Quantitative modeling of a gene's expression from its intergenic sequence

Mechanistic analysis of enhancer sequences in the estrogen receptor transcriptional program

Estrogen Receptor α (ERα) is a major lineage determining transcription factor (TF) in mammary gland development. Dysregulation of ERα-mediated transcriptional program results in cancer. Transcriptomic and epigenomic profiling of breast cancer cell lines has revealed large numbers of enhancers involved in this regulatory program, but how these enhancers encode function in their sequence remains poorly understood. A subset of ERα-bound enhancers are transcribed into short bidirectional RNA (enhancer RNA or eRNA), and this property is believed to be a reliable marker of active enhancers. We therefore analyze thousands of ERα-bound enhancers and build quantitative, mechanism-aware models to discriminate eRNAs from non-transcribing enhancers based on their sequence. Our thermodynamics-based models provide insights into the roles of specific TFs in ERα-mediated transcriptional program, many of which are supported by the literature. We use in silico perturbations to predict TF-enhancer regulatory relationships and integrate these findings with experimentally determined enhancer-promoter interactions to construct a gene regulatory network. We also demonstrate that the model can prioritize breast cancer-related sequence variants while providing mechanistic explanations for their function. Finally, we experimentally validate the model-proposed mechanisms underlying three such variants.

Nonequilibrium model of short-range repression in gene transcription regulation

Transcription factors are proteins that regulate gene activity by activating or repressing gene transcription. A special class of transcriptional repressors operates via a short-range mechanism, making local DNA regions inaccessible to binding by activators, and thus providing an indirect repressive action on the target gene. This mechanism is commonly modeled assuming that repressors interact with DNA under thermodynamic equilibrium and neglecting some configurations of the gene regulatory region. We elaborate on a more general nonequilibrium model of short-range repression using the graph formalism for transitions between gene states, and we apply analytical calculations to compare it with the equilibrium model in terms of the repression strength and expression noise. In contrast to the equilibrium approach, the new model allows us to separate two basic mechanisms of short-range repression. The first mechanism is associated with the recruiting of factors that mediate chromatin condensation, and the second one concerns the blocking of factors that mediate chromatin loosening. The nonequilibrium model demonstrates better performance on previously published gene expression data obtained for transcription factors controlling Drosophila development, and furthermore it predicts that the first repression mechanism is the most favorable in this system. The presented approach can be scaled to larger gene networks and can be used to infer specific modes and parameters of transcriptional regulation from gene expression data.

Fully interpretable deep learning model of transcriptional control

Motivation

The universal expressibility assumption of Deep Neural Networks (DNNs) is the key motivation behind recent worksin the systems biology community to employDNNs to solve important problems in functional genomics and moleculargenetics. Typically, such investigations have taken a ‘black box’ approach in which the internal structure of themodel used is set purely by machine learning considerations with little consideration of representing the internalstructure of the biological system by the mathematical structure of the DNN. DNNs have not yet been applied to thedetailed modeling of transcriptional control in which mRNA production is controlled by the binding of specific transcriptionfactors to DNA, in part because such models are in part formulated in terms of specific chemical equationsthat appear different in form from those used in neural networks.

Results

In this paper, we give an example of a DNN whichcan model the detailed control of transcription in a precise and predictive manner. Its internal structure is fully interpretableand is faithful to underlying chemistry of transcription factor binding to DNA. We derive our DNN from asystems biology model that was not previously recognized as having a DNN structure. Although we apply our DNNto data from the early embryo of the fruit fly Drosophila, this system serves as a test bed for analysis of much larger datasets obtained by systems biology studies on a genomic scale. .

Availability and implementation

The implementation and data for the models used in this paper are in a zip file in the supplementary material.

Supplementary information

Supplementary data are available at Bioinformatics online.

An in silico analysis of robust but fragile gene regulation links enhancer length to robustness

Organisms must ensure that expression of genes is directed to the appropriate tissues at the correct times, while simultaneously ensuring that these gene regulatory systems are robust to perturbation. This idea is captured by a mathematical concept called r-robustness, which says that a system is robust to a perturbation in up to r - 1 randomly chosen parameters. r-robustness implies that the biological system has a small number of sensitive parameters and that this number can be used as a robustness measure. In this work we use this idea to investigate the robustness of gene regulation using a sequence level model of the Drosophila melanogaster gene even-skipped. We consider robustness with respect to mutations of the enhancer sequence and with respect to changes of the transcription factor concentrations. We find that gene regulation is r-robust with respect to mutations in the enhancer sequence and identify a number of sensitive nucleotides. In both natural and in silico predicted enhancers, the number of nucleotides that are sensitive to mutation correlates negatively with the length of the sequence, meaning that longer sequences are more robust. The exact degree of robustness obtained is dependent not only on DNA sequence, but also on the local concentration of regulatory factors. We find that gene regulation can be remarkably sensitive to changes in transcription factor concentrations at the boundaries of expression features, while it is robust to perturbation elsewhere.

The regulatory control of Cebpa enhancers and silencers in the myeloid and red-blood cell lineages

Cebpa encodes a transcription factor (TF) that plays an instructive role in the development of multiple myeloid lineages. The expression of Cebpa itself is finely modulated, as Cebpa is expressed at high and intermediate levels in neutrophils and macrophages respectively and downregulated in non-myeloid lineages. The cis-regulatory logic underlying the lineage-specific modulation of Cebpa's expression level is yet to be fully characterized. Previously, we had identified 6 new cis-regulatory modules (CRMs) in a 78kb region surrounding Cebpa. We had also inferred the TFs that regulate each CRM by fitting a sequence-based thermodynamic model to a comprehensive reporter activity dataset. Here, we report the cis-regulatory logic of Cebpa CRMs at the resolution of individual binding sites. We tested the binding sites and functional roles of inferred TFs by designing and constructing mutated CRMs and comparing theoretical predictions of their activity against empirical measurements in a myeloid cell line. The enhancers were confirmed to be activated by combinations of PU.1, C/EBP family TFs, Egr1, and Gfi1 as predicted by the model. We show that silencers repress the activity of the proximal promoter in a dominant manner in G1ME cells, which are derived from the red-blood cell lineage. Dominant repression in G1ME cells can be traced to binding sites for GATA and Myb, a motif shared by all of the silencers. Finally, we demonstrate that GATA and Myb act redundantly to silence the proximal promoter. These results indicate that dominant repression is a novel mechanism for resolving hematopoietic lineages. Furthermore, Cebpa has a fail-safe cis-regulatory architecture, featuring several functionally similar CRMs, each of which contains redundant binding sites for multiple TFs. Lastly, by experimentally demonstrating the predictive ability of our sequence-based thermodynamic model, this work highlights the utility of this computational approach for understanding mammalian gene regulation.

Spatially varying cis-regulatory divergence in Drosophila embryos elucidates cis-regulatory logic

Spatial patterning of gene expression is a key process in development, yet how it evolves is still poorly understood. Both cis- and trans-acting changes could participate in complex interactions, so to isolate the cis-regulatory component of patterning evolution, we measured allele-specific spatial gene expression patterns in D. melanogaster × simulans hybrid embryos. RNA-seq of cryo-sectioned slices revealed 66 genes with strong spatially varying allele-specific expression. We found that hunchback, a major regulator of developmental patterning, had reduced expression of the D. simulans allele specifically in the anterior tip of hybrid embryos. Mathematical modeling of hunchback cis-regulation suggested a candidate transcription factor binding site variant, which we verified as causal using CRISPR-Cas9 genome editing. In sum, even comparing morphologically near-identical species we identified surprisingly extensive spatial variation in gene expression, suggesting not only that development is robust to many such changes, but also that natural selection may have ample raw material for evolving new body plans via changes in spatial patterning.

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.

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.

Synthetic enhancer design by in silico compensatory evolution reveals flexibility and constraint in cis-regulation

BACKGROUND

Models that incorporate specific chemical mechanisms have been successful in describing the activity of Drosophila developmental enhancers as a function of underlying transcription factor binding motifs. Despite this, the minimum set of mechanisms required to reconstruct an enhancer from its constituent parts is not known. Synthetic biology offers the potential to test the sufficiency of known mechanisms to describe the activity of enhancers, as well as to uncover constraints on the number, order, and spacing of motifs.

RESULTS

Using a functional model and in silico compensatory evolution, we generated putative synthetic even-skipped stripe 2 enhancers with varying degrees of similarity to the natural enhancer. These elements represent the evolutionary trajectories of the natural stripe 2 enhancer towards two synthetic enhancers designed ab initio. In the first trajectory, spatially regulated expression was maintained, even after more than a third of binding sites were lost. In the second, sequences with high similarity to the natural element did not drive expression, but a highly diverged sequence about half the length of the minimal stripe 2 enhancer drove ten times greater expression. Additionally, homotypic clusters of Zelda or Stat92E motifs, but not Bicoid, drove expression in developing embryos.

CONCLUSIONS

Here, we present a functional model of gene regulation to test the degree to which the known transcription factors and their interactions explain the activity of the Drosophila even-skipped stripe 2 enhancer. Initial success in the first trajectory showed that the gene regulation model explains much of the function of the stripe 2 enhancer. Cases where expression deviated from prediction indicates that undescribed factors likely act to modulate expression. We also showed that activation driven Bicoid and Hunchback is highly sensitive to spatial organization of binding motifs. In contrast, Zelda and Stat92E drive expression from simple homotypic clusters, suggesting that activation driven by these factors is less constrained. Collectively, the 40 sequences generated in this work provides a powerful training set for building future models of gene regulation.

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.

Summary: This Review highlights how high-resolution quantitative tools and theoretical models have formed our current view of the mechanisms determining precision and accuracy in the timing, location and level of transcription in the Drosophila embryo.

A sequence level model of an intact locus predicts the location and function of nonadditive enhancers

Metazoan gene expression is controlled through the action of long stretches of noncoding DNA that contain enhancers-shorter sequences responsible for controlling a single aspect of a gene's expression pattern. Models built on thermodynamics have shown how enhancers interpret protein concentration in order to determine specific levels of gene expression, but the emergent regulatory logic of a complete regulatory locus shows qualitative and quantitative differences from isolated enhancers. Such differences may arise from steric competition limiting the quantity of DNA that can simultaneously influence the transcription machinery. We incorporated this competition into a mechanistic model of gene regulation, generated efficient algorithms for this computation, and applied it to the regulation of Drosophila even-skipped (eve). This model finds the location of enhancers and identifies which factors control the boundaries of eve expression. This model predicts a new enhancer that, when assayed in vivo, drives expression in a non-eve pattern. Incorporation of chromatin accessibility eliminates this inconsistency.

Different modes of enhancer-specific regulation by Runt and Even-skipped during Drosophila segmentation

Expression of the Drosophila slp1 gene depends on nonadditive interactions between two cis-regulatory enhancers. These enhancers are repressed by preventing either Pol II recruitment or release of promoter-proximal paused Pol II in a manner that is both enhancer and transcription factor specific and can account for their nonadditive interaction.

The initial metameric expression of the Drosophila sloppy paired 1 (slp1) gene is controlled by two distinct cis-regulatory DNA elements that interact in a nonadditive manner to integrate inputs from transcription factors encoded by the pair-rule segmentation genes. We performed chromatin immunoprecipitation on reporter genes containing these elements in different embryonic genotypes to investigate the mechanism of their regulation. The distal early stripe element (DESE) mediates both activation and repression by Runt. We find that the differential response of DESE to Runt is due to an inhibitory effect of Fushi tarazu (Ftz) on P-TEFb recruitment and the regulation of RNA polymerase II (Pol II) pausing. The proximal early stripe element (PESE) is also repressed by Runt, but in this case, Runt prevents PESE-dependent Pol II recruitment and preinitiation complex (PIC) assembly. PESE is also repressed by Even-skipped (Eve), but, of interest, this repression involves regulation of P-TEFb recruitment and promoter-proximal Pol II pausing. These results demonstrate that the mode of slp1 repression by Runt is enhancer specific, whereas the mode of repression of the slp1 PESE enhancer is transcription factor specific. We propose a model based on these differential regulatory interactions that accounts for the nonadditive interactions between the PESE and DESE enhancers during Drosophila segmentation.

Incorporating chromatin accessibility data into sequence-to-expression modeling

Prediction of gene expression levels from regulatory sequences is one of the major challenges of genomic biology today. A particularly promising approach to this problem is that taken by thermodynamics-based models that interpret an enhancer sequence in a given cellular context specified by transcription factor concentration levels and predict precise expression levels driven by that enhancer. Such models have so far not accounted for the effect of chromatin accessibility on interactions between transcription factor and DNA and consequently on gene-expression levels. Here, we extend a thermodynamics-based model of gene expression, called GEMSTAT (Gene Expression Modeling Based on Statistical Thermodynamics), to incorporate chromatin accessibility data and quantify its effect on accuracy of expression prediction. In the new model, called GEMSTAT-A, accessibility at a binding site is assumed to affect the transcription factor's binding strength at the site, whereas all other aspects are identical to the GEMSTAT model. We show that this modification results in significantly better fits in a data set of over 30 enhancers regulating spatial expression patterns in the blastoderm-stage Drosophila embryo. It is important to note that the improved fits result not from an overall elevated accessibility in active enhancers but from the variation of accessibility levels within an enhancer. With whole-genome DNA accessibility measurements becoming increasingly popular, our work demonstrates how such data may be useful for sequence-to-expression models. It also calls for future advances in modeling accessibility levels from sequence and the transregulatory context, so as to predict accurately the effect of cis and trans perturbations on gene expression.

Dynamics of Transcription Factor Binding Site Evolution

Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model for directional selection on gene expression to estimate the rates of gain and loss of transcription factor binding sites (TFBS) in finite populations under both point and insertion/deletion mutations. Our results show that these rates are typically slow for a single TFBS in an isolated DNA region, unless the selection is extremely strong. These rates decrease drastically with increasing TFBS length or increasingly specific protein-DNA interactions, making the evolution of sites longer than ∼ 10 bp unlikely on typical eukaryotic speciation timescales. Similarly, evolution converges to the stationary distribution of binding sequences very slowly, making the equilibrium assumption questionable. The availability of longer regulatory sequences in which multiple binding sites can evolve simultaneously, the presence of “pre-sites” or partially decayed old sites in the initial sequence, and biophysical cooperativity between transcription factors, can all facilitate gain of TFBS and reconcile theoretical calculations with timescales inferred from comparative genomics.

Evolution has produced a remarkable diversity of living forms that manifests in qualitative differences as well as quantitative traits. An essential factor that underlies this variability is transcription factor binding sites, short pieces of DNA that control gene expression levels. Nevertheless, we lack a thorough theoretical understanding of the evolutionary times required for the appearance and disappearance of these sites. By combining a biophysically realistic model for how cells read out information in transcription factor binding sites with model for DNA sequence evolution, we explore these timescales and ask what factors crucially affect them. We find that the emergence of binding sites from a random sequence is generically slow under point and insertion/deletion mutational mechanisms. Strong selection, sufficient genomic sequence in which the sites can evolve, the existence of partially decayed old binding sites in the sequence, as well as certain biophysical mechanisms such as cooperativity, can accelerate the binding site gain times and make them consistent with the timescales suggested by comparative analyses of genomic data.

Dynamics of chromatin accessibility and epigenetic state in response to UV damage

Epigenetic mechanisms determine the access of regulatory factors to DNA during events such as transcription and the DNA damage response. However, the global response of histone modifications and chromatin accessibility to UV exposure remains poorly understood. Here, we report that UV exposure results in a genome-wide reduction in chromatin accessibility, while the distribution of the active regulatory mark H3K27ac undergoes massive reorganization. Genomic loci subjected to epigenetic reprogramming upon UV exposure represent target sites for sequence-specific transcription factors. Most of these are distal regulatory regions, highlighting their importance in the cellular response to UV exposure. Furthermore, UV exposure results in an extensive reorganization of super-enhancers, accompanied by expression changes of associated genes, which may in part contribute to the stress response. Taken together, our study provides the first comprehensive resource for genome-wide chromatin changes upon UV irradiation in relation to gene expression and elucidates new aspects of this relationship.

Global sensitivity analysis of a dynamic model for gene expression in Drosophila embryos

It is well known that gene regulation is a tightly controlled process in early organismal development. However, the roles of key processes involved in this regulation, such as transcription and translation, are less well understood, and mathematical modeling approaches in this field are still in their infancy. In recent studies, biologists have taken precise measurements of protein and mRNA abundance to determine the relative contributions of key factors involved in regulating protein levels in mammalian cells. We now approach this question from a mathematical modeling perspective. In this study, we use a simple dynamic mathematical model that incorporates terms representing transcription, translation, mRNA and protein decay, and diffusion in an early Drosophila embryo. We perform global sensitivity analyses on this model using various different initial conditions and spatial and temporal outputs. Our results indicate that transcription and translation are often the key parameters to determine protein abundance. This observation is in close agreement with the experimental results from mammalian cells for various initial conditions at particular time points, suggesting that a simple dynamic model can capture the qualitative behavior of a gene. Additionally, we find that parameter sensitivites are temporally dynamic, illustrating the importance of conducting a thorough global sensitivity analysis across multiple time points when analyzing mathematical models of gene regulation.

Dynamics and function of distal regulatory elements during neurogenesis and neuroplasticity

Gene regulation in mammals involves a complex interplay between promoters and distal regulatory elements that function in concert to drive precise spatiotemporal gene expression programs. However, the dynamics of the distal gene regulatory landscape and its function in the transcriptional reprogramming that underlies neurogenesis and neuronal activity remain largely unknown. Here, we performed a combinatorial analysis of genome-wide data sets for chromatin accessibility (FAIRE-seq) and the enhancer mark H3K27ac, revealing the highly dynamic nature of distal gene regulation during neurogenesis, which gets progressively restricted to distinct genomic regions as neurons acquire a post-mitotic, terminally differentiated state. We further find that the distal accessible and active regions serve as target sites for distinct transcription factors that function in a stage-specific manner to contribute to the transcriptional program underlying neuronal commitment and maturation. Mature neurons respond to a sustained activity of NMDA receptors by epigenetic reprogramming at a large number of distal regulatory regions as well as dramatic reorganization of super-enhancers. Such massive remodeling of the distal regulatory landscape in turn results in a transcriptome that confers a transient loss of neuronal identity and gain of cellular plasticity. Furthermore, NMDA receptor activity also induces many novel prosurvival genes that function in neuroprotective pathways. Taken together, these findings reveal the dynamics of the distal regulatory landscape during neurogenesis and uncover novel regulatory elements that function in concert with epigenetic mechanisms and transcription factors to generate the transcriptome underlying neuronal development and activity.

What does it take to evolve an enhancer? A simulation-based study of factors influencing the emergence of combinatorial regulation

There is widespread interest today in understanding enhancers, which are regulatory elements typically harboring several transcription factor binding sites and mediating the combinatorial effect of transcription factors on gene expression. The evolution of enhancers poses interesting unanswered questions, for example, the evolutionary time taken for a typical enhancer to emerge or the factors shaping its evolution. Existing approaches to cis-regulatory evolution have often ignored the combinatorial nature and varied biochemical mechanisms of gene regulation encoded in enhancers. We report on our investigation of enhancer evolution through the use of PEBCRES, a framework for evolutionary simulation of enhancers that employs a mechanistic and well-supported sequence-to-expression model to assign fitness to the evolving enhancer genotype. We estimated the time necessary to evolve, from genomic background, enhancers capable of driving complex gene expression patterns similar to those involved in early development in Drosophila. We found the time-to-evolve to range between 0.5 and 10 Myr, and to vary greatly with the target expression pattern, complexity of the real enhancer known to encode that pattern, and the strength of input from specific transcription factors. To our knowledge, this is the first estimate of waiting times for realistic enhancers to evolve. The in silico evolved enhancers had, with a few interesting exceptions, site compositions similar to those seen in real enhancers for the same patterns. Our simulations also revealed that certain features of an enhancer might evolve not due to their biological function but as aids to the evolutionary process itself.

Mid-embryo patterning and precision in Drosophila segmentation: Krüppel dual regulation of hunchback

In early development, genes are expressed in spatial patterns which later define cellular identities and tissue locations. The mechanisms of such pattern formation have been studied extensively in early Drosophila (fruit fly) embryos. The gap gene hunchback (hb) is one of the earliest genes to be expressed in anterior-posterior (AP) body segmentation. As a transcriptional regulator for a number of downstream genes, the spatial precision of hb expression can have significant effects in the development of the body plan. To investigate the factors contributing to hb precision, we used fine spatial and temporal resolution data to develop a quantitative model for the regulation of hb expression in the mid-embryo. In particular, modelling hb pattern refinement in mid nuclear cleavage cycle 14 (NC14) reveals some of the regulatory contributions of simultaneously-expressed gap genes. Matching the model to recent data from wild-type (WT) embryos and mutants of the gap gene Krüppel (Kr) indicates that a mid-embryo Hb concentration peak important in thoracic development (at parasegment 4, PS4) is regulated in a dual manner by Kr, with low Kr concentration activating hb and high Kr concentration repressing hb. The processes of gene expression (transcription, translation, transport) are intrinsically random. We used stochastic simulations to characterize the noise generated in hb expression. We find that Kr regulation can limit the positional variability of the Hb mid-embryo border. This has been recently corroborated in experimental comparisons of WT and Kr- mutant embryos. Further, Kr regulation can decrease uncertainty in mid-embryo hb expression (i.e. contribute to a smooth Hb boundary) and decrease between-copy transcriptional variability within nuclei. Since many tissue boundaries are first established by interactions between neighbouring gene expression domains, these properties of Hb-Kr dynamics to diminish the effects of intrinsic expression noise may represent a general mechanism contributing to robustness in early development.

Spurious transcription factor binding: non-functional or genetically redundant?

Transcription factor binding sites (TFBSs) on the DNA are generally accepted as the key nodes of gene control. However, the multitudes of TFBSs identified in genome-wide studies, some of them seemingly unconstrained in evolution, have prompted the view that in many cases TF binding may serve no biological function. Yet, insights from transcriptional biochemistry, population genetics and functional genomics suggest that rather than segregating into 'functional' or 'non-functional', TFBS inputs to their target genes may be generally cumulative, with varying degrees of potency and redundancy. As TFBS redundancy can be diminished by mutations and environmental stress, some of the apparently 'spurious' sites may turn out to be important for maintaining adequate transcriptional regulation under these conditions. This has significant implications for interpreting the phenotypic effects of TFBS mutations, particularly in the context of genome-wide association studies for complex traits.