Global repression by tailless during segmentation.

The orphan nuclear receptor Tailless (Tll) exhibits conserved roles in brain formation and maintenance that are shared, for example, with vertebrate orthologous forms (Tlx). However, the early expression of tll in two gap domains in the segmentation cascade of Drosophila is unusual even for most other insects. Here we investigate tll regulation on pair-rule stripes. With ectopic misexpression of tll we detected unexpected repression of almost all pair-rule stripes of hairy (h), even-skipped (eve), runt (run), and fushi-tarazu (ftz). Examining Tll embryonic ChIP-chip data with regions mapped as Cis-Regulatory Modules (CRMs) of pair-rule stripes we verified Tll interactions to these regions. With the ChIP-chip data we also verified Tll interactions to the CRMs of gap domains and in the misexpression assay, Tll-mediated repression on Kruppel (Kr), kni (kni) and giant (gt) according to their differential sensitivity to Tll. These results with gap genes confirmed previous data from the literature and argue against indirect repression roles of Tll in the striped pattern. Moreover, the prediction of Tll binding sites in the CRMs of eve stripes and the mathematical modeling of their removal using an experimentally validated theoretical framework shows effects on eve stripes compatible with the absence of a repressor binding to the CRMs. In addition, modeling increased tll levels in the embryo results in the differential repression of eve stripes, agreeing well with the results of the misexpression assay. In genetic assays we investigated eve 5, that is strongly repressed by the ectopic domain and representative of more central stripes not previously implied to be under direct regulation of tll. While this stripe is little affected in tll-, its posterior border is expanded in gt- but detected with even greater expansion in gt-;tll-. We end up by discussing tll with key roles in combinatorial repression mechanisms to contain the expression of medial patterns of the segmentation cascade in the extremities of the embryo.

The effect of mutational robustness on the evolvability of multicellular organisms and eukaryotic cells.

Canalization involves mutational robustness, the lack of phenotypic change as a result of genetic mutations. Given the large divergence in phenotype across species, understanding the relationship between high robustness and evolvability has been of interest to both theorists and experimentalists. Although canalization was originally proposed in the context of multicellular organisms, the effect of multicellularity and other classes of hierarchical organization on evolvability has not been considered by theoreticians. We address this issue using a Boolean population model with explicit representation of an environment in which individuals with explicit genotype and a hierarchical phenotype representing multicellularity evolve. Robustness is described by a single real number between zero and one which emerges from the genotype-phenotype map. We find that high robustness is favoured in constant environments, and lower robustness is favoured after environmental change. Multicellularity and hierarchical organization severely constrain robustness: peak evolvability occurs at an absolute level of robustness of about 0.99 compared with values of about 0.5 in a classical neutral network model. These constraints result in a sharp peak of evolvability in which the maximum is set by the fact that the fixation of adaptive mutations becomes more improbable as robustness decreases. When robustness is put under genetic control, robustness levels leading to maximum evolvability are selected for, but maximal relative fitness appears to require recombination.

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.

Physical implications of so(2, 1) symmetry in exact solutions for a self-repressing gene.

We chemically characterize the symmetries underlying the exact solutions of a stochastic negatively self-regulating gene. The breaking of symmetry at a low molecular number causes three effects. Two branches of the solution exist, having high and low switching rates, such that the low switching rate branch approaches deterministic behavior and the high switching rate branch exhibits sub-Fano behavior. The average protein number differs from the deterministically expected value. Bimodal probability distributions appear as the protein number becomes a readout of the ON/OFF state of the gene.

DNA Occupancy of Polymerizing Transcription Factors: A Chemical Model of the ETS Family Factor Yan.

Transcription factors use both protein-DNA and protein-protein interactions to assemble appropriate complexes to regulate gene expression. Although most transcription factors operate as monomers or dimers, a few, including the E26 transformation-specific family repressors Drosophila melanogaster Yan and its human homolog TEL/ETV6, can polymerize. Although polymerization is required for both the normal and oncogenic function of Yan and TEL/ETV6, the mechanisms by which it influences the recruitment, organization, and stability of transcriptional complexes remain poorly understood. Further, a quantitative description of the DNA occupancy of a polymerizing transcription factor is lacking, and such a description would have broader applications to the conceptually related area of polymerizing chromatin regulators. To expand the theoretical basis for understanding how the oligomeric state of a transcriptional regulator influences its chromatin occupancy and function, we leveraged the extensive biochemical characterization of E26 transformation-specific factors to develop a mathematical model of Yan occupancy at chemical equilibrium. We find that spreading condensation from a specific binding site can take place in a path-independent manner given reasonable values of the free energies of specific and non-specific DNA binding and protein-protein cooperativity. Our calculations show that polymerization confers upon a transcription factor the unique ability to extend occupancy across DNA regions far from specific binding sites. In contrast, dimerization promotes recruitment to clustered binding sites and maximizes discrimination between specific and non-specific sites. We speculate that the association with non-specific DNA afforded by polymerization may enable regulatory behaviors that are well-suited to transcriptional repressors but perhaps incompatible with precise activation.

The analysis of novel distal Cebpa enhancers and silencers using a transcriptional model reveals the complex regulatory logic of hematopoietic lineage specification.

C/EBPα plays an instructive role in the macrophage-neutrophil cell-fate decision and its expression is necessary for neutrophil development. How Cebpa itself is regulated in the myeloid lineage is not known. We decoded the cis-regulatory logic of Cebpa, and two other myeloid transcription factors, Egr1 and Egr2, using a combined experimental-computational approach. With a reporter design capable of detecting both distal enhancers and silencers, we analyzed 46 putative cis-regulatory modules (CRMs) in cells representing myeloid progenitors, and derived early macrophages or neutrophils. In addition to novel enhancers, this analysis revealed a surprisingly large number of silencers. We determined the regulatory roles of 15 potential transcriptional regulators by testing 32,768 alternative sequence-based transcriptional models against CRM activity data. This comprehensive analysis allowed us to infer the cis-regulatory logic for most of the CRMs. Silencer-mediated repression of Cebpa was found to be effected mainly by TFs expressed in non-myeloid lineages, highlighting a previously unappreciated contribution of long-distance silencing to hematopoietic lineage resolution. The repression of Cebpa by multiple factors expressed in alternative lineages suggests that hematopoietic genes are organized into densely interconnected repressive networks instead of hierarchies of mutually repressive pairs of pivotal TFs. More generally, our results demonstrate that de novo cis-regulatory dissection is feasible on a large scale with the aid of transcriptional modeling. Current address: Department of Biology, University of North Dakota, 10 Cornell Street, Stop 9019, Grand Forks, ND 58202-9019, USA.

Natural variation of the expression pattern of the segmentation gene even-skipped in melanogaster.

The evolution of canalized traits is a central question in evolutionary biology. Natural variation in highly conserved traits can provide clues about their evolutionary potential. Here we investigate natural variation in a conserved trait-even-skipped (eve) expression at the cellular blastoderm stage of embryonic development in Drosophila melanogaster. Expression of the pair-rule gene eve was quantitatively measured in three inbred lines derived from a natural population of D. melanogaster. One line showed marked differences in the spacing, amplitude and timing of formation of the characteristic seven-striped pattern over a 50-min period prior to the onset of gastrulation. Stripe 5 amplitude and the width of the interstripe between stripes 4 and 5 were both reduced in this line, while the interstripe distance between stripes 3 and 4 was increased. Engrailed expression in stage 10 embryos revealed a statistically significant increase in the length of parasegment 6 and a decrease in the length of parasegments 8 and 9. These changes are larger than those previously reported between D. melanogaster and D. pseudoobscura, two species that are thought to have diverged from a common ancestor over 25 million years ago. This line harbors a rare 448 bp deletion in the first intron of knirps (kni). This finding suggested that reduced Kni levels caused the deviant eve expression, and indeed we observed lower levels of Kni protein at early cycle 14A in L2 compared to the other two lines. A second of the three lines displayed an approximately 20% greater level of expression for all seven eve stripes. The three lines are each viable and fertile, and none display a segmentation defect as adults, suggesting that early-acting variation in eve expression is ameliorated by developmental buffering mechanisms acting later in development. Canalization of the segmentation pathway may reduce the fitness consequences of genetic variation, thus allowing the persistence of mutations with unexpectedly strong gene expression phenotypes.

Rearrangements of 2.5 kilobases of noncoding DNA from the Drosophila even-skipped locus define predictive rules of genomic cis-regulatory logic.

Rearrangements of about 2.5 kilobases of regulatory DNA located 5' of the transcription start site of the Drosophila even-skipped locus generate large-scale changes in the expression of even-skipped stripes 2, 3, and 7. The most radical effects are generated by juxtaposing the minimal stripe enhancers MSE2 and MSE3 for stripes 2 and 3 with and without small "spacer" segments less than 360 bp in length. We placed these fusion constructs in a targeted transformation site and obtained quantitative expression data for these transformants together with their controlling transcription factors at cellular resolution. These data demonstrated that the rearrangements can alter expression levels in stripe 2 and the 2-3 interstripe by a factor of more than 10. We reasoned that this behavior would place tight constraints on possible rules of genomic cis-regulatory logic. To find these constraints, we confronted our new expression data together with previously obtained data on other constructs with a computational model. The model contained representations of thermodynamic protein-DNA interactions including steric interference and cooperative binding, short-range repression, direct repression, activation, and coactivation. The model was highly constrained by the training data, which it described within the limits of experimental error. The model, so constrained, was able to correctly predict expression patterns driven by enhancers for other Drosophila genes; even-skipped enhancers not included in the training set; stripe 2, 3, and 7 enhancers from various Drosophilid and Sepsid species; and long segments of even-skipped regulatory DNA that contain multiple enhancers. The model further demonstrated that elevated expression driven by a fusion of MSE2 and MSE3 was a consequence of the recruitment of a portion of MSE3 to become a functional component of MSE2, demonstrating that cis-regulatory "elements" are not elementary objects.

Parallel Simulated Annealing Using an Adaptive Resampling Interval.

This paper presents a parallel simulated annealing algorithm that is able to achieve 90% parallel efficiency in iteration on up to 192 processors and up to 40% parallel efficiency in time when applied to a 5000-dimension Rastrigin function. Our algorithm breaks scalability barriers in the method of Chu et al. (1999) by abandoning adaptive cooling based on variance. The resulting gains in parallel efficiency are much larger than the loss of serial efficiency from lack of adaptive cooling. Our algorithm resamples the states across processors periodically. The resampling interval is tuned according to the success rate for each specific number of processors. We further present an adaptive method to determine the resampling interval based on the adoption rate. This adaptive method is able to achieve nearly identical parallel efficiency but higher success rates compared to the fixed interval one using the best interval found.

Ancestral resurrection of the Drosophila S2E enhancer reveals accessible evolutionary paths through compensatory change.

Upstream regulatory sequences that control gene expression evolve rapidly, yet the expression patterns and functions of most genes are typically conserved. To address this paradox, we have reconstructed computationally and resurrected in vivo the cis-regulatory regions of the ancestral Drosophila eve stripe 2 element and evaluated its evolution using a mathematical model of promoter function. Our feed-forward transcriptional model predicts gene expression patterns directly from enhancer sequence. We used this functional model along with phylogenetics to generate a set of possible ancestral eve stripe 2 sequences for the common ancestors of 1) D. simulans and D. sechellia; 2) D. melanogaster, D. simulans, and D. sechellia; and 3) D. erecta and D. yakuba. These ancestral sequences were synthesized and resurrected in vivo. Using a combination of quantitative and computational analysis, we find clear support for functional compensation between the binding sites for Bicoid, Giant, and Krüppel over the course of 40-60 My of Drosophila evolution. We show that this compensation is driven by a coupling interaction between Bicoid activation and repression at the anterior and posterior border necessary for proper placement of the anterior stripe 2 border. A multiplicity of mechanisms for binding site turnover exemplified by Bicoid, Giant, and Krüppel sites, explains how rapid sequence change may occur while maintaining the function of the cis-regulatory element.

Quantitative and predictive model of transcriptional control of the Drosophila melanogaster even skipped gene.

Here we present a quantitative and predictive model of the transcriptional readout of the proximal 1.7 kb of the control region of the Drosophila melanogaster gene even skipped (eve). The model is based on the positions and sequence of individual binding sites on the DNA and quantitative, time-resolved expression data at cellular resolution. These data demonstrated new expression features, first reported here. The model correctly predicts the expression patterns of mutations in trans, as well as point mutations, insertions and deletions in cis. It also shows that the nonclassical expression of stripe 7 driven by this fragment is activated by the protein Caudal (Cad), and repressed by the proteins Tailless (Tll) and Giant (Gt).

Quantitative dynamics and increased variability of segmentation gene expression in the Drosophila Krüppel and knirps mutants.

Here we characterize the response of the Drosophila segmentation system to mutations in two gap genes, Kr and kni, in the form of single or double homozygotes and single heterozygotes. Segmentation gene expression in these genotypes was quantitatively monitored with cellular resolution in space and 6.5 to 13min resolution in time. As is the case with wild type, we found that gene expression domains in the posterior portion of the embryo shift to the anterior over time. In certain cases, such as the gt posterior domain in Kr mutants, the shifts are significantly larger than is seen in wild type embryos. We also investigated the effects of Kr and kni on the variability of gene expression. Mutations often produce variable phenotypes, and it is well known that the cuticular phenotype of Kr mutants is variable. We sought to understand the molecular basis of this effect. We find that throughout cycle 14A the relative levels of eve and ftz expression in stripes 2 and 3 are variable among individual embryos. Moreover, in Kr and kni mutants, unlike wild type, the variability in positioning of the posterior Hb domain and eve stripe 7 is not decreased or filtered with time. The posterior Gt domain in Kr mutants is highly variable at early times, but this variability decreases when this domain shifts in the anterior direction to the position of the neighboring Kni domain. In contrast to these findings, positional variability throughout the embryo does not decrease over time in double Kr;kni mutants. In heterozygotes the early expression patterns of segmentation genes resemble patterns seen in homozygous mutants but by the onset of gastrulation they become similar to the wild type patterns. Finally, we note that gene expression levels are reduced in Kr and kni mutant embryos and have a tendency to decrease over time. This is a surprising result in view of the role that mutual repression is thought to play in the gap gene system.

A synthetic biology approach to the development of transcriptional regulatory models and custom enhancer design.

Synthetic biology offers novel opportunities for elucidating transcriptional regulatory mechanisms and enhancer logic. Complex cis-regulatory sequences--like the ones driving expression of the Drosophila even-skipped gene--have proven difficult to design from existing knowledge, presumably due to the large number of protein-protein interactions needed to drive the correct expression patterns of genes in multicellular organisms. This work discusses two novel computational methods for the custom design of enhancers that employ a sophisticated, empirically validated transcriptional model, optimization algorithms, and synthetic biology. These synthetic elements have both utilitarian and academic value, including improving existing regulatory models as well as evolutionary questions. The first method involves the use of simulated annealing to explore the sequence space for synthetic enhancers whose expression output fit a given search criterion. The second method uses a novel optimization algorithm to find functionally accessible pathways between two enhancer sequences. These paths describe a set of mutations wherein the predicted expression pattern does not significantly vary at any point along the path. Both methods rely on a predictive mathematical framework that maps the enhancer sequence space to functional output.

Evolution of biological cooperation: an algorithmic approach.

This manuscript presents an algorithmic approach to cooperation in biological systems, drawing on fundamental ideas from statistical mechanics and probability theory. Fisher's geometric model of adaptation suggests that the evolution of organisms well adapted to multiple constraints comes at a significant complexity cost. By utilizing combinatorial models of fitness, we demonstrate that the probability of adapting to all constraints decreases exponentially with the number of constraints, thereby generalizing Fisher's result. Our main focus is understanding how cooperation can overcome this adaptivity barrier. Through these combinatorial models, we demonstrate that when an organism needs to adapt to a multitude of environmental variables, division of labor emerges as the only viable evolutionary strategy.

Modeling of gap gene expression in Drosophila Kruppel mutants.

The segmentation gene network in Drosophila embryo solves the fundamental problem of embryonic patterning: how to establish a periodic pattern of gene expression, which determines both the positions and the identities of body segments. The gap gene network constitutes the first zygotic regulatory tier in this process. Here we have applied the systems-level approach to investigate the regulatory effect of gap gene Kruppel (Kr) on segmentation gene expression. We acquired a large dataset on the expression of gap genes in Kr null mutants and demonstrated that the expression levels of these genes are significantly reduced in the second half of cycle 14A. To explain this novel biological result we applied the gene circuit method which extracts regulatory information from spatial gene expression data. Previous attempts to use this formalism to correctly and quantitatively reproduce gap gene expression in mutants for a trunk gap gene failed, therefore here we constructed a revised model and showed that it correctly reproduces the expression patterns of gap genes in Kr null mutants. We found that the remarkable alteration of gap gene expression patterns in Kr mutants can be explained by the dynamic decrease of activating effect of Cad on a target gene and exclusion of Kr gene from the complex network of gap gene interactions, that makes it possible for other interactions, in particular, between hb and gt, to come into effect. The successful modeling of the quantitative aspects of gap gene expression in mutant for the trunk gap gene Kr is a significant achievement of this work. This result also clearly indicates that the oversimplified representation of transcriptional regulation in the previous models is one of the reasons for unsuccessful attempts of mutant simulations.

Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation.

Developing embryos exhibit a robust capability to reduce phenotypic variations that occur naturally or as a result of experimental manipulation. This reduction in variation occurs by an epigenetic mechanism called canalization, a phenomenon which has resisted understanding because of a lack of necessary molecular data and of appropriate gene regulation models. In recent years, quantitative gene expression data have become available for the segment determination process in the Drosophila blastoderm, revealing a specific instance of canalization. These data show that the variation of the zygotic segmentation gene expression patterns is markedly reduced compared to earlier levels by the time gastrulation begins, and this variation is significantly lower than the variation of the maternal protein gradient Bicoid. We used a predictive dynamical model of gene regulation to study the effect of Bicoid variation on the downstream gap genes. The model correctly predicts the reduced variation of the gap gene expression patterns and allows the characterization of the canalizing mechanism. We show that the canalization is the result of specific regulatory interactions among the zygotic gap genes. We demonstrate the validity of this explanation by showing that variation is increased in embryos mutant for two gap genes, Krüppel and knirps, disproving competing proposals that canalization is due to an undiscovered morphogen, or that it does not take place at all. In an accompanying article in PLoS Computational Biology (doi:10.1371/journal.pcbi.1000303), we show that cross regulation between the gap genes causes their expression to approach dynamical attractors, reducing initial variation and providing a robust output. These results demonstrate that the Bicoid gradient is not sufficient to produce gap gene borders having the low variance observed, and instead this low variance is generated by gap gene cross regulation. More generally, we show that the complex multigenic phenomenon of canalization can be understood at a quantitative and predictive level by the application of a precise dynamical model.

FlyEx, the quantitative atlas on segmentation gene expression at cellular resolution.

The datasets on gene expression are the valuable source of information about the functional state of an organism. Recently, we have acquired the large dataset on expression of segmentation genes in the Drosophila blastoderm. To provide efficient access to the data, we have developed the FlyEx database (http://urchin.spbcas.ru/flyex). FlyEx contains 4716 images of 14 segmentation gene expression patterns obtained from 1579 embryos and 9,500,000 quantitative data records. Reference data are available for all segmentation genes in cycles 11-13 and all temporal classes of cycle 14A. FlyEx supports operations on images of gene expression patterns. The database can be used to examine the quality of data, analyze the dynamics of formation of segmentation gene expression domains, as well as to estimate the variability of gene expression patterns. Currently, a user is able to monitor and analyze the dynamics of formation of segmentation gene expression domains over the whole period of segment determination, that amounts to 1.5 h of development. FlyEx supports the data downloads and construction of personal reference datasets, that makes it possible to more effectively use and analyze data.

Estimation of errors introduced by confocal imaging into the data on segmentation gene expression in Drosophila.

MOTIVATION: Currently the confocal scanning microscopy of fluorescently tagged molecules is extensively employed to acquire quantitative data on gene expression at cellular resolution. Following this approach, we generated a large dataset on the expression of segmentation genes in the Drosophila blastoderm, that is widely used in systems biology studies. As data accuracy is of critical importance for the success of studies in this field, we took a shot to evaluate possible errors introduced in the data by acquisition and processing methods. This article deals with errors introduced by confocal microscope. RESULTS: In confocal imaging, the inevitable photon noise is commonly reduced by the averaging of multiple frames. The averaging may introduce errors into the data, if single frames are clipped by microscope hardware. A method based on censoring technique is used to estimate and correct this type of errors. Additional source of errors is the quantification of blurred images. To estimate and correct these errors, the Richardson-Lucy deconvolution method was modified to provide the higher accuracy of data read off from blurred images of the Drosophila blastoderm. We have found that the sizes of errors introduced by confocal imaging make up approximately 5-7% of the mean intensity values and do not disguise the dynamic behavior and characteristic features of gene expression patterns. We also defined a range of microscope parameters for the acquisition of sufficiently accurate data. AVAILABILITY: http://urchin.spbcas.ru/downloads/step/step.htm