivial since one risks creating new sites in the process of deleting or moving others. Here we present an online binding site removal tool, SiteOut, that enables users to design arbitrary DNA sequences that entirely lack binding sites for factors of interest. SiteOut can also be used to delete sites from a specific sequence, or to introduce site-free spacers between functional sequences without creating new sites at the junctions. In combination with commercial DNA synthesis services, SiteOut provides a powerful and flexible platform for synthetic projects that interrogate regulatory DNA. Here we describe the algorithm and illustrate the ways in which SiteOut can be used; it is publicly available at https://depace.med.harvard.edu/siteout/.

The appeasement of Doug: a synthetic approach to enhancer biology.

Genetic approaches have been instrumental in dissecting developmental enhancers by characterizing their transcription factor binding sites. Though some enhancers have been well-studied in this regard, we cannot currently build developmental enhancers from scratch. Reconstitution experiments can provide important complementary tests of our understanding of enhancer function, but these experiments are exceedingly rare in the literature, possibly due to the difficulty of publishing negative results. In this perspective, we argue that the time is right for a synthetic approach to enhancer biology. Focusing primarily on Drosophila enhancers as examples, we review classic and modern methods for dissecting enhancer function as well as computational tools for enhancer design. We include our own negative results from attempts to reconstitute the stripe 2 enhancer from the even-skipped locus and discuss possible ways forward. We believe that with a communal effort in open data sharing, we can make substantial progress toward a complete understanding of enhancer function.

Krüppel Expression Levels Are Maintained through Compensatory Evolution of Shadow Enhancers.

Many developmental genes are controlled by shadow enhancers­pairs of enhancers that drive overlapping expression patterns. We hypothesized that compensatory evolution can maintain the total expression of a gene, while individual shadow enhancers diverge between species. To test this hypothesis, we analyzed expression driven by orthologous pairs of shadow enhancers from Drosophila melanogaster, Drosophila yakuba, and Drosophila pseudoobscura that control expression of Krüppel, a transcription factor that patterns the anterior-posterior axis of blastoderm embryos. We found that the expression driven by the pair of enhancers is conserved between these three species, but expression levels driven by the individual enhancers are not. Using sequence analysis and experimental perturbation, we show that each shadow enhancer is regulated by different transcription factors. These results support the hypothesis that compensatory evolution can occur between shadow enhancers, which has implications for mechanistic and evolutionary studies of gene regulation.