Multiscale diffusion in the mitotic Drosophila melanogaster syncytial blastoderm

Nature of barriers determines first passage times in heterogeneous media

Intuition suggests that passage times across a region increase with the number of barriers along the path. Can this fail depending on the nature of the barrier? To probe this fundamental question, we exactly solve for the first passage time in general d-dimensions for diffusive transport through a spatially patterned array of obstacles - either entropic or energetic, depending on the nature of the obstacles. For energetic barriers, we show that first passage times vary non-monotonically with the number of barriers, while for entropic barriers it increases monotonically. This non-monotonicity for energetic barriers is further reflected in the behaviour of effective diffusivity as well. We then design a simple experiment where a robotic bug navigates in a heterogeneous environment through a spatially patterned array of obstacles to validate our predictions. Finally, using numerical simulations, we show that this non-monotonic behaviour for energetic barriers is general and extends to even super-diffusive transport.

Reshaping the Syncytial Drosophila Embryo with Cortical Actin Networks: Four Main Steps of Early Development

Drosophila development begins as a syncytium. The large size of the one-cell embryo makes it ideal for studying the structure, regulation, and effects of the cortical actin cytoskeleton. We review four main steps of early development that depend on the actin cortex. At each step, dynamic remodelling of the cortex has specific effects on nuclei within the syncytium. During axial expansion, a cortical actomyosin network assembles and disassembles with the cell cycle, generating cytoplasmic flows that evenly distribute nuclei along the ovoid cell. When nuclei move to the cell periphery, they seed Arp2/3-based actin caps which grow into an array of dome-like compartments that house the nuclei as they divide at the cell cortex. To separate germline nuclei from the soma, posterior germ plasm induces full cleavage of mono-nucleated primordial germ cells from the syncytium. Finally, zygotic gene expression triggers formation of the blastoderm epithelium via cellularization and simultaneous division of ~6000 mono-nucleated cells from a single internal yolk cell. During these steps, the cortex is regulated in space and time, gains domain and sub-domain structure, and undergoes mesoscale interactions that lay a structural foundation of animal development.

Pseudocleavage furrows restrict plasma membrane-associated PH domain in syncytial Drosophila embryos

Syncytial cells contain multiple nuclei and have local distribution and function of cellular components despite being synthesized in a common cytoplasm. The syncytial Drosophila blastoderm embryo shows reduced spread of organelle and plasma membrane-associated proteins between adjacent nucleo-cytoplasmic domains. Anchoring to the cytoarchitecture within a nucleo-cytoplasmic domain is likely to decrease the spread of molecules; however, its role in restricting this spread has not been assessed. In order to analyze the cellular mechanisms that regulate the rate of spread of plasma membrane-associated molecules in the syncytial Drosophila embryos, we express a pleckstrin homology (PH) domain in a localized manner at the anterior of the embryo by tagging it with the bicoid mRNA localization signal. Anteriorly expressed PH domain forms an exponential gradient in the anteroposterior axis with a longer length scale compared with Bicoid. Using a combination of experiments and theoretical modeling, we find that the characteristic distribution and length scale emerge due to plasma membrane sequestration and restriction within an energid. Loss of plasma membrane remodeling to form pseudocleavage furrows shows an enhanced spread of PH domain but not Bicoid. Modeling analysis suggests that the enhanced spread of the PH domain occurs due to the increased spread of the cytoplasmic population of the PH domain in pseudocleavage furrow mutants. Our analysis of cytoarchitecture interaction in regulating plasma membrane protein distribution and constraining its spread has implications on the mechanisms of spread of various molecules, such as morphogens in syncytial cells.

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

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

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

Cytoskeletal mechanics and dynamics in the Drosophila syncytial embryo

Cell and tissue functions rely on the genetic programmes and cascades of biochemical signals. It has become evident during the past decade that the physical properties of soft material that govern the mechanics of cells and tissues play an important role in cellular function and morphology. The biophysical properties of cells and tissues are determined by the cytoskeleton, consisting of dynamic networks of F-actin and microtubules, molecular motors, crosslinkers and other associated proteins, among other factors such as cell-cell interactions. The Drosophila syncytial embryo represents a simple pseudo-tissue, with its nuclei orderly embedded in a structured cytoskeletal matrix at the embryonic cortex with no physical separation by cellular membranes. Here, we review the stereotypic dynamics and regulation of the cytoskeleton in Drosophila syncytial embryos and how cytoskeletal dynamics underlies biophysical properties and the emergence of collective features. We highlight the specific features and processes of syncytial embryos and discuss the applicability of biophysical approaches.

Just passing through: The auxin gradient of the root meristem

The root meristem-one of the plant's centers of continuous growth-is a conveyer belt in which cells of different identities are pushed through gradients along the root's longitudinal axis. An auxin gradient has long been implicated in controlling the progression of cell states in the root meristem. Recent work has shown that a PLETHORA (PLT) protein transcription factor gradient, which is under a delayed auxin response, has a dose-dependent effect on the differentiation state of cells. The direct effect of auxin concentration on differential transcriptional outputs remains unclear. Genomic and other analyses of regulatory sequences show that auxin responses are likely controlled by combinatorial inputs from transcription factors outside the core auxin signaling pathway. The passage through the meristem exposes cells to varying positional signals that could help them interpret auxin inputs independent of gradient effects. One open question is whether cells process information from the changes in the gradient over time as they move through the auxin gradient.

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.

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

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

On the importance of protein diffusion in biological systems: The example of the Bicoid morphogen gradient

Morphogens are proteins that form concentration gradients in embryos and developing tissues, where they act as postal codes, providing cells with positional information and allowing them to behave accordingly. Bicoid was the first discovered morphogen, and remains one of the most studied. It regulates segmentation in flies, forming a striking exponential gradient along the anterior-posterior axis of early Drosophila embryos, and activating the transcription of multiple target genes in a concentration-dependent manner. In this review, the work done by us and by others to characterize the mobility of Bicoid in D. melanogaster embryos is presented. The central role played by the diffusion of Bicoid in both the establishment of the gradient and the activation of target genes is discussed, and placed in the context of the need for these processes to be all at once rapid, precise and robust. The Bicoid system, and morphogen gradients in general, remain amongst the most amazing examples of the coexistence, often observed in living systems, of small-scale disorder and large-scale spatial order. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Syndapin promotes pseudocleavage furrow formation by actin organization in the syncytial Drosophila embryo

F-BAR domain–containing proteins link the actin cytoskeleton to the membrane during membrane remodeling. Syndapin associates with the pseudocleavage furrow membrane and is essential for furrow morphology, actin organization, and extension downstream of initiation factor RhoGEF2.

Coordinated membrane and cytoskeletal remodeling activities are required for membrane extension in processes such as cytokinesis and syncytial nuclear division cycles in Drosophila. Pseudocleavage furrow membranes in the syncytial Drosophila blastoderm embryo show rapid extension and retraction regulated by actin-remodeling proteins. The F-BAR domain protein Syndapin (Synd) is involved in membrane tubulation, endocytosis, and, uniquely, in F-actin stability. Here we report a role for Synd in actin-regulated pseudocleavage furrow formation. Synd localized to these furrows, and its loss resulted in short, disorganized furrows. Synd presence was important for the recruitment of the septin Peanut and distribution of Diaphanous and F-actin at furrows. Synd and Peanut were both absent in furrow-initiation mutants of RhoGEF2 and Diaphanous and in furrow-progression mutants of Anillin. Synd overexpression in rhogef2 mutants reversed its furrow-extension phenotypes, Peanut and Diaphanous recruitment, and F-actin organization. We conclude that Synd plays an important role in pseudocleavage furrow extension, and this role is also likely to be crucial in cleavage furrow formation during cell division.

Semi-permeable Diffusion Barriers Enhance Patterning Robustness in the C. elegans Germline

Positional information derived from local morphogen concentration plays an important role in patterning. A key question is how morphogen diffusion and gene expression regulation shape positional information into an appropriate profile with suitably low noise. We address this question using a model system--the C. elegans germline--whose regulatory network has been well characterized genetically but whose spatiotemporal dynamics are poorly understood. We show that diffusion within the germline syncytium is a critical control of stem cell differentiation and that semi-permeable diffusion barriers present at key locations make it possible--in combination with a feedback loop in the germline regulatory network--for mitotic zone size to be robust against spatial noise in Notch signaling. Spatial averaging within compartments defined by diffusion barriers is an advantageous patterning strategy, which attenuates noise while still allowing for sharp transitions between compartments. This strategy could apply to other organs.

Evidence for internuclear signaling in drosophila embryogenesis

BACKGROUND

Syncytial nuclei in Drosophila embryos undergo their first 13 divisions nearly synchronously. In the last several cell cycles, these division events travel across the anterior-posterior axis of the syncytial blastoderm in a wave. The phenomenon is well documented but the underlying mechanisms are not yet understood.

RESULTS

We study timing and positional data obtained from in vivo imaging of Drosophila embryos. We determine the statistical properties of the distribution of division times within and across generations with the null hypothesis that timing of division events is an independent random variable for each nucleus. We also compare timing data with a model of Drosophila cell cycle regulation that does not include internuclear signaling, and to a universal model of phase-dependent signaling to determine the probable form of internuclear signaling in the syncytial embryo.

CONCLUSIONS

The statistical variance of division times is lower than one would expect from uncoordinated activity. In fact, the variance decreases between the 10th and 11th divisions, which demonstrates a contribution of internuclear signaling to the observed synchrony and division waves. Our comparison with a coupled oscillator model leads us to conclude that internuclear signaling must be of Response/Signaling type with a positive impulse.

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

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

Mobility of signaling molecules: the key to deciphering plant organogenesis

Signaling molecules move between cells to form a characteristic distribution pattern within a developing organ; thereafter, they spatiotemporally regulate organ development. A key question in this process is how the signaling molecules robustly form the precise distribution on a tissue scale in a reproducible manner. Despite of an increasing number of quantitative studies regarding the mobility of signaling molecules, the detail mechanism of organogenesis via intercellular signaling is still unclear. We here review the potential advantages of plant development to address this question, focusing on the cytoplasmic continuity of plant cells through the plasmodesmata. The plant system would provide a unique opportunity to define the simple transportation mode of diffusion process, and, hence, the mechanism of organogenesis via intercellular signaling. Based on the advances in the understanding of intercellular signaling at the molecular level and in the quantitative imaging techniques, we discuss our current challenges in measuring the mobility of signaling molecules for deciphering plant organogenesis.

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

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

Messages do diffuse faster than messengers: reconciling disparate estimates of the morphogen bicoid diffusion coefficient

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times.

Understanding the mechanisms by which equivalent cells develop into different body parts is a fundamental question in biology. One well-studied example is the patterning along the anterior-posterior axis of Drosophila melanogaster embryos for which the spatial gradient of the protein Bicoid is determinant. The localized production of Bicoid is implicated in its inhomogeneous distribution. Diffusion then determines the time and spatial scales of the gradient as it is formed. Estimates of Bicoid diffusion coefficients made with the optical techniques, FRAP and FCS resulted in largely different values, one of which was too slow to account for the observed time of gradient formation. In this paper, we present a model in which Bicoid diffuses and interacts with binding sites so that its transport is described by a "single molecule'' and a "collective'' diffusion coefficient. The latter can be arbitrarily larger than the former coefficient and sets the rate for bulk processes such as the formation of the gradient. In this way we obtain a self-consistent picture in which the FRAP and FCS estimates are accurate and where the gradient can be established within the experimentally observed times.

Paused Pol II coordinates tissue morphogenesis in the Drosophila embryo

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

Morphogen transport

The graded distribution of morphogens underlies many of the tissue patterns that form during development. How morphogens disperse from a localized source and how gradients in the target tissue form has been under debate for decades. Recent imaging studies and biophysical measurements have provided evidence for various morphogen transport models ranging from passive mechanisms, such as free or hindered extracellular diffusion, to cell-based dispersal by transcytosis or cytonemes. Here, we analyze these transport models using the morphogens Nodal, fibroblast growth factor and Decapentaplegic as case studies. We propose that most of the available data support the idea that morphogen gradients form by diffusion that is hindered by tortuosity and binding to extracellular molecules.

Investigating the principles of morphogen gradient formation: from tissues to cells

Morphogen gradients regulate the patterning and growth of many tissues, hence a key question is how they are established and maintained during development. Theoretical descriptions have helped to explain how gradient shape is controlled by the rates of morphogen production, spreading and degradation. These effective rates have been measured using fluorescence recovery after photobleaching (FRAP) and photoactivation. To unravel which molecular events determine the effective rates, such tissue-level assays have been combined with genetic analysis, high-resolution assays, and models that take into account interactions with receptors, extracellular components and trafficking. Nevertheless, because of the natural and experimental data variability, and the underlying assumptions of transport models, it remains challenging to conclusively distinguish between cellular mechanisms.