Gene expression noise in spatial patterning: hunchback promoter structure affects noise amplitude and distribution in Drosophila segmentation

Quantification reveals early dynamics in Drosophila maternal gradients

The Bicoid (Bcd) protein is a primary determinant of early anterior-posterior (AP) axis specification in Drosophila embryogenesis. This morphogen is spatially distributed in an anterior-high gradient, and affects particular AP cell fates in a concentration-dependent manner. The early distribution and dynamics of the bicoid (bcd) mRNA, the source for the Bcd protein gradient, is not well understood, leaving a number of open questions for how Bcd positional information develops and is regulated. Confocal microscope images of whole early embryos, stained for bcd mRNA or the Staufen (Stau) protein involved in its transport, were processed to extract quantitative AP intensity profiles at two depths (apical-under the embryo surface but above the nuclear layer; and basal-below the nuclei). Each profile was quantified by a two- (or three-) exponential equation. The parameters of these equations were used to analyze the early developmental dynamics of bcd. Analysis of 1D profiles was compared with 2D intensity surfaces from the same images. This approach reveals strong early changes in bcd and Stau, which appear to be coordinated. We can unambiguously discriminate three stages in early development using the exponential parameters: pre-blastoderm (1-9 cleavage cycle, cc), syncytial blastoderm (10-13 cc) and cellularization (from 14A cc). Key features which differ in this period are how fast the first exponential (anterior component) of the apical profile drops with distance and whether it is higher or lower than the basal first exponential. We can further discriminate early and late embryos within the pre-blastoderm stage, depending on how quickly the anterior exponential drops. This relates to the posterior-wards spread of bcd in the first hour of development. Both bcd and Stau show several redistributions in the head cytoplasm, quite probably related to nuclear activity: first shifting inwards towards the core plasm, forming either protrusions (early pre-blastoderm) or round aggregations (early nuclear cleavage cycles, cc, 13 and 14), then moving to the embryo surface and spreading posteriorly. These movements are seen both with the 2D surface study and the 1D profile analysis. The continued spreading of bcd can be tracked from the time of nuclear layer formation (later pre-blastoderm) to the later syncytial blastoderm stages by the progressive loss of steepness of the apical anterior exponential (for both bcd and Stau). Finally, at the beginning of cc14 (cellularization stage) we see a distinctive flip from the basal anterior gradient being higher to the apical gradient being higher (for both bcd and Stau). Quantitative analysis reveals substantial (and correlated) bcd and Stau redistributions during early development, supporting that the distribution and dynamics of bcd mRNA are key factors in the formation and maintenance of the Bcd protein morphogenetic gradient. This analysis reveals the complex and dynamic nature of bcd redistribution, particularly in the head cytoplasm. These resemble observations in oogenesis; their role and significance have yet to be clarified. The observed co-localization during redistribution of bcd and Stau may indicate the involvement of active transport.

Constraints and limitations on the transcriptional response downstream of the Bicoid morphogen gradient

The regulation of the hunchback promoter expression by the maternal Bicoid gradient has been studied as a model system in development for many years. Yet, at the level of quantitative agreement between data and theoretical models, even the first step of this regulation, transcription, continues to be challenging. This situation is slowly progressing, thanks to quantitative live-imaging techniques coupled to advanced statistical data analysis and modeling. Here, we outline the current state of our knowledge of this apparently "simple" step, highlighting the newly appreciated role of bursty transcription dynamics and its regulation.

Analyzing the stability of gene expression using a simple reaction-diffusion model in an early Drosophila embryo

In all complex organisms, the precise levels and timing of gene expression controls vital biological processes. In higher eukaryotes, including the fruit fly Drosophila melanogaster, the complex molecular control of transcription (the synthesis of RNA from DNA) and translation (the synthesis of proteins from RNA) events driving this gene expression are not fully understood. In particular, for Drosophila melanogaster, there is a plethora of experimental data, including quantitative measurements of both RNA and protein concentrations, but the precise mechanisms that control the dynamics of gene expression during early development and the processes which lead to steady-state levels of certain proteins remain elusive. This study analyzes a current mathematical modeling approach in an attempt to better understand the long-term behavior of gene regulation. The model is a modified reaction-diffusion equation which has been previously employed in predicting gene expression levels and studying the relative contributions of transcription and translation events to protein abundance [10,11,24]. Here, we use Matrix Algebra and Analysis techniques to study the stability of the gene expression system and analyze equilibria, using very general assumptions regarding the parameter values incorporated into the model. We prove that, given realistic biological parameter values, the system will result in a unique, stable equilibrium solution. Additionally, we give an example of this long-term behavior using the model alongside actual experimental data obtained from Drosophila embryos.

Noise model estimation with application to gene expression

Algorithms for the estimation of noise level and the detection of noise model are proposed. They are applied to gene expression data for Drosophila embryos. The 2D data on gene expression and the extracted 1D profiles are considered. Since the 1D data contain processing errors, an algorithm for separation of these processing errors is constructed to estimate the biological noise level. An approach to discrimination between the additive and multiplicative models is suggested for the 1D and 2D cases. Singular spectrum analysis and its 2D extension are exploited for the pattern extraction. The algorithms are tested on artificial data similar to the real data. Comparison of the results, which are obtained by the 1D and 2D methods, is performed for Krüppel and giant genes.

Control of Hox transcription factor concentration and cell-to-cell variability by an auto-regulatory switch

The variability in transcription factor concentration among cells is an important developmental determinant, yet how variability is controlled remains poorly understood. Studies of variability have focused predominantly on monitoring mRNA production noise. Little information exists about transcription factor protein variability, as this requires the use of quantitative methods with single-molecule sensitivity. Using Fluorescence Correlation Spectroscopy (FCS), we have characterized the concentration and variability of 14 endogenously tagged TFs in live Drosophila imaginal discs. For the Hox TF Antennapedia, we investigated whether protein variability results from random stochastic events or is developmentally regulated. We found that Antennapedia transitioned from low concentration/high variability early, to high concentration/low variability later, in development. FCS and temporally resolved genetic studies uncovered that Antennapedia itself is necessary and sufficient to drive a developmental regulatory switch from auto-activation to auto-repression, thereby reducing variability. This switch is controlled by progressive changes in relative concentrations of preferentially activating and repressing Antennapedia isoforms, which bind chromatin with different affinities. Mathematical modeling demonstrated that the experimentally supported auto-regulatory circuit can explain the increase of Antennapedia concentration and suppression of variability over time.

Summary: Preferentially repressing and activating isoforms of the Hox transcription factor Antennapedia elicit a developmental regulatory switch from auto-activation to auto-repression that increases concentration and suppresses cell-to-cell variability over time.

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.

Landscape reveals critical network structures for sharpening gene expression boundaries

Background

Spatial pattern formation is a critical issue in developmental biology. Gene expression boundary sharpening has been observed from both experiments and modeling simulations. However, the mechanism to determine the sharpness of the boundary is not fully elucidated.

Results

We investigated the boundary sharpening resulted by three biological motifs, interacting with morphogens, and uncovered their probabilistic landscapes. The landscape view, along with calculated average switching time between attractors, provides a natural explanation for the boundary sharpening behavior relying on the noise induced gene state switchings. To possess boundary sharpening potential, a gene network needs to generate an asymmetric bistable state, i.e. one of the two stable states is less stable than the other. We found that the mutual repressed self-activation model displays more robust boundary sharpening ability against parameter perturbation, compared to the mutual repression or the self-activation model. This is supported by the results of switching time calculated from the landscape, which indicate that the mutual repressed self-activation model has shortest switching time, among three models. Additionally, introducing cross gradients of morphogens provides a more stable mechanism for the boundary sharpening of gene expression, due to a two-way switching mechanism.

Conclusions

Our results reveal the underlying principle for the gene expression boundary sharpening, and pave the way for the mechanistic understanding of cell fate decisions in the pattern formation processes of development.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0595-5) contains supplementary material, which is available to authorized users.

Mean-Independent Noise Control of Cell Fates via Intermediate States

Stochasticity affects accurate signal detection and robust generation of correct cell fates. Although many known regulatory mechanisms may reduce fluctuations in signals, most simultaneously influence their mean dynamics, leading to unfaithful cell fates. Through analysis and computation, we demonstrate that a reversible signaling mechanism acting through intermediate states can reduce noise while maintaining the mean. This mean-independent noise control (MINC) mechanism is investigated in the context of an intracellular binding protein that regulates retinoic acid (RA) signaling during zebrafish hindbrain development. By comparing our models with experimental data, we find that the MINC mechanism allows for sharp boundaries of gene expression without sacrificing boundary accuracy. In addition, this MINC mechanism can modulate noise to levels that we show are beneficial to spatial patterning through noise-induced cell fate switching. These results reveal a design principle that may be important for noise regulation in many systems that control cell fate determination.

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Mean-independent noise control allows noise attenuation without affecting the mean

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Intermediate states enable such control through proportional coupling

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This controls spatial gene expression noise without shifting boundary locations

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Specific noise levels are required for successful downstream boundary sharpening

Novel Traits, Flower Symmetry, and Transcriptional Autoregulation: New Hypotheses From Bioinformatic and Experimental Data

A common feature in developmental networks is the autoregulation of transcription factors which, in turn, positively or negatively regulate additional genes critical for developmental patterning. When a transcription factor regulates its own expression by binding to cis-regulatory sites in its gene, the regulation is direct transcriptional autoregulation (DTA). Indirect transcriptional autoregulation (ITA) involves regulation by proteins expressed downstream of the target transcription factor. We review evidence for a hypothesized role of DTA in the evolution and development of novel flowering plant phenotypes. We additionally provide new bioinformatic and experimental analyses that support a role for transcriptional autoregulation in the evolution of flower symmetry. We find that 5' upstream non-coding regions are significantly enriched for predicted autoregulatory sites in Lamiales CYCLOIDEA genes-an upstream regulator of flower monosymmetry. This suggests a possible correlation between autoregulation of CYCLOIDEA and the origin of monosymmetric flowers near the base of Lamiales, a pattern that may be correlated with independently derived monosymmetry across eudicot lineages. We find additional evidence for transcriptional autoregulation in the flower symmetry program, and report that Antirrhinum DRIF2 may undergo ITA. In light of existing data and new data presented here, we hypothesize how cis-acting autoregulatory sites originate, and find evidence that such sites (and DTA) can arise subsequent to the evolution of a novel phenotype.

Optimizing bicoid signal extraction

Signal extraction and analysis is of great importance, not only in fields such as economics and meteorology, but also in genetics and even biomedicine. There exists a range of parametric and nonparametric techniques which can perform signal extractions. However, the aim of this paper is to define a new approach for optimising signal extraction from bicoid gene expression profile. Having studied both parametric and nonparametric signal extraction techniques, we identified the lack of specific criteria enabling users to select the optimal signal extraction parameters. Exploiting the expression profile of bicoid gene, which is a maternal segmentation coordinate gene found in Drosophila melanogaster, we introduce a new approach for optimising the signal extraction using a nonparametric technique. The underlying criteria are based on the distribution of the residual, more specifically its skewness.

Partially compromised specification causes stochastic effects on gut development in C. elegans

The C. elegans gut descends from the E progenitor cell through a series of stereotyped cell divisions and morphogenetic events. Effects of perturbations of upstream cell specification on downstream organogenesis have not been extensively investigated. Here we have assembled an allelic series of strains that variably compromise specification of E by perturbing the activation of the gut-specifying end-1 and end-3 genes. Using a marker that allows identification of all E descendants regardless of fate, superimposed with markers that identify cells that have adopted a gut fate, we have examined the fate of E lineage descendants among hundreds of embryos. We find that when specification is partially compromised, the E lineage undergoes hyperplasia accompanied by stochastic and variable specification of gut fate among the E descendants. As anticipated by prior work, the activation of the gut differentiation factor elt-2 becomes delayed in these strains, although ultimate protein levels of a translational ELT-2::GFP reporter resemble those of the wild type. By comparing these effects among the various specification mutants, we find that the stronger the defect in specification (i.e. the fewer number of embryos specifying gut), the stronger the defects in the E lineage and delay in activation of elt-2. Despite the changes in the E lineage in these strains, we find that supernumerary E descendants that adopt a gut fate are accommodated into a relatively normal-looking intestine. Hence, upstream perturbation of specification dramatically affects the E lineage, but as long as sufficient descendants adopt a gut fate, organogenesis overcomes these effects to form a relatively normal intestine.

Transcriptional bursting in Drosophila development: Stochastic dynamics of eve stripe 2 expression

Anterior-posterior (AP) body segmentation of the fruit fly (Drosophila) is first seen in the 7-stripe spatial expression patterns of the pair-rule genes, which regulate downstream genes determining specific segment identities. Regulation of pair-rule expression has been extensively studied for the even-skipped (eve) gene. Recent live imaging, of a reporter for the 2^ndeve stripe, has demonstrated the stochastic nature of this process, with ‘bursts’ in the number of RNA transcripts being made over time. We developed a stochastic model of the spatial and temporal expression of eve stripe 2 (binding by transcriptional activators (Bicoid and Hunchback proteins) and repressors (Giant and Krüppel proteins), transcriptional initiation and termination; with all rate parameters constrained by features of the experimental data) in order to analyze the noisy experimental time series and test hypotheses for how eve transcription is regulated. These include whether eve transcription is simply OFF or ON, with a single ON rate, or whether it proceeds by a more complex mechanism, with multiple ON rates. We find that both mechanisms can produce long (multi-minute) RNA bursts, but that the short-time (minute-to-minute) statistics of the data is indicative of eve being transcribed with at least two distinct ON rates, consistent with data on the joint activation of eve by Bicoid and Hunchback. We also predict distinct statistical signatures for cases in which eve is repressed (e.g. along the edges of the stripe) vs. cases in which activation is reduced (e.g. by mutagenesis of transcription factor binding sites). Fundamental developmental processes such as gene transcription are intrinsically noisy; our approach presents a new way to quantify and analyze time series data during developmental patterning in order to understand regulatory mechanisms and how they propagate noise and impact embryonic robustness.

Macromolecular Crowding Regulates the Gene Expression Profile by Limiting Diffusion

We seek to elucidate the role of macromolecular crowding in transcription and translation. It is well known that stochasticity in gene expression can lead to differential gene expression and heterogeneity in a cell population. Recent experimental observations by Tan et al. have improved our understanding of the functional role of macromolecular crowding. It can be inferred from their observations that macromolecular crowding can lead to robustness in gene expression, resulting in a more homogeneous cell population. We introduce a spatial stochastic model to provide insight into this process. Our results show that macromolecular crowding reduces noise (as measured by the kurtosis of the mRNA distribution) in a cell population by limiting the diffusion of transcription factors (i.e. removing the unstable intermediate states), and that crowding by large molecules reduces noise more efficiently than crowding by small molecules. Finally, our simulation results provide evidence that the local variation in chromatin density as well as the total volume exclusion of the chromatin in the nucleus can induce a homogenous cell population.

The cellular nucleus is packed with macromolecules such as DNAs and proteins, which leaves limited space for other molecules to move around. Recent experimental results by C. Tan et al. have shown that macromolecular crowding can regulate gene expression, resulting in a more homogenous cell population. We introduce a computational model to uncover the mechanism by which macromolecular crowding functions. Our results suggest that macromolecular crowding limits the diffusion of the transcription factors and attenuates the transcriptional bursting, which leads to a more homogenous cell population. Regulation of gene expression noise by macromolecules depends on the size of the crowders, i.e. larger macromolecules can reduce the noise more effectively than smaller macromolecules. We also demonstrate that local variation of chromatin density can affect the noise of gene expression. This shows the importance of the chromatin structure in gene expression regulation.

Sequential construction of a model for modular gene expression control, applied to spatial patterning of theDrosophilagenehunchback

Gene network simulations are increasingly used to quantify mutual gene regulation in biological tissues. These are generally based on linear interactions between single-entity regulatory and target genes. Biological genes, by contrast, commonly have multiple, partially independent, cis-regulatory modules (CRMs) for regulator binding, and can produce variant transcription and translation products. We present a modeling framework to address some of the gene regulatory dynamics implied by this biological complexity. Spatial patterning of the hunchback (hb) gene in Drosophila development involves control by three CRMs producing two distinct mRNA transcripts. We use this example to develop a differential equations model for transcription which takes into account the cis-regulatory architecture of the gene. Potential regulatory interactions are screened by a genetic algorithms (GAs) approach and compared to biological expression data.

A glance at the applications of Singular Spectrum Analysis in gene expression data

In recent years Singular Spectrum Analysis (SSA) has been used to solve many biomedical issues and is currently accepted as a potential technique in quantitative genetics studies. Presented in this article is a review of recent published genetics studies which have taken advantage of SSA. Since Singular Value Decomposition (SVD) is an important stage of this technique which can also be used as an independent analytical method in gene expression data, we also briefly touch upon some areas of the application of SVD. The review finds that at present, the most prominent area of applying SSA in genetics is filtering and signal extraction, which proves that SSA can be considered as a valuable aid and promising method for genetics analysis.

Noise modulation in retinoic acid signaling sharpens segmental boundaries of gene expression in the embryonic zebrafish hindbrain

Morphogen gradients induce sharply defined domains of gene expression in a concentration-dependent manner, yet how cells interpret these signals in the face of spatial and temporal noise remains unclear. Using fluorescence lifetime imaging microscopy (FLIM) and phasor analysis to measure endogenous retinoic acid (RA) directly in vivo, we have investigated the amplitude of noise in RA signaling, and how modulation of this noise affects patterning of hindbrain segments (rhombomeres) in the zebrafish embryo. We demonstrate that RA forms a noisy gradient during critical stages of hindbrain patterning and that cells use distinct intracellular binding proteins to attenuate noise in RA levels. Increasing noise disrupts sharpening of rhombomere boundaries and proper patterning of the hindbrain. These findings reveal novel cellular mechanisms of noise regulation, which are likely to play important roles in other aspects of physiology and disease.

DOI:http://dx.doi.org/10.7554/eLife.14034.001

Animal cells need to be able to communicate with each other so that they can work together in tissues and organs. To do so, cells release signaling molecules that can move around within a tissue and be detected by receptors on other cells.

We tend to assume that the signaling molecules are evenly distributed across a tissue and affect all the receiving cells in the same way. However, random variations (noise) that affect how many of these molecules are produced, how they move through the space between cells and how they bind to receptors makes the reality much more complex. Cells responding to the signal somehow can ignore this noise and establish sharp boundaries between different cell types so that neighboring cells have distinct roles in the tissue. Few studies have attempted to measure such noise or address how cells manage to respond to noisy signals in a consistent manner.

Retinoic acid is a signaling molecule that plays an important role in the development of the brain in animal embryos. It forms a gradient along the body of the embryo from the head end to the tail end, but it has proved difficult to measure this gradient directly. Sosnik et al. exploited the fact that this molecule is weakly fluorescent and used microscopy to directly detect it in zebrafish embryos. The experiments show that retinoic acid forms a gradient in the embryos, with high levels at the tail end and lower levels at the head end.

Sosnik et al. also found that there is a large amount of noise in the retinoic acid gradient. Two cells in the same position can have very different retinoic acid levels, and the levels in a particular cell can vary from one minute to the next. The experiments also show that proteins that interact with retinoic acid help to reduce noise within a cell. This noise reduction is important for sharpening the boundaries between different brain regions in the embryo to allow the brain to develop normally. A future challenge will be to see if similar retinoic acid gradients and noise control occur in other tissues, and if the noise has any positive role to play in development.

DOI:http://dx.doi.org/10.7554/eLife.14034.002

Shaped 3D singular spectrum analysis for quantifying gene expression, with application to the early zebrafish embryo

Recent progress in microscopy technologies, biological markers, and automated processing methods is making possible the development of gene expression atlases at cellular-level resolution over whole embryos. Raw data on gene expression is usually very noisy. This noise comes from both experimental (technical/methodological) and true biological sources (from stochastic biochemical processes). In addition, the cells or nuclei being imaged are irregularly arranged in 3D space. This makes the processing, extraction, and study of expression signals and intrinsic biological noise a serious challenge for 3D data, requiring new computational approaches. Here, we present a new approach for studying gene expression in nuclei located in a thick layer around a spherical surface. The method includes depth equalization on the sphere, flattening, interpolation to a regular grid, pattern extraction by Shaped 3D singular spectrum analysis (SSA), and interpolation back to original nuclear positions. The approach is demonstrated on several examples of gene expression in the zebrafish egg (a model system in vertebrate development). The method is tested on several different data geometries (e.g., nuclear positions) and different forms of gene expression patterns. Fully 3D datasets for developmental gene expression are becoming increasingly available; we discuss the prospects of applying 3D-SSA to data processing and analysis in this growing field.

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.

Bicoid signal extraction with a selection of parametric and nonparametric signal processing techniques

The maternal segmentation coordinate gene bicoid plays a significant role during Drosophila embryogenesis. The gradient of Bicoid, the protein encoded by this gene, determines most aspects of head and thorax development. This paper seeks to explore the applicability of a variety of signal processing techniques at extracting bicoid expression signal, and whether these methods can outperform the current model. We evaluate the use of six different powerful and widely-used models representing both parametric and nonparametric signal processing techniques to determine the most efficient method for signal extraction in bicoid. The results are evaluated using both real and simulated data. Our findings show that the Singular Spectrum Analysis technique proposed in this paper outperforms the synthesis diffusion degradation model for filtering the noisy protein profile of bicoid whilst the exponential smoothing technique was found to be the next best alternative followed by the autoregressive integrated moving average.

Optimizing information flow in small genetic networks. IV. Spatial coupling

We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the input) by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively different regulatory strategy emerges where individual cells respond to the input in a nearly steplike fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.

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.

Shaped singular spectrum analysis for quantifying gene expression, with application to the early Drosophila embryo

In recent years, with the development of automated microscopy technologies, the volume and complexity of image data on gene expression have increased tremendously. The only way to analyze quantitatively and comprehensively such biological data is by developing and applying new sophisticated mathematical approaches. Here, we present extensions of 2D singular spectrum analysis (2D-SSA) for application to 2D and 3D datasets of embryo images. These extensions, circular and shaped 2D-SSA, are applied to gene expression in the nuclear layer just under the surface of the Drosophila (fruit fly) embryo. We consider the commonly used cylindrical projection of the ellipsoidal Drosophila embryo. We demonstrate how circular and shaped versions of 2D-SSA help to decompose expression data into identifiable components (such as trend and noise), as well as separating signals from different genes. Detection and improvement of under- and overcorrection in multichannel imaging is addressed, as well as the extraction and analysis of 3D features in 3D gene expression patterns.

In silico evolution of the hunchback gene indicates redundancy in cis-regulatory organization and spatial gene expression

Biological development depends on the coordinated expression of genes in time and space. Developmental genes have extensive cis-regulatory regions which control their expression. These regions are organized in a modular manner, with different modules controlling expression at different times and locations. Both how modularity evolved and what function it serves are open questions. We present a computational model for the cis-regulation of the hunchback (hb) gene in the fruit fly (Drosophila). We simulate evolution (using an evolutionary computation approach from computer science) to find the optimal cis-regulatory arrangements for fitting experimental hb expression patterns. We find that the cis-regulatory region tends to readily evolve modularity. These cis-regulatory modules (CRMs) do not tend to control single spatial domains, but show a multi-CRM/multi-domain correspondence. We find that the CRM-domain correspondence seen in Drosophila evolves with a high probability in our model, supporting the biological relevance of the approach. The partial redundancy resulting from multi-CRM control may confer some biological robustness against corruption of regulatory sequences. The technique developed on hb could readily be applied to other multi-CRM developmental genes.

Eco-evo-devo: the time has come

The major goal of ecological evolutionary developmental biology, also known as "eco-evo-devo," is to uncover the rules that underlie the interactions between an organism's environment, genes, and development and to incorporate these rules into evolutionary theory. In this chapter, we discuss some key and emerging concepts within eco-evo-devo. These concepts show that the environment is a source and inducer of genotypic and phenotypic variation at multiple levels of biological organization, while development acts as a regulator that can mask, release, or create new combinations of variation. Natural selection can subsequently fix this variation, giving rise to novel phenotypes. Combining the approaches of eco-evo-devo and ecological genomics will mutually enrich these fields in a way that will not only enhance our understanding of evolution, but also of the genetic mechanisms underlying the responses of organisms to their natural environments.

Noise minimisation in gene expression switches

Gene expression is subject to stochastic variation which leads to fluctuations in the rate of protein production. Recently, a study in yeast at a genomic scale showed that, in some cases, gene expression variability alters phenotypes while, in other cases, these remain unchanged despite fluctuations in the expression of other genes. These studies suggested that noise in gene expression is a physiologically relevant trait and, to prevent harmful stochastic variation in the expression levels of some genes, it can be subject to minimisation. However, the mechanisms for noise minimisation are still unclear. In the present work, we analysed how noise expression depends on the architecture of the cis-regulatory system, in particular on the number of regulatory binding sites. Using analytical calculations and stochastic simulations, we found that the fluctuation level in noise expression decreased with the number of regulatory sites when regulatory transcription factors interacted with only one other bound transcription factor. In contrast, we observed that there was an optimal number of binding sites when transcription factors interacted with many bound transcription factors. This finding suggested a new mechanism for preventing large fluctuations in the expression of genes which are sensitive to the concentration of regulators.

Precise developmental gene expression arises from globally stochastic transcriptional activity

Early embryonic patterning events are strikingly precise, a fact that appears incompatible with the stochastic gene expression observed across phyla. Using single-molecule mRNA quantification in Drosophila embryos, we determine the magnitude of fluctuations in the expression of four critical patterning genes. The accumulation of mRNAs is identical across genes and fluctuates by only ∼8% between neighboring nuclei, generating precise protein distributions. In contrast, transcribing loci exhibit an intrinsic noise of ∼45% independent of specific promoter-enhancer architecture or fluctuating inputs. Precise transcript distribution in the syncytium is recovered via straightforward spatiotemporal averaging, i.e., accumulation and diffusion of transcripts during nuclear cycles, without regulatory feedback. Common expression characteristics shared between genes suggest that fluctuations in mRNA production are context independent and are a fundamental property of transcription. The findings shed light on how the apparent paradox between stochastic transcription and developmental precision is resolved.

A spatial point pattern analysis in Drosophila blastoderm embryos evaluating the potential inheritance of transcriptional states

The Drosophila blastoderm embryo undergoes rapid cycles of nuclear division. This poses a challenge to genes that need to reliably sense the concentrations of morphogen molecules to form desired expression patterns. Here we investigate whether the transcriptional state of hunchback (hb), a target gene directly activated by the morphogenetic protein Bicoid (Bcd), exhibits properties indicative of inheritance between mitotic cycles. To achieve this, we build a dataset of hb transcriptional states at the resolution of individual nuclei in embryos at early cycle 14. We perform a spatial point pattern (SPP) analysis to evaluate the spatial relationships among the nuclei that have distinct numbers of hb gene copies undergoing active transcription in snapshots of embryos. Our statistical tests and simulation studies reveal properties of dispersed clustering for nuclei with both or neither copies of hb undergoing active transcription. Modeling of nuclear lineages from cycle 11 to cycle 14 suggests that these two types of nuclei can achieve spatial clustering when, and only when, the transcriptional states are allowed to propagate between mitotic cycles. Our results are consistent with the possibility where the positional information encoded by the Bcd morphogen gradient may not need to be decoded de novo at all mitotic cycles in the Drosophila blastoderm embryo.

How cells know where they are

Development, regeneration, and even day-to-day physiology require plant and animal cells to make decisions based on their locations. The principles by which cells may do this are deceptively straightforward. But when reliability needs to be high--as often occurs during development--successful strategies tend to be anything but simple. Increasingly, the challenge facing biologists is to relate the diverse diffusible molecules, control circuits, and gene regulatory networks that help cells know where they are to the varied, sometimes stringent, constraints imposed by the need for real-world precision and accuracy.

Evaluation of gene association methods for coexpression network construction and biological knowledge discovery

BACKGROUND

Constructing coexpression networks and performing network analysis using large-scale gene expression data sets is an effective way to uncover new biological knowledge; however, the methods used for gene association in constructing these coexpression networks have not been thoroughly evaluated. Since different methods lead to structurally different coexpression networks and provide different information, selecting the optimal gene association method is critical.

METHODS AND RESULTS

In this study, we compared eight gene association methods - Spearman rank correlation, Weighted Rank Correlation, Kendall, Hoeffding's D measure, Theil-Sen, Rank Theil-Sen, Distance Covariance, and Pearson - and focused on their true knowledge discovery rates in associating pathway genes and construction coordination networks of regulatory genes. We also examined the behaviors of different methods to microarray data with different properties, and whether the biological processes affect the efficiency of different methods.

CONCLUSIONS

We found that the Spearman, Hoeffding and Kendall methods are effective in identifying coexpressed pathway genes, whereas the Theil-sen, Rank Theil-Sen, Spearman, and Weighted Rank methods perform well in identifying coordinated transcription factors that control the same biological processes and traits. Surprisingly, the widely used Pearson method is generally less efficient, and so is the Distance Covariance method that can find gene pairs of multiple relationships. Some analyses we did clearly show Pearson and Distance Covariance methods have distinct behaviors as compared to all other six methods. The efficiencies of different methods vary with the data properties to some degree and are largely contingent upon the biological processes, which necessitates the pre-analysis to identify the best performing method for gene association and coexpression network construction.

Precision of hunchback expression in the Drosophila embryo

Activation of the gap gene hunchback (hb) by the maternal Bicoid gradient is one of the most intensively studied gene regulatory interactions in animal development. Most efforts to understand this process have focused on the classical Bicoid target enhancer located immediately upstream of the P2 promoter. However, hb is also regulated by a recently identified distal shadow enhancer as well as a neglected "stripe" enhancer, which mediates expression in both central and posterior regions of cellularizing embryos. Here, we employ BAC transgenesis and quantitative imaging methods to investigate the individual contributions of these different enhancers to the dynamic hb expression pattern. These studies reveal that the stripe enhancer is crucial for establishing the definitive border of the anterior Hb expression pattern, just beyond the initial border delineated by Bicoid. Removal of this enhancer impairs dynamic expansion of hb expression and results in variable cuticular defects in the mesothorax (T2) due to abnormal patterns of segmentation gene expression. The stripe enhancer is subject to extensive regulation by gap repressors, including Kruppel, Knirps, and Hb itself. We propose that this repression helps ensure precision of the anterior Hb border in response to variations in the Bicoid gradient.

Mutual repression enhances the steepness and precision of gene expression boundaries

Embryonic development is driven by spatial patterns of gene expression that determine the fate of each cell in the embryo. While gene expression is often highly erratic, embryonic development is usually exceedingly precise. In particular, gene expression boundaries are robust not only against intra-embryonic fluctuations such as noise in gene expression and protein diffusion, but also against embryo-to-embryo variations in the morphogen gradients, which provide positional information to the differentiating cells. How development is robust against intra- and inter-embryonic variations is not understood. A common motif in the gene regulation networks that control embryonic development is mutual repression between pairs of genes. To assess the role of mutual repression in the robust formation of gene expression patterns, we have performed large-scale stochastic simulations of a minimal model of two mutually repressing gap genes in Drosophila, hunchback (hb) and knirps (kni). Our model includes not only mutual repression between hb and kni, but also the stochastic and cooperative activation of hb by the anterior morphogen Bicoid (Bcd) and of kni by the posterior morphogen Caudal (Cad), as well as the diffusion of Hb and Kni between neighboring nuclei. Our analysis reveals that mutual repression can markedly increase the steepness and precision of the gap gene expression boundaries. In contrast to other mechanisms such as spatial averaging and cooperative gene activation, mutual repression thus allows for gene-expression boundaries that are both steep and precise. Moreover, mutual repression dramatically enhances their robustness against embryo-to-embryo variations in the morphogen levels. Finally, our simulations reveal that diffusion of the gap proteins plays a critical role not only in reducing the width of the gap gene expression boundaries via the mechanism of spatial averaging, but also in repairing patterning errors that could arise because of the bistability induced by mutual repression.

The role of Bicoid cooperative binding in the patterning of sharp borders in Drosophila melanogaster

In Drosophila embryonic development, the Bicoid (Bcd) protein establishes positional information of downstream developmental genes like hunchback (hb), which has a strong anterior expression and a sharp on-off boundary in the mid-embryo. The role of Bcd cooperative binding in the positioning of the Hb pattern has been previously demonstrated. However, there are discrepancies in the reported results about the role of this mechanism in the sharp Hb border. Here, we determined the Hill coefficient (nH) required for Bcd to generate the sharp border of Hb in wild-type (WT) embryos. We found that an n(H) of approximately 6.3 (s.d. 1.4) and 10.8 (s.d. 4.0) is required to account for Hb sharpness at early and late cycle 14A, respectively. Additional mechanisms are possibly required because the high nH is likely unachievable for Bcd binding to the hb promoter. To test this idea, we determined the nH required to pattern the Hb profile of 15 embryos expressing an hb14F allele that is defective in self-activation and found nH to be 3.0 (s.d. 1.0). This result indicates that in WT embryos, the hb self-activation is important for Hb sharpness. Corroborating our results, we also found a progressive increase in the required value of n(H) spanning from 4.0 to 9.2 by determining this coefficient from averaged profiles of eight temporal classes at cycle 14A (T1 to T8). Our results indicate that there is a transition in the mechanisms responsible for the sharp Hb border during cycle 14A: in early stages of this cycle, Bcd cooperative binding is primarily responsible for Hb sharpness; in late cycle 14A, hb self-activation becomes the dominant mechanism.

Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

Stochastic reaction-diffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-diffusion simulation algorithm that samples realizations from the exact solution of the reaction-diffusion master equation. The present algorithm, called partial-propensity stochastic reaction-diffusion (PSRD) method, uses an on-lattice discretization of the reaction-diffusion system and relies on partial-propensity methods for computational efficiency. We describe the algorithm in detail, provide a theoretical analysis of its computational cost, and demonstrate its computational performance in benchmarks. We then illustrate the application of PSRD to two- and three-dimensional pattern-forming Gray-Scott systems, highlighting the role of intrinsic noise in these systems.

Evaluating the Drosophila Bicoid morphogen gradient system through dissecting the noise in transcriptional bursts

MOTIVATION

We describe a statistical model to dissect the noise in transcriptional bursts in a developmental system.

RESULTS

We assume that, at any given moment of time, each copy of a native gene inside a cell can exist in either a bursting (active) or non-bursting (inactive) state. The experimentally measured total noise in the transcriptional states of a gene in a population of cells can be mathematically dissected into two contributing components: internal and external. While internal noise quantifies the stochastic nature of transcriptional bursts, external noise is caused by cell-to-cell differences including fluctuations in activator concentration. We use our developed methods to analyze the Drosophila Bicoid (Bcd) morphogen gradient system. For its target gene hunchback (hb), the noise properties can be recapitulated by a simplified gene regulatory model in which Bcd acts as the only input, suggesting that the external noise in hb transcription is primarily derived from fluctuations in the Bcd activator input. However, such a simplified gene regulatory model is insufficient to predict the noise properties of another Bcd target gene, orthodenticle (otd), suggesting that otd transcription is sensitive to additional external fluctuations beyond those in Bcd. Our results show that analysis of the relationship between input and output noise can reveal important insights into how a morphogen gradient system works. Our study also advances the knowledge about transcription at a fundamental level.

CONTACT

jun.ma@cchmc.org

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Measuring gene expression noise in early Drosophila embryos: nucleus-to-nucleus variability

In recent years the analysis of noise in gene expression has widely attracted the attention of experimentalists and theoreticians. Experimentally, the approaches based on in vivo fluorescent reporters in single cells appear to be straightforward and effective tools for bacteria and yeast. However, transferring these approaches to multicellular organisms presents many methodological problems. Here we describe our approach to measure between-nucleus variability (noise) in the primary morphogenetic gradient of Bicoid (Bcd) in the precellular blastoderm stage of fruit fly (Drosophila) embryos. The approach is based on the comparison of results for fixed immunostained embryos with observations of live embryos carrying fluorescent Bcd (Bcd-GFP). We measure the noise using two-dimensional Singular Spectrum Analysis (2D SSA). We have found that the nucleus-to-nucleus noise in Bcd intensity, both for live (Bcd-GFP) and for fixed immunstained embryos, tends to be signal-independent. In addition, the character of the noise is sensitive to the nuclear masking technique used to extract quantitative intensities. Further, the method of decomposing the raw quantitative expression data into a signal (expression surface) and residual noise affects the character of the residual noise. We find that careful masking of confocal images and use of appropriate computational tools to decompose raw expression data into trend and noise makes it possible to extract and study the biological noise of gene expression.

Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain

Morphogens provide positional information for spatial patterns of gene expression during development. However, stochastic effects such as local fluctuations in morphogen concentration and noise in signal transduction make it difficult for cells to respond to their positions accurately enough to generate sharp boundaries between gene expression domains. During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5. Fluorescent in situ hybridization reveals rough edges around these gene expression domains, in which cells co-express hoxb1a and krox20 on either side of the boundary, and these sharpen within a few hours. Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments. In particular, fluctuations in RA initially induce a rough boundary that requires noise in hoxb1a/krox20 expression to sharpen. This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

Evolutionary origins of transcription factor binding site clusters

Empirical studies have revealed that regulatory DNA sequences such as enhancers or promoters often harbor multiple binding sites for the same transcription factor. Such "homotypic site clustering" has been hypothesized as arising out of functional requirements of the sequences. Here, we propose an alternative explanation of this phenomenon that multisite enhancers are common because they are favored by evolutionary sampling of the genotype-phenotype landscape. To test this hypothesis, we developed a new computational framework specialized for population genetic simulations of enhancer evolution. It uses a thermodynamics-based model of enhancer function, integrating information from strong as well as weak binding sites, to determine the strength of selection. Using this framework, we found that even when simpler genotypes exist for a desired strength of regulation, relatively complex genotypes (enhancers with more sites) are more readily reached by the simulated evolutionary process. We show that there are more ways to "build" a fit genotype with many weak sites than with a few strong sites, and this is why evolution finds complex genotypes more often. Our claims are consistent with an empirical analysis of binding site content in enhancers characterized in Drosophila melanogaster and their orthologs in other Drosophila species. We also characterized a subtle but significant difference between genotypes likely to be sampled by evolution and equally fit genotypes one would obtain by uniform sampling of the fitness landscape, that is, an "evolutionary signature" in enhancer sequences. Finally, we investigated potential effects of other factors, such as rugged fitness landscapes, short local duplications, and noise characteristics of enhancers, on the emergence of homotypic site clustering. Homotypic site clustering is an important contributor to the complexity and function of cis-regulatory sequences. This work provides a simple null hypothesis for its origin, against which alternative adaptationist explanations may be evaluated, and cautions against "evolutionary mirages" present in common features of genomic sequence. The quantitative framework we develop here can be used more generally to understand how mechanisms of enhancer action influence their composition and evolution.

The Drosophila gap gene network is composed of two parallel toggle switches

Drosophila “gap” genes provide the first response to maternal gradients in the early fly embryo. Gap genes are expressed in a series of broad bands across the embryo during first hours of development. The gene network controlling the gap gene expression patterns includes inputs from maternal gradients and mutual repression between the gap genes themselves. In this study we propose a modular design for the gap gene network, involving two relatively independent network domains. The core of each network domain includes a toggle switch corresponding to a pair of mutually repressive gap genes, operated in space by maternal inputs. The toggle switches present in the gap network are evocative of the phage lambda switch, but they are operated positionally (in space) by the maternal gradients, so the synthesis rates for the competing components change along the embryo anterior-posterior axis. Dynamic model, constructed based on the proposed principle, with elements of fractional site occupancy, required 5–7 parameters to fit quantitative spatial expression data for gap gradients. The identified model solutions (parameter combinations) reproduced major dynamic features of the gap gradient system and explained gap expression in a variety of segmentation mutants.

Morphogen gradient formation and action: insights from studying Bicoid protein degradation

In a recent publication, we identified a novel F-box protein, encoded by fates-shifted (fsd), that plays a role in targeting Bcd for ubiquitination and degradation. Our analysis of mutant Drosophila embryos suggests that Bcd protein degradation is important for proper gradient formation and developmental fate specification. Here we describe further experiments that lead to an estimate of Bcd half-life, < 15 min, in embryos during the time of gradient formation. We use our findings to evaluate different models of Bcd gradient formation. With this new estimate, we simulate the Bcd gradient formation process in our own biologically realistic 2-D model. Finally, we discuss the role of Bcd-encoded positional information in controlling the positioning and precision of developmental decisions.