The bicoid morphogen system

Quantifying Information of Dynamical Biochemical Reaction Networks

A large number of complex biochemical reaction networks are included in the gene expression, cell development, and cell differentiation of in vivo cells, among other processes. Biochemical reaction-underlying processes are the ones transmitting information from cellular internal or external signaling. However, how this information is measured remains an open question. In this paper, we apply the method of information length, based on the combination of Fisher information and information geometry, to study linear and nonlinear biochemical reaction chains, respectively. Through a lot of random simulations, we find that the amount of information does not always increase with the length of the linear reaction chain; instead, the amount of information varies significantly when this length is not very large. When the length of the linear reaction chain reaches a certain value, the amount of information hardly changes. For nonlinear reaction chains, the amount of information changes not only with the length of this chain, but also with reaction coefficients and rates, and this amount also increases with the length of the nonlinear reaction chain. Our results will help to understand the role of the biochemical reaction networks in cells.

Aurora kinases: Generators of spatial control during mitosis

Cell division events require regulatory systems to ensure that events happen in a distinct order. The classic view of temporal control of the cell cycle posits that cells order events by linking them to changes in Cyclin Dependent Kinase (CDK) activities. However, a new paradigm is emerging from studies of anaphase where chromatids separate at the central metaphase plate and then move to opposite poles of the cell. These studies suggest that distinct events are ordered depending upon the location of each chromosome along its journey from the central metaphase plate to the elongated spindle poles. This system is dependent upon a gradient of Aurora B kinase activity that emerges during anaphase and acts as a spatial beacon to control numerous anaphase/telophase events and cytokinesis. Recent studies also suggest that Aurora A kinase activity specifies proximity of chromosomes or proteins to spindle poles during prometaphase. Together these studies argue that a key role for Aurora kinases is to provide spatial information that controls events depending upon the location of chromosomes or proteins along the mitotic spindle.

Shaping the scaling characteristics of gap gene expression patterns in Drosophila

How patterns are formed to scale with tissue size remains an unresolved problem. Here we investigate embryonic patterns of gap gene expression along the anterior-posterior (AP) axis in Drosophila. We use embryos that greatly differ in length and, importantly, possess distinct length-scaling characteristics of the Bicoid (Bcd) gradient. We systematically analyze the dynamic movements of gap gene expression boundaries in relation to both embryo length and Bcd input as a function of time. We document the process through which such dynamic movements drive both an emergence of a global scaling landscape and evolution of boundary-specific scaling characteristics. We show that, despite initial differences in pattern scaling characteristics that mimic those of Bcd in the anterior, such characteristics of final patterns converge. Our study thus partitions the contributions of Bcd input and regulatory dynamics inherent to the AP patterning network in shaping embryonic pattern's scaling characteristics.

Twenty-seven ZAD-ZNF genes of Drosophila melanogaster are orthologous to the embryo polarity determining mosquito gene cucoid

The C2H2 zinc finger gene cucoid establishes anterior-posterior (AP) polarity in the early embryo of culicine mosquitoes. This gene is unrelated to genes that establish embryo polarity in other fly species (Diptera), such as the homeobox gene bicoid, which serves this function in the traditional model organism Drosophila melanogaster. The cucoid gene is a conserved single copy gene across lower dipterans but nothing is known about its function in other species, and its evolution in higher dipterans, including Drosophila, is unresolved. We found that cucoid is a member of the ZAD-containing C2H2 zinc finger (ZAD-ZNF) gene family and is orthologous to 27 of the 91 members of this family in D. melanogaster, including M1BP, ranshi, ouib, nom, zaf1, odj, Nnk, trem, Zif, and eighteen uncharacterized genes. Available knowledge of the functions of cucoid orthologs in Drosophila melanogaster suggest that the progenitor of this lineage specific expansion may have played a role in regulating chromatin. We also describe many aspects of the gene duplication history of cucoid in the brachyceran lineage of D. melanogaster, thereby providing a framework for predicting potential redundancies among these genes in D. melanogaster.

Steady-State Operation of a Cell-Free Genetic Band-Detection Circuit

Pattern formation processes play a decisive role during embryogenesis and involve the precise spatial and temporal orchestration of intricate gene regulatory processes. Synthetic gene circuits modeled after their biological counterparts can be used to investigate such processes under well-controlled conditions and may, in the future, be utilized for autonomous position determination in synthetic biological materials. Here, we investigated a three-node feed-forward gene regulatory circuit in vitro that generates three distinct fluorescent outputs in response to varying concentrations of a single externally supplied morphogen. The circuit acts as a band detector for the morphogen concentration and, in a spatial context, could serve as a stripe-forming gene circuit. We simulated the behavior of the genetic circuit in the presence of a morphogen gradient using a system of ordinary differential equations and determined optimal parameters for stripe-pattern formation using an evolutionary algorithm. To analyze the subcircuits of the system, we conducted cell-free characterization experiments and finally tested the whole genetic circuit in nanoliter-scale microfluidic flow reactors that provided a continuous supply of cell extract and metabolites and allowed removal of degradation products. To make use of the widely employed promoters P_LlacO-1 and P_LtetO-1 in our design, we removed LacI from our bacterial cell extract by genome engineering Escherichia coli using a pORTMAGE workflow. Our results show that the band-detector works as designed when operated out of equilibrium within the flow reactors. On the other hand, subcircuits of the system and the whole circuit fail to generate the desired gene expression response when operated in a closed reactor. Our work thus underlines the importance of out-of-equilibrium operation of complex gene circuits, which cannot settle to a steady-state expression pattern within the finite lifetime of a cell-free expression system.

Hunchback activates Bicoid in Pair1 neurons to regulate synapse number and locomotor circuit function

Neural circuit function underlies cognition, sensation, and behavior. Proper circuit assembly depends on the identity of the neurons in the circuit (gene expression, morphology, synapse targeting, and biophysical properties). Neuronal identity is established by spatial and temporal patterning mechanisms, but little is known about how these mechanisms drive circuit formation in postmitotic neurons. Temporal patterning involves the sequential expression of transcription factors (TFs) in neural progenitors to diversify neuronal identity, in part through the initial expression of homeodomain TF combinations. Here, we address the role of the Drosophila temporal TF Hunchback and the homeodomain TF Bicoid in the assembly of the Pair1 (SEZ_DN1) descending neuron locomotor circuit, which promotes larval pausing and head casting. We find that both Hunchback and Bicoid are expressed in larval Pair1 neurons, Hunchback activates Bicoid in Pair1 (opposite of their embryonic relationship), and the loss of Hunchback function or Bicoid function from Pair1 leads to ectopic presynapse numbers in Pair1 axons and an increase in Pair1-induced pausing behavior. These phenotypes are highly specific, as the loss of Bicoid or Hunchback has no effect on Pair1 neurotransmitter identity, dendrite morphology, or axonal morphology. Importantly, the loss of Hunchback or Bicoid in Pair1 leads to the addition of new circuit partners that may underlie the exaggerated locomotor pausing behavior. These data are the first to show a role for Bicoid outside of embryonic patterning and the first to demonstrate a cell-autonomous role for Hunchback and Bicoid in interneuron synapse targeting and locomotor behavior.

Suboptimal Intermediates Underlie Evolution of the Bicoid Homeodomain

Changes in regulatory networks generate materials for evolution to create phenotypic diversity. For transcription networks, multiple studies have shown that alterations in binding sites of cis-regulatory elements correlate well with the gain or loss of specific features of the body plan. Less is known about alterations in the amino acid sequences of the transcription factors (TFs) that bind these elements. Here we study the evolution of Bicoid (Bcd), a homeodomain (HD) protein that is critical for anterior embryo patterning in Drosophila. The ancestor of Bcd (AncBcd) emerged after a duplication of a Zerknullt (Zen)-like ancestral protein (AncZB) in a suborder of flies. AncBcd diverged from AncZB, gaining novel transcriptional and translational activities. We focus on the evolution of the HD of AncBcd, which binds to DNA and RNA, and is comprised of four subdomains: an N-terminal arm (NT) and three helices; H1, H2, and Recognition Helix (RH). Using chimeras of subdomains and gene rescue assays in Drosophila, we show that robust patterning activity of the Bcd HD (high frequency rescue to adulthood) is achieved only when amino acid substitutions in three separate subdomains (NT, H1, and RH) are combined. Other combinations of subdomains also yield full rescue, but with lower penetrance, suggesting alternative suboptimal activities. Our results suggest a multistep pathway for the evolution of the Bcd HD that involved intermediate HD sequences with suboptimal activities, which constrained and enabled further evolutionary changes. They also demonstrate critical epistatic forces that contribute to the robust function of a DNA-binding domain.

Cis-regulatory chromatin loops arise before TADs and gene activation, and are independent of cell fate during early Drosophila development

Acquisition of cell fate is thought to rely on the specific interaction of remote cis-regulatory modules (CRMs), for example, enhancers and target promoters. However, the precise interplay between chromatin structure and gene expression is still unclear, particularly within multicellular developing organisms. In the present study, we employ Hi-M, a single-cell spatial genomics approach, to detect CRM-promoter looping interactions within topologically associating domains (TADs) during early Drosophila development. By comparing cis-regulatory loops in alternate cell types, we show that physical proximity does not necessarily instruct transcriptional states. Moreover, multi-way analyses reveal that multiple CRMs spatially coalesce to form hubs. Loops and CRM hubs are established early during development, before the emergence of TADs. Moreover, CRM hubs are formed, in part, via the action of the pioneer transcription factor Zelda and precede transcriptional activation. Our approach provides insight into the role of CRM-promoter interactions in defining transcriptional states, as well as distinct cell types.

The development of body and organ shape

Background

Organisms show an incredibly diverse array of body and organ shapes that are both unique to their taxon and important for adapting to their environment. Achieving these specific shapes involves coordinating the many processes that transform single cells into complex organs, and regulating their growth so that they can function within a fully-formed body.

Main text

Conceptually, body and organ shape can be separated in two categories, although in practice these categories need not be mutually exclusive. Body shape results from the extent to which organs, or parts of organs, grow relative to each other. The patterns of relative organ size are characterized using allometry. Organ shape, on the other hand, is defined as the geometric features of an organ’s component parts excluding its size. Characterization of organ shape is frequently described by the relative position of homologous features, known as landmarks, distributed throughout the organ. These descriptions fall into the domain of geometric morphometrics.

Conclusion

In this review, we discuss the methods of characterizing body and organ shape, the developmental programs thought to underlie each, highlight when and how the mechanisms regulating body and organ shape might overlap, and provide our perspective on future avenues of research.

Subdiffusion-limited fractional reaction-subdiffusion equations with affine reactions: Solution, stochastic paths, and applications

In contrast to normal diffusion, there is no canonical model for reactions between chemical species which move by anomalous subdiffusion. Indeed, the type of mesoscopic equation describing reaction-subdiffusion systems depends on subtle assumptions about the microscopic behavior of individual molecules. Furthermore, the correspondence between mesoscopic and microscopic models is not well understood. In this paper, we study the subdiffusion-limited model, which is defined by mesoscopic equations with fractional derivatives applied to both the movement and the reaction terms. Assuming that the reaction terms are affine functions, we show that the solution to the fractional system is the expectation of a random time change of the solution to the corresponding integer order system. This result yields a simple and explicit algebraic relationship between the fractional and integer order solutions in Laplace space. We then find the microscopic Langevin description of individual molecules that corresponds to such mesoscopic equations and give a computer simulation method to generate their stochastic trajectories. This analysis identifies some precise microscopic conditions that dictate when this type of mesoscopic model is or is not appropriate. We apply our results to several scenarios in cell biology which, despite the ubiquity of subdiffusion in cellular environments, have been modeled almost exclusively by normal diffusion. Specifically, we consider subdiffusive models of morphogen gradient formation, fluctuating mobility, and fluorescence recovery after photobleaching (FRAP) experiments. We also apply our results to fractional ordinary differential equations.

The dynamic transmission of positional information in stau- mutants during Drosophila embryogenesis

It has been suggested that Staufen (Stau) is key in controlling the variability of the posterior boundary of the Hb anterior domain (xHb). However, the mechanism that underlies this control is elusive. Here, we quantified the dynamic 3D expression of segmentation genes in Drosophila embryos. With improved control of measurement errors, we show that the xHb of stau- mutants reproducibly moves posteriorly by 10% of the embryo length (EL) to the wild type (WT) position in the nuclear cycle (nc) 14, and that its variability over short time windows is comparable to that of the WT. Moreover, for stau- mutants, the upstream Bicoid (Bcd) gradients show equivalent relative intensity noise to that of the WT in nc12-nc14, and the downstream Even-skipped (Eve) and cephalic furrow (CF) show the same positional errors as these factors in WT. Our results indicate that threshold-dependent activation and self-organized filtering are not mutually exclusive and could both be implemented in early Drosophila embryogenesis.

Can the French flag and reaction-diffusion models explain flower patterning? Celebrating the 50th anniversary of the French flag model

It has been 50 years since Lewis Wolpert introduced the French flag model proposing the patterning of different cell types based on threshold concentrations of a morphogen diffusing in the tissue. Sixty-seven years ago, Alan Turing introduced the idea of patterns initiating de novo from a reaction-diffusion network. Together these models have been used to explain many patterning events in animal development, so here we take a look at their applicability to flower development. First, although many plant transcription factors move through plasmodesmata from cell to cell, in the flower there is little evidence that they specify fate in a concentration-dependent manner, so they cannot yet be described as morphogens. Secondly, the reaction-diffusion model appears to be a reasonably good description of the formation of spots of pigment on petals, although additional nuances are present. Thirdly, aspects of both of these combine in a new fluctuation-based patterning system creating the scattered pattern of giant cells in Arabidopsis sepals. In the future, more precise imaging and manipulations of the dynamics of patterning networks combined with mathematical modeling will allow us to better understand how the multilayered complex and beautiful patterns of flowers emerge de novo.

A matter of time: Formation and interpretation of the Bicoid morphogen gradient

Spatially distributed signaling molecules, known as morphogens, provide spatial information during development. A host of different morphogens have now been identified, from subcellular gradients through to morphogens that act across a whole embryo. These gradients form over a wide-range of timescales, from seconds to hours, and their time windows for interpretation are also highly variable; the processes of morphogen gradient formation and interpretation are highly dynamic. The morphogen Bicoid (Bcd), present in the early Drosophila embryo, is essential for setting up the future Drosophila body segments. Due to its accessibility for both genetic perturbations and imaging, this system has provided key insights into how precise patterning can occur within a highly dynamic system. Here, we review the temporal scales of Bcd gradient formation and interpretation. In particular, we discuss the quantitative evidence for different models of Bcd gradient formation, outline the time windows for Bcd interpretation, and describe how Bcd temporally adapts its own ability to be interpreted. The utilization of temporal information in morphogen readout may provide crucial inputs to ensure precise spatial patterning, particularly in rapidly developing systems.

Optogenetic approaches to investigate spatiotemporal signaling during development

Embryogenesis is coordinated by signaling pathways that pattern the developing organism. Many aspects of this process are not fully understood, including how signaling molecules spread through embryonic tissues, how signaling amplitude and dynamics are decoded, and how multiple signaling pathways cooperate to pattern the body plan. Optogenetic approaches can be used to address these questions by providing precise experimental control over a variety of biological processes. Here, we review how these strategies have provided new insights into developmental signaling and discuss how they could contribute to future investigations.

Setting up for gastrulation: D. melanogaster

Drosophila melanogaster embryos develop initially as a syncytium of totipotent nuclei and subsequently, once cellularized, undergo morphogenetic movements associated with gastrulation to generate the three somatic germ layers of the embryo: mesoderm, ectoderm, and endoderm. In this chapter, we focus on the first phase of gastrulation in Drosophila involving patterning of early embryos when cells differentiate their gene expression programs. This patterning process requires coordination of multiple developmental processes including genome reprogramming at the maternal-to-zygotic transition, combinatorial action of transcription factors to support distinct gene expression, and dynamic feedback between this genetic patterning by transcription factors and changes in cell morphology. We discuss the gene regulatory programs acting during patterning to specify the three germ layers, which involve the regulation of spatiotemporal gene expression coupled to physical tissue morphogenesis.

Protein concentration gradients and switching diffusions

Morphogen gradients play a vital role in developmental biology by enabling embryonic cells to infer their spatial location and determine their developmental fate accordingly. The standard mechanism for generating a morphogen gradient involves a morphogen being produced from a localized source and subsequently degrading. While this mechanism is effective over the length and time scales of tissue development, it fails over typical subcellular length scales due to the rapid dissipation of spatial asymmetries. In a recent theoretical work, we found an alternative mechanism for generating concentration gradients of diffusing molecules, in which the molecules switch between spatially constant diffusivities at switching rates that depend on the spatial location of a molecule. Independently, an experimental and computational study later found that Caenorhabditis elegans zygotes rely on this mechanism for cell polarization. In this paper, we extend our analysis of switching diffusivities to determine its role in protein concentration gradient formation. In particular, we determine how switching diffusivities modifies the standard theory and show how space-dependent switching diffusivities can yield a gradient in the absence of a localized source. Our mathematical analysis yields explicit formulas for the intracellular concentration gradient which closely match the results of previous experiments and numerical simulations.

Inference of Transcription Factor Regulation Patterns Using Gene Expression Covariation in Natural Populations of Drosophila melanogaster

Gene regulatory networks control the complex programs that drive development. Deciphering the connections between transcription factors (TFs) and target genes is challenging, in part because TFs bind to thousands of places in the genome but control expression through a subset of these binding events. We hypothesize that we can combine natural variation of expression levels and predictions of TF binding sites to identify TF targets. We gather RNA-seq data from 71 genetically distinct F1 Drosophila melanogaster embryos and calculate the correlations between TF and potential target genes' expression levels, which we call "regulatory strength." To separate direct and indirect TF targets, we hypothesize that direct TF targets will have a preponderance of binding sites in their upstream regions. Using 14 TFs active during embryogenesis, we find that 12 TFs showed a significant correlation between their binding strength and regulatory strength on downstream targets, and 10 TFs showed a significant correlation between the number of binding sites and the regulatory effect on target genes. The general roles, e.g. bicoid's role as an activator, and the particular interactions we observed between our TFs, e.g. twist's role as a repressor of sloppy paired and odd paired, generally coincide with the literature.

The Physiology of Homeoprotein Transduction

The homeoprotein family comprises ~300 transcription factors and was long seen as primarily involved in developmental programs through cell autonomous regulation. However, recent evidence reveals that many of these factors are also expressed in the adult where they exert physiological functions not yet fully deciphered. Furthermore, the DNA-binding domain of most homeoproteins contains two signal sequences allowing their secretion and internalization, thus intercellular transfer. This review focuses on this new-found signaling in cell migration, axon guidance, and cerebral cortex physiological homeostasis and speculates on how it may play important roles in early arealization of the neuroepithelium. It also describes the use of homeoproteins as therapeutic proteins in mouse models of diseases affecting the central nervous system, in particular Parkinson disease and glaucoma.

Spatial gradient of bicoid is well explained by Birnbaum-Saunders distribution

bicoid is a maternally transcribed gene which plays a pivotal role during the early developmental stage of Drosophila melanogaster by acting as an essential input to the segmentation network. Therefore, fundamental insights into gene cross-regulations of segmentation network expect to be unveiled by presenting an accurate mathematical model for bicoid gene expression profile. In this paper, an extended version of Birnbaum-Saunders with four parameters is introduced and evaluated to describe the spatial gradient of this gene. Theoretical aspects of four-parameter Birnbaum-Saunders and the estimated parameters are presented and thoroughly assessed for different embryos. The reliability and validity of the results are evaluated via both simulation studies and real data sets and thereby adding more confidence and value to the findings of this research.

Programmable protein circuits in living cells

Synthetic protein-level circuits could enable engineering of powerful new cellular behaviors. Rational protein circuit design would be facilitated by a composable protein-protein regulation system in which individual protein components can regulate one another to create a variety of different circuit architectures. In this study, we show that engineered viral proteases can function as composable protein components, which can together implement a broad variety of circuit-level functions in mammalian cells. In this system, termed CHOMP (circuits of hacked orthogonal modular proteases), input proteases dock with and cleave target proteases to inhibit their function. These components can be connected to generate regulatory cascades, binary logic gates, and dynamic analog signal-processing functions. To demonstrate the utility of this system, we rationally designed a circuit that induces cell death in response to upstream activators of the Ras oncogene. Because CHOMP circuits can perform complex functions yet be encoded as single transcripts and delivered without genomic integration, they offer a scalable platform to facilitate protein circuit engineering for biotechnological applications.

Precision in a rush: Trade-offs between reproducibility and steepness of the hunchback expression pattern

Fly development amazes us by the precision and reproducibility of gene expression, especially since the initial expression patterns are established during very short nuclear cycles. Recent live imaging of hunchback promoter dynamics shows a stable steep binary expression pattern established within the three minute interphase of nuclear cycle 11. Considering expression models of different complexity, we explore the trade-off between the ability of a regulatory system to produce a steep boundary and minimize expression variability between different nuclei. We show how a limited readout time imposed by short developmental cycles affects the gene’s ability to read positional information along the embryo’s anterior posterior axis and express reliably. Comparing our theoretical results to real-time monitoring of the hunchback transcription dynamics in live flies, we discuss possible regulatory strategies, suggesting an important role for additional binding sites, gradients or non-equilibrium binding and modified transcription factor search strategies.

Despite very limited time, organisms develop in reproducible ways. In the early stages of fly development the information about maternal signals is read out in a few minutes to produce steep and precise gene expression patterns. Motivated by recent live imaging experiments in fly embryos, we explore the consequences of the trade-off between a rushed but reproducible readout and a steep expression pattern on the regulatory modules of gene expression. We show that the current view of one anterior gradient morphogen binding to six binding sites is quantitatively inconsistent with the experimental data given the short readout time, suggesting other regulatory features.

3 minutes to precisely measure morphogen concentration

Morphogen gradients provide concentration-dependent positional information along polarity axes. Although the dynamics of the establishment of these gradients is well described, precision and noise in the downstream activation processes remain elusive. A simple paradigm to address these questions is the Bicoid morphogen gradient that elicits a rapid step-like transcriptional response in young fruit fly embryos. Focusing on the expression of the major Bicoid target, hunchback (hb), at the onset of zygotic transcription, we used the MS2-MCP approach which combines fluorescent labeling of nascent mRNA with live imaging at high spatial and temporal resolution. Removing 36 putative Zelda binding sites unexpectedly present in the original MS2 reporter, we show that the 750 bp of the hb promoter are sufficient to recapitulate endogenous expression at the onset of zygotic transcription. After each mitosis, in the anterior, expression is turned on to rapidly reach a plateau with all nuclei expressing the reporter. Consistent with a Bicoid dose-dependent activation process, the time period required to reach the plateau increases with the distance to the anterior pole. Despite the challenge imposed by frequent mitoses and high nuclei-to-nuclei variability in transcription kinetics, it only takes 3 minutes at each interphase for the MS2 reporter loci to distinguish subtle differences in Bicoid concentration and establish a steadily positioned and steep (Hill coefficient ~ 7) expression boundary. Modeling based on the cooperativity between the 6 known Bicoid binding sites in the hb promoter region, assuming rate limiting concentrations of the Bicoid transcription factor at the boundary, is able to capture the observed dynamics of pattern establishment but not the steepness of the boundary. This suggests that a simple model based only on the cooperative binding of Bicoid is not sufficient to describe the spatiotemporal dynamics of early hb expression.

Live Imaging of mRNA Transcription in Drosophila Embryos

Live imaging has been used in recent years for the understanding of dynamic processes in biology, such as embryo development. This was made possible by a combination of advancements in microscopy, leading to improved signal-to-noise ratios and better spatial and temporal resolutions, and by the development of new fluorescence markers, allowing for the quantification of protein expression and transcriptional dynamics in vivo. Here we describe a general protocol, which can be used in standard confocal microscopes to image early Drosophila melanogaster embryos, in order to learn about the transcriptional dynamics of a fluorescently labeled RNA.

LiveFly: A Toolbox for the Analysis of Transcription Dynamics in Live Drosophila Embryos

We present the LiveFly toolbox for quantitative analysis of transcription dynamics in live Drosophila embryos. The toolbox allows users to process two-color 3D confocal movies acquired using nuclei-labeling and the fluorescent RNA-tagging system described in the previous chapter and export the nuclei's position as a function of time, their lineages and the intensity traces of the active loci. The toolbox, which is tailored for the context of Drosophila early development, is semiautomatic, and requires minimal user intervention. It also includes a tool to combine data from multiple movies and visualize several features of the intensity traces and the expression pattern.

Cell Sorting and Noise-Induced Cell Plasticity Coordinate to Sharpen Boundaries between Gene Expression Domains

A fundamental question in biology is how sharp boundaries of gene expression form precisely in spite of biological variation/noise. Numerous mechanisms position gene expression domains across fields of cells (e.g. morphogens), but how these domains are refined remains unclear. In some cases, domain boundaries sharpen through differential adhesion-mediated cell sorting. However, boundaries can also sharpen through cellular plasticity, with cell fate changes driven by up- or down-regulation of gene expression. In this context, we have argued that noise in gene expression can help cells transition to the correct fate. Here we investigate the efficacy of cell sorting, gene expression plasticity, and their combination in boundary sharpening using multi-scale, stochastic models. We focus on the formation of hindbrain segments (rhombomeres) in the developing zebrafish as an example, but the mechanisms investigated apply broadly to many tissues. Our results indicate that neither sorting nor plasticity is sufficient on its own to sharpen transition regions between different rhombomeres. Rather the two have complementary strengths and weaknesses, which synergize when combined to sharpen gene expression boundaries.

In many developing systems, chemical gradients control the formation of segmental domains of gene expression, specifying distinct domains that go on to form different tissues and structures, in a concentration-dependent manner. These gradients are noisy however, raising the question of how sharply delineated boundaries between distinct segments form. It is crucial that developing systems be able to cope with stochasticity and generate well-defined boundaries between different segmented domains. Previous work suggests that cell sorting and cellular plasticity help sharpen boundaries between segments. However, it remains unclear how effective each of these mechanisms is and what their role in sharpening may be. Motivated by recent experimental observations, we construct a hybrid stochastic model to investigate these questions. We find that neither mechanism is sufficient on its own to sharpen boundaries between different segments. Rather, results indicate each has its own strengths and weaknesses, and that they work together synergistically to promote the development of precise, well defined segment boundaries. Formation of segmented rhombomeres in the zebrafish hindbrain, which later form different components of the central nervous system, is a motivating case for this study.

Scaling of pattern formations and morphogen gradients

The concentration gradient of morphogens provides positional information for an embryo and plays a pivotal role in pattern formation of tissues during the developmental processes. Morphogen-dependent pattern formations show robustness despite various perturbations. Although tissues usually grow and dynamically change their size during histogenesis, proper patterns are formed without the influence of size variations. Furthermore, even when the blastula embryo of Xenopus laevis is bisected into dorsal and ventral halves, the dorsal half of the embryo leads to proportionally patterned half-sized embryos. This robustness of pattern formation despite size variations is termed as scaling. In this review, I focused on the morphogen-dependent dorsal-ventral axis formation in Xenopus and described how morphogens form a proper gradient shape according to the embryo size.

Gene expression boundary scaling and organ size regulation in the Drosophila embryo

How the shape and size of tissues and organs is regulated during development is a major question in developmental biology. Such regulation relies upon both intrinsic cues (such as signaling networks) and extrinsic inputs (such as from neighboring tissues). Here, we focus on pattern formation and organ development during Drosophila embryogenesis. In particular, we outline the importance of both biochemical and mechanical tissue-tissue interactions in size regulation. We describe how the Drosophila embryo can potentially provide novel insights into how shape and size are regulated during development. We focus on gene expression boundary scaling in the early embryo and how size is regulated in three organs (hindgut, trachea, and ventral nerve cord) later in development, with particular focus on the role of tissue-tissue interactions. Overall, we demonstrate that Drosophila embryogenesis provides a suitable model system for studying spatial and temporal scaling and size control in vivo.

BMP4 acts as a dorsal telencephalic morphogen in a mouse embryonic stem cell culture system

The concept of a morphogen - a molecule that specifies two or more cell fates in a concentration-dependent manner - is paradigmatic in developmental biology. Much remains unknown, however, about the existence of morphogens in the developing vertebrate central nervous system (CNS), including the mouse dorsal telencephalic midline (DTM). Bone morphogenetic proteins (BMPs) are candidate DTM morphogens, and our previous work demonstrated BMP4 sufficiency to induce one DTM cell fate - that of choroid plexus epithelial cells (CPECs) - in a mouse embryonic stem cell (mESC) culture system. Here we used BMP4 in a modified mESC culture system to derive a second DTM fate, the cortical hem (CH). CH and CPEC markers were induced by BMP4 in a concentration-dependent manner consistent with in vivo development. BMP4 concentrations that led to CH fate also promoted markers for Cajal-Retzius neurons, which are known CH derivatives. Interestingly, single BMP4 administrations also sufficed for appropriate temporal regulation of CH, CPEC, and cortical genes, with initially broad and overlapping dose-response profiles that sharpened over time. BMP4 concentrations that yielded CH- or CPEC-enriched populations also had different steady-state levels of phospho-SMAD1/5/8, suggesting that differences in BMP signaling intensity underlie DTM fate choice. Surprisingly, inactivation of the cortical selector gene Lhx2 did not affect DTM expression levels, dose-response profiles, or timing in response to BMP4, although neural progenitor genes were downregulated. These data indicate that BMP4 can act as a classic morphogen to orchestrate both spatial and temporal aspects of DTM fate acquisition, and can do so in the absence of Lhx2.

Precision of Readout at the hunchback Gene: Analyzing Short Transcription Time Traces in Living Fly Embryos

The simultaneous expression of the hunchback gene in the numerous nuclei of the developing fly embryo gives us a unique opportunity to study how transcription is regulated in living organisms. A recently developed MS2-MCP technique for imaging nascent messenger RNA in living Drosophila embryos allows us to quantify the dynamics of the developmental transcription process. The initial measurement of the morphogens by the hunchback promoter takes place during very short cell cycles, not only giving each nucleus little time for a precise readout, but also resulting in short time traces of transcription. Additionally, the relationship between the measured signal and the promoter state depends on the molecular design of the reporting probe. We develop an analysis approach based on tailor made autocorrelation functions that overcomes the short trace problems and quantifies the dynamics of transcription initiation. Based on live imaging data, we identify signatures of bursty transcription initiation from the hunchback promoter. We show that the precision of the expression of the hunchback gene to measure its position along the anterior-posterior axis is low both at the boundary and in the anterior even at cycle 13, suggesting additional post-transcriptional averaging mechanisms to provide the precision observed in fixed embryos.

The fly embryo provides a natural laboratory to study the dynamics of transcription and its implications for the developing organism. Using live imaging experiments we investigate the nature of transcription regulation of the hunchback gene—the first to read out the maternal Bicoid gradient. While traditional time trace analysis methods based on OFF time distributions or autocorrelation functions fail for short signals, our tailored autocorrelation function overcomes these limitations revealing bursty dynamics that is reproducible between cell cycles and embryos. The inferred rates result in a lot of variability in the readout of nuclei sensing similar Bicoid concentrations, suggesting additional readout mechanisms than a one-to-one mapping of the input onto the output.

Maternal AP determinants in the Drosophila oocyte and embryo

An animal embryo cannot initiate its journey of forming a new life on its own. It must rely on maternally provided resources and inputs to kick-start its developmental process. In Drosophila, the initial polarities of the embryo along both the anterior-posterior (AP) and dorsal-ventral (DV) axes are also specified by maternal determinants. Over the past several decades, genetic and molecular studies have identified and characterized such determinants, as well as the zygotic genetic regulatory networks that control patterning in the early embryo. Extensive studies of oogenesis have also led to a detailed knowledge of the cellular and molecular interactions that control the formation of a mature egg. Despite these efforts, oogenesis and embryogenesis have been studied largely as separate problems, except for qualitative aspects with regard to maternal regulation of the asymmetric localization of maternal determinants. Can oogenesis and embryogenesis be viewed from a unified perspective at a quantitative level, and can that improve our understanding of how robust embryonic patterning is achieved? Here, we discuss the basic knowledge of the regulatory mechanisms controlling oogenesis and embryonic patterning along the AP axis. We explore properties of the maternal Bicoid gradient in relation to embryo size in search for a unified framework for robust AP patterning. WIREs Dev Biol 2016, 5:562-581. doi: 10.1002/wdev.235 For further resources related to this article, please visit the WIREs website.

Theoretical analysis of degradation mechanisms in the formation of morphogen gradients

Fundamental biological processes of development of tissues and organs in multicellular organisms are governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in the concentration profiles of signaling molecules, which are frequently referred as morphogen gradients, lead to a cell differentiation via activating specific genes in a concentration-dependent manner. It is widely accepted that the establishment of the morphogen gradients involves multiple biochemical reactions and diffusion processes. One of the critical elements in the formation of morphogen gradients is a degradation of signaling molecules. We develop a new theoretical approach that provides a comprehensive description of the degradation mechanisms. It is based on the idea that the degradation works as an effective potential that drives the signaling molecules away from the source region. Utilizing the method of first-passage processes, the dynamics of the formation of morphogen gradients for various degradation mechanisms is explicitly evaluated. It is found that linear degradation processes lead to a dynamic behavior specified by times to form the morphogen gradients that depend linearly on the distance from the source. This is because the effective potential due to the degradation is quite strong. At the same time, nonlinear degradation mechanisms yield a quadratic scaling in the morphogen gradients formation times since the effective potentials are much weaker. Physical-chemical explanations of these phenomena are presented.

Transcriptional Responses to the Auxin Hormone

Auxin is arguably the most important signaling molecule in plants, and the last few decades have seen remarkable breakthroughs in understanding its production, transport, and perception. Recent investigations have focused on transcriptional responses to auxin, providing novel insight into the functions of the domains of key transcription regulators in responses to the hormonal cue and prominently implicating chromatin regulation in these responses. In addition, studies are beginning to identify direct targets of the auxin-responsive transcription factors that underlie auxin modulation of development. Mechanisms to tune the response to different auxin levels are emerging, as are first insights into how this single hormone can trigger diverse responses. Key unanswered questions center on the mechanism for auxin-directed transcriptional repression and the identity of additional determinants of auxin response specificity. Much of what has been learned in model plants holds true in other species, including the earliest land plants.

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.

New Model for Understanding Mechanisms of Biological Signaling: Direct Transport via Cytonemes

Biological signaling is a crucial natural process that governs the formation of all multicellular organisms. It relies on efficient and fast transfer of information between different cells and tissues. It has been presumed for a long time that these long-distance communications in most systems can take place only indirectly via the diffusion of signaling molecules, also known as morphogens, through the extracellular fluid; however, recent experiments indicate that there is also an alternative direct delivery mechanism. It utilizes dynamic tubular cellular extensions, called cytonemes, that directly connect cells, supporting the flux of morphogens to specific locations. We present a first quantitative analysis of the cytoneme-mediated mechanism of biological signaling. Dynamics of the formation of signaling molecule profiles, which are also known as morphogen gradients, is discussed. It is found that the direct-delivery mechanism is more robust with respect to fluctuations in comparison with the passive diffusion mechanism. In addition, we show that the direct transport of morphogens through cytonemes simultaneously delivers the information to all cells, which is also different from the diffusional indirect delivery; however, it requires energy dissipation and it might be less efficient at large distances due to intermolecular interactions of signaling molecules.

Temporal and spatial dynamics of scaling-specific features of a gene regulatory network in Drosophila

A widely appreciated aspect of developmental robustness is pattern formation in proportion to size. But how such scaling features emerge dynamically remains poorly understood. Here we generate a data set of the expression profiles of six gap genes in Drosophila melanogaster embryos that differ significantly in size. Expression patterns exhibit size-dependent dynamics both spatially and temporally. We uncover a dynamic emergence of under-scaling in the posterior, accompanied by reduced expression levels of gap genes near the middle of large embryos. Simulation results show that a size-dependent Bicoid gradient input can lead to reduced Krüppel expression that can have long-range and dynamic effects on gap gene expression in the posterior. Thus, for emergence of scaled patterns, the entire embryo may be viewed as a single unified dynamic system where maternally derived size-dependent information interpreted locally can be propagated in space and time as governed by the dynamics of a gene regulatory network.

How pattern formation is regulated relative to the size of an organism is unclear. Here, Wu et al. take data from gap gene expression in flies of different sizes together with simulations, identifying how scaling emerges dynamically and that local patterning influences global gene regulatory networks.

Probing the impact of temperature on molecular events in a developmental system

A well-appreciated general feature of development is the ability to achieve a normal outcome despite the inevitable variability at molecular, genetic, or environmental levels. But it is not well understood how changes in a global factor such as temperature bring about specific challenges to a developmental system in molecular terms. Here we address this question using early Drosophila embryos where the maternal gradient Bicoid (Bcd) instructs anterior-patterning (AP) patterning. We show that temperature can impact the amplitude of the Bcd gradient in the embryo. To evaluate how molecular decisions are made at different temperatures, we quantify Bcd concentrations and the expression of its target gene hunchback (hb) in individual embryos. Our results suggest a relatively robust Bcd concentration threshold in inducing hb transcription within a temperature range. Our results also reveal a complex nature of the effects of temperature on the progressions of developmental and molecular events of the embryo. Our study thus advances the concept of developmental robustness by quantitatively elaborating specific features and challenges—imposed by changes in temperature—that an embryo must resolve.

Mechanical Forces and Growth in Animal Tissues

Mechanical forces shape biological tissues. They are the effectors of the developmental programs that orchestrate morphogenesis. A lot of effort has been devoted to understanding morphogenetic processes in mechanical terms. In this review, we focus on the interplay between tissue mechanics and growth. We first describe how tissue mechanics affects growth, by influencing the orientation of cell divisions and the signaling pathways that control the rate of volume increase and proliferation. We then address how the mechanical state of a tissue is affected by the patterns of growth. The forward and reverse interactions between growth and mechanics must be investigated in an integrative way if we want to understand how tissues grow and shape themselves. To illustrate this point, we describe examples in which growth homeostasis is achieved by feedback mechanisms that use mechanical forces.

The role of source delocalization in the development of morphogen gradients

Successful biological development via spatial regulation of cell differentiation relies on the action of multiple signaling molecules that are known as morphogens. It is now well-established that signaling molecules create non-uniform concentration profiles, morphogen gradients, that activate different genes, leading to patterning in the developing embryos. The current view of the formation of morphogen gradients is that it is a result of complex reaction-diffusion processes that include the strongly localized production, diffusion and uniform degradation of signaling molecules. However, multiple experimental studies also suggest that the production of morphogen in many cases is delocalized. We develop a theoretical method that allows us to investigate the role of the delocalization in the formation of morphogen gradients. The approach is based on discrete-state stochastic models that can be solved exactly for arbitrary production lengths and production rates of morphogen molecules. Our analysis shows that the delocalization might have a strong effect on mechanisms of the morphogen gradient formation. The physical origin of this effect is discussed.

Fundamental origins and limits for scaling a maternal morphogen gradient

Tissue expansion and patterning are integral to development, but it is unknown quantitatively how a mother accumulates molecular resources to invest in the future of instructing robust embryonic patterning. Here we develop a model, Tissue Expansion-Modulated Maternal Morphogen Scaling (TEM³S), to study scaled anterior-posterior patterning in Drosophila embryos. Using both ovaries and embryos, we measure a core quantity of the model, the scaling power of the Bicoid (Bcd) morphogen gradient’s amplitude n_A. We also evaluate directly model-derived predictions about Bcd gradient and patterning properties. Our results show that scaling of the Bcd gradient in the embryo originates from, and is constrained fundamentally by, a dynamic relationship between maternal tissue expansion and bcd gene copy number expansion in the ovary. This delicate connection between the two transitioning stages of a life cycle, stemming from a finite value of n_A ~ 3, underscores a key feature of developmental systems depicted by TEM³S.

A theoretical framework for the regulation of Shh morphogen-controlled gene expression

How morphogen gradients govern the pattern of gene expression in developing tissues is not well understood. Here, we describe a statistical thermodynamic model of gene regulation that combines the activity of a morphogen with the transcriptional network it controls. Using Sonic hedgehog (Shh) patterning of the ventral neural tube as an example, we show that the framework can be used together with the principled parameter selection technique of approximate Bayesian computation to obtain a dynamical model that accurately predicts tissue patterning. The analysis indicates that, for each target gene regulated by Gli, which is the transcriptional effector of Shh signalling, there is a neutral point in the gradient, either side of which altering the Gli binding affinity has opposite effects on gene expression. This explains recent counterintuitive experimental observations. The approach is broadly applicable and provides a unifying framework to explain the temporospatial pattern of morphogen-regulated gene expression.

Development of morphogen gradient: the role of dimension and discreteness

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances, and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuum descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.

On the GFP-based analysis of dynamic concentration profiles

Studies with GFP-tagged proteins can be used to investigate the dynamics of concentration profiles of regulatory proteins in cells and tissues. Analysis of these experiments must account for the finite rate with which the GFP-tagged proteins mature to the fluorescent state. Toward this end, we present an analytical framework that provides an explicit connection between the apparent kinetics of concentration gradients and the rates of GFP maturation.