The shapes of elongating gastruloids are consistent with convergent extension driven by a combination of active cell crawling and differential adhesion.

Gastruloids have emerged as highly useful in vitro models 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 process in vitro. Here, we measure and quantify the shapes of elongating gastruloids and show, by Cellular Potts model simulations based on a novel, optimized algorithm, that convergent extension, driven by a combination of active cell crawling 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 extension in vivo. All in all, our study demonstrates, how gastruloids can be used to elucidate morphogenic processes in embryonic development.

2'-Fucosyllactose helps butyrate producers outgrow competitors in infant gut microbiota simulations.

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 in metabolic detail. It represents the community as a grid of bacterial populations that exchange 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 of Bifidobacterium, whereas butyrate producing bacteria are only consistently abundant in the presence of propane-1,2-diol, a product of 2'-FL metabolism. In absence of prebiotics or in presence of only GOS, however, Bacteroides vulgatus and Cutibacterium acnes outcompete butyrate producers by consuming intermediate metabolites.

A life-history allele of large effect shortens developmental time in a wild insect population.

Developmental time is a key life-history trait with large effects on Darwinian fitness. In many insects, developmental time is currently under strong selection to minimize ecological mismatches in seasonal timing induced by climate change. The genetic basis of responses to such selection, however, is poorly understood. To address this problem, we set up a long-term evolve-and-resequence experiment in the beetle Tribolium castaneum and selected replicate, outbred populations for fast or slow embryonic development. The response to this selection was substantial and embryonic developmental timing of the selection lines started to diverge during dorsal closure. Pooled whole-genome resequencing, gene expression analysis and an RNAi screen pinpoint a 222 bp deletion containing binding sites for Broad and Tramtrack upstream of the ecdysone degrading enzyme Cyp18a1 as a main target of selection. Using CRISPR/Cas9 to reconstruct this allele in the homogenous genetic background of a laboratory strain, we unravel how this single deletion advances the embryonic ecdysone peak inducing dorsal closure and show that this allele accelerates larval development but causes a trade-off with fecundity. Our study uncovers a life-history allele of large effect and reveals the evolvability of developmental time in a natural insect population.

Deformability and collision-induced reorientation enhance cell topotaxis in dense microenvironments.

In vivo, cells navigate through complex environments filled with obstacles such as other cells and the extracellular matrix. Recently, the term "topotaxis" has been introduced for navigation along topographic cues such as obstacle density gradients. Experimental and mathematical efforts have analyzed topotaxis of single cells in pillared grids with pillar density gradients. A previous model based on active Brownian particles (ABPs) has shown that ABPs perform topotaxis, i.e., drift toward lower pillar densities, due to decreased effective persistence lengths at high pillar densities. The ABP model predicted topotactic drifts of up to 1% of the instantaneous speed, whereas drifts of up to 5% have been observed experimentally. We hypothesized that the discrepancy between the ABP and the experimental observations could be in 1) cell deformability and 2) more complex cell-pillar interactions. Here, we introduce a more detailed model of topotaxis based on the cellular Potts model (CPM). To model persistent cells we use the Act model, which mimics actin-polymerization-driven motility, and a hybrid CPM-ABP model. Model parameters were fitted to simulate the experimentally found motion of Dictyostelium discoideum on a flat surface. For starved D. discoideum, the topotactic drifts predicted by both CPM variants are closer to the experimental results than the previous ABP model due to a larger decrease in persistence length. Furthermore, the Act model outperformed the hybrid model in terms of topotactic efficiency, as it shows a larger reduction in effective persistence time in dense pillar grids. Also pillar adhesion can slow down cells and decrease topotaxis. For slow and less-persistent vegetative D. discoideum cells, both CPMs predicted a similar small topotactic drift. We conclude that deformable cell volume results in higher topotactic drift compared with ABPs, and that feedback of cell-pillar collisions on cell persistence increases drift only in highly persistent cells.

Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix.

The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is a challenge that cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has nontrivial structure and mechanics. Here, we extend the CPM with a bead-spring model of ECM fiber networks modeled using molecular dynamics. We model a contractile cell pulling with discrete focal adhesion-like sites on the fiber network and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that at high network cross-linking, contractile cell forces propagate over at least eight cell diameters, decaying with distance with power law exponent n= 0.35 - 0.65 typical of viscoelastic ECMs. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation for investigating how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

Computational modeling of cambium activity provides a regulatory framework for simulating radial plant growth.

Precise organization of growing structures is a fundamental process in developmental biology. In plants, radial growth is mediated by the cambium, a stem cell niche continuously producing wood (xylem) and bast (phloem) in a strictly bidirectional manner. While this process contributes large parts to terrestrial biomass, cambium dynamics eludes direct experimental access due to obstacles in live-cell imaging. Here, we present a cell-based computational model visualizing cambium activity and integrating the function of central cambium regulators. Performing iterative comparisons of plant and model anatomies, we conclude that the receptor-like kinase PXY and its ligand CLE41 are part of a minimal framework sufficient for instructing tissue organization. By integrating tissue-specific cell wall stiffness values, we moreover probe the influence of physical constraints on tissue geometry. Our model highlights the role of intercellular communication within the cambium and shows that a limited number of factors are sufficient to create radial growth by bidirectional tissue production.

Evolution of genome fragility enables microbial division of labor.

Division of labor can evolve when social groups benefit from the functional specialization of its members. Recently, a novel means of coordinating the division of labor was found in the antibiotic-producing bacterium Streptomyces coelicolor, where specialized cells are generated through large-scale genomic re-organization. We investigate how the evolution of a genome architecture enables such mutation-driven division of labor, using a multiscale computational model of bacterial evolution. In this model, bacterial behavior-antibiotic production or replication-is determined by the structure and composition of their genome, which encodes antibiotics, growth-promoting genes, and fragile genomic loci that can induce chromosomal deletions. We find that a genomic organization evolves, which partitions growth-promoting genes and antibiotic-coding genes into distinct parts of the genome, separated by fragile genomic loci. Mutations caused by these fragile sites mostly delete growth-promoting genes, generating sterile, and antibiotic-producing mutants from weakly-producing progenitors, in agreement with experimental observations. This division of labor enhances the competition between colonies by promoting antibiotic diversity. These results show that genomic organization can co-evolve with genomic instabilities to enable reproductive division of labor.

A new model of Notch signalling: Control of Notch receptor cis-inhibition via Notch ligand dimers.

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.

A Multiscale Spatiotemporal Model Including a Switch from Aerobic to Anaerobic Metabolism Reproduces Succession in the Early Infant Gut Microbiota.

The human intestinal microbiota starts to form immediately after birth and is important for the health of the host. During the first days, facultatively anaerobic bacterial species generally dominate, such as Enterobacteriaceae. These are succeeded by strictly anaerobic species, particularly Bifidobacterium species. An early transition to Bifidobacterium species is associated with health benefits; for example, Bifidobacterium species repress growth of pathogenic competitors and modulate the immune response. Succession to Bifidobacterium is thought to be due to consumption of intracolonic oxygen present in newborns by facultative anaerobes, including Enterobacteriaceae. To study if oxygen depletion suffices for the transition to Bifidobacterium species, here we introduced a multiscale mathematical model that considers metabolism, spatial bacterial population dynamics, and cross-feeding. Using publicly available metabolic network data from the AGORA collection, the model simulates ab initio the competition of strictly and facultatively anaerobic species in a gut-like environment under the influence of lactose and oxygen. The model predicts that individual differences in intracolonic oxygen in newborn infants can explain the observed individual variation in succession to anaerobic species, in particular Bifidobacterium species. Bifidobacterium species became dominant in the model by their use of the bifid shunt, which allows Bifidobacterium to switch to suboptimal yield metabolism with fast growth at high lactose concentrations, as predicted here using flux balance analysis. The computational model thus allows us to test the internal plausibility of hypotheses for bacterial colonization and succession in the infant colon. IMPORTANCE The composition of the infant microbiota has a great impact on infant health, but its controlling factors are still incompletely understood. The frequently dominant anaerobic Bifidobacterium species benefit health, e.g., they can keep harmful competitors under control and modulate the intestinal immune response. Controlling factors could include nutritional composition and intestinal mucus composition, as well as environmental factors, such as antibiotics. We introduce a modeling framework of a metabolically realistic intestinal microbial ecology in which hypothetical scenarios can be tested and compared. We present simulations that suggest that greater levels of intraintestinal oxygenation more strongly delay the dominance of Bifidobacterium species, explaining the observed variety of microbial composition and demonstrating the use of the model for hypothesis generation. The framework allowed us to test a variety of controlling factors, including intestinal mixing and transit time. Future versions will also include detailed modeling of oligosaccharide and mucin metabolism.

Scaling relations for auxin waves.

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.

Implementing Computational Modeling in Tissue Engineering: Where Disciplines Meet.

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic setups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights. Impact Statement Although in recent years the use of mathematical and computational sciences has increased in the Tissue Engineering and Regenerative Medicine (TERM) field, we believe that a further integration of experimental and computational approaches has a huge potential for advancing the field due to the ability of models to explain and predict experimental results and efficiently optimize TERM product and process designs. By providing an overview of existing computational models, how they have contributed to the field, as well as a future perspective, this review represents an important step to help realize TERM's ultimate goal: a cure instead of care.

Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics.

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 motility without attaching to the ECM, or sliding and stepping motility 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 predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility 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.

Modeling Plant Tissue Development Using VirtualLeaf.

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.

A Novel Function of TLR2 and MyD88 in the Regulation of Leukocyte Cell Migration Behavior During Wounding in Zebrafish Larvae.

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 explore in vivo whether 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 in tlr2 and myd88 mutants 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 both tlr2-/- and myd88-/- 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 both tlr2 and myd88 control the migration direction of distant neutrophils upon wounding. Furthermore, in both the tlr2 and the myd88 mutants, macrophages migrated more slowly toward the wound edge. Taken together, our findings show that tlr2 and myd88 are involved in responses to tail wounding by regulating the behavior and speed of leukocyte migration in vivo.

Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics.

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.

Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in the absence of growth.

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 from in vitro observations of the behaviour of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGF[Formula: see text]1 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'.

Mechanical interplay between cell shape and actin cytoskeleton organization.

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 (GDß1, GDß3) and epithelioid (GEß1, GEß3) cells.

Topotaxis of active Brownian particles.

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, has been extensively studied for topographical gradients at the subcellular scale, but can also occur in the presence of a spatially varying density of cell-sized features. Such a large-scale topotaxis has recently been observed in highly motile cells that persistently crawl within an array of obstacles with smoothly varying lattice spacing. We introduce a toy model of large-scale topotaxis, based on active Brownian particles. 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 large-scale topotaxis and could serve as a starting point for more detailed studies on self-propelled particles and cells.

Somite Division and New Boundary Formation by Mechanical Strain.

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.