Jacqueline M. Dresch

Deciphering a transcriptional regulatory code: modeling short-range repression in the Drosophila embryo.

Systems biology seeks a genomic‐level interpretation of transcriptional regulatory information represented by patterns of protein‐binding sites. Obtaining this information without direct experimentation is challenging; minor alterations in binding sites can have profound effects on gene expression, and underlie important aspects of disease and evolution. Quantitative modeling offers an alternative path to develop a global understanding of the transcriptional regulatory code. Recent studies have focused on endogenous regulatory sequences; however, distinct enhancers differ in many features, making it difficult to generalize to other cis‐regulatory elements. We applied a systematic approach to simpler elements and present here the first quantitative analysis of short‐range transcriptional repressors, which have central functions in metazoan development. Our fractional occupancy‐based modeling uncovered unexpected features of these proteins’ activity that allow accurate predictions of regulation by the Giant, Knirps, Krüppel, and Snail repressors, including modeling of an endogenous enhancer. This study provides essential elements of a transcriptional regulatory code that will allow extensive analysis of genomic information in Drosophila melanogaster and related organisms.

Thermodynamic modeling of transcription: sensitivity analysis differentiates biological mechanism from mathematical model-induced effects.

BackgroundQuantitative models of gene expression generate parameter values that can shed light on biological features such as transcription factor activity, cooperativity, and local effects of repressors. An important element in such investigations is sensitivity analysis, which determines how strongly a models output reacts to variations in parameter values. Parameters of low sensitivity may not be accurately estimated, leading to unwarranted conclusions. Low sensitivity may reflect the nature of the biological data, or it may be a result of the model structure. Here, we focus on the analysis of thermodynamic models, which have been used extensively to analyze gene transcription. Extracted parameter values have been interpreted biologically, but until now little attention has been given to parameter sensitivity in this context.ResultsWe apply local and global sensitivity analyses to two recent transcriptional models to determine the sensitivity of individual parameters. We show that in one case, values for repressor efficiencies are very sensitive, while values for protein cooperativities are not, and provide insights on why these differential sensitivities stem from both biological effects and the structure of the applied models. In a second case, we demonstrate that parameters that were thought to prove the systems dependence on activator-activator cooperativity are relatively insensitive. We show that there are numerous parameter sets that do not satisfy the relationships proferred as the optimal solutions, indicating that structural differences between the two types of transcriptional enhancers analyzed may not be as simple as altered activator cooperativity.ConclusionsOur results emphasize the need for sensitivity analysis to examine model construction and forms of biological data used for modeling transcriptional processes, in order to determine the significance of estimated parameter values for thermodynamic models. Knowledge of parameter sensitivities can provide the necessary context to determine how modeling results should be interpreted in biological systems.

TWO-LAYER MATHEMATICAL MODELING OF GENE EXPRESSION: INCORPORATING DNA-LEVEL INFORMATION AND SYSTEM DYNAMICS

High-throughput genome sequencing and transcriptome analysis have provided researchers with a quantitative basis for detailed modeling of gene expression using a wide variety of mathematical models. Two of the most commonly employed approaches used to model eukaryotic gene regulation are systems of differential equations, which describe time-dependent interactions of gene networks, and thermodynamic equilibrium approaches that can explore DNA-level transcriptional regulation. To combine the strengths of these approaches, we have constructed a new two-layer mathematical model that provides a dynamical description of gene regulatory systems, using detailed DNA-based information, as well as spatial and temporal transcription factor concentration data. We also developed a semi-implicit numerical algorithm for solving the model equations and demonstrate here the efficiency of this algorithm through stability and convergence analyses. To test the model, we used it together with the semi-implicit algorithm to simulate a Drosophila gene regulatory circuit that drives development in the dorsal-ventral axis of the blastoderm-stage embryo, involving three genes. For model validation, we have done both mathematical and statistical comparisons between the experimental data and the models simulated data. Where protein and cis-regulatory information is available, our two-layer model provides a method for recapitulating and predicting dynamic aspects of eukaryotic transcriptional systems that will greatly improve our understanding of gene regulation at a global level.

Flanking sequence context-dependent transcription factor binding in early Drosophila development

BackgroundGene expression in the Drosophila embryo is controlled by functional interactions between a large network of protein transcription factors (TFs) and specific sequences in DNA cis-regulatory modules (CRMs). The binding site sequences for any TF can be experimentally determined and represented in a position weight matrix (PWM). PWMs can then be used to predict the location of TF binding sites in other regions of the genome, although there are limitations to this approach as currently implemented.ResultsIn this proof-of-principle study, we analyze 127 CRMs and focus on four TFs that control transcription of target genes along the anterio-posterior axis of the embryo early in development. For all four of these TFs, there is some degree of conserved flanking sequence that extends beyond the predicted binding regions. A potential role for these conserved flanking sequences may be to enhance the specificity of TF binding, as the abundance of these sequences is greatly diminished when we examine only predicted high-affinity binding sites.ConclusionsExpanding PWMs to include sequence context-dependence will increase the information content in PWMs and facilitate a more efficient functional identification and dissection of CRMs.

Quantitative perturbation-based analysis of gene expression predicts enhancer activity in early Drosophila embryo

Enhancers constitute one of the major components of regulatory machinery of metazoans. Although several genome-wide studies have focused on finding and locating enhancers in the genomes, the fundamental principles governing their internal architecture and cis-regulatory grammar remain elusive. Here, we describe an extensive, quantitative perturbation analysis targeting the dorsal-ventral patterning gene regulatory network (GRN) controlled by Drosophila NF-κB homolog Dorsal. To understand transcription factor interactions on enhancers, we employed an ensemble of mathematical models, testing effects of cooperativity, repression, and factor potency. Models trained on the dataset correctly predict activity of evolutionarily divergent regulatory regions, providing insights into spatial relationships between repressor and activator binding sites. Importantly, the collective predictions of sets of models were effective at novel enhancer identification and characterization. Our study demonstrates how experimental dataset and modeling can be effectively combined to provide quantitative insights into cis-regulatory information on a genome-wide scale. DOI: http://dx.doi.org/10.7554/eLife.08445.001

MARZ: an algorithm to combinatorially analyze gapped n-mer models of transcription factor binding

BackgroundA key challenge in understanding the molecular mechanisms that control gene regulation is the characterization of the specificity with which transcription factor proteins bind to specific DNA sequences. A number of computational approaches have been developed to examine these interactions, including simple mononucleotide and dinucleotide position weight matrix models.ResultsHere we develop a novel, unbiased computational algorithm, MARZ, that systematically analyzes all possible gapped matrices across a fixed number of nucleotides. In addition, to evaluate the ability of these matrix models to predict in vivo binding sites, we utilize a new scoring system and, in combination with established scoring methods and statistical analysis, test the performance of 32 different gapped matrices on the well characterized HUNCHBACK transcription factor in Drosophila.ConclusionsOur results indicate that in many cases gapped matrix models can outperform traditional models, but that the relative strength of the binding sites considered in the analysis can profoundly influence the predictive ability of specific models.

Deciphering the combinatorial architecture of a Drosophila homeotic gene enhancer

In Drosophila, the 330 kb bithorax complex regulates cellular differentiation along the anterior–posterior axis during development in the thorax and abdomen and is comprised of three homeotic genes: Ultrabithorax, abdominal-A, and Abdominal-B. The expression of each of these genes is in turn controlled through interactions between transcription factors and a number of cis-regulatory modules in the neighboring intergenic regions. In this study, we examine how the sequence architecture of transcription factor binding sites mediates the functional activity of one of these cis-regulatory modules. Using computational, mathematical modeling and experimental molecular genetic approaches we investigate the IAB7b enhancer, which regulates Abdominal-B expression specifically in the presumptive seventh and ninth abdominal segments of the early embryo. A cross-species comparison of the IAB7b enhancer reveals an evolutionarily conserved signature motif containing two FUSHI-TARAZU activator transcription factor binding sites. We find that the transcriptional repressors KNIRPS, KRUPPEL and GIANT are able to restrict reporter gene expression to the posterior abdominal segments, using different molecular mechanisms including short-range repression and competitive binding. Additionally, we show the functional importance of the spacing between the two FUSHI-TARAZU binding sites and discuss the potential importance of cooperativity for transcriptional activation. Our results demonstrate that the transcriptional output of the IAB7b cis-regulatory module relies on a complex set of combinatorial inputs mediated by specific transcription factor binding and that the sequence architecture at this enhancer is critical to maintain robust regulatory function.

Global parameter estimation for thermodynamic models of transcriptional regulation

Deciphering the mechanisms involved in gene regulation holds the key to understanding the control of central biological processes, including human disease, population variation, and the evolution of morphological innovations. New experimental techniques including whole genome sequencing and transcriptome analysis have enabled comprehensive modeling approaches to study gene regulation. In many cases, it is useful to be able to assign biological significance to the inferred model parameters, but such interpretation should take into account features that affect these parameters, including model construction and sensitivity, the type of fitness calculation, and the effectiveness of parameter estimation. This last point is often neglected, as estimation methods are often selected for historical reasons or for computational ease. Here, we compare the performance of two parameter estimation techniques broadly representative of local and global approaches, namely, a quasi-Newton/Nelder-Mead simplex (QN/NMS) method and a covariance matrix adaptation-evolutionary strategy (CMA-ES) method. The estimation methods were applied to a set of thermodynamic models of gene transcription applied to regulatory elements active in the Drosophila embryo. Measuring overall fit, the global CMA-ES method performed significantly better than the local QN/NMS method on high quality data sets, but this difference was negligible on lower quality data sets with increased noise or on data sets simplified by stringent thresholding. Our results suggest that the choice of parameter estimation technique for evaluation of gene expression models depends both on quality of data, the nature of the models [again, remains to be established] and the aims of the modeling effort.

A primer on thermodynamic-based models for deciphering transcriptional regulatory logic.

A rigorous analysis of transcriptional regulation at the DNA level is crucial to the understanding of many biological systems. Mathematical modeling has offered researchers a new approach to understanding this central process. In particular, thermodynamic-based modeling represents the most biophysically informed approach aimed at connecting DNA level regulatory sequences to the expression of specific genes. The goal of this review is to give biologists a thorough description of the steps involved in building, analyzing, and implementing a thermodynamic-based model of transcriptional regulation. The data requirements for this modeling approach are described, the derivation for a specific regulatory region is shown, and the challenges and future directions for the quantitative modeling of gene regulation are discussed.

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.