Dynamic control of positional information in the early Drosophila embryo

Automatic design of gene regulatory mechanisms for spatial pattern formation

Gene regulatory mechanisms (GRMs) control the formation of spatial and temporal expression patterns that can serve as regulatory signals for the development of complex shapes. Synthetic developmental biology aims to engineer such genetic circuits for understanding and producing desired multicellular spatial patterns. However, designing synthetic GRMs for complex, multi-dimensional spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given two-dimensional spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms-including the number of genes necessary for the formation of the target spatial pattern-we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover complex genetic circuits producing spatial patterns.

Evolution of patterning

Developing tissues are patterned in space and time; this enables them to differentiate their cell types and form complex structures to support different body plans. Although space and time are two independent entities, there are many examples of spatial patterns that originate from temporal ones. The most prominent example is the expression of the genes hunchback, Krüppel, pdm, and castor, which are expressed temporally in the neural stem cells of the Drosophila ventral nerve cord and spatially along the anteroposterior axis of the blastoderm stage embryo. In this Viewpoint, we investigate the relationship between space and time in specific examples of spatial and temporal patterns with the aim of gaining insight into the evolutionary history of patterning.

Automatic design of gene regulatory mechanisms for spatial pattern formation

Synthetic developmental biology aims to engineer gene regulatory mechanisms (GRMs) for understanding and producing desired multicellular patterns and shapes. However, designing GRMs for spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms-including the number of genes necessary for the formation of the target pattern-we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover pattern-producing genetic circuits.

A bistable autoregulatory module in the developing embryo commits cells to binary expression fates

Bistable autoactivation has been proposed as a mechanism for cells to adopt binary fates during embryonic development. However, it is unclear whether the autoactivating modules found within developmental gene regulatory networks are bistable, unless their parameters are quantitatively determined. Here, we combine in vivo live imaging with mathematical modeling to dissect the binary cell fate dynamics of the fruit fly pair-rule gene fushi tarazu (ftz), which is regulated by two known enhancers: the early (non-autoregulating) element and the autoregulatory element. Live imaging of transcription and protein concentration in the blastoderm revealed that binary Ftz fates are achieved as Ftz expression rapidly transitions from being dictated by the early element to the autoregulatory element. Moreover, we discovered that Ftz concentration alone is insufficient to activate the autoregulatory element, and that this element only becomes responsive to Ftz at a prescribed developmental time. Based on these observations, we developed a dynamical systems model and quantitated its kinetic parameters directly from experimental measurements. Our model demonstrated that the ftz autoregulatory module is indeed bistable and that the early element transiently establishes the content of the binary cell fate decision to which the autoregulatory module then commits. Further in silico analysis revealed that the autoregulatory element locks the Ftz fate quickly, within 35 min of exposure to the transient signal of the early element. Overall, our work confirms the widely held hypothesis that autoregulation can establish developmental fates through bistability and, most importantly, provides a framework for the quantitative dissection of cellular decision-making.

Developmental Biology: Computational and Experimental Approaches

Developmental biology studies ontogenesis, the individual development of an organism from the time of fertilization in sexual reproduction or its expelling from the maternal organism in asexual reproduction to the end of an organism's life, with all phenotypical characters typical of this biological species and supporting the normal course of all biochemical processes and morphogenesis [...].

Cellular compartmentalisation and receptor promiscuity as a strategy for accurate and robust inference of position during morphogenesis

Precise spatial patterning of cell fate during morphogenesis requires accurate inference of cellular position. In making such inferences from morphogen profiles, cells must contend with inherent stochasticity in morphogen production, transport, sensing and signalling. Motivated by the multitude of signalling mechanisms in various developmental contexts, we show how cells may utilise multiple tiers of processing (compartmentalisation) and parallel branches (multiple receptor types), together with feedback control, to bring about fidelity in morphogenetic decoding of their positions within a developing tissue. By simultaneously deploying specific and nonspecific receptors, cells achieve a more accurate and robust inference. We explore these ideas in the patterning of Drosophila melanogaster wing imaginal disc by Wingless morphogen signalling, where multiple endocytic pathways participate in decoding the morphogen gradient. The geometry of the inference landscape in the high dimensional space of parameters provides a measure for robustness and delineates stiff and sloppy directions. This distributed information processing at the scale of the cell highlights how local cell autonomous control facilitates global tissue scale design.

Stability of Pattern Formation in Systems with Dynamic Source Regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with a step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

Evo-devo beyond development: Generalizing evo-devo to all levels of the phenotypic evolution

A foundational idea of evo-devo is that morphological variation is not isotropic, that is, it does not occur in all directions. Instead, some directions of morphological variation are more likely than others from DNA-level variation and these largely depend on development. We argue that this evo-devo perspective should apply not only to morphology but to evolution at all phenotypic levels. At other phenotypic levels there is no development, but there are processes that can be seen, in analogy to development, as constructing the phenotype (e.g., protein folding, learning for behavior, etc.). We argue that to explain the direction of evolution two types of arguments need to be combined: generative arguments about which phenotypic variation arises in each generation and selective arguments about which of it passes to the next generation. We explain how a full consideration of the two types of arguments improves the explanatory power of evolutionary theory. Also see the video abstract here: https://youtu.be/Egbvma_uaKc.

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.

A timer gene network is spatially regulated by the terminal system in the Drosophila embryo

In insect embryos, anteroposterior patterning is coordinated by the sequential expression of the 'timer' genes caudal, Dichaete, and odd-paired, whose expression dynamics correlate with the mode of segmentation. In Drosophila, the timer genes are expressed broadly across much of the blastoderm, which segments simultaneously, but their expression is delayed in a small 'tail' region, just anterior to the hindgut, which segments during germband extension. Specification of the tail and the hindgut depends on the terminal gap gene tailless, but beyond this the regulation of the timer genes is poorly understood. We used a combination of multiplexed imaging, mutant analysis, and gene network modelling to resolve the regulation of the timer genes, identifying 11 new regulatory interactions and clarifying the mechanism of posterior terminal patterning. We propose that a dynamic Tailless expression gradient modulates the intrinsic dynamics of a timer gene cross-regulatory module, delineating the tail region and delaying its developmental maturation.

Cellular reaction gene regulation network for swarm robots with pattern formation maneuvering control

Self-organized pattern formation enables swarm robots to interact with local environments to self-organize into intricate structures generated by gene regulatory network (GRN) control methods without global knowledge. Previous studies have reported that it is challenging to maintain pattern formation stability during maneuvering in the environment due to local morphogenetic reaction rules. Motivated by the mechanism of the GRN in multi-cellular organisms, we propose a novel cellular reaction gene regulatory network (CR-GRN) for pattern formation maneuvering control. In CR-GRN, a cellular reaction network is creatively proposed to depict the robots, environment, virtual target pattern, and their interaction to generate emergent swarm behavior in multi-robot systems. A novel diffusion equation is proposed to simulate the process of morphogen diffusion among cells to ensure stable adaptive pattern generation. In addition, genes, proteins, and morphogens are used to define the internal and external states of cells and form a feedback regulation network. Simulation experiments are conducted to validate the proposed method. The results show that the CR-GRN can satisfy the requirements of turning curvature and maintain the robot's uniformity based on the proposed algorithm. This proves that robots using the CR-GRN can cooperate more effectively to cope in a complicated environment, and maintain a stable formation during maneuvering.

Patterning principles of morphogen gradients

Metazoan embryos develop from a single cell into three-dimensional structured organisms while groups of genetically identical cells attain specialized identities. Cells of the developing embryo both create and accurately interpret morphogen gradients to determine their positions and make specific decisions in response. Here, we first cover intellectual roots of morphogen and positional information concepts. Focusing on animal embryos, we then provide a review of current understanding on how morphogen gradients are established and how their spans are controlled. Lastly, we cover how gradients evolve in time and space during development, and how they encode information to control patterning. In sum, we provide a list of patterning principles for morphogen gradients and review recent advances in quantitative methodologies elucidating information provided by morphogens.

Beyond genotype-phenotype maps: Toward a phenotype-centered perspective on evolution

Evolutionary biology is paying increasing attention to the mechanisms that enable phenotypic plasticity, evolvability, and extra-genetic inheritance. Yet, there is a concern that these phenomena remain insufficiently integrated within evolutionary theory. Understanding their evolutionary implications would require focusing on phenotypes and their variation, but this does not always fit well with the prevalent genetic representation of evolution that screens off developmental mechanisms. Here, we instead use development as a starting point, and represent it in a way that allows genetic, environmental and epigenetic sources of phenotypic variation to be independent. We show why this representation helps to understand the evolutionary consequences of both genetic and non-genetic phenotype determinants, and discuss how this approach can instigate future areas of empirical and theoretical research.

Latent space of a small genetic network: Geometry of dynamics and information

The high-dimensional character of most biological systems presents genuine challenges for modeling and prediction. Here we propose a neural network-based approach for dimensionality reduction and analysis of biological gene expression data, using, as a case study, a well-known genetic network in the early Drosophila embryo, the gap gene patterning system. We build an autoencoder compressing the dynamics of spatial gap gene expression into a two-dimensional (2D) latent map. The resulting 2D dynamics suggests an almost linear model, with a small bare set of essential interactions. Maternally defined spatial modes control gap genes positioning, without the classically assumed intricate set of repressive gap gene interactions. This, surprisingly, predicts minimal changes of neighboring gap domains when knocking out gap genes, consistent with previous observations. Latent space geometries in maternal mutants are also consistent with the existence of such spatial modes. Finally, we show how positional information is well defined and interpretable as a polar angle in latent space. Our work illustrates how optimization of small neural networks on medium-sized biological datasets is sufficiently informative to capture essential underlying mechanisms of network function.

The macroscopic limit to synchronization of cellular clocks in single cells of Neurospora crassa

We determined the macroscopic limit for phase synchronization of cellular clocks in an artificial tissue created by a “big chamber” microfluidic device to be about 150,000 cells or less. The dimensions of the microfluidic chamber allowed us to calculate an upper limit on the radius of a hypothesized quorum sensing signal molecule of 13.05 nm using a diffusion approximation for signal travel within the device. The use of a second microwell microfluidic device allowed the refinement of the macroscopic limit to a cell density of 2166 cells per fixed area of the device for phase synchronization. The measurement of averages over single cell trajectories in the microwell device supported a deterministic quorum sensing model identified by ensemble methods for clock phase synchronization. A strong inference framework was used to test the communication mechanism in phase synchronization of quorum sensing versus cell-to-cell contact, suggesting support for quorum sensing. Further evidence came from showing phase synchronization was density-dependent.

Optogenetic control of the Bicoid morphogen reveals fast and slow modes of gap gene regulation

Developmental patterning networks are regulated by multiple inputs and feedback connections that rapidly reshape gene expression, limiting the information that can be gained solely from slow genetic perturbations. Here we show that fast optogenetic stimuli, real-time transcriptional reporters, and a simplified genetic background can be combined to reveal the kinetics of gene expression downstream of a developmental transcription factor in vivo. We engineer light-controlled versions of the Bicoid transcription factor and study their effects on downstream gap genes in embryos. Our results recapitulate known relationships, including rapid Bicoid-dependent transcription of giant and hunchback and delayed repression of Krüppel. In addition, we find that the posterior pattern of knirps exhibits a quick but inverted response to Bicoid perturbation, suggesting a noncanonical role for Bicoid in directly suppressing knirps transcription. Acute modulation of transcription factor concentration while recording output gene activity represents a powerful approach for studying developmental gene networks in vivo.

System drift and speciation

Even if a species' phenotype does not change over evolutionary time, the underlying mechanism may change, as distinct molecular pathways can realize identical phenotypes. Here we use linear system theory to explore the consequences of this idea, describing how a gene network underlying a conserved phenotype evolves, as the genetic drift of small changes to these molecular pathways causes a population to explore the set of mechanisms with identical phenotypes. To do this, we model an organism's internal state as a linear system of differential equations for which the environment provides input and the phenotype is the output, in which context there exists an exact characterization of the set of all mechanisms that give the same input-output relationship. This characterization implies that selectively neutral directions in genotype space should be common and that the evolutionary exploration of these distinct but equivalent mechanisms can lead to the reproductive incompatibility of independently evolving populations. This evolutionary exploration, or system drift, is expected to proceed at a rate proportional to the amount of intrapopulation genetic variation divided by the effective population size ( Ne$N_e$ ). At biologically reasonable parameter values this could lead to substantial interpopulation incompatibility, and thus speciation, on a time scale of Ne$N_e$ generations. This model also naturally predicts Haldane's rule, thus providing a concrete explanation of why heterogametic hybrids tend to be disrupted more often than homogametes during the early stages of speciation.

Data-driven modeling predicts gene regulatory network dynamics during the differentiation of multipotential hematopoietic progenitors

Cellular differentiation during hematopoiesis is guided by gene regulatory networks (GRNs) comprising transcription factors (TFs) and the effectors of cytokine signaling. Based largely on analyses conducted at steady state, these GRNs are thought to be organized as a hierarchy of bistable switches, with antagonism between Gata1 and PU.1 driving red- and white-blood cell differentiation. Here, we utilize transient gene expression patterns to infer the genetic architecture—the type and strength of regulatory interconnections—and dynamics of a twelve-gene GRN including key TFs and cytokine receptors. We trained gene circuits, dynamical models that learn genetic architecture, on high temporal-resolution gene-expression data from the differentiation of an inducible cell line into erythrocytes and neutrophils. The model is able to predict the consequences of gene knockout, knockdown, and overexpression experiments and the inferred interconnections are largely consistent with prior empirical evidence. The inferred genetic architecture is densely interconnected rather than hierarchical, featuring extensive cross-antagonism between genes from alternative lineages and positive feedback from cytokine receptors. The analysis of the dynamics of gene regulation in the model reveals that PU.1 is one of the last genes to be upregulated in neutrophil conditions and that the upregulation of PU.1 and other neutrophil genes is driven by Cebpa and Gfi1 instead. This model inference is confirmed in an independent single-cell RNA-Seq dataset from mouse bone marrow in which Cebpa and Gfi1 expression precedes the neutrophil-specific upregulation of PU.1 during differentiation. These results demonstrate that full PU.1 upregulation during neutrophil development involves regulatory influences extrinsic to the Gata1-PU.1 bistable switch. Furthermore, although there is extensive cross-antagonism between erythroid and neutrophil genes, it does not have a hierarchical structure. More generally, we show that the combination of high-resolution time series data and data-driven dynamical modeling can uncover the dynamics and causality of developmental events that might otherwise be obscured.

The supply of blood cells is replenished by the maturation of hematopoietic progenitor cells into different cell types. Which cell type a progenitor cell develops into is determined by a complex network of genes whose protein products directly or indirectly regulate each others’ expression and that of downstream genes characteristic of the cell type. We inferred the nature and causality of the regulatory connections in a 12-gene network known to affect the decision between erythrocyte and neutrophil cell fates using a predictive machine-learning approach. Our analysis showed that the overall architecture of the network is densely interconnected and not hierarchical. Furthermore, the model inferred that PU.1, considered a master regulator of all white-blood cell lineages, is upregulated during neutrophil development by two other proteins, Cebpa and Gfi1. We validated this prediction by showing that Cebpa and Gfi1 expression precedes that of PU.1 in single-cell gene expression data from mouse bone marrow. These results revise the architecture of the gene network and the causality of regulatory events guiding hematopoiesis. The results also show that combining machine learning approaches with time course data can help resolve causality during development.

Unraveling the heritage of lost traits

We synthesize ontogenetic work spanning the past century that show evolutionarily lost structures are rarely entirely absent from earlier developmental stages. We discuss morphological and genetic insights from developmental studies reveal about the evolution of trait loss and regain.

Application of Domain- and Genotype-Specific Models to Infer Post-Transcriptional Regulation of Segmentation Gene Expression in Drosophila

Unlike transcriptional regulation, the post-transcriptional mechanisms underlying zygotic segmentation gene expression in early Drosophila embryo have been insufficiently investigated. Condition-specific post-transcriptional regulation plays an important role in the development of many organisms. Our recent study revealed the domain- and genotype-specific differences between mRNA and the protein expression of Drosophila hb, gt, and eve genes in cleavage cycle 14A. Here, we use this dataset and the dynamic mathematical model to recapitulate protein expression from the corresponding mRNA patterns. The condition-specific nonuniformity in parameter values is further interpreted in terms of possible post-transcriptional modifications. For hb expression in wild-type embryos, our results predict the position-specific differences in protein production. The protein synthesis rate parameter is significantly higher in hb anterior domain compared to the posterior domain. The parameter sets describing Gt protein dynamics in wild-type embryos and Kr mutants are genotype-specific. The spatial discrepancy between gt mRNA and protein posterior expression in Kr mutants is well reproduced by the whole axis model, thus rejecting the involvement of post-transcriptional mechanisms. Our models fail to describe the full dynamics of eve expression, presumably due to its complex shape and the variable time delays between mRNA and protein patterns, which likely require a more complex model. Overall, our modeling approach enables the prediction of regulatory scenarios underlying the condition-specific differences between mRNA and protein expression in early embryo.

Fitting thermodynamic-based models: Incorporating parameter sensitivity improves the performance of an evolutionary algorithm

A detailed comprehension of transcriptional regulation is critical to understanding the genetic control of development and disease across many different organisms. To more fully investigate the complex molecular interactions controlling the precise expression of genes, many groups have constructed mathematical models to complement their experimental approaches. A critical step in such studies is choosing the most appropriate parameter estimation algorithm to enable detailed analysis of the parameters that contribute to the models. In this study, we develop a novel set of evolutionary algorithms that use a pseudo-random Sobol Set to construct the initial population and incorporate parameter sensitivities into the adaptation of mutation rates, using local, global, and hybrid strategies. Comparison of the performance of these new algorithms to a number of current state-of-the-art global parameter estimation algorithms on a range of continuous test functions, as well as synthetic biological data representing models of gene regulatory systems, reveals improved performance of the new algorithms in terms of runtime, error and reproducibility. In addition, by analyzing the ability of these algorithms to fit datasets of varying quality, we provide the experimentalist with a guide to how the algorithms perform across a range of noisy data. These results demonstrate the improved performance of the new set of parameter estimation algorithms and facilitate meaningful integration of model parameters and predictions in our understanding of the molecular mechanisms of gene regulation.

Using phenotypic plasticity to understand the structure and evolution of the genotype-phenotype map

Deciphering the genotype-phenotype map necessitates relating variation at the genetic level to variation at the phenotypic level. This endeavour is inherently limited by the availability of standing genetic variation, the rate of spontaneous mutation to novo genetic variants, and possible biases associated with induced mutagenesis. An interesting alternative is to instead rely on the environment as a source of variation. Many phenotypic traits change plastically in response to the environment, and these changes are generally underlain by changes in gene expression. Relating gene expression plasticity to the phenotypic plasticity of more integrated organismal traits thus provides useful information about which genes influence the development and expression of which traits, even in the absence of genetic variation. We here appraise the prospects and limits of such an environment-for-gene substitution for investigating the genotype-phenotype map. We review models of gene regulatory networks, and discuss the different ways in which they can incorporate the environment to mechanistically model phenotypic plasticity and its evolution. We suggest that substantial progress can be made in deciphering this genotype-environment-phenotype map, by connecting theory on gene regulatory network to empirical patterns of gene co-expression, and by more explicitly relating gene expression to the expression and development of phenotypes, both theoretically and empirically.

Patterning with clocks and genetic cascades: Segmentation and regionalization of vertebrate versus insect body plans

Oscillatory and sequential processes have been implicated in the spatial patterning of many embryonic tissues. For example, molecular clocks delimit segmental boundaries in vertebrates and insects and mediate lateral root formation in plants, whereas sequential gene activities are involved in the specification of regional identities of insect neuroblasts, vertebrate neural tube, vertebrate limb, and insect and vertebrate body axes. These processes take place in various tissues and organisms, and, hence, raise the question of what common themes and strategies they share. In this article, we review 2 processes that rely on the spatial regulation of periodic and sequential gene activities: segmentation and regionalization of the anterior-posterior (AP) axis of animal body plans. We study these processes in species that belong to 2 different phyla: vertebrates and insects. By contrasting 2 different processes (segmentation and regionalization) in species that belong to 2 distantly related phyla (arthropods and vertebrates), we elucidate the deep logic of patterning by oscillatory and sequential gene activities. Furthermore, in some of these organisms (e.g., the fruit fly Drosophila), a mode of AP patterning has evolved that seems not to overtly rely on oscillations or sequential gene activities, providing an opportunity to study the evolution of pattern formation mechanisms.

The early Drosophila embryo as a model system for quantitative biology

With the rise of new tools, from controlled genetic manipulations and optogenetics to improved microscopy, it is now possible to make clear, quantitative and reproducible measurements of biological processes. The humble fruit fly Drosophila melanogaster, with its ease of genetic manipulation combined with excellent imaging accessibility, has become a major model system for performing quantitative in vivo measurements. Such measurements are driving a new wave of interest from physicists and engineers, who are developing a range of testable dynamic models of active systems to understand fundamental biological processes. The reproducibility of the early Drosophila embryo has been crucial for understanding how biological systems are robust to unavoidable noise during development. Insights from quantitative in vivo experiments in the Drosophila embryo are having an impact on our understanding of critical biological processes, such as how cells make decisions and how complex tissue shape emerges. Here, to highlight the power of using Drosophila embryogenesis for quantitative biology, I focus on three main areas: (1) formation and robustness of morphogen gradients; (2) how gene regulatory networks ensure precise boundary formation; and (3) how mechanical interactions drive packing and tissue folding. I further discuss how such data has driven advances in modelling.

Multiple morphogens and rapid elongation promote segmental patterning during development

The vertebrate hindbrain is segmented into rhombomeres (r) initially defined by distinct domains of gene expression. Previous studies have shown that noise-induced gene regulation and cell sorting are critical for the sharpening of rhombomere boundaries, which start out rough in the forming neural plate (NP) and sharpen over time. However, the mechanisms controlling simultaneous formation of multiple rhombomeres and accuracy in their sizes are unclear. We have developed a stochastic multiscale cell-based model that explicitly incorporates dynamic morphogenetic changes (i.e. convergent-extension of the NP), multiple morphogens, and gene regulatory networks to investigate the formation of rhombomeres and their corresponding boundaries in the zebrafish hindbrain. During pattern initiation, the short-range signal, fibroblast growth factor (FGF), works together with the longer-range morphogen, retinoic acid (RA), to specify all of these boundaries and maintain accurately sized segments with sharp boundaries. At later stages of patterning, we show a nonlinear change in the shape of rhombomeres with rapid left-right narrowing of the NP followed by slower dynamics. Rapid initial convergence improves boundary sharpness and segment size by regulating cell sorting and cell fate both independently and coordinately. Overall, multiple morphogens and tissue dynamics synergize to regulate the sizes and boundaries of multiple segments during development.

In segmental pattern formation, chemical gradients control gene expression in a concentration-dependent manner to specify distinct gene expression domains. Despite the stochasticity inherent to such biological processes, precise and accurate borders form between segmental gene expression domains. Previous work has revealed synergy between gene regulation and cell sorting in sharpening borders that are initially rough. However, it is still poorly understood how size and boundary sharpness of multiple segments are regulated in a tissue that changes dramatically in its morphology as the embryo develops. Here we develop a stochastic multiscale cell-base model to investigate these questions. Two novel strategies synergize to promote accurate segment formation, a combination of long- and short-range morphogens plus rapid tissue convergence, with one responsible for pattern initiation and the other enabling pattern refinement.

Homology of process: developmental dynamics in comparative biology

Comparative biology builds up systematic knowledge of the diversity of life, across evolutionary lineages and levels of organization, starting with evidence from a sparse sample of model organisms. In developmental biology, a key obstacle to the growth of comparative approaches is that the concept of homology is not very well defined for levels of organization that are intermediate between individual genes and morphological characters. In this paper, we investigate what it means for ontogenetic processes to be homologous, focusing specifically on the examples of insect segmentation and vertebrate somitogenesis. These processes can be homologous without homology of the underlying genes or gene networks, since the latter can diverge over evolutionary time, while the dynamics of the process remain the same. Ontogenetic processes like these therefore constitute a dissociable level and distinctive unit of comparison requiring their own specific criteria of homology. In addition, such processes are typically complex and nonlinear, such that their rigorous description and comparison requires not only observation and experimentation, but also dynamical modelling. We propose six criteria of process homology, combining recognized indicators (sameness of parts, morphological outcome and topological position) with novel ones derived from dynamical systems modelling (sameness of dynamical properties, dynamical complexity and evidence for transitional forms). We show how these criteria apply to animal segmentation and other ontogenetic processes. We conclude by situating our proposed dynamical framework for homology of process in relation to similar research programmes, such as process structuralism and developmental approaches to morphological homology.

Time and space in segmentation

Arthropod segmentation and vertebrate somitogenesis are leading fields in the experimental and theoretical interrogation of developmental patterning. However, despite the sophistication of current research, basic conceptual issues remain unresolved. These include: (i) the mechanistic origins of spatial organization within the segment addition zone (SAZ); (ii) the mechanistic origins of segment polarization; (iii) the mechanistic origins of axial variation; and (iv) the evolutionary origins of simultaneous patterning. Here, I explore these problems using coarse-grained models of cross-regulating dynamical processes. In the morphogenetic framework of a row of cells undergoing axial elongation, I simulate interactions between an 'oscillator', a 'switch' and up to three 'timers', successfully reproducing essential patterning behaviours of segmenting systems. By comparing the output of these largely cell-autonomous models to variants that incorporate positional information, I find that scaling relationships, wave patterns and patterning dynamics all depend on whether the SAZ is regulated by temporal or spatial information. I also identify three mechanisms for polarizing oscillator output, all of which functionally implicate the oscillator frequency profile. Finally, I demonstrate significant dynamical and regulatory continuity between sequential and simultaneous modes of segmentation. I discuss these results in the context of the experimental literature.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

Implications of diffusion and time-varying morphogen gradients for the dynamic positioning and precision of bistable gene expression boundaries

The earliest models for how morphogen gradients guide embryonic patterning failed to account for experimental observations of temporal refinement in gene expression domains. Following theoretical and experimental work in this area, dynamic positional information has emerged as a conceptual framework to discuss how cells process spatiotemporal inputs into downstream patterns. Here, we show that diffusion determines the mathematical means by which bistable gene expression boundaries shift over time, and therefore how cells interpret positional information conferred from morphogen concentration. First, we introduce a metric for assessing reproducibility in boundary placement or precision in systems where gene products do not diffuse, but where morphogen concentrations are permitted to change in time. We show that the dynamics of the gradient affect the sensitivity of the final pattern to variation in initial conditions, with slower gradients reducing the sensitivity. Second, we allow gene products to diffuse and consider gene expression boundaries as propagating wavefronts with velocity modulated by local morphogen concentration. We harness this perspective to approximate a PDE model as an ODE that captures the position of the boundary in time, and demonstrate the approach with a preexisting model for Hunchback patterning in fruit fly embryos. We then propose a design that employs antiparallel morphogen gradients to achieve accurate boundary placement that is robust to scaling. Throughout our work we draw attention to tradeoffs among initial conditions, boundary positioning, and the relative timescales of network and gradient evolution. We conclude by suggesting that mathematical theory should serve to clarify not just our quantitative, but also our intuitive understanding of patterning processes.

Finding gene network topologies for given biological function with recurrent neural network

Searching for possible biochemical networks that perform a certain function is a challenge in systems biology. For simple functions and small networks, this can be achieved through an exhaustive search of the network topology space. However, it is difficult to scale this approach up to larger networks and more complex functions. Here we tackle this problem by training a recurrent neural network (RNN) to perform the desired function. By developing a systematic perturbative method to interrogate the successfully trained RNNs, we are able to distill the underlying regulatory network among the biological elements (genes, proteins, etc.). Furthermore, we show several cases where the regulation networks found by RNN can achieve the desired biological function when its edges are expressed by more realistic response functions, such as the Hill-function. This method can be used to link topology and function by helping uncover the regulation logic and network topology for complex tasks.

Networks are useful ways to describe interactions between molecules in a cell, but predicting the real topology of large networks can be challenging. Here, the authors use deep learning to predict the topology of networks that perform biologically-plausible functions.

Dynamic regulation of anterior-posterior patterning genes in living Drosophila embryos

Expression of the gap and pair-rule genes plays an essential role in body segmentation during Drosophila embryogenesis.^1-5 However, it remains unclear how precise expression patterns of these key developmental genes arise from stochastic transcriptional activation at the single-cell level. Here, I employed genome-editing and live-imaging approaches to comprehensively visualize regulation of the gap and pair-rule genes at the endogenous loci. Quantitative image analysis revealed that the total duration of active transcription (transcription period) is a major determinant of spatial patterning of gene expression in early embryos. The length of the transcription period is determined by the continuity of bursting activities in individual nuclei, with the core expression domain producing more bursts than boundary regions. Each gene exhibits a distinct rate of nascent RNA production during transcriptional bursting, which contributes to gene-to-gene variability in the total output. I also provide evidence for "enhancer interference," wherein a distal weak enhancer interferes with transcriptional activation by a strong proximal enhancer to downregulate the length of the transcription period without changing the transcription rate. Analysis of the endogenous hunchback (hb) locus revealed that the removal of the distal shadow enhancer induces strong ectopic transcriptional activation, which suppresses refinement of the initial broad expression domain into narrower stripe patterns at the anterior part of embryos. This study provides key insights into the link between transcriptional bursting, enhancer-promoter interaction, and spatiotemporal patterning of gene expression during animal development.

Bootstrapping and Pinning down the Root Meristem; the Auxin-PLT-ARR Network Unites Robustness and Sensitivity in Meristem Growth Control

After germination, the meristem of the embryonic plant root becomes activated, expands in size and subsequently stabilizes to support post-embryonic root growth. The plant hormones auxin and cytokinin, together with master transcription factors of the PLETHORA (PLT) family have been shown to form a regulatory network that governs the patterning of this root meristem. Still, which functional constraints contributed to shaping the dynamics and architecture of this network, has largely remained unanswered. Using a combination of modeling approaches we reveal how the interplay between auxin and PLTs enables meristem activation in response to above-threshold stimulation, while its embedding in a PIN-mediated auxin reflux loop ensures localized PLT transcription and thereby, a finite meristem size. We furthermore demonstrate how this constrained PLT transcriptional domain enables independent control of meristem size and division rates, further supporting a division of labor between auxin and PLT. We subsequently reveal how the weaker auxin antagonism of the earlier active Arabidopsis response regulator 12 (ARR12) may arise from the absence of a DELLA protein interaction domain. Our model indicates that this reduced strength is essential to prevent collapse in the early stages of meristem expansion while at later stages the enhanced strength of Arabidopsis response regulator 1 (ARR1) is required for sufficient meristem size control. Summarizing, our work indicates that functional constraints significantly contribute to shaping the auxin-cytokinin-PLT regulatory network.

Roadmap for the multiscale coupling of biochemical and mechanical signals during development

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

Inference of dynamic spatial GRN models with multi-GPU evolutionary computation

Reverse engineering mechanistic gene regulatory network (GRN) models with a specific dynamic spatial behavior is an inverse problem without analytical solutions in general. Instead, heuristic machine learning algorithms have been proposed to infer the structure and parameters of a system of equations able to recapitulate a given gene expression pattern. However, these algorithms are computationally intensive as they need to simulate millions of candidate models, which limits their applicability and requires high computational resources. Graphics processing unit (GPU) computing is an affordable alternative for accelerating large-scale scientific computation, yet no method is currently available to exploit GPU technology for the reverse engineering of mechanistic GRNs from spatial phenotypes. Here we present an efficient methodology to parallelize evolutionary algorithms using GPU computing for the inference of mechanistic GRNs that can develop a given gene expression pattern in a multicellular tissue area or cell culture. The proposed approach is based on multi-CPU threads running the lightweight crossover, mutation and selection operators and launching GPU kernels asynchronously. Kernels can run in parallel in a single or multiple GPUs and each kernel simulates and scores the error of a model using the thread parallelism of the GPU. We tested this methodology for the inference of spatiotemporal mechanistic gene regulatory networks (GRNs)-including topology and parameters-that can develop a given 2D gene expression pattern. The results show a 700-fold speedup with respect to a single CPU implementation. This approach can streamline the extraction of knowledge from biological and medical datasets and accelerate the automatic design of GRNs for synthetic biology applications.

Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits

Qualitative modeling approaches are promising and still underexploited tools for the analysis and design of synthetic circuits. They can make predictions of circuit behavior in the absence of precise, quantitative information. Moreover, they provide direct insight into the relation between the feedback structure and the dynamical properties of a network. We review qualitative modeling approaches by focusing on two specific formalisms, Boolean networks and piecewise-linear differential equations, and illustrate their application by means of three well-known synthetic circuits. We describe various methods for the analysis of state transition graphs, discrete representations of the network dynamics that are generated in both modeling frameworks. We also briefly present the problem of controlling synthetic circuits, an emerging topic that could profit from the capacity of qualitative modeling approaches to rapidly scan a space of design alternatives.

Fully interpretable deep learning model of transcriptional control

Motivation

The universal expressibility assumption of Deep Neural Networks (DNNs) is the key motivation behind recent worksin the systems biology community to employDNNs to solve important problems in functional genomics and moleculargenetics. Typically, such investigations have taken a ‘black box’ approach in which the internal structure of themodel used is set purely by machine learning considerations with little consideration of representing the internalstructure of the biological system by the mathematical structure of the DNN. DNNs have not yet been applied to thedetailed modeling of transcriptional control in which mRNA production is controlled by the binding of specific transcriptionfactors to DNA, in part because such models are in part formulated in terms of specific chemical equationsthat appear different in form from those used in neural networks.

Results

In this paper, we give an example of a DNN whichcan model the detailed control of transcription in a precise and predictive manner. Its internal structure is fully interpretableand is faithful to underlying chemistry of transcription factor binding to DNA. We derive our DNN from asystems biology model that was not previously recognized as having a DNN structure. Although we apply our DNNto data from the early embryo of the fruit fly Drosophila, this system serves as a test bed for analysis of much larger datasets obtained by systems biology studies on a genomic scale. .

Availability and implementation

The implementation and data for the models used in this paper are in a zip file in the supplementary material.

Supplementary information

Supplementary data are available at Bioinformatics online.

Dynamical systems approach to evolution-development congruence: Revisiting Haeckel's recapitulation theory

It is acknowledged that embryonic development has a tendency to proceed from common toward specific. Ernst Haeckel raised the question of why that tendency prevailed through evolution, and the question remains unsolved. Here, we revisit Haeckel's recapitulation theory, that is, the parallelism between evolution and development through numerical evolution and dynamical systems theory. By using intracellular gene expression dynamics with cell‐to‐cell interaction over spatially aligned cells to represent the developmental process, gene regulation networks (GRN) that govern these dynamics evolve under the selection pressure to achieve a prescribed spatial gene expression pattern. For most numerical evolutionary experiments, the evolutionary pattern changes over generations, as well as the developmental pattern changes governed by the evolved GRN exhibit remarkable similarity. Changes in both patterns consisted of several epochs where stripes are formed in a short time, whereas for other temporal regimes, the pattern hardly changes. In evolution, these quasi‐stationary generations are needed to achieve relevant mutations, whereas, in development, they are due to some gene expressions that vary slowly and control the pattern change. These successive epochal changes in development and evolution are represented as common bifurcations in dynamical systems theory, regulating working network structure from feedforward subnetwork to those containing feedback loops. The congruence is the correspondence between successive acquisitions of subnetworks through evolution and changes in working subnetworks in development. Consistency of the theory with the segmentation gene‐expression dynamics is discussed. Novel outlook on recapitulation and heterochrony are provided, testable experimentally by the transcriptome and network analysis.

We confirmed recapitulation, parallelism between evolution and development, by evolutionary simulation of pattern formation. Its origin is analyzed in terms of bifurcation in dynamical systems theory, slow‐mode control, and network structures.

Spatio-Temporal Dynamics of the Patterning of Arabidopsis Flower Meristem

The qualitative model presented in this work recovers the onset of the four fields that correspond to those of each floral organ whorl of Arabidopsis flower, suggesting a mechanism for the generation of the positional information required for the differential expression of the A, B, and C identity genes according to the ABC model for organ determination during early stages of flower development. Our model integrates a previous model for the emergence of WUS pattern in the floral meristem, and shows that this pre-pattern is a necessary but not sufficient condition for the posterior information of the four fields predicted by the ABC model. Furthermore, our model predicts that LFY diffusion along the L1 layer of cells is not a necessary condition for the patterning of the floral meristem.

On the evolution and development of morphological complexity: A view from gene regulatory networks

How does morphological complexity evolve? This study suggests that the likelihood of mutations increasing phenotypic complexity becomes smaller when the phenotype itself is complex. In addition, the complexity of the genotype-phenotype map (GPM) also increases with the phenotypic complexity. We show that complex GPMs and the above mutational asymmetry are inevitable consequences of how genes need to be wired in order to build complex and robust phenotypes during development. We randomly wired genes and cell behaviors into networks in EmbryoMaker. EmbryoMaker is a mathematical model of development that can simulate any gene network, all animal cell behaviors (division, adhesion, apoptosis, etc.), cell signaling, cell and tissues biophysics, and the regulation of those behaviors by gene products. Through EmbryoMaker we simulated how each random network regulates development and the resulting morphology (i.e. a specific distribution of cells and gene expression in 3D). This way we obtained a zoo of possible 3D morphologies. Real gene networks are not random, but a random search allows a relatively unbiased exploration of what is needed to develop complex robust morphologies. Compared to the networks leading to simple morphologies, the networks leading to complex morphologies have the following in common: 1) They are rarer; 2) They need to be finely tuned; 3) Mutations in them tend to decrease morphological complexity; 4) They are less robust to noise; and 5) They have more complex GPMs. These results imply that, when complexity evolves, it does so at a progressively decreasing rate over generations. This is because as morphological complexity increases, the likelihood of mutations increasing complexity decreases, morphologies become less robust to noise, and the GPM becomes more complex. We find some properties in common, but also some important differences, with non-developmental GPM models (e.g. RNA, protein and gene networks in single cells).

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?

Dynamic patterning by morphogens illuminated by cis-regulatory studies

Morphogen concentration changes in space as well as over time during development. However, how these dynamics are interpreted by cells to specify fate is not well understood. Here, we focus on two morphogens: the maternal transcription factors Bicoid and Dorsal, which directly regulate target genes to pattern Drosophila embryos. The actions of these factors at enhancers has been thoroughly dissected and provides a rich platform for understanding direct input by morphogens and their changing roles over time. Importantly, Bicoid and Dorsal do not work alone; we also discuss additional inputs that work with morphogens to control spatiotemporal gene expression in embryos.

Dynamic Modeling of Transcriptional Gene Regulatory Networks

Diverse cellular phenotypes are determined by groups of transcription factors (TFs) and other regulators that influence each others' gene expression, forming transcriptional gene regulatory networks (GRNs). In many biological contexts, especially in development and associated diseases, the expression of the genes in GRNs is not static but evolves in time. Modeling the dynamics of GRN state is an important approach for understanding diverse cellular phenomena such as cell-fate specification, pluripotency and cell-fate reprogramming, oncogenesis, and tissue regeneration. In this protocol, we describe how to model GRNs using a data-driven dynamic modeling methodology, gene circuits. Gene circuits do not require knowledge of the GRN topology and connectivity but instead learn them from training data, making them very general and applicable to diverse biological contexts. We utilize the MATLAB-based gene circuit modeling software Fast Inference of Gene Regulation (FIGR) for training the model on quantitative gene expression data and simulating the GRN. We describe all the steps in the modeling life cycle, from formulating the model, training the model using FIGR, simulating the GRN, to analyzing and interpreting the model output. This protocol highlights these steps with the example of a dynamical model of the gap gene GRN involved in Drosophila segmentation and includes example MATLAB statements for each step.

Kinetic sculpting of the seven stripes of the Drosophila even-skipped gene

We used live imaging to visualize the transcriptional dynamics of the Drosophila melanogaster even-skipped gene at single-cell and high-temporal resolution as its seven stripe expression pattern forms, and developed tools to characterize and visualize how transcriptional bursting varies over time and space. We find that despite being created by the independent activity of five enhancers, even-skipped stripes are sculpted by the same kinetic phenomena: a coupled increase of burst frequency and amplitude. By tracking the position and activity of individual nuclei, we show that stripe movement is driven by the exchange of bursting nuclei from the posterior to anterior stripe flanks. Our work provides a conceptual, theoretical and computational framework for dissecting pattern formation in space and time, and reveals how the coordinated transcriptional activity of individual nuclei shapes complex developmental patterns.

Quantitative dissection of transcription in development yields evidence for transcription-factor-driven chromatin accessibility

Thermodynamic models of gene regulation can predict transcriptional regulation in bacteria, but in eukaryotes, chromatin accessibility and energy expenditure may call for a different framework. Here, we systematically tested the predictive power of models of DNA accessibility based on the Monod-Wyman-Changeux (MWC) model of allostery, which posits that chromatin fluctuates between accessible and inaccessible states. We dissected the regulatory dynamics of hunchback by the activator Bicoid and the pioneer-like transcription factor Zelda in living Drosophila embryos and showed that no thermodynamic or non-equilibrium MWC model can recapitulate hunchback transcription. Therefore, we explored a model where DNA accessibility is not the result of thermal fluctuations but is catalyzed by Bicoid and Zelda, possibly through histone acetylation, and found that this model can predict hunchback dynamics. Thus, our theory-experiment dialogue uncovered potential molecular mechanisms of transcriptional regulatory dynamics, a key step toward reaching a predictive understanding of developmental decision-making.

PDEparams: parameter fitting toolbox for partial differential equations in python

MOTIVATION

Partial differential equations (PDEs) is a well-established and powerful tool to simulate multi-cellular biological systems. However, available free tools for validation against data are on development.

RESULTS

The PDEparams module provides a flexible interface and readily accommodates different parameter analysis tools in PDE models such as computation of likelihood profiles, and parametric bootstrapping, along with direct visualization of the results. To our knowledge, it is the first open, freely available tool for parameter fitting of PDE models.

AVAILABILITY AND IMPLEMENTATION

PDEparams is distributed under the MIT license. The source code, usage instructions and examples are freely available on GitHub at github.com/systemsmedicine/PDE_params.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Gli3 utilizes Hand2 to synergistically regulate tissue-specific transcriptional networks

Despite a common understanding that Gli TFs are utilized to convey a Hh morphogen gradient, genetic analyses suggest craniofacial development does not completely fit this paradigm. Using the mouse model (Mus musculus), we demonstrated that rather than being driven by a Hh threshold, robust Gli3 transcriptional activity during skeletal and glossal development required interaction with the basic helix-loop-helix TF Hand2. Not only did genetic and expression data support a co-factorial relationship, but genomic analysis revealed that Gli3 and Hand2 were enriched at regulatory elements for genes essential for mandibular patterning and development. Interestingly, motif analysis at sites co-occupied by Gli3 and Hand2 uncovered mandibular-specific, low-affinity, 'divergent' Gli-binding motifs (dGBMs). Functional validation revealed these dGBMs conveyed synergistic activation of Gli targets essential for mandibular patterning and development. In summary, this work elucidates a novel, sequence-dependent mechanism for Gli transcriptional activity within the craniofacial complex that is independent of a graded Hh signal.

Cell sorting and morphogenesis in early Drosophila embryos

The regionalisation of growing tissues into compartments that do not mix is thought to be a common motif of animal development. Compartments and compartmental boundaries were discovered by lineage studies in the model organism Drosophila. Since then, many compartment boundaries have been identified in developing tissues, from insects to vertebrates. These are important for animal development, because boundaries localize signalling centres that control tissue morphogenesis. Compartment boundaries are boundaries of lineage restriction, where specific mechanisms keep boundaries straight and cells segregated. Here, we review the mechanisms of cell sorting at boundaries found in early Drosophila embryos. The parasegmental boundaries, separating anterior from posterior compartments in the embryo, keep cells segregated by increasing actomyosin contractility at boundary cell-cell interfaces. Differential actomyosin contractility in turn promotes fold formation and orients cell division. Earlier in development, actomyosin differentials are also important for cell sorting during axis extension. Specific cell surface asymmetries and signalling pathways are required to initiate and maintain these actomyosin differentials.

Gene regulatory networks in Drosophila early embryonic development as a model for the study of the temporal identity of neuroblasts

Genes belonging to the "gap" and "gap-like" family constitute the best-studied gene regulatory networks (GRNs) in Drosophila embryogenesis. Gap genes are a core of two subnetworks controlling embryonic segmentation: (hunchback, hb; Krüppel, Kr; giant, gt; and knirps, kni) and (hb; Kr; pou-domain, pdm; and, probably, castor, cas). Of particular interest is that (hb, Kr, pdm, cas) also specifies the temporal identity of stem cells, neuroblasts, in Drosophila neurogenesis. This GRN controls the sequential differentiation of neuroblasts during the asymmetric cell division. In the last decades, modeling of the patterning of gene ensemble (hb, Kr, gt, kni) in segmentation was in the center of attention. We show that our previously published and extensively studied model at a certain level of external factors is able to reproduce temporal patterns of (hb, Kr, pdm, cas) in neurogenesis with minor evolutionary explicable modifications. This result testifies in favor of a hypothesis that the similarity of two gene ensembles active in segmentation and neurogenesis is a result of co-option of the network architecture in evolution from the common ancestral form. By means of the model dynamical analysis, it is shown that the establishment of the robust patterns in both systems could be explained in terms of the action of attractors in the gap gene dynamical system. We formulate the common principles underlying the robustness of both GRNs in segmentation and neurogenesis due to the similar functional organization of the gene ensembles as having the same evolutionary origin.