Adaptation of the length scale and amplitude of the Bicoid gradient profile to achieve robust patterning in abnormally large Drosophila melanogaster embryos

Rapid response of fly populations to gene dosage across development and generations

Although the effects of genetic and environmental perturbations on multicellular organisms are rarely restricted to single phenotypic layers, our current understanding of how developmental programs react to these challenges remains limited. Here, we have examined the phenotypic consequences of disturbing the bicoid regulatory network in early Drosophila embryos. We generated flies with two extra copies of bicoid, which causes a posterior shift of the network's regulatory outputs and a decrease in fitness. We subjected these flies to EMS mutagenesis, followed by experimental evolution. After only 8-15 generations, experimental populations have normalized patterns of gene expression and increased survival. Using a phenomics approach, we find that populations were normalized through rapid increases in embryo size driven by maternal changes in metabolism and ovariole development. We extend our results to additional populations of flies, demonstrating predictability. Together, our results necessitate a broader view of regulatory network evolution at the systems level.

Size regulation of the lateral organ initiation zone and its role in determining cotyledon number in conifers

Introduction

Unlike monocots and dicots, many conifers, particularly Pinaceae, form three or more cotyledons. These are arranged in a whorl, or ring, at a particular distance from the embryo tip, with cotyledons evenly spaced within the ring. The number of cotyledons, n_c, varies substantially within species, both in clonal cultures and in seed embryos. n_c variability reflects embryo size variability, with larger diameter embryos having higher n_c. Correcting for growth during embryo development, we extract values for the whorl radius at each n_c. This radius, corresponding to the spatial pattern of cotyledon differentiation factors, varies over three-fold for the naturally observed range of n_c. The current work focuses on factors in the patterning mechanism that could produce such a broad variability in whorl radius. Molecularly, work in Arabidopsis has shown that the initiation zone for leaf primordia occurs at a minimum between inhibitor zones of HD-ZIP III at the shoot apical meristem (SAM) tip and KANADI (KAN) encircling this farther from the tip. PIN1-auxin dynamics within this uninhibited ring form auxin maxima, specifying primordia initiation sites. A similar mechanism is indicated in conifer embryos by effects on cotyledon formation with overexpression of HD-ZIP III inhibitors and by interference with PIN1-auxin patterning.

Methods

We develop a mathematical model for HD-ZIP III/KAN spatial localization and use this to characterize the molecular regulation that could generate (a) the three-fold whorl radius variation (and associated n_c variability) observed in conifer cotyledon development, and (b) the HD-ZIP III and KAN shifts induced experimentally in conifer embryos and in Arabidopsis.

Results

This quantitative framework indicates the sensitivity of mechanism components for positioning lateral organs closer to or farther from the tip. Positional shifting is most readily driven by changes to the extent of upstream (meristematic) patterning and changes in HD-ZIP III/KAN mutual inhibition, and less efficiently driven by changes in upstream dosage or the activation of HD-ZIP III. Sharper expression boundaries can also be more resistant to shifting than shallower expression boundaries.

Discussion

The strong variability seen in conifer n_c (commonly from 2 to 10) may reflect a freer variation in regulatory interactions, whereas monocot (n_c = 1) and dicot (n_c = 2) development may require tighter control of such variation. These results provide direction for future quantitative experiments on the positional control of lateral organ initiation, and consequently on plant phyllotaxy and architecture.

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.

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.

Quantitative Analysis of the Dynamics of Maternal Gradients in the Early Drosophila Embryo

Predetermination, formation, and maintenance of the primary morphogenetic gradient (bicoid, bcd) of the early Drosophila embryo involves many interrelated processes. Here we focus on the biological systems analysis of the bcd mRNA redistribution in an early embryo. The results of the quantitative analysis of experimental data, together with the results of their dynamic modeling, substantiate the role of active transport in the redistribution of the bcd mRNA. The role of the nonlinearity of degradation mechanisms in the mRNA pattern robustness is discussed.

The many bits of positional information

Half a century after Lewis Wolpert's seminal conceptual advance on how cellular fates distribute in space, we provide a brief historical perspective on how the concept of positional information emerged and influenced the field of developmental biology and beyond. We focus on a modern interpretation of this concept in terms of information theory, largely centered on its application to cell specification in the early Drosophila embryo. We argue that a true physical variable (position) is encoded in local concentrations of patterning molecules, that this mapping is stochastic, and that the processes by which positions and corresponding cell fates are determined based on these concentrations need to take such stochasticity into account. With this approach, we shift the focus from biological mechanisms, molecules, genes and pathways to quantitative systems-level questions: where does positional information reside, how it is transformed and accessed during development, and what fundamental limits it is subject to?

Growing Up in a Changing World: Environmental Regulation of Development in Insects

All organisms are exposed to changes in their environment throughout their life cycle. When confronted with these changes, they adjust their development and physiology to ensure that they can produce the functional structures necessary for survival and reproduction. While some traits are remarkably invariant, or robust, across environmental conditions, others show high degrees of variation, known as plasticity. Generally, developmental processes that establish cell identity are thought to be robust to environmental perturbation, while those relating to body and organ growth show greater degrees of plasticity. However, examples of plastic patterning and robust organ growth demonstrate that this is not a hard-and-fast rule.In this review, we explore how the developmental context and the gene regulatory mechanisms underlying trait formation determine the impacts of the environment on development in insects. Furthermore, we outline future issues that need to be resolved to understand how the structure of signaling networks defines whether a trait displays plasticity or robustness.

Integrating cellular dimensions with cell differentiation during early development

Early embryo development is characterized by alteration of cellular dimensions and fating of blastomeres. An emerging concept is that cell size and shape drive cellular differentiation during early embryogenesis in a variety of model organisms. In this review, we summarize recent advances that elucidate the contribution of the physical dimensions of a cell to major embryonic transitions and cell fate specification in vivo. We also highlight techniques and newly evolving methods for manipulating the sizes and shapes of cells and whole embryos in situ and ex vivo. Finally, we provide an outlook for addressing fundamental questions in the field and more broadly uncovering how changes to cell size control decision making in a variety of biological contexts.

Embryonic geometry underlies phenotypic variation in decanalized conditions

During development, many mutations cause increased variation in phenotypic outcomes, a phenomenon termed decanalization. Phenotypic discordance is often observed in the absence of genetic and environmental variations, but the mechanisms underlying such inter-individual phenotypic discordance remain elusive. Here, using the anterior-posterior (AP) patterning of the Drosophila embryo, we identified embryonic geometry as a key factor predetermining patterning outcomes under decanalizing mutations. With the wild-type AP patterning network, we found that AP patterning is robust to variations in embryonic geometry; segmentation gene expression remains reproducible even when the embryo aspect ratio is artificially reduced by more than twofold. In contrast, embryonic geometry is highly predictive of individual patterning defects under decanalized conditions of either increased bicoid (bcd) dosage or bcd knockout. We showed that the phenotypic discordance can be traced back to variations in the gap gene expression, which is rendered sensitive to the geometry of the embryo under mutations.

Positional information and tissue scaling during development and regeneration

In order to contribute to the appropriate tissues during development, cells need to know their position within the embryo. This positional information is conveyed by gradients of signaling molecules, termed morphogens, that are produced in specific regions of the embryo and induce concentration-dependent responses in target tissues. Positional information is remarkably robust, and embryos often develop with the correct proportions even if large parts of the embryo are removed. In this Review, we discuss classical embryological experiments and modern quantitative analyses that have led to mechanistic insights into how morphogen gradients adapt, scale and properly pattern differently sized domains. We analyze these experimental findings in the context of mathematical models and synthesize general principles that apply to multiple systems across species and developmental stages.

Detection and Quantification of the Bicoid Concentration Gradient in Drosophila Embryos

We describe methods for detecting and quantifying the concentration gradient of the morphogenetic protein Bicoid through fluorescent immunostaining in fixed Drosophila embryos. We introduce image-processing steps using MATLAB functions, and discuss how the measured signal intensities can be analyzed to extract quantitative information. The described procedures permit robust detection of the endogenous Bicoid concentration gradient at a cellular resolution.

A model of neocortical area patterning in the lissencephalic mouse may hold for larger gyrencephalic brains

In the mouse, two telencephalic signaling centers orchestrate embryonic patterning of the cerebral cortex. From the rostral patterning center in the telencephalon, the Fibroblast Growth Factor, FGF8, disperses as a morphogen to establish the rostral to caudal axis of the neocortical area map. FGF8 coordinates with Wnt3a from the cortical hem to regulate graded expression of transcription factors that position neocortical areas, and control hippocampal development. Whether similar signaling centers pattern the much larger cortices of carnivore and primate species, however, is unclear. The limited dispersion range of FGF8 and Wnt3a is inconsistent with patterning larger cortical primordia. Yet the implication that different mechanisms organize cortex in different mammals flies in the face of the tenet that developmental patterning mechanisms are conserved across vertebrate species. In the present study, both signaling centers were identified in the ferret telencephalon, as were expression gradients of the patterning transcription factor genes regulated by FGF8 and Wnt3a. Notably, at the stage corresponding to the peak period of FGF8 signaling in the mouse neocortical primordium (NP), the NP was the same size in ferret and mouse, which would allow morphogen patterning of the ferret NP. Subsequently, the size of ferret neocortex shot past that of the mouse. Images from online databases further suggest that NP growth in humans, too, is slowed in early cortical development. We propose that if early growth in larger brains is held back, mechanisms that pattern the neocortical area map in the mouse could be conserved across mammalian species.

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.

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.

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.

Scaling Pattern to Variations in Size during Development of the Vertebrate Neural Tube

Anatomical proportions are robustly maintained in individuals that vary enormously in size, both within a species and between members of related taxa. However, the mechanisms underlying scaling are still poorly understood. We have examined this phenomenon in the context of the patterning of the ventral neural tube in response to a gradient of the morphogen Sonic hedgehog (SHH) in the chick and zebra finch, two species that differ in size during the time of neural tube patterning. We find that scaling is achieved, at least in part, by altering the sensitivity of the target cells to SHH and appears to be achieved by modulating the ratio of the repressive and activating transcriptional regulators, GLI2 and GLI3. This mechanism contrasts with previous experimental and theoretical analyses of morphogenic scaling that have focused on compensatory changes in the morphogen gradient itself.

Developmental Pattern Formation in Phases

Cells in developing organs undergo a series of changes in their transcriptional state until a complete repertoire of cell types is specified. These changes in cell identity, together with the control of tissue growth, determine the pattern of gene expression in the tissue. Recent studies explore the dynamics of pattern formation during development and provide new insights into the control mechanisms. Changes in morphogen signalling and transcriptional networks control the specification of cell types. This is often followed by a distinct second phase, where pattern is elaborated by tissue growth. Here, we discuss the transitions between distinct phases in pattern formation. We consider the implications of the underlying mechanisms for understanding how reproducible patterns form during development.

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.

Time to move on: Modeling transcription dynamics during an embryonic transition away from maternal control

In a recent study, we investigated the regulation of hunchback (hb) transcription dynamics in Drosophila embryos. Our results suggest that shutdown of hb transcription at early nuclear cycle (nc) 14 is an event associated with the global changes taking place during the mid-blastula transition (MBT). Here we have developed a simple model of hb transcription dynamics during this transition time. With kinetic parameters estimated from our published experimental data, the model describes the dynamical processes of hb gene transcription and hb mRNA accumulation. With two steps, transcription onset upon exiting the previous mitosis followed by a sudden impact that blocks gene activation, the model recapitulates the observed dynamics of hb transcription during the nc14 interphase. The timing of gene inactivation is essential, as its alterations lead to changes in both hb transcription dynamics and hb mRNA levels. Our model provides a clear dynamical picture of hb transcription regulation as one of the many, actively regulated events concurrently taking place during the MBT.

Modeling somite scaling in small embryos in the framework of Turing patterns

The adaptation of prevertebra size to embryo size is investigated in the framework of a reaction-diffusion model involving a Turing pattern. The reaction scheme and Fick's first law of diffusion are modified in order to take into account the departure from dilute conditions induced by confinement in smaller embryos. In agreement with the experimental observations of scaling in somitogenesis, our model predicts the formation of smaller prevertebrae or somites in smaller embryos. These results suggest that models based on Turing patterns cannot be automatically disregarded by invoking the question of maintaining proportions in embryonic development. Our approach highlights the nontrivial role that the solvent can play in biology.

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.

Morphogen rules: design principles of gradient-mediated embryo patterning

The Drosophila blastoderm and the vertebrate neural tube are archetypal examples of morphogen-patterned tissues that create precise spatial patterns of different cell types. In both tissues, pattern formation is dependent on molecular gradients that emanate from opposite poles. Despite distinct evolutionary origins and differences in time scales, cell biology and molecular players, both tissues exhibit striking similarities in the regulatory systems that establish gene expression patterns that foreshadow the arrangement of cell types. First, signaling gradients establish initial conditions that polarize the tissue, but there is no strict correspondence between specific morphogen thresholds and boundary positions. Second, gradients initiate transcriptional networks that integrate broadly distributed activators and localized repressors to generate patterns of gene expression. Third, the correct positioning of boundaries depends on the temporal and spatial dynamics of the transcriptional networks. These similarities reveal design principles that are likely to be broadly applicable to morphogen-patterned tissues.

Modulation of temporal dynamics of gene transcription by activator potency in the Drosophila embryo

The Drosophila embryo at the mid-blastula transition (MBT) concurrently experiences a receding first wave of zygotic transcription and the surge of a massive second wave. It is not well understood how genes in the first wave become turned off transcriptionally and how their precise timing may impact embryonic development. Here we perturb the timing of the shutdown of Bicoid (Bcd)-dependent hunchback (hb) transcription in the embryo through the use of a Bcd mutant that has heightened activating potency. A delayed shutdown specifically increases Bcd-activated hb levels, and this alters spatial characteristics of the patterning outcome and causes developmental defects. Our study thus documents a specific participation of maternal activator input strength in the timing of molecular events in precise accordance with MBT morphological progression.

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.

Critical waves and the length problem of biology

It is pointed out that the mystery of how biological systems measure their lengths vanishes away if one premises that they have discovered a way to generate linear waves analogous to compressional sound. These can be used to detect length at either large or small scales using echo timing and fringe counting. It is shown that suitable linear chemical potential waves can, in fact, be manufactured by tuning to criticality conventional reaction-diffusion with a small number substance. Min oscillations in Escherichia coli are cited as precedent resonant length measurement using chemical potential waves analogous to laser detection. Mitotic structures in eukaryotes are identified as candidates for such an effect at higher frequency. The engineering principle is shown to be very general and functionally the same as that used by hearing organs.

Intracellular Scaling Mechanisms

Organelle function is often directly related to organelle size. However, it is not necessarily absolute size but the organelle-to-cell-size ratio that is critical. Larger cells generally have increased metabolic demands, must segregate DNA over larger distances, and require larger cytokinetic rings to divide. Thus, organelles often must scale to the size of the cell. The need for scaling is particularly acute during early development during which cell size can change rapidly. Here, we highlight scaling mechanisms for cellular structures as diverse as centrosomes, nuclei, and the mitotic spindle, and distinguish them from more general mechanisms of size control. In some cases, scaling is a consequence of the underlying mechanism of organelle size control. In others, size-control mechanisms are not obviously related to cell size, implying that scaling results indirectly from cell-size-dependent regulation of size-control mechanisms.

Pom1 gradient buffering through intermolecular auto-phosphorylation

Concentration gradients provide spatial information for tissue patterning and cell organization, and their robustness under natural fluctuations is an evolutionary advantage. In rod-shaped Schizosaccharomyces pombe cells, the DYRK-family kinase Pom1 gradients control cell division timing and placement. Upon dephosphorylation by a Tea4-phosphatase complex, Pom1 associates with the plasma membrane at cell poles, where it diffuses and detaches upon auto-phosphorylation. Here, we demonstrate that Pom1 auto-phosphorylates intermolecularly, both in vitro and in vivo, which confers robustness to the gradient. Quantitative imaging reveals this robustness through two system's properties: The Pom1 gradient amplitude is inversely correlated with its decay length and is buffered against fluctuations in Tea4 levels. A theoretical model of Pom1 gradient formation through intermolecular auto-phosphorylation predicts both properties qualitatively and quantitatively. This provides a telling example where gradient robustness through super-linear decay, a principle hypothesized a decade ago, is achieved through autocatalysis. Concentration-dependent autocatalysis may be a widely used simple feedback to buffer biological activities.

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.

Coordination of progenitor specification and growth in mouse and chick spinal cord

Development requires tissue growth as well as cell diversification. To address how these processes are coordinated, we analyzed the development of molecularly distinct domains of neural progenitors in the mouse and chick neural tube. We show that during development, these domains undergo changes in size that do not scale with changes in overall tissue size. Our data show that domain proportions are first established by opposing morphogen gradients and subsequently controlled by domain-specific regulation of differentiation rate but not differences in proliferation rate. Regulation of differentiation rate is key to maintaining domain proportions while accommodating both intra- and interspecies variations in size. Thus, the sequential control of progenitor specification and differentiation elaborates pattern without requiring that signaling gradients grow as tissues expand.

Modeling of the dorsal gradient across species reveals interaction between embryo morphology and Toll signaling pathway during evolution

Morphogenetic gradients are essential to allocate cell fates in embryos of varying sizes within and across closely related species. We previously showed that the maternal NF-κB/Dorsal (Dl) gradient has acquired different shapes in Drosophila species, which result in unequally scaled germ layers along the dorso-ventral axis and the repositioning of the neuroectodermal borders. Here we combined experimentation and mathematical modeling to investigate which factors might have contributed to the fast evolutionary changes of this gradient. To this end, we modified a previously developed model that employs differential equations of the main biochemical interactions of the Toll (Tl) signaling pathway, which regulates Dl nuclear transport. The original model simulations fit well the D. melanogaster wild type, but not mutant conditions. To broaden the applicability of this model and probe evolutionary changes in gradient distributions, we adjusted a set of 19 independent parameters to reproduce three quantified experimental conditions (i.e. Dl levels lowered, nuclear size and density increased or decreased). We next searched for the most relevant parameters that reproduce the species-specific Dl gradients. We show that adjusting parameters relative to morphological traits (i.e. embryo diameter, nuclear size and density) alone is not sufficient to reproduce the species Dl gradients. Since components of the Tl pathway simulated by the model are fast-evolving, we next asked which parameters related to Tl would most effectively reproduce these gradients and identified a particular subset. A sensitivity analysis reveals the existence of nonlinear interactions between the two fast-evolving traits tested above, namely the embryonic morphological changes and Tl pathway components. Our modeling further suggests that distinct Dl gradient shapes observed in closely related melanogaster sub-group lineages may be caused by similar sequence modifications in Tl pathway components, which are in agreement with their phylogenetic relationships.

Embryo size can vary greatly among closely related species. How tissue specification either scales or is modified in the developing embryo in different species is an ongoing investigation in developmental biology. Here we asked how embryo morphology and specific molecular pathways influence tissue specification by altering the distribution of morphogens. Morphogens are molecules that form gradients that regulate gene expression patterns in a dosage-dependent fashion that result in tissue specification, and therefore are a prime target for evolution in order to adjust or maintain tissue proportions in relation to overall embryo size. We used a mathematical model to identify factors that influence the distribution of the Dorsal morphogen gradient that is responsible for patterning the dorsal-ventral axis of the Drosophila fruit fly embryo. We obtained experimental data from mutant conditions and different species of Drosophila to calibrate our model and found an interaction between embryo morphology and regulation of the Toll pathway, which regulates the Dorsal gradient. Furthermore, the model predicts that closely related species share similar modifications in Toll pathway components resulting in their species-specific gradient shapes, which are supported by interspecies amino acid comparison of the components Dorsal and Cactus.

Dampened regulates the activating potency of Bicoid and the embryonic patterning outcome in Drosophila

The Drosophila morphogen gradient of Bicoid (Bcd) initiates anterior-posterior (AP) patterning; however, it is poorly understood how its ability to activate a target gene may have an impact on this process. Here we report an F-box protein, Dampened (Dmpd) as a nuclear cofactor of Bcd that can enhance its activating potency. We establish a quantitative platform to specifically investigate two parameters of a Bcd target gene response, expression amplitude and boundary position. We show that embryos lacking Dmpd have a reduced amplitude of Bcd-activated hunchback (hb) expression at a critical time of development. This is because of a reduced Bcd-dependent transcribing probability. This defect is faithfully propagated further downstream of the AP-patterning network to alter the spatial characteristics of even-skipped (eve) stripes. Thus, unlike another Bcd-interacting F-box protein Fate-shifted (Fsd), which controls AP patterning through regulating the Bcd gradient profile, Dmpd achieves its patterning role through regulating the activating potency of Bcd.