A computational statistics approach for estimating the spatial range of morphogen gradients

A reaction-diffusion network model predicts a dual role of Cactus/IκB to regulate Dorsal/NFκB nuclear translocation in Drosophila

Dorsal-ventral patterning of the Drosophila embryo depends on the NFκB superfamily transcription factor Dorsal (Dl). Toll receptor activation signals for degradation of the IκB inhibitor Cactus (Cact), leading to a ventral-to-dorsal nuclear Dl gradient. Cact is critical for Dl nuclear import, as it binds to and prevents Dl from entering the nuclei. Quantitative analysis of cact mutants revealed an additional Cact function to promote Dl nuclear translocation in ventral regions of the embryo. To investigate this dual Cact role, we developed a predictive model based on a reaction-diffusion regulatory network. This network distinguishes non-uniform Toll-dependent Dl nuclear import and Cact degradation, from the Toll-independent processes of Cact degradation and reversible nuclear-cytoplasmic Dl flow. In addition, it incorporates translational control of Cact levels by Dl. Our model successfully reproduces wild-type data and emulates the Dl nuclear gradient in mutant dl and cact allelic combinations. Our results indicate that the dual role of Cact depends on the dynamics of Dl-Cact trimers along the dorsal-ventral axis: In the absence of Toll activation, free Dl-Cact trimers retain Dl in the cytoplasm, limiting the flow of Dl into the nucleus; in ventral-lateral regions, Dl-Cact trimers are recruited by Toll activation into predominant signaling complexes and promote Dl nuclear translocation. Simulations suggest that the balance between Toll-dependent and Toll-independent processes are key to this dynamics and reproduce the full assortment of Cact effects. Considering the high evolutionary conservation of these pathways, our analysis should contribute to understanding NFκB/c-Rel activation in other contexts such as in the vertebrate immune system and disease.

In Drosophila, Toll pathway establishes spatially distinct gene expression territories that define the embryonic dorsal-ventral axis. Toll activation leads to degradation of the IκB inhibitor Cactus, releasing the NFκB superfamily transcription factor Dorsal for nuclear entry. Recently, quantitative analysis of cact mutants revealed that Cact displays an additional function to promote Dl nuclear translocation in ventral regions of the embryo. To understand this novel activity, we developed a predictive theoretical model that shows that the kinetics of Dorsal-Cactus complex formation prior to their recruitment to Toll-signaling complexes is an essential regulatory hub. Cactus controls the balance between the recruitment of these complexes by active Toll receptor and association-dissociation events that generate free Dorsal for direct nuclear import.

French flag gradients and Turing reaction-diffusion versus differentiation waves as models of morphogenesis

The Turing reaction-diffusion model and the French Flag Model are widely accepted in the field of development as the best models for explaining embryogenesis. Virtually all current attempts to understand cell differentiation in embryos begin and end with the assumption that some combination of these two models works. The result may become a bias in embryogenesis in assuming the problem has been solved by these two-chemical substance-based models. Neither model is applied consistently. We review the differences between the French Flag, Turing reaction-diffusion model, and a mechanochemical model called the differentiation wave/cell state splitter model. The cytoskeletal cell state splitter and the embryonic differentiation waves was first proposed in 1987 as a combined physics and chemistry model for cell differentiation in embryos, based on empirical observations on urodele amphibian embryos. We hope that the development of theory can be advanced and observations relevant to distinguishing the embryonic differentiation wave model from the French Flag model and reaction-diffusion equations will be taken up by experimentalists. Experimentalists rely on mathematical biologists for theory, and therefore depend on them for what parameters they choose to measure and ignore. Therefore, mathematical biologists need to fully understand the distinctions between these three models.

Formation, interpretation, and regulation of the Drosophila Dorsal/NF-κB gradient

The morphogen gradient of the transcription factor Dorsal in the early Drosophila embryo has become one of the most widely studied tissue patterning systems. Dorsal is a Drosophila homolog of mammalian NF-κB and patterns the dorsal-ventral axis of the blastoderm embryo into several tissue types by spatially regulating upwards of 100 zygotic genes. Recent studies using fluorescence microscopy and live imaging have quantified the Dorsal gradient and its target genes, which has paved the way for mechanistic modeling of the gradient. In this review, we describe the mechanisms behind the initiation of the Dorsal gradient and its regulation of target genes. The main focus of the review is a discussion of quantitative and computational studies of the Dl gradient system, including regulation of the Dl gradient. We conclude with a discussion of potential future directions.

Two-Exponential Models of Gene Expression Patterns for Noisy Experimental Data

Spatial pattern formation of the primary anterior-posterior morphogenetic gradient of the transcription factor Bicoid (Bcd) has been studied experimentally and computationally for many years. Bcd specifies positional information for the downstream segmentation genes, affecting the fly body plan. More recently, a number of researchers have focused on the patterning dynamics of the underlying bcd messenger RNA (mRNA) gradient, which is translated into Bcd protein. New, more accurate techniques for visualizing bcd mRNA need to be combined with quantitative signal extraction techniques to reconstruct the bcd mRNA distribution. Here, we present a robust technique for quantifying gradients with a two-exponential model. This approach (1) has natural, biologically relevant parameters and (2) is invariant to linear transformations of the data arising due to variation in experimental conditions (e.g., microscope settings, nonspecific background signal). This allows us to quantify bcd mRNA gradient variability from embryo to embryo (important for studying the robustness of developmental regulatory networks); sort out atypical gradients; and classify embryos to developmental stage by quantitative gradient parameters.

Biochemical and in silico evaluation of recombinant E. coli aminopeptidase and in vitro processed human interferon α-2b

Escherichia coli is an extensively used host for the production of recombinant proteins, making its N-terminal methionine aminopeptidase (MAP) an attractive candidate for studies on posttranslational protein processing. The present study describes the recombinant production and properties of MAP from the DH5α strain of E. coli. The soluble and active enzyme was produced in E. coli BL21 (DE3) RIL - codon plus cells under a T7 promoter system and purified by anion-exchange chromatography. It exhibited a molecular weight of 29,200.94 Da by MALDI-TOF analysis. The purified enzyme showed specific activity of 1.64 U/mg with methionylp-nitroanilide and 1.51 U/mg with synthetic tetrapeptide substrate 'MGMM' in a discontinuous HPLC-based assay. In vitro studies showed the processing of up to 36% of Met-INFα-2b in 40 min. In silico studies revealed that the ES-complex formation between the enzyme and interferon has a ΔG -683.07 kJ/mol. Molecular docking results showed that the processed INFα-2b has greater binding affinity with IFNAR2 receptor as indicated by ΔG -784.53 kJ/mol, significantly lower than that of methionine containing INFα-2b (ΔG -717.63 kJ/mol). These findings emphasize the functional superiority or better efficacy of N-terminal methionine processed recombinant interferon.

The organelle of differentiation in embryos: the cell state splitter

The cell state splitter is a membraneless organelle at the apical end of each epithelial cell in a developing embryo. It consists of a microfilament ring and an intermediate filament ring subtending a microtubule mat. The microtubules and microfilament ring are in mechanical opposition as in a tensegrity structure. The cell state splitter is bistable, perturbations causing it to contract or expand radially. The intermediate filament ring provides metastability against small perturbations. Once this snap-through organelle is triggered, it initiates signal transduction to the nucleus, which changes gene expression in one of two readied manners, causing its cell to undergo a step of determination and subsequent differentiation. The cell state splitter also triggers the cell state splitters of adjacent cells to respond, resulting in a differentiation wave. Embryogenesis may be represented then as a bifurcating differentiation tree, each edge representing one cell type. In combination with the differentiation waves they propagate, cell state splitters explain the spatiotemporal course of differentiation in the developing embryo. This review is excerpted from and elaborates on "Embryogenesis Explained" (World Scientific Publishing, Singapore, 2016).

Microfluidics for High-Throughput Quantitative Studies of Early Development

Developmental biology has traditionally relied on qualitative analyses; recently, however, as in other fields of biology, researchers have become increasingly interested in acquiring quantitative knowledge about embryogenesis. Advances in fluorescence microscopy are enabling high-content imaging in live specimens. At the same time, microfluidics and automation technologies are increasing experimental throughput for studies of multicellular models of development. Furthermore, computer vision methods for processing and analyzing bioimage data are now leading the way toward quantitative biology. Here, we review advances in the areas of fluorescence microscopy, microfluidics, and data analysis that are instrumental to performing high-content, high-throughput studies in biology and specifically in development. We discuss a case study of how these techniques have allowed quantitative analysis and modeling of pattern formation in the Drosophila embryo.

An integrated platform for large-scale data collection and precise perturbation of live Drosophila embryos

Understanding the fundamental principles governing embryogenesis is a key goal of developmental biology. Direct observation of embryogenesis via in vivo live imaging is vital to understanding embryogenesis; yet, tedious sample preparation makes it difficult to acquire large-scale imaging data that is often required to overcome experimental and biological noises for quantitative studies. Furthermore, it is often difficult, and sometimes impossible, to incorporate environmental perturbation for understanding developmental responses to external stimuli. To address this issue, we have developed a method for high-throughput imaging of live embryos, delivering precise environmental perturbations, and unbiased data extraction. This platform includes an optimized microfluidic device specifically for live embryos and also for precise perturbations in the microenvironment of the developing embryos. In addition, we developed software for simple, yet accurate, automated segmentation of fluorescent images, and automated data extraction. Using a quantitative assessment we find that embryos develop normally within the microfluidic device. Finally, we show an application of the high-throughput assay for monitoring developmental responses to external stimuli: anoxia-induced developmental arrest in Drosophila embryos. With slight modifications, the method developed in this work can be applied to many other models of development and other stimulus-response behaviors during development.

Efficient processing and analysis of large-scale light-sheet microscopy data

Light-sheet microscopy is a powerful method for imaging the development and function of complex biological systems at high spatiotemporal resolution and over long time scales. Such experiments typically generate terabytes of multidimensional image data, and thus they demand efficient computational solutions for data management, processing and analysis. We present protocols and software to tackle these steps, focusing on the imaging-based study of animal development. Our protocols facilitate (i) high-speed lossless data compression and content-based multiview image fusion optimized for multicore CPU architectures, reducing image data size 30-500-fold; (ii) automated large-scale cell tracking and segmentation; and (iii) visualization, editing and annotation of multiterabyte image data and cell-lineage reconstructions with tens of millions of data points. These software modules are open source. They provide high data throughput using a single computer workstation and are readily applicable to a wide spectrum of biological model systems.

The presence of nuclear cactus in the early Drosophila embryo may extend the dynamic range of the dorsal gradient

In a developing embryo, the spatial distribution of a signaling molecule, or a morphogen gradient, has been hypothesized to carry positional information to pattern tissues. Recent measurements of morphogen distribution have allowed us to subject this hypothesis to rigorous physical testing. In the early Drosophila embryo, measurements of the morphogen Dorsal, which is a transcription factor responsible for initiating the earliest zygotic patterns along the dorsal-ventral axis, have revealed a gradient that is too narrow to pattern the entire axis. In this study, we use a mathematical model of Dorsal dynamics, fit to experimental data, to determine the ability of the Dorsal gradient to regulate gene expression across the entire dorsal-ventral axis. We found that two assumptions are required for the model to match experimental data in both Dorsal distribution and gene expression patterns. First, we assume that Cactus, an inhibitor that binds to Dorsal and prevents it from entering the nuclei, must itself be present in the nuclei. And second, we assume that fluorescence measurements of Dorsal reflect both free Dorsal and Cactus-bound Dorsal. Our model explains the dynamic behavior of the Dorsal gradient at lateral and dorsal positions of the embryo, the ability of Dorsal to regulate gene expression across the entire dorsal-ventral axis, and the robustness of gene expression to stochastic effects. Our results have a general implication for interpreting fluorescence-based measurements of signaling molecules.

Imaging the dorsal-ventral axis of live and fixed Drosophila melanogaster embryos

Optimal imaging conditions are of critical importance in developmental biology, as much of the data in the discipline is acquired through microscopy. However, imaging deep sections of tissue, especially live tissue, can be a technical challenge due to light scattering and difficulties in mounting the sample. In particular, capturing high-quality images of dorsal-ventral cross sections requires "end-on" mounting to orient the anterior-posterior axis vertically. Here we present methods to mount and image dorsal-ventral cross sections of both live and fixed Drosophila melanogaster embryos. Our methods have the advantages of being rapid, allowing deep optical sections, and not requiring expensive, specialized equipment.

Zelda potentiates morphogen activity by increasing chromatin accessibility

Zygotic genome activation (ZGA) is a major genome programming event whereby the cells of the embryo begin to adopt specified fates. Experiments in Drosophila and zebrafish have revealed that ZGA depends on transcription factors that provide large-scale control of gene expression by direct and specific binding to gene regulatory sequences. Zelda (Zld) plays such a role in the Drosophila embryo, where it has been shown to control the action of patterning signals; however, the mechanisms underlying this effect remain largely unclear. A recent model proposed that Zld binding sites act as quantitative regulators of the spatiotemporal expression of genes activated by Dorsal (Dl), the morphogen that patterns the dorsoventral axis. Here we tested this model experimentally, using enhancers of brinker (brk) and short gastrulation (sog), both of which are directly activated by Dl, but at different concentration thresholds. In agreement with the model, we show that there is a clear positive correlation between the number of Zld binding sites and the spatial domain of enhancer activity. Likewise, the timing of expression could be advanced or delayed. We present evidence that Zld facilitates binding of Dl to regulatory DNA, and that this is associated with increased chromatin accessibility. Importantly, the change in chromatin accessibility is strongly correlated with the change in Zld binding, but not Dl. We propose that the ability of genome activators to facilitate readout of transcriptional input is key to widespread transcriptional induction during ZGA.

Paused Pol II coordinates tissue morphogenesis in the Drosophila embryo

Paused RNA polymerase (Pol II) is a pervasive feature of Drosophila embryos and mammalian stem cells, but its role in development is uncertain. Here, we demonstrate that a spectrum of paused Pol II determines the "time to synchrony"-the time required to achieve coordinated gene expression across the cells of a tissue. To determine whether synchronous patterns of gene activation are significant in development, we manipulated the timing of snail expression, which controls the coordinated invagination of ∼1,000 mesoderm cells during gastrulation. Replacement of the strongly paused snail promoter with moderately paused or nonpaused promoters causes stochastic activation of snail expression and increased variability of mesoderm invagination. Computational modeling of the dorsal-ventral patterning network recapitulates these variable and bistable gastrulation profiles and emphasizes the importance of timing of gene activation in development. We conclude that paused Pol II and transcriptional synchrony are essential for coordinating cell behavior during morphogenesis.

Size-dependent regulation of dorsal-ventral patterning in the early Drosophila embryo

How natural variation in embryo size affects patterning of the Drosophila embryo dorsal-ventral (DV) axis is not known. Here we examined quantitatively the relationship between nuclear distribution of the Dorsal transcription factor, boundary positions for several target genes, and DV axis length. Data were obtained from embryos of a wild-type background as well as from mutant lines inbred to size select embryos of smaller or larger sizes. Our data show that the width of the nuclear Dorsal gradient correlates with DV axis length. In turn, for some genes expressed along the DV axis, the boundary positions correlate closely with nuclear Dorsal levels and with DV axis length; while the expression pattern of others is relatively constant and independent of the width of the Dorsal gradient. In particular, the patterns of snail (sna) and ventral nervous system defective (vnd) correlate with nuclear Dorsal levels and exhibit scaling to DV length; while the pattern of intermediate neuroblasts defective (ind) remains relatively constant with respect to changes in Dorsal and DV length. However, in mutants that exhibit an abnormal expansion of the Dorsal gradient which fails to scale to DV length, only sna follows the Dorsal distribution and exhibits overexpansion; in contrast, vnd and ind do not overexpand suggesting some additional mechanism acts to refine the dorsal boundaries of these two genes. Thus, our results argue against the idea that the Dorsal gradient works as a global system of relative coordinates along the DV axis and suggest that individual targets respond to changes in embryo size in a gene-specific manner.

Kinetics of gene derepression by ERK signaling

ERK controls gene expression in development, but mechanisms that link ERK activation to changes in transcription are not well understood. We used high-resolution analysis of signaling dynamics to study transcriptional interpretation of ERK signaling during Drosophila embryogenesis, at a stage when ERK induces transcription of intermediate neuroblasts defective (ind), a gene essential for patterning of the nerve cord. ERK induces ind by antagonizing its repression by Capicua (Cic), a transcription factor that acts as a sensor of receptor tyrosine kinases in animal development and human diseases. A recent study established that active ERK reduces the nuclear levels of Cic, but it remained unclear whether this is required for the induction of Cic target genes. We provide evidence that Cic binding sites within the regulatory DNA of ind control the spatial extent and the timing of ind expression. At the same time, we demonstrate that ERK induces ind before Cic levels in the nucleus are reduced. Based on this, we propose that ERK-dependent relief of gene repression by Cic is a two-step process, in which fast reduction of repressor activity is followed by slower changes in nuclear localization and overall protein levels. This may be a common feature of systems in which ERK induces genes by relief of transcriptional repression.

Microfluidic trap array for massively parallel imaging of Drosophila embryos

Here we describe a protocol for the fabrication and use of a microfluidic device to rapidly orient >700 Drosophila embryos in parallel for end-on imaging. The protocol describes master microfabrication (∼1 d), polydimethylsiloxane molding (few hours), system setup and device operation (few minutes) and imaging (depending on application). Our microfluidics-based approach described here is one of the first to facilitate rapid orientation for end-on imaging, and it is a major breakthrough for quantitative studies on Drosophila embryogenesis. The operating principle of the embryo trap is based on passive hydrodynamics, and it does not require direct manipulation of embryos by the user; biologists following the protocol should be able to repeat these procedures. The compact design and fabrication materials used allow the device to be used with traditional microscopy setups and do not require specialized fixtures. Furthermore, with slight modification, this array can be applied to the handling of other model organisms and oblong objects.

Temporal dynamics, spatial range, and transcriptional interpretation of the Dorsal morphogen gradient

Dorsoventral pattern of Drosophila embryo is specified by the nuclear localization gradient of the transcription factor Dorsal. Genetic and genomic studies of this morphogen gradient provided important insights into spatial control of gene expression in development. Recent live imaging experiments revealed hitherto unappreciated dynamics of the Dorsal gradient and posed new questions about the mechanisms of its transcriptional interpretation. Some of these questions can be answered by models in which the morphogenetic capacity of the Dorsal gradient is potentiated by spatially uniform factors, such as Zelda, a transcription factor that plays a key role in the activation of zygotic transcription. Combinatorial effects of uniform and graded factors play an important role in the transcriptional and signaling cascades initiated by Dorsal and may explain differential positioning of gene expression borders by other morphogen gradients.

RTK signaling modulates the Dorsal gradient

The dorsoventral (DV) axis of the Drosophila embryo is patterned by a nuclear gradient of the Rel family transcription factor, Dorsal (Dl), that activates or represses numerous target genes in a region-specific manner. Here, we demonstrate that signaling by receptor tyrosine kinases (RTK) reduces nuclear levels and transcriptional activity of Dl, both at the poles and in the mid-body of the embryo. These effects depend on wntD, which encodes a Dl antagonist belonging to the Wingless/Wnt family of secreted factors. Specifically, we show that, via relief of Groucho- and Capicua-mediated repression, the Torso and EGFR RTK pathways induce expression of WntD, which in turn limits Dl nuclear localization at the poles and along the DV axis. Furthermore, this RTK-dependent control of Dl is important for restricting expression of its targets in both contexts. Thus, our results reveal a new mechanism of crosstalk, whereby RTK signals modulate the spatial distribution and activity of a developmental morphogen in vivo.

Pattern formation by graded and uniform signals in the early Drosophila embryo

The early Drosophila embryo is patterned by graded distributions of maternal transcription factors. Recent studies revealed that pattern formation by these graded signals depends on uniformly expressed transcriptional activators, such as Zelda. Removal of Zelda influences both the timing and the spatial expression domains for most of the genes controlled by maternal gradients. We demonstrate that some of these patterning defects, which range from temporal delay to loss of expression, can be rationalized with the use of a mathematical model based on cooperative binding of graded and uniform factors. This model makes a number of predictions, which we confirm experimentally by analyzing the expression of short gastrulation (sog), a gene that is controlled by a combination of the Dorsal morphogen gradient and Zelda. The proposed model suggests a general mechanism for the formation of nested gene expression domains, which is a hallmark of tissue patterning by morphogen gradients. According to this mechanism, the differential effects of a morphogen on its target genes can depend on their differential sensitivity to uniform factors.