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Gastruloids have emerged as highly usefulin vitromodels of mammalian gastrulation. One of the most striking features of 3D gastruloids is their elongation, which mimics the extension of the embryonic anterior-posterior axis. Although axis extension is crucial for development, the underlying mechanism has not been fully elucidated in mammalian species. Gastruloids provide an opportunity to study this morphogenic processin vitro. Here, we measure and quantify the shapes of elongating gastruloids and show, by Cellular Potts model simulations, that a combination of convergent extension and differential adhesion can explain the observed shapes. We reveal that differential adhesion alone is insufficient and also directly observe hallmarks of convergent extension by time-lapse imaging of gastruloids. Finally, we show that gastruloid elongation can be abrogated by inhibition of the Rho kinase pathway, which is involved in convergent extensionin vivo. All in all, our study demonstrates, how gastruloids can be used to elucidate morphogenic processes in embryonic development.

A reduced capacity for butyrate production by the early infant gut microbiota is associated with negative health effects, such as inflammation and the development of allergies. Here we develop new hypotheses on the effect of the prebiotic galacto-oligosaccharides (GOS) or 2’-fucosyllactose (2’-FL) on butyrate production by the infant gut microbiota using a multiscale, spatiotemporal mathematical model of the infant gut. The model simulates a community of cross-feeding gut bacteria at metabolic detail. It represents the gut microbiome as a grid of bacterial populations that exchange intermediary metabolites, using 20 different subspecies-specific metabolic networks taken from the AGORA database. The simulations predict that both GOS and 2’-FL promote the growth ofBifidobacterium, whereas butyrate producing bacteria are only consistently abundant in the presence of propane-1,2-diol, a product of 2’-FL metabolism. The results suggest that in absence of prebiotics or in presence of only GOS, bacterial species, includingCutibacterium acnesandBacteroides vulgatus, outcompete butyrate producers by feeding on intermediary metabolites. In presence of 2’-FL, however, production of propane-1,2-diol specifically supports butyrate producers.

All tissue development and replenishment relies upon the breaking of symmetries leading to the morphological and operational differentiation of progenitor cells into more specialized cells. One of the main engines driving this process is the Notch signal transduction pathway, a ubiquitous signalling system found in the vast majority of metazoan cell types characterized to date. Broadly speaking, Notch receptor activity is governed by a balance between two processes: 1) intercellular Notch transactivation triggered via interactions between receptors and ligands expressed in neighbouring cells; 2) intracellular cis inhibition caused by ligands binding to receptors within the same cell. Additionally, recent reports have also unveiled evidence of cis activation. Whilst context-dependent Notch receptor clustering has been hypothesized, to date, Notch signalling has been assumed to involve an interplay between receptor and ligand monomers. In this study, we demonstrate biochemically, through a mutational analysis of DLL4, both in vitro and in tissue culture cells, that Notch ligands can efficiently self-associate. We found that the membrane proximal EGF-like repeat of DLL4 was necessary and sufficient to promote oligomerization/dimerization. Mechanistically, our experimental evidence supports the view that DLL4 ligand dimerization is specifically required for cis-inhibition of Notch receptor activity. To further substantiate these findings, we have adapted and extended existing ordinary differential equation-based models of Notch signalling to take account of the ligand dimerization-dependent cis-inhibition reported here. Our new model faithfully recapitulates our experimental data and improves predictions based upon published data. Collectively, our work favours a model in which net output following Notch receptor/ligand binding results from ligand monomer-driven Notch receptor transactivation (and cis activation) counterposed by ligand dimer-mediated cis-inhibition.Author summaryThe growth and maintenance of tissues is a fundamental characteristic of metazoan life, controlled by a highly conserved core of cell signal transduction networks. One such pathway, the Notch signalling system, plays a unique role in these phenomena by orchestrating the generation of the phenotypic and genetic asymmetries which underlie tissue development and remodeling. At the molecular level, it achieves this via two specific types of receptor/ligand interaction: intercellular binding of receptors and ligands expressed in neighbouring cells, which triggers receptor activation (transactivation); intracellular receptor/ligand binding within the same cell which blocks receptor activation (cis inhibition). Together, these counterposed mechanisms determine the strength, the direction and the specificity of Notch signalling output. Whilst, the basic mechanisms of receptor transactivation have been delineated in some detail, the precise nature of cis inhibition has remained enigmatic. Through a combination of experimental approaches and computational modelling, in this study, we present a new model of Notch signalling in which ligand monomers promote Notch receptor transactivation, whereas cis inhibition is induced optimally via ligand dimers. This is the first model to include a concrete molecular distinction, in terms of ligand configuration, between the main branches of Notch signalling. Our model faithfully recapitulates both our presented experimental results as well as the recently published work of others, and provides a novel perspective for understanding Notch-regulated biological processes such as embryo development and angiogenesis.

We analyze an ‘up-the-gradient’ model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show that this model admits a family of travelling wave solutions that is parameterized by the height of the auxin-pulse. We uncover scaling relations for the speed and width of these waves and verify these rigorous results with numerical computations. In addition, we provide explicit expressions for the leading-order wave profiles, which allows the influence of the biological parameters in the problem to be readily identified. Our proofs are based on a generalization of the scaling principle developed by Friesecke and Pego to construct pulse solutions to the classic Fermi–Pasta–Ulam–Tsingou model, which describes a one-dimensional chain of coupled nonlinear springs.

Cell-based computational modeling and simulation are becoming invaluable tools in analyzing plant development. In a cell-based simulation model, the inputs are behaviors and dynamics of individual cells and the rules describing responses to signals from adjacent cells. The outputs are the growing tissues, shapes, and cell-differentiation patterns that emerge from the local, chemical, and biomechanical cell-cell interactions. In this updated and extended version of our previous chapter on VirtualLeaf (Merks and Guravage, Methods in Molecular Biology 959, 333–352), we present a step-by-step, practical tutorial for building cell-based simulations of plant development and for analyzing the influence of parameters on simulation outcomes by systematically changing the values of the parameters and analyzing each outcome. We show how to build a model of a growing tissue, a reaction–diffusion system on a growing domain, and an auxin transport model. Moreover, in addition to the previous publication, we demonstrate how to run a Turing system on a regular, rectangular lattice, and how to run parameter sweeps. The aim of VirtualLeaf is to make computational modeling more accessible to experimental plant biologists with relatively little computational background.

Cell-based computational modeling and simulation are becoming invaluable tools in analyzing plant development. In a cell-based simulation model, the inputs are behaviors and dynamics of individual cells and the rules describing responses to signals from adjacent cells. The outputs are the growing tissues, shapes, and cell-differentiation patterns that emerge from the local, chemical, and biomechanical cell-cell interactions. In this updated and extended version of our previous chapter on VirtualLeaf (Merks and Guravage, Methods in Molecular Biology 959, 333-352), we present a step-by-step, practical tutorial for building cell-based simulations of plant development and for analyzing the influence of parameters on simulation outcomes by systematically changing the values of the parameters and analyzing each outcome. We show how to build a model of a growing tissue, a reaction-diffusion system on a growing domain, and an auxin transport model. Moreover, in addition to the previous publication, we demonstrate how to run a Turing system on a regular, rectangular lattice, and how to run parameter sweeps. The aim of VirtualLeaf is to make computational modeling more accessible to experimental plant biologists with relatively little computational background.

Organ laterality refers to the left-right asymmetry in disposition and conformation of internal organs and is established during embryogenesis. The heart is the first organ to display visible left-right asymmetries through its left-sided positioning and rightward looping. Here, we present a new zebrafish loss-of-function allele for tbx5a, which displays defective rightward cardiac looping morphogenesis. By mapping individual cardiomyocyte behavior during cardiac looping, we establish that ventricular and atrial cardiomyocytes rearrange in distinct directions. As a consequence, the cardiac chambers twist around the atrioventricular canal resulting in torsion of the heart tube, which is compromised in tbx5a mutants. Pharmacological treatment and ex vivo culture establishes that the cardiac twisting depends on intrinsic mechanisms and is independent from cardiac growth. Furthermore, genetic experiments indicate that looping requires proper tissue patterning. We conclude that cardiac looping involves twisting of the chambers around the atrioventricular canal, which requires correct tissue patterning by Tbx5a.

Zebrafish is a useful modeling organism for the study of vertebrate development, immune response, and metabolism. Metabolic studies can be aided by mathematical reconstructions of the metabolic network of zebrafish. These list the substrates and products of all biochemical reactions that occur in the zebrafish. Mathematical techniques such as flux-balance analysis then make it possible to predict the possible metabolic flux distributions that optimize, for example, the turnover of food into biomass. The only available genome-scale reconstruction of zebrafish metabolism is ZebraGEM. In this study, we present ZebraGEM 2.0, an updated and validated version of ZebraGEM. ZebraGEM 2.0 is extended with gene-protein-reaction associations (GPRs) that are required to integrate genetic data with the metabolic model. To demonstrate the use of these GPRs, we performed an in silico genetic screening for knockouts of metabolic genes and validated the results against published in vivo genetic knockout and knockdown screenings. Among the single knockout simulations, we identified 74 essential genes, whose knockout stopped growth completely. Among these, 11 genes are known have an abnormal knockout or knockdown phenotype in vivo (partial), and 41 have human homologs associated with metabolic diseases. We also added the oxidative phosphorylation pathway, which was unavailable in the published version of ZebraGEM. The updated model performs better than the original model on a predetermined list of metabolic functions. We also determined a minimal feed composition. The oxidative phosphorylation pathways were validated by comparing with published experiments in which key components of the oxidative phosphorylation pathway were pharmacologically inhibited. To test the utility of ZebraGEM2.0 for obtaining new results, we integrated gene expression data from control and Mycobacterium marinum-infected zebrafish larvae. The resulting model predicts impeded growth and altered histidine metabolism in the infected larvae.

Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles, and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell-cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell-cell boundaries can buckle. In this paper we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the Cellular Potts Model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell-cell shear or sliding, from which T1 and T2 transitions emerge naturally, allowing application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential-adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks., Comment: 28 pages, 4 figures; accepted for publication in Bulletin of Mathematical Biology

Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motion without attaching to the ECM, or sliding and stepping motion with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells’ speed and persistence decreases. Additionally, the model can predict short-term persistent with long-term subdiffusive motility, showing a pivoting motion. For small adhesion areas, we observe that the spatial distribution of adhesions influences cell motility. Small adhesions at the front allow for more persistent motion than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.Author summaryDuring immunosurveillance, lymphocytes patrol through tissues to interact with cancer cells, other immune cells, and pathogens. The efficiency of this process depends on the kinds of trajectories taken, ranging from simple Brownian walks to Lévy walks. The composition of the extracellular matrix (ECM), a network of macromolecules, affects the formation of cell-matrix adhesions, thus strongly influencing the way lymphocytes move. Here, we present a model of lymphocyte motility driven by adhesions that grow, shrink and rupture in response to the ECM and cellular forces. Compared to other models, our model is computationally light making it suitable for generating long term cell track data, while still capturing actin dynamics and adhesion turnover. Our model suggests that cell motility is affected by the force required to break adhesions and the rate at which new adhesions form. Adhesions can promote cell protrusion by inhibiting retrograde actin flow. After introducing this effect into the model, we found that it reduces the cellular diffusivity and that it promotes stick-slip behaviour. Furthermore, location and size of adhesion clusters determined cell persistence. Overall, our model explains the plasticity of lymphocyte behaviour in response to the ECM.

Toll-like receptor (TLR) signaling via myeloid differentiation factor 88 protein (MyD88) has been indicated to be involved in the response to wounding. It remains unknown whether the putative role of MyD88 in wounding responses is due to a control of leukocyte cell migration. The aim of this study was to explorein vivowhether TLR2 and MyD88 are involved in modulating neutrophil and macrophage cell migration behavior upon zebrafish larval tail wounding. Live cell imaging of tail-wounded larvae was performed intlr2andmyd88mutants and their corresponding wild type siblings. In order to visualize cell migration following tissue damage, we constructed double transgenic lines with fluorescent markers for macrophages and neutrophils in all mutant and sibling zebrafish lines. Three days post fertilization (dpf), tail-wounded larvae were studied using confocal laser scanning microscopy (CLSM) to quantify the number of recruited cells at the wounding area. We found that in bothtlr2–/–andmyd88–/–groups the recruited neutrophil and macrophage numbers are decreased compared to their wild type sibling controls. Through analyses of neutrophil and macrophage migration patterns, we demonstrated that bothtlr2andmyd88control the migration direction of distant neutrophils upon wounding. Furthermore, in both thetlr2and themyd88mutants, macrophages migrated more slowly toward the wound edge. Taken together, our findings show thattlr2andmyd88are involved in responses to tail wounding by regulating the behavior and speed of leukocyte migrationin vivo.

Epithelial branching morphogenesis drives the development of organs such as the lung, salivary gland, kidney and the mammary gland. It involves cell proliferation, cell differentiation and cell migration. An elaborate network of chemical and mechanical signals between the epithelium and the surrounding mesenchymal tissues regulates the formation and growth of branching organs. Surprisingly, when cultured in isolation from mesenchymal tissues, many epithelial tissues retain the ability to exhibit branching morphogenesis even in the absence of proliferation. In this work, we propose a simple, experimentally plausible mechanism that can drive branching morphogenesis in the absence of proliferation and cross-talk with the surrounding mesenchymal tissue. The assumptions of our mathematical model derive fromin vitroobservations of the behaviour of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGFβ1 inhibits the formation of cell protrusions, leading to curvature-dependent inhibition of sprouting. Our hybrid cellular Potts and partial-differential equation model correctly reproduces the experimentally observed tissue-geometry-dependent determination of the sites of branching, and it suffices for the formation of self-avoiding branching structures in the absence and also in the presence of cell proliferation.This article is part of the theme issue ‘Multi-scale analysis and modelling of collective migration in biological systems’.

We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses. Upon modeling the actin cytoskeleton as a nematic liquid crystal, we further show that the geometry of the cell edge feeds back on the organization of the stress fibers by altering the length scale at which these are confined. This feedback mechanism is controlled by a dimensionless number, the anchoring number, representing the relative weight of surface-anchoring and bulk-aligning torques. Our model allows to predict both cellular shape and the internal structure of the actin cytoskeleton and is in good quantitative agreement with experiments on fibroblastoid (GDβ1, GDβ3) and epithelioid (GEβ1, GEβ3) cells.

Epithelial branching morphogenesis drives the development of organs such as the lung, salivary gland, kidney and the mammary gland. It involves cell proliferation, cell differentiation and cell migration. An elaborate network of chemical and mechanical signals between the epithelium and the surrounding mesenchymal tissues regulates the formation and growth of branching organs. Surprisingly, when cultured in isolation from mesenchymal tissues, many epithelial tissues retain the ability to exhibit branching morphogenesis even in absence of proliferation. In this work, we propose a simple, experimentally-plausible mechanism that can drive branching morphogenesis in absence of proliferation and cross-talk with the surrounding mesenchymal tissue. The assumptions of our mathematical model derive fromin vitroobservations of the behavior of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGFβ1 inhibits the formation of cell protrusions, leading to curvature dependent inhibition of sprouting. Our hybrid cellular Potts and partial-differential equation model correctly reproduces the experimentally observed tissue-geometry dependent determination of the sites of branching, and it suffices for the formation of self-avoiding branching structures in absence and also in presence of cell proliferation.

Summary Somitogenesis, the primary segmentation of the vertebrate embryo, is associated with oscillating genes that interact with a wave of cell differentiation. The necessity of cell-matrix adherence and embryonic tension, however, suggests that mechanical cues are also involved. To explicitly investigate this, we applied surplus axial strain to live chick embryos. Despite substantial deformations, the embryos developed normally and somite formation rate was unaffected. Surprisingly, however, we observed slow cellular reorganizations of the most elongated somites into two or more well-shaped daughter somites. In what appeared to be a regular process of boundary formation, somites divided and fibronectin was deposited in between. Cell counts and morphology indicated that cells from the somitocoel underwent mesenchymal-epithelial transition; this was supported by a Cellular Potts model of somite division. Thus, although somitogenesis appeared to be extremely robust, we observed new boundary formation in existing somites and conclude that mechanical strain can be morphologically instructive., Graphical Abstract, Highlights • Live chick embryos develop normally under substantial axial strain (>50%) • Mature somites divide into daughter somites, and fibronectin is deposited in between • Mesenchymal cells from the somitocoel transition into epithelial border cells • Mechanical strain can induce border formation and thus affect morphogenesis, Poultry Embryology; Mechanical Modeling; Developmental Biology

Many animal cells change their shape depending on the stiffness of the substrate on which they are cultured: they assume small, rounded shapes in soft ECMs, they elongate within stiffer ECMs, and flatten out on hard substrates. Cells tend to prefer stiffer parts of the substrate, a phenomenon known as durotaxis. Such mechanosensitive responses to ECM mechanics are key to understanding the regulation of biological tissues by mechanical cues, as it occurs, e.g., during angiogenesis and the alignment of cells in muscles and tendons. Although it is well established that the mechanical cell-ECM interactions are mediated by focal adhesions, the mechanosensitive molecular complexes linking the cytoskeleton to the substrate, it is poorly understood how the stiffness-dependent kinetics of the focal adhesions eventually produce the observed interdependence of substrate stiffness and cell shape and cell behavior. Here we show that the mechanosensitive behavior of single-focal adhesions, cell contractility and substrate adhesivity together suffice to explain the observed stiffness-dependent behavior of cells. We introduce a multiscale computational model that is based upon the following assumptions: (1) cells apply forces onto the substrate through FAs; (2) the FAs grow and stabilize due to these forces; (3) within a given time-interval, the force that the FAs experience is lower on soft substrates than on stiffer substrates due to the time it takes to reach mechanical equilibrium; and (4) smaller FAs are pulled from the substrate more easily than larger FAs. Our model combines the cellular Potts model for the cells with a finite-element model for the substrate, and describes each FA using differential equations. Together these assumptions provide a unifying model for cell spreading, cell elongation and durotaxis in response to substrate mechanics., 31 pages, 5 figures, 8 supplementary figures

Mathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tis- sue morphogenesis. Here, we review the cellular Potts model (CPM; also known as the Glazier-Graner-Hoge- weg model), an effective computational modeling framework. We discuss its usability for modeling complex developmental phenomena by examining four fundamental examples of tissue morphogenesis: (i) cell sorting, (ii) cyst formation, (iii) tube morphogenesis in kidney development, and (iv) blood vessel formation. The review provides an introduction for biologists for starting simulation analysis using the CPM framework.

During animal development and homeostasis, the structure of tissues, including muscles, blood vessels and connective tissues adapts to mechanical strains in the extracellular matrix (ECM). These strains originate from the differential growth of tissues or forces due to muscle contraction or gravity. Here we show using a computational model that by amplifying local strain cues, active cell contractility can facilitate and accelerate the reorientation of single cells to static strains. At the collective cell level, the model simulations show that active cell contractility can facilitate the formation of strings along the orientation of stretch. The computational model is based on a hybrid cellular Potts and finite-element simulation framework describing a mechanical cell-substrate feedback, where: 1) cells apply forces on the ECM, such that 2) local strains are generated in the ECM, and 3) cells preferentially extend protrusions along the strain orientation. In accordance with experimental observations, simulated cells align and form string-like structures parallel to static uniaxial stretch. Our model simulations predict that the magnitude of the uniaxial stretch and the strength of the contractile forces regulate a gradual transition between string-like patterns and vascular network-like patterns. Our simulations also suggest that at high population densities, less cell cohesion promotes string formation., 24 pages, 6 figures; 12 pages of supplementary information with 11 supplementary figures and 2 supplementary tables

Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monolayers and investigate how chirality affects the motion of topological defects, as well as the collective motion in stripe-shaped domains. We find that chirality introduces a characteristic asymmetry in the collective cellular flow, from which the ratio between chiral and non-chiral active stresses can be inferred by particle-image-velocimetry measurements. Furthermore, we find that chirality changes the nature of the spontaneous flow transition under confinement and that, for specific anchoring conditions, the latter has the structure of an imperfect pitchfork bifurcation., Comment: 12 pages, 5 figures. Version accepted for publication in Soft Matter

Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as topotaxis, is especially prominent among cells persistently crawling within a spatially varying distribution of cell-sized obstacles. In this article we introduce a toy model of topotaxis based on active Brownian particles constrained to move in a lattice of obstacles, with space-dependent lattice spacing. Using numerical simulations and analytical arguments, we demonstrate that topographical gradients introduce a spatial modulation of the particles' persistence, leading to directed motion toward regions of higher persistence. Our results demonstrate that persistent motion alone is sufficient to drive topotaxis and could serve as a starting point for more detailed studies on self-propelled particles and cells., Comment: 10 pages, 6 figures

Zebrafish is a useful modeling organism for the study of vertebrate development, immune response, and metabolism. Metabolic studies can be aided by mathematical reconstructions of the metabolic network of zebrafish. These list the substrates and products of all biochemical reactions that occur in the zebrafish. Mathematical techniques such as flux-balance analysis then make it possible to predict the possible metabolic flux distributions that optimize, for example, the turnover of food into biomass. The only available genome-scale reconstruction of zebrafish metabolism is ZebraGEM. In this study, we present ZebraGEM 2.0, an updated and validated version of ZebraGEM. ZebraGEM 2.0 is extended with gene-protein-reaction associations (GPRs) that are required to integrate genetic data with the metabolic model. To demonstrate the use of these GPRs, we performed an in silico genetic screening for knockouts of metabolic genes and validated the results against published in vivo genetic knockout and knockdown screenings. Among the single knockout simulations, we identified 74 essential genes, whose knockout stopped growth completely. Among these, 11 genes are known have an abnormal knockout or knockdown phenotype in vivo (partial), and 41 have human homologs associated with metabolic diseases. We also added the oxidative phosphorylation pathway, which was unavailable in the published version of ZebraGEM. The updated model performs better than the original model on a predetermined list of metabolic functions. We also determined a minimal feed composition. The oxidative phosphorylation pathways were validated by comparing with published experiments in which key components of the oxidative phosphorylation pathway were pharmacologically inhibited. To test the utility of ZebraGEM2.0 for obtaining new results, we integrated gene expression data from control and Mycobacterium marinum-infected zebrafish larvae. The resulting model predicts impeded growth and altered histidine metabolism in the infected larvae.

Summary Many cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions., Graphical Abstract, Highlights • A cellular Potts model is extended with the mechanical response of focal adhesions • Mechanical cell-ECM reciprocity leads to cell spreading, elongation, and durotaxis • Cell-generated planar stresses may cooperatively strengthen focal adhesion patches • Predicted durotaxis speed increases with gradient steepness until saturation point, Biological Sciences; Cell Biology; Biophysics; In Silico Biology; Biomaterials; Structural Biology; Biochemistry; Biocomputational Method

In experimental assays of angiogenesis in three-dimensional fibrin matrices, a temporary scaffold formed during wound healing, the type and composition of fibrin impacts the level of sprouting. More sprouts form on high molecular weight (HMW) than on low molecular weight (LMW) fibrin. It is unclear what mechanisms regulate the number and the positions of the vascular-like structures in cell cultures. To address this question, we propose a mechanistic simulation model of endothelial cell migration and fibrin proteolysis by the plasmin system. The model is a hybrid, cell-based and continuum, computational model based on the cellular Potts model and sets of partial-differential equations. Based on the model results, we propose that a positive feedback mechanism between uPAR, plasmin and transforming growth factor β1 (TGFβ1) selects cells in the monolayer for matrix invasion. Invading cells releases TGFβ1 from the extracellular matrix through plasmin-mediated fibrin degradation. The activated TGFβ1 further stimulates fibrin degradation and keeps proteolysis active as the sprout invades the fibrin matrix. The binding capacity for TGFβ1 of LMW is reduced relative to that of HMW. This leads to reduced activation of proteolysis and, consequently, reduced cell ingrowth in LMW fibrin compared to HMW fibrin. Thus our model predicts that endothelial cells in LMW fibrin matrices compared to HMW matrices show reduced sprouting due to a lower bio-availability of TGFβ1., Author summary Therapies for a range of medical conditions, including cancer, wound healing and diabetic retinopathy can benefit from a better control over the growth of blood vessels. The chemical properties of fibrin, the material that forms scabs in wounds and can also occur in large concentrations in tumors, can regulate the degree of blood vessel growth (angiogenesis). Angiogenesis can be mimicked in cell cultures. These allow us to modulate the chemical properties of fibrin and study the effect on angiogenesis. Fibrin occurs in high molecular weight (HMW) and in low molecular weight (LMW) forms. Interestingly, there is more ingrowth of angiogenic-like structures into HMW than in LMW fibrin, but the mechanisms are poorly understood. To get more insight into these, we constructed a computational model. Using the model, we propose and analyse a hypothetical mechanism for sprouting that could explain the differences in endothelial cell sprouting in LMW and HMW fibrin matrices. Our model suggests that cells digest fibrin, thus creating space for ingrowth. At the same time, digestion frees growth factors bound to fibrin, that activates further secretion of digestive enzymes by the cells. We propose that the resulting positive feedback loop spontaneously selects cells in the endothelial monolayer for ingrowth and helps the blood vessel sprout move deeper into the fibrin. This could be a complementary mechanism to lateral-inhibition by Delta-Notch for the selection of leader cells, also called ‘tip cells’. Our model predicts that endothelial cells in LMW fibrin compared to HMW fibrin show reduced sprouting due to a lower bio-availability of TGFβ1.

The cellular Potts model (CPM, a.k.a. Glazier–Graner–Hogeweg or GGH model) is a somewhat liberal extension of probabilistic cellular automata. The model is derived from the Ising and Potts models and represents biological cells as domains of CA-sites of the same state. A Hamiltonian energy is used to describe the balance of forces that the biological cells apply onto one another and their local environment. A Metropolis algorithm iteratively copies the state from one site into one of the adjacent sites, thus shifting the domain interfaces and moving the biological cells along the lattice. The approach is commonly used in applications of developmental biology, where the CPM often interacts with systems of ordinary-differential equations that model the intracellular chemical kinetics and partial-differential equations that model the extracellular chemical signal dynamics to constitute a hybrid and multiscale description of the biological system. In this chapter we will introduce the cellular Potts model and discuss its use in developmental biology, focusing on the development of blood vessels, a process called vascular morphogenesis. We will start by introducing a range of models focusing on uncovering the basic mechanisms of vascular morphogenesis: network formation and sprouting and then show how these models are extended with models of intracellular regulation and with interactions with the extracellular micro-environment. We then briefly review the integration of models of vascular morphogenesis in several examples of organ development in health and disease, including development, cancer, and age-related macular degeneration. We end by discussing the computational efficiency of the CPM and the available strategies for the validation of CPM-based simulation models.

In January 1970, computer scientist Leo Geurts walked into Swart Gallery in Amsterdam, The Netherlands, to see the solo exhibition by Dutch artist Peter Struycken (The Netherlands, 1939). He was struck by Struycken’s black and white works “Computerstructuren” (1969), which were painted after grid patterns generated by algorithms. Geurts assumed that they must have been produced using cellular automata. He started working with Lambert Meertens at Mathematisch Centrum (now CWI) in Amsterdam to make a similar work.

Computational modelling is helpful for elucidating the cellular mechanisms driving biological morphogenesis. Previous simulation studies of blood vessel growth based on the Cellular Potts model (CPM) proposed that elongated, adhesive or mutually attractive endothelial cells suffice for the formation of blood vessel sprouts and vascular networks. Because each mathematical representation of a model introduces potential artifacts, it is important that model results are reproduced using alternative modelling paradigms. Here, we present a lattice-free, particle-based simulation of the cell elongation model of vasculogenesis. The new, particle-based simulations confirm the results obtained from the previous Cellular Potts simulations. Furthermore, our current findings suggest that the emergence of order is possible with the application of a high enough attractive force or, alternatively, a longer attraction radius. The methodology will be applicable to a range of problems in morphogenesis and noisy particle aggregation in which cell shape is a key determining factor., Comment: 9 pages, 11 figures, 2 supplementary videos (on Youtube), submitted to Computational Particle Mechanics, special issue: Jos\'e-Manuel Garcia Aznar (Ed.) Particle-based simulations on cell and biomolecular mechanics

Vertebrates are characterized by their segmented structure, first visible in the somites that form along the embryonic body axis. Somites are the predecessors of the vertebrae, ribs, muscles and the skin and impose a segmented organization on the peripheral nervous system. The variability in somite number between species has presumably evolved by genetic rearrangements, leading to changes in the ratio of the segmentation clock rate to the developmental growth rate. However, it is known that physical cues, like temperature, salinity or light conditions, can modify the vertebrate body plan and change the vertebral number. Here we show that mechanical stretching, another physical cue, can induce the formation of additional somites in the developing chicken embryo. Stretching of live chick embryos and the resulting deformation of somites induces a slow cellular reorganization of somites to form two or more well-shaped and stable daughter somites. Mesenchymal cells from the somite core thereby undergo mesenchymal-to-epithelial transitions (MET), thus meeting the geometrical demand for more border cells. Our simulations, using a Cellular Potts Model of somite remodeling, suggest that this MET occurs through lateral induction by existing epithelial cells. Our results strengthen the idea that somitic mesoderm self-organizes, and show that it is phenotypically plastic under variations in the mechanical environment. These somite qualities could play out as a selective advantage by preventing the formation of transitional vertebrae and give rise to another possibility how the vertebrate body axis might have evolved towards different vertebral numbers, next to the previously proposed genetic rearrangements.

BackgroundThe human gut contains approximately 1014bacteria, belonging to hundreds of different species. Together, these microbial species form a complex food web that can break down food sources that our own digestive enzymes cannot handle, including complex polysaccharides, producing short chain fatty acids and additional metabolites,e.g., vitamin K. The diversity of microbial diversity is important for colonic health: Changes in the composition of the microbiota have been associated with inflammatory bowel disease, diabetes, obestity and Crohn’s disease, and make the microbiota more vulnerable to infestation by harmful species,e.g., Clostridium difficile. To get a grip on the controlling factors of microbial diversity in the gut, we here propose a multi-scale, spatiotemporal dynamic flux-balance analysis model to study the emergence of metabolic diversity in a spatial gut-like, tubular environment. The model features genome-scale metabolic models of microbial populations, resource sharing via extracellular metabolites, and spatial population dynamics and evolution.ResultsIn this model, cross-feeding interactions emerge readily, despite the species’ ability to metabolize sugars autonomously. Interestingly, the community requires cross-feeding for producing a realistic set of short-chain fatty acids from an input of glucose, If we let the composition of the microbial subpopulations change during invasion of adjacent space, a complex and stratifed microbiota evolves, with subspecies specializing on cross-feeding interactions via a mechanism of compensated trait loss. The microbial diversity and stratification collapse if the flux through the gut is enhanced to mimic diarrhea.ConclusionsIn conclusion, thisin silicomodel is a helpful tool in systems biology to predict and explain the controlling factors of microbial diversity in the gut. It can be extended to include,e.g., complex food source, and host-microbiota interactions via the gut wall.

We investigate the geometrical and mechanical properties of adherent cells characterized by a highly anisotropic actin cytoskeleton. Using a combination of theoretical work and experiments on micropillar arrays, we demonstrate that the shape of the cell edge is accurately described by elliptical arcs, whose eccentricity expresses the degree of anisotropy of the internal cell stresses. This results in a spatially varying tension along the cell edge, that significantly affects the traction forces exerted by the cell on the substrate. Our work highlights the strong interplay between cell mechanics and geometry and paves the way towards the reconstruction of cellular forces from geometrical data., 5 pages, 3 figures

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the differences between tip cells and stalk cells. To predict potential differences, we looked for parameter values that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the model prediction we inhibited Apelin signaling in our model and in an \emph{in vitro} model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting. Based on the prediction of the computational model, we propose that the differential expression of Apelin and APJ yields a "self-generated" gradient mechanisms that accelerates the extension of the sprout., Comment: 48 pages, 10 figures, 8 supplementary figures. Accepted for publication in PLoS ONE

Cell shape influences function, and the current model suggests that such shape effect is transient. However, cells dynamically change their shapes, thus, the critical question is whether shape information remains influential on future cell function even after the original shape is lost. We address this question by integrating experimental and computational approaches. Quantitative live imaging of asymmetric cell-fate decision-making and their live shape manipulation demonstrates that cellular eccentricity of progenitor cell indeed biases stochastic fate decisions of daughter cells despite mitotic rounding. Modelling and simulation indicates that polarized localization of Delta protein instructs by the progenitor eccentricity is an origin of the bias. Simulation with varying parameters predicts that diffusion rate and abundance of Delta molecules quantitatively influence the bias. These predictions are experimentally validated by physical and genetic methods, showing that cells exploit a mechanism reported herein to influence their future fates based on their past shape despite dynamic shape changes., Cell shape influences function but during mitotic cell rounding the original shape is lost. Here the authors show that the cellular eccentricity of progenitor cell biases stochastic fate-decisions using a combination of quantitative live imaging, genetic manipulations and computational simulations.

How does the genetic information encoded in the DNA direct the growth and form of multicellular organisms? The genome directs a cell’s biophysical properties and its response to signals from adjacent cells. To analyze how these cell behaviors drive embryogenesis, insights into the collective behavior of multicellular aggregates is crucial. This article describes computational approaches to the study of collective cell behavior. Four examples (cell sorting, angiogenesis, somitogenesis, and root development) illustrate how computational insights into collective cell behavior are incorporated into experimental studies to unravel the mechanisms of development.