The enteric nervous system (ENS) is the main branch of the peripheral nervous system that innervates the gastrointestinal tract controlling vital functions. It arises during embryogenesis via migration, proliferation and differentiation of neural crest-derived ENS progenitors. Perturbation of these processes, caused by mutations in key signalling pathway components and transcription factors, prevents progenitor colonisation of the distal gut causing aganglionic phenotypes and enteric neuropathies such as Hirschsprung (HSCR) disease. While animal models implicate Notch signalling in ENS specification, its role in human ENS progenitor cell fate decisions remains unclear. Here, we employ a human pluripotent stem cell-based model to show that Notch signalling is a key regulator of human ENS progenitor dynamics. Quantitative modelling of our in vitro data indicates that Notch inhibition accelerates progenitor differentiation without substantially altering neuronal versus glial lineage bias. Furthermore, we establish that Notch signalling controls human ENS progenitor migration by influencing migration velocity and directionality. Together, these findings provide mechanistic insights into how Notch signalling disruption may contribute to the pathogenesis of human intestinal aganglionosis.

The notochord is a defining feature of chordates. It acts as mechanical support and a source of signals to surrounding tissues during development. In mammals, notochord-derived cells persist within intervertebral discs, where they form the nucleus pulposus, the cartilage in between vertebrae units that provides the spine with flexibility. Here, we synthesise developmental knowledge with recent advances in notochord biology and insights from single-cell molecular approaches. We discuss the developmental processes from notochord initiation during gastrulation through to disc formation, highlighting signalling pathways that govern axial mesoderm specification and notochordal lineage commitment. Knowledge gained from in vivo studies has guided the development of pluripotent stem cell-based models in mice and humans, including monolayer and micropatterned systems and 3D organoids. These models recapitulate key developmental aspects of notochord formation and pave the way for disease modelling and regenerative applications. We discuss their relevance to the study of developmental disorders arising from notochord dysfunction and notochordal cell roles in disc homeostasis. Finally, we outline remaining questions and examine how developmental insights and stem cell innovations can advance our understanding of tissue formation, function and homeostasis while fostering the integration of basic mechanistic insights with translational applications.

The spine is a fascinating structure originating from just a few embryonic precursors appearing early during embryo implantation and developing into a complex multi-component architecture, evolutionary selected to ensure structural support, protect the spinal cord and enable bipedal mobility in humans. A broad range of developmental disorders can affect the spine leading to malformed vertebrae, neurological impairments and premature degeneration. The developmental mechanisms causing these disorders remain poorly understood, thus limiting therapeutic interventions to palliative treatments. In this short review, we cover the fundamentals of spinal embryogenesis and highlight developmental mechanisms associated with selected spinal developmental disorders observed in the clinic in the hope that the reader will gain a better grasp of the origins of complex spinal developmental abnormalities.

Patterning of cell fates is central to embryonic development, tissue homeostasis, and disease. Quantitative analysis of patterning reveals the logic by which cell-cell interactions orchestrate changes in cell fate. However, it is challenging to quantify patterning when graded changes in identity occur over complex 4D trajectories, or where different cell states are intermingled. Furthermore, comparing patterns across multiple individual embryos, tissues, or organoids is difficult because these often vary in shape and size. This problem is further exacerbated when comparing patterning between species. Here we present a toolkit of computational approaches to tackle these problems. These strategies are based on measuring properties of each cell in relation to the properties of its neighbors to quantify patterning, and on using embryonic landmarks in order to compare these patterns between embryos. We perform detailed neighbor-analysis of the caudal lateral epiblast of E8.5 mouse embryos, revealing local patterning in emergence of early mesoderm cells that is sensitive to inhibition of Notch activity. We extend this toolkit to compare mouse and chick embryos, revealing conserved 3D patterning of the caudal-lateral epiblast that scales across an order of magnitude difference in size between these two species. We also examine 3D patterning of gene expression boundaries across the length of Drosophila embryos. We present a flexible approach to examine the reproducibility of patterning between individuals, to measure phenotypic changes in patterning after experimental manipulation, and to compare of patterning across different scales and tissue architectures.

Loss of pluripotency is an essential step in post-implantation development that facilitates the emergence of somatic cell identities essential for gastrulation. Before implantation, pluripotent cell identity is governed by a gene regulatory network that includes the key transcription factors SOX2 and NANOG. However, it is unclear how the pluripotency gene regulatory network is dissolved to enable lineage restriction. Here, we show that SOX2 is required for post-implantation pluripotent identity in the mouse, and cells that lose SOX2 expression in the posterior epiblast are no longer pluripotent. Using in vitro and in vivo analyses, we demonstrate anticorrelated expression of NANOG and SOX2 preceding gastrulation, culminating in an early disappearance of pluripotent identity from posterior NANOGhigh/SOX2low epiblast. Surprisingly, Sox2 expression is repressed by NANOG and embryos with post-implantation deletion of Nanog maintain posterior SOX2 expression. Our results demonstrate that the distinctive features of post-implantation pluripotency are underpinned by altered functionality of pluripotency transcription factors, ensuring correct spatio-temporal loss of embryonic pluripotency.

Notochord progenitors (NotoPs) represent a scarce yet crucial embryonic cell population, playing important roles in embryo patterning and eventually giving rise to the cells that form and maintain intervertebral discs. The mechanisms regulating NotoPs emergence are unclear. This knowledge gap persists due to the inherent complexity of cell fate patterning during gastrulation, particularly within the anterior primitive streak (APS), where NotoPs first arise alongside neuro-mesoderm and endoderm. To gain insights into this process, we use micropatterning together with FGF and the WNT pathway activator CHIR9901 to guide the development of human embryonic stem cells into reproducible patterns of APS cell fates. We show that CHIR9901 dosage dictates the downstream dynamics of endogenous TGFβ signalling, which in turn controls cell fate decisions. While sustained NODAL signalling defines endoderm and NODAL inhibition is imperative for neuro-mesoderm emergence, timely inhibition of NODAL signalling with spatial confinement potentiates WNT activity and enables us to generate NotoPs efficiently. Our work elucidates the signalling regimes underpinning NotoP emergence and provides insights into the regulatory mechanisms controlling the balance of APS cell fates during gastrulation.

Cell-cell interactions are central to development, but exploring how a change in any given cell relates to changes in the neighbour of that cell can be technically challenging. Here, we review recent developments in synthetic biology and image analysis that are helping overcome this problem. We highlight the opportunities presented by these advances and discuss opportunities and limitations in applying them to developmental model systems.

Patterning of cell fates is central to embryonic development, tissue homeostasis, and disease. Quantitative analysis of patterning reveals the logic by which cell-cell interactions orchestrate changes in cell fate. However, it is challenging to quantify patterning when graded changes in identity occur over complex 4D trajectories, or where different cell states are intermingled. Furthermore, comparing patterns across multiple individual embryos, tissues, or organoids is difficult because these often vary in shape and size. Here we present a toolkit of computational approaches to tackle these problems. These strategies are based on measuring properties of each cell in relation to the properties of its neighbours to quantify patterning, and on using embryonic landmarks in order to compare these patterns between embryos. We use this toolkit to characterise patterning of cell identities within the caudal lateral epiblast of E8.5 embryos, revealing local patterning in emergence of early mesoderm cells that is sensitive to inhibition of Notch activity. ### Competing Interest Statement The authors have declared no competing interest.

Minimizing the level of material consumption in textile production is a major concern. The cornerstone of this optimization task is the nesting problem, whose goal is to lay a set of irregular 2D parts out onto a rectangular surface, called the nesting zone, while respecting a set of constraints. Knowing the efficiency—ratio of usable to used up material enables the optimization of several textile production problems. Unfortunately, knowing the efficiency requires the nesting problem to be solved, which is computationally intensive and has been proven to be NP -hard. This paper introduces a regression approach to estimate efficiency without solving the nesting problem. Our approach models the 2D nesting problem as a graph where the nodes are images derived from parts and the edges hold the constraints. The method then consists of combining convolutional neural networks for addressing the image-based aspects and graph neural networks (GNNs) for the constraint aspects. We evaluate several neural message passing approaches on our dataset and obtain results that are sufficiently accurate for enabling several business use cases, where our model best solves this task with a mean absolute error of 1.65. We provide open access to our dataset, whose properties differ from those of other graph datasets found in the literature. This dataset is constructed on 100,000 real customers’ nesting data. Along the way, we compare the performance and generalization capabilities of four GNN architectures obtained from the literature on this dataset.

Notochord progenitors (NotoPs) represent a scarce yet crucial embryonic cell population, playing important roles in embryo patterning and eventually giving rise to the cells that form and maintain intervertebral discs. The mechanisms regulating NotoPs emergence are unclear. This knowledge gap persists due to the inherent complexity of cell fate patterning during gastrulation, particularly within the anterior primitive streak (APS), where NotoPs first arise alongside other important progenitors including neuro-mesodermal and endodermal progenitors. To gain insights into this process, we use micropatterning together with FGF and the WNT pathway activator CHIR9901, to guide the development of human embryonic stem cells into reproducible patterns of APS cell fates. We show that small variations in CHIR9901 dosage dictate the downstream dynamics of endogenous TGFbeta signalling which in turn controls cell fate decisions. We show that sustained NODAL signalling induces endoderm while NODAL inhibition is needed for NMP specification. Furthermore, we unveil a crosstalk between TGFbeta and WNT signaling pathways, wherein TGFbeta inhibition enhances WNT activity. Finally, we demonstrate that the timely inhibition of TGFbeta signalling is imperative for the emergence of NotoPs. Our work elucidates the signalling regimes underpinning NotoPs emergence and provides novel insights into the regulatory mechanisms controlling the balance of APS cell fates during gastrulation.

Amir et al. (CPM 2017) introduce the approximate string cover problem (ACP) motivated by applications including molecular biology, coding, automata theory, formal language theory and combinatorics. A cover of a string T is a string C for which every letter of T lies within some occurrence of C. The input of the ACP consists of a string T and the goal is to find a string C of length less than the length of T that covers a string T' , which is as close to T as possible (under some predefined distance). Amir et al. study this problem for the Hamming distance and show that it is NP-hard. In this paper we continue the work of Amir et al. and show the following results for the cover length relaxation of the ACP. After observing that the NP-hardness proof by Amir et al. (CPM 2017, TCS 2019) suffers from several lapses, we propose an amendment to the proof. We then introduce an approximation algorithm for a variant of the ACP, in which we aim to maximize the length of the input string minus the distance to the string covered by the approximate cover returned by the algorithm. This problem is naturally as hard as the ACP. We prove an asymptotic approximation ratio of 𝒪(√(|T|)) , where |T| is the size of the input string. Finally, we present an FPT algorithm with respect to the alphabet size and the size of the cover based on a dynamic programming framework.

To enhance their practice, healthcare professionals need to cross-link various usage recommendations provided by heterogeneous vocabularies that must be retrieved and integrated conjointly. This is the aim of the Knowledge Warehouse / K-Ware platform. It enables establishing relevant bridges between different knowledge sources (structured vocabularies, thesaurus, ontologies) expressed in the semantic web standard languages (i.e. SKOS, OWL, RDF). This poster presents the strategy applied in K-Ware to hide the different aspects of linking literals with medical entities encoded in these knowledge sources to fetch some publications abstracts from Pubmed.

Much of the beauty and mystery of development comes down to the question of how embryos set up patterns of gene expression. Four recent preprints tackle this fascinating question by combining quantitative imaging, modelling, experimental embryology and careful conceptual thinking.One particularly beautiful example of patterning occurs during somitogenesis. During this process, regular stripes in gene expression emerge sequentially along the pre-somitic mesoderm (PSM), prefiguring the formation of ribs and associated muscles. This event is governed by two factors: a cell-autonomous ‘clock’ (i.e. repeated ‘tick-tock’ oscillations of gene expression) and a coordinated ‘wavefront’ (i.e. a differentiation event that occurs at defined anterior-posterior locations; Gomez et al., 2008; Palmeirim et al., 1997).The position of the differentiation wavefront has been proposed to be dictated entirely by extrinsic signals, yet when Rohde and colleagues (Rohde et al., 2021 preprint) isolated individual zebrafish PSM cells in the absence of exogenous growth factors, they found that these cells exhibit a trajectory of transient oscillatory clock dynamics and differentiation similar to that seen in intact embryos, albeit with a higher variance. This surprising result, which is based on experimental data from live reporters and interpreted using mathematical modelling, indicates that PSM cells possess not only an intrinsic oscillator but also an intrinsic timer that is started upon exit of a cell from the tailbud and ultimately tells cells when to differentiate. This noisy timer can be influenced by extrinsic cues but is not dependent on them. The molecular basis for this intrinsic timer is not yet known and remains an area ripe for future investigation.The story continues with a pair of interconnected preprints (Fulton et al., 2022 preprint; Spiess et al., 2022 preprint) that address the intriguing question of how a stable pattern, such as that associated with the spatially defined ‘wavefront’ of differentiation in the PSM, can emerge amid highly dynamic cell movements.Fulton et al. first performed experiments broadly similar to those carried out by Rohde et al. to confirm that PSM cells possess a cell-intrinsic differentiation timer. They then labelled coherent groups of cells in the progenitor zone to investigate how cells move over time. After 3 h, some particularly speedy cells had already raced away into the differentiation zone, whereas others had barely moved from their starting point. So, to achieve coherent patterning of cell fate, it seems that the far-ranging cells must somehow accelerate their intrinsic differentiation timer by just the right amount, whereas more sluggish cells must down-tune their own timer to a correspondingly sluggish rate.In general, the timing of differentiation is governed by gene regulatory networks (GRNs). In some systems, such as the fly blastoderm (Crombach et al., 2016; Verd et al., 2014) and the vertebrate neural tube (Kicheva et al., 2014; Sagner and Briscoe, 2017), the logic of GRNs has been deduced based on measurements of signalling activity and transcription factor expression over time. Cell movements in these tissues are so slow that they can be ignored, but that is not the case in the PSM (Thomson et al., 2021). To infer GRNs in the PSM, Spiess et al. therefore needed to measure the expression of multiple transcription factors and signalling pathways in cells as they are moving around in live tissues, an endeavor hampered by the limited number of live reporters that can be imaged simultaneously. They overcame this problem by measuring a broader panel of markers in ‘snapshot’ images and then superimposing these measurements onto individual cell trajectories, obtained by tracking cells within an in toto-imaged embryo, in order to approximate dynamic changes in gene expression.From these data, they inferred a range of possible GRNs, which they could then test using ‘live modelling’, i.e. by simulating the effects of candidate GRNs in individual cells over time. This enabled the authors to identify a simple GRN that could account for the experimental observations (not only from embryos but also from isolated PSM cells) and that was consistent with information from the literature. They propose that, because cells move relative to defined signalling centres, cell movements dictate the strength and duration of signalling exposure – information that is then interpreted by the intracellular GRN in just the right way to generate a coherent pattern. Impressively, this GRN went beyond explaining the broad regionalisation of cell identities. It also predicted low-level ‘aberrant’ heterogeneity of cell fates within the progenitor zone, a prediction that was subsequently confirmed using sensitive detection methods.In summary, this new methodology reveals a simple GRN that explains how stable patterns of gene expression can emerge in the context of extensive cell movements. Given that cells tend to move around a lot during many other stages of embryonic development, and probably also during the formation of organoids (Huch et al., 2017) and in other ex vivo models of development (Hashmi et al., 2021 preprint), this approach will be broadly applicable. Furthermore, because the method generates a range of plausible alternative GRNs, it could be used to explore how GRNs evolve over evolutionary time to adapt the body plan to novel environments.Some questions remain. For example, the model of Fulton et al. explains patterning based on cell movements, long-range signalling and an intrinsic timer, but could there be an additional influence from local cell-cell communication?Another recent preprint (Lee et al., 2022 preprint) tells us that cells do indeed talk to their neighbours to refine patterning at least in some contexts. In this study, Lee et al. focussed on the formation of the primitive streak at gastrulation. This process is governed by gradients of long-range signals, similar to those that influence differentiation in the PSM. Do cells interpret their position in these gradients autonomously? This may be possible, but an alternative is a ‘neighbourhood watch’ model, in which cells sense and respond to signalling differences from their neighbours. Using mathematical modelling, Lee et al. identified particular manipulations of exogenous signals that should produce different consequences depending on which model is correct. These manipulations, performed in the experimentally tractable chick model, confirmed that the neighbourhood watch model best fits the experimental observations.Taken together, these four preprints exemplify the power of combining quantitative imaging and modelling in the context of model systems that are readily amenable to manipulation. Moreover, they reveal the internal logic of programmes that integrate dynamically changing sources of information to generate the body plan.It is particularly intriguing that these programmes produce certain imperfections in the coherence of patterning (Fulton et al., 2022 preprint). This leaves us with one final question: is this heterogeneity entirely ‘aberrant’ or could it be helpful in some way? David Bowie once said, ‘I thrive on mistakes’. Is it possible that the embryo does too?We are grateful to Linus Schumacher, Val Wilson, Berta Verd, Ben Steventon, Andy Oates and Claudio Stern for helpful comments.

The wide adoption of digital technologies has increased the availability of coding systems and other metadata to annotate health-related data. However, most of these resources are based on the W3C RDF standard language. Their levels of formalism are pretty heterogeneous, making them challenging to handle jointly in the scope of a particular project (aligning/mapping, browsing/navigating, visualizing, etc.). Indeed, these vocabularies having different objectives, are based on standards such as RDF for their persistence, and even use extensions such as SKOS to manipulate terminologies or OWL for ontologies that we want to preserve. Our Knowledge Warehouse platform provides a framework for managing these differences without distorting them. As an example, we will see in this article how K-Ware manages semantic metadata in an abstract way within the OWL Gene Ontology GO resource for handling browsing relations and be able to define pattern for some of the GO reasoning rules.

Nesting efficiency dataset This is the raw dataset associated with the paper “Graph Neural Networks Comparison for 2D-Nesting Efficiency Estimation”, by C.Lallier, L. Vézard, B. Pinaud and G. Blin, 2022. Consisting of 100,000 nesting tasks. Usage: The files are: tasks.gz, parts.gz, constraints.gz, and shapes.gz. They are in PICKLE file format version 5 with a gzip compression. Example to load a file : import pandas as pd tasks = pd.read_pickle('tasks.gz') Description: Tasks.gz file contains nestings high-level descriptors. It is composed of the following columns: Column Type Description efficiency float The variable to predict (label). Given in % duration integer input data. The nesting algorithm convergence time. Given in s. sheet_width integer input data. The width of the nesting area. Given in m-4 sheet_length integer input data. Facultative. The height of the nesting area. Given in m-4 sheet_type integer input data. Kind of the nesting. tasks_index integer Generated data. Join key between tables. is_train, is_val, is_test boolean Generated data. Can be used as mask for the train, val and test subsets. Parts.gz contains description of the parts to be nested : Column Type Description tasks_index integer Reference to the join key from the Task table. parts_id integer Generated part id. shape_hash integer Reference to the hash of the part's shape, join key from the Shape table. Shapes.gz is the description of the shapes of the parts to be nested : Column Type Description shape_hash integer Generated data. Join key between tables. raw list of integers List of x, y tuples for each point. Unit is m-4 sizes list of integers List of sub-shapes sizes. Constraints.gz describes constraints and their parameters: Column Type Description type string Generated constraint type. tasks_index integer Reference to the join key from the Task table. parts_1, parts_2 list of integers References to the parts_id from the Parts table. p1_x, p1_y and p2_x, p2_y list of floats Input data. Origin position (x, y) of the constraint on parts. For each part of the constraint. r1_start, r1_end, r1_flip_x list of floats Input data. Rotation (start, end, and flip_x) parameters of the constraint. Multiple ranges accepted. y_min, y_max list of floats Input data. Range from (y_min, y_max). Multiple ranges accepted. x_offset, y_offset, motif_order, x_alignment_type, y_alignment_type, proximity_type, max_distance, groups_relative_orientation, is_frozen float Input data. Other constraint parameters.

Cell-cell interactions govern differentiation and cell competition in pluripotent cells during early development, but the investigation of such processes is hindered by a lack of efficient analysis tools. Here, we introduce SyNPL: clonal pluripotent stem cell lines that employ optimised Synthetic Notch (SynNotch) technology to report cell-cell interactions between engineered 'sender' and 'receiver' cells in cultured pluripotent cells and chimaeric mouse embryos. A modular design makes it straightforward to adapt the system for programming differentiation decisions non-cell-autonomously in receiver cells in response to direct contact with sender cells. We demonstrate the utility of this system by enforcing neuronal differentiation at the boundary between two cell populations. In summary, we provide a new adaptation of SynNotch technology that could be used to identify cell interactions and to profile changes in gene or protein expression that result from direct cell-cell contact with defined cell populations in culture and in early embryos, and that can be customised to generate synthetic patterning of cell fate decisions.

The ${\rm M{\small INIMUM}~W\small{EIGHT}}$ $t$-${\rm {\small PARTITE}~C{\small LIQUE}~P{\small ROBLEM}~MW} t {\rm CP}$ is the problem of finding a $t$-clique with minimum weight in a complete edge-weighted $t$-partite graph. The motivation for studying this problem is its potential in modelling the problem of identifying sets of commonly existing putative co-regulated, co-expressed genes, called gene clusters. In this paper, we show that ${\rm MW} t {\rm CP}$ is NP-hard, APX-hard in the general case. We also present a 2-approximation algorithm that runs in $O(n^2)$ for the metric case and has 1+$ \frac{1}{t}$-approximation performance guarantee for the ultrametric subclass of instances. We further show how relaxing or tightening the application of the metricity property affects the approximation ratio. Finally insights on the application ${\rm MW} t {\rm CP}$ to gene cluster discovery are presented.

The mechanisms of pattern formation during embryonic development remain poorly understood. Embryonic stem cells in culture self-organise to form spatial patterns of gene expression upon geometrical confinement indicating that patterning is an emergent phenomenon that results from the many interactions between the cells. Here, we applied an agent-based modelling approach in order to identify plausible biological rules acting at the meso-scale within stem cell collectives that may explain spontaneous patterning. We tested different models involving differential motile behaviours with or without biases due to neighbour interactions. We introduced a new metric, termed stem cell aggregate pattern distance (SCAPD) to probabilistically assess the fitness of our models with empirical data. The best of our models improves fitness by 70% and 77% over the random models for a discoidal or an ellipsoidal stem cell confinement respectively. Collectively, our findings show that a parsimonious mechanism that involves differential motility is sufficient to explain the spontaneous patterning of the cells upon confinement. Our work also defines a region of the parameter space that is compatible with patterning. We hope that our approach will be applicable to many biological systems and will contribute towards facilitating progress by reducing the need for extensive and costly experiments.

Embryonic stem cells (ESCs) studies play an important role for understanding the molecular events that underlie cell lineage commitment and serve as models for the development of disease. However, the interactions between neighboring embryonic stem cells are not fully understood. Assessing proximity between different types of embryonic stem cells might provide more information about distinct behaviors of embryonic stem cells. In this study, we processed 186 cell colonies on disc constrained microdomains and 152 cell colonies on ellipse. We grouped cell colonies based on different observed patterns and grouped cells by their locations. By applying two measurements on embryonic stem cell colonies, minimum spanning tree and average distance to the five closest objects, we investigated the difference of proximity between different types of embryonic stem cells, the difference between grouped cell colonies and the difference between grouped cells. We found one type of ESC has a smaller average path based on minimum spanning tree and higher proximity than the other type. We report consistent results for different types of embryonic stem cells: these findings may be useful to set benchmarks for empirical models which replicate ESC behaviors.