LBIBCell: a cell-based simulation environment for morphogenetic problems

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets

In living and synthetic active matter systems, the constituents can self-propel and interact with each other and with the environment through various physicochemical mechanisms. Among these mechanisms, chemotactic and auto-chemotactic effects are widely observed. The impact of (auto-)chemotactic effects on achiral active matter has been a recent research focus. However, the influence of these effects on chiral active matter remains elusive. Here, we develop a Brownian dynamics model coupled with a diffusion equation to examine the dynamics of auto-chemotactic chiral active droplets in both quasi-two-dimensional (2D) and three-dimensional (3D) systems. By quantifying the droplet trajectory as a function of the dimensionless Péclet number and chemotactic strength, our simulations well reproduce the curling and helical trajectories of nematic droplets in a surfactant-rich solution reported by Krüger et al. [Phys. Rev. Lett. 117, 048003 (2016)]. The modeled curling trajectory in 2D exhibits an emergent chirality, also consistent with the experiment. We further show that the geometry of the chiral droplet trajectories, characterized by the pitch and diameter, can be used to infer the velocities of the droplet. Interestingly, we find that, unlike the achiral case, the velocities of chiral active droplets show dimensionality dependence: its mean instantaneous velocity is higher in 3D than in 2D, whereas its mean migration velocity is lower in 3D than in 2D. Taken together, our particle-based simulations provide new insights into the dynamics of auto-chemotactic chiral active droplets, reveal the effects of dimensionality, and pave the way toward their applications, such as drug delivery, sensors, and micro-reactors.

SimuCell3D: three-dimensional simulation of tissue mechanics with cell polarization

The three-dimensional (3D) organization of cells determines tissue function and integrity, and changes markedly in development and disease. Cell-based simulations have long been used to define the underlying mechanical principles. However, high computational costs have so far limited simulations to either simplified cell geometries or small tissue patches. Here, we present SimuCell3D, an efficient open-source program to simulate large tissues in three dimensions with subcellular resolution, growth, proliferation, extracellular matrix, fluid cavities, nuclei and non-uniform mechanical properties, as found in polarized epithelia. Spheroids, vesicles, sheets, tubes and other tissue geometries can readily be imported from microscopy images and simulated to infer biomechanical parameters. Doing so, we show that 3D cell shapes in layered and pseudostratified epithelia are largely governed by a competition between surface tension and intercellular adhesion. SimuCell3D enables the large-scale in silico study of 3D tissue organization in development and disease at a great level of detail.

A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth

The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study mechanisms involved in growth regulation. Most existing computational models for studying tissue growth focus specifically on either chemical signals or mechanical forces. Here we developed a multiscale chemical-mechanical model to investigate the growth regulation mechanism based on the dynamics of a morphogen gradient. By comparing the spatial distribution of dividing cells and the overall tissue shape obtained in model simulations with experimental data of the wing disc, it is shown that the size of the domain of the Dpp morphogen is critical in determining tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with Dpp absorbance at the peripheral zone, the feedback regulation that downregulates Dpp receptors on the cell membrane allows for further spreading of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate.

FGF8 induces chemokinesis and regulates condensation of mouse nephron progenitor cells

Kidneys develop via iterative branching of the ureteric epithelial tree and subsequent nephrogenesis at the branch points. Nephrons form in the cap mesenchyme as the metanephric mesenchyme (MM) condenses around the epithelial ureteric buds (UBs). Previous work has demonstrated that FGF8 is important for the survival of nephron progenitor cells (NPCs), and early deletion of Fgf8 leads to the cessation of nephron formation, which results in post-natal lethality. We now reveal a previously unreported function of FGF8. By combining transgenic mouse models, quantitative imaging assays and data-driven computational modelling, we show that FGF8 has a strong chemokinetic effect and that this chemokinetic effect is important for the condensation of NPCs to the UB. The computational model shows that the motility must be lower close to the UB to achieve NPC attachment. We conclude that the FGF8 signalling pathway is crucial for the coordination of NPC condensation at the UB. Chemokinetic effects have also been described for other FGFs and may be generally important for the formation of mesenchymal condensates.

The Role of in silico Research in Developing Nanoparticle-Based Therapeutics

Nanoparticles (NPs) hold great potential as therapeutics, particularly in the realm of drug delivery. They are effective at functional cargo delivery and offer a great degree of amenability that can be used to offset toxic side effects or to target drugs to specific regions in the body. However, there are many challenges associated with the development of NP-based drug formulations that hamper their successful clinical translation. Arguably, the most significant barrier in the way of efficacious NP-based drug delivery systems is the tedious and time-consuming nature of NP formulation—a process that needs to account for downstream effects, such as the onset of potential toxicity or immunogenicity, in vivo biodistribution and overall pharmacokinetic profiles, all while maintaining desirable therapeutic outcomes. Computational and AI-based approaches have shown promise in alleviating some of these restrictions. Via predictive modeling and deep learning, in silico approaches have shown the ability to accurately model NP-membrane interactions and cellular uptake based on minimal data, such as the physicochemical characteristics of a given NP. More importantly, machine learning allows computational models to predict how specific changes could be made to the physicochemical characteristics of a NP to improve functional aspects, such as drug retention or endocytosis. On a larger scale, they are also able to predict the in vivo pharmacokinetics of NP-encapsulated drugs, predicting aspects such as circulatory half-life, toxicity, and biodistribution. However, the convergence of nanomedicine and computational approaches is still in its infancy and limited in its applicability. The interactions between NPs, the encapsulated drug and the body form an intricate network of interactions that cannot be modeled with absolute certainty. Despite this, rapid advancements in the area promise to deliver increasingly powerful tools capable of accelerating the development of advanced nanoscale therapeutics. Here, we describe computational approaches that have been utilized in the field of nanomedicine, focusing on approaches for NP design and engineering.

Quantitative modeling identifies critical cell mechanics driving bile duct lumen formation

Biliary ducts collect bile from liver lobules, the smallest functional and anatomical units of liver, and carry it to the gallbladder. Disruptions in this process caused by defective embryonic development, or through ductal reaction in liver disease have a major impact on life quality and survival of patients. A deep understanding of the processes underlying bile duct lumen formation is crucial to identify intervention points to avoid or treat the appearance of defective bile ducts. Several hypotheses have been proposed to characterize the biophysical mechanisms driving initial bile duct lumen formation during embryogenesis. Here, guided by the quantification of morphological features and expression of genes in bile ducts from embryonic mouse liver, we sharpened these hypotheses and collected data to develop a high resolution individual cell-based computational model that enables to test alternative hypotheses in silico. This model permits realistic simulations of tissue and cell mechanics at sub-cellular scale. Our simulations suggest that successful bile duct lumen formation requires a simultaneous contribution of directed cell division of cholangiocytes, local osmotic effects generated by salt excretion in the lumen, and temporally-controlled differentiation of hepatoblasts to cholangiocytes, with apical constriction of cholangiocytes only moderately affecting luminal size.

The initial step in bile duct development is the formation of a biliary lumen, a process which involves several cellular mechanisms, such as cell division and polarization, and secretion of fluid. However, how these mechanisms are orchestrated in time and space is difficult to understand. Here, we built a computational model of biliary lumen formation which represents every cell and its function in detail. With the model we can simulate the effect of biophysical aspects that affect duct formation. We have tested the individual and combined effects of directed cell division, apical constriction, and osmotic effects on lumen expansion by varying the parameters that control their relative strength. Our simulations suggest that successful bile duct lumen formation requires the simultaneous contribution of directed cell division of cholangiocytes, local osmotic effects generated by salt excretion in the lumen, and temporally-controlled differentiation of hepatoblasts to cholangiocytes, with apical constriction of cholangiocytes only moderately affecting luminal size.

Seven challenges in the multiscale modeling of multicellular tissues

The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.

A Sight on Single-Cell Transcriptomics in Plants Through the Prism of Cell-Based Computational Modeling Approaches: Benefits and Challenges for Data Analysis

Single-cell technology is a relatively new and promising way to obtain high-resolution transcriptomic data mostly used for animals during the last decade. However, several scientific groups developed and applied the protocols for some plant tissues. Together with deeply-developed cell-resolution imaging techniques, this achievement opens up new horizons for studying the complex mechanisms of plant tissue architecture formation. While the opportunities for integrating data from transcriptomic to morphogenetic levels in a unified system still present several difficulties, plant tissues have some additional peculiarities. One of the plants' features is that cell-to-cell communication topology through plasmodesmata forms during tissue growth and morphogenesis and results in mutual regulation of expression between neighboring cells affecting internal processes and cell domain development. Undoubtedly, we must take this fact into account when analyzing single-cell transcriptomic data. Cell-based computational modeling approaches successfully used in plant morphogenesis studies promise to be an efficient way to summarize such novel multiscale data. The inverse problem's solutions for these models computed on the real tissue templates can shed light on the restoration of individual cells' spatial localization in the initial plant organ-one of the most ambiguous and challenging stages in single-cell transcriptomic data analysis. This review summarizes new opportunities for advanced plant morphogenesis models, which become possible thanks to single-cell transcriptome data. Besides, we show the prospects of microscopy and cell-resolution imaging techniques to solve several spatial problems in single-cell transcriptomic data analysis and enhance the hybrid modeling framework opportunities.

Turning Nature's own processes into design strategies for living bone implant biomanufacturing: a decade of Developmental Engineering

A decade after the term developmental engineering (DE) was coined to indicate the use of developmental processes as blueprints for the design and development of engineered living implants, a myriad of proof-of-concept studies demonstrate the potential of this approach in small animal models. This review provides an overview of DE work, focusing on applications in bone regeneration. Enabling technologies allow to quantify the distance between in vitro processes and their developmental counterpart, as well as to design strategies to reduce that distance. By embedding Nature's robust mechanisms of action in engineered constructs, predictive large animal data and subsequent positive clinical outcomes can be gradually achieved. To this end, the development of next generation biofabrication technologies should provide the necessary scale and precision for robust living bone implant biomanufacturing.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

SBML Level 3: an extensible format for the exchange and reuse of biological models

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

Modeling of Wnt-mediated tissue patterning in vertebrate embryogenesis

During embryogenesis, morphogens form a concentration gradient in responsive tissue, which is then translated into a spatial cellular pattern. The mechanisms by which morphogens spread through a tissue to establish such a morphogenetic field remain elusive. Here, we investigate by mutually complementary simulations and in vivo experiments how Wnt morphogen transport by cytonemes differs from typically assumed diffusion-based transport for patterning of highly dynamic tissue such as the neural plate in zebrafish. Stochasticity strongly influences fate acquisition at the single cell level and results in fluctuating boundaries between pattern regions. Stable patterning can be achieved by sorting through concentration dependent cell migration and apoptosis, independent of the morphogen transport mechanism. We show that Wnt transport by cytonemes achieves distinct Wnt thresholds for the brain primordia earlier compared with diffusion-based transport. We conclude that a cytoneme-mediated morphogen transport together with directed cell sorting is a potentially favored mechanism to establish morphogen gradients in rapidly expanding developmental systems.

Cell-based simulations of biased epithelial lung growth

During morphogenesis, epithelial tubes elongate. In the case of the mammalian lung, biased elongation has been linked to a bias in cell shape and cell division, but it has remained unclear whether a bias in cell shape along the axis of outgrowth is sufficient for biased outgrowth and how it arises. Here, we use our 2D cell-based tissue simulation software [Formula: see text] to investigate the conditions for biased epithelial outgrowth. We show that the observed bias in cell shape and cell division can result in the observed bias in outgrowth only in the case of strong cortical tension, and comparison to biological data suggests that the cortical tension in epithelia is likely sufficient. We explore mechanisms that may result in the observed bias in cell division and cell shapes. To this end, we test the possibility that the surrounding tissue or extracellular matrix acts as a mechanical constraint that biases growth in the longitudinal direction. While external compressive forces can result in the observed bias in outgrowth, we find that they do not result in the observed bias in cell shapes. We conclude that other mechanisms must exist that generate the bias in lung epithelial outgrowth.

A quantitative high-resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. This paper considers as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells' response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important.

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

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 cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the 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.

Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids over various growth conditions and cell lines

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function.

Image-based modeling of kidney branching morphogenesis reveals GDNF-RET based Turing-type mechanism and pattern-modulating WNT11 feedback

Branching patterns and regulatory networks differ between branched organs. It has remained unclear whether a common regulatory mechanism exists and how organ-specific patterns can emerge. Of all previously proposed signalling-based mechanisms, only a ligand-receptor-based Turing mechanism based on FGF10 and SHH quantitatively recapitulates the lung branching patterns. We now show that a GDNF-dependent ligand-receptor-based Turing mechanism quantitatively recapitulates branching of cultured wildtype and mutant ureteric buds, and achieves similar branching patterns when directing domain outgrowth in silico. We further predict and confirm experimentally that the kidney-specific positive feedback between WNT11 and GDNF permits the dense packing of ureteric tips. We conclude that the ligand-receptor based Turing mechanism presents a common regulatory mechanism for lungs and kidneys, despite the differences in the molecular implementation. Given its flexibility and robustness, we expect that the ligand-receptor-based Turing mechanism constitutes a likely general mechanism to guide branching morphogenesis and other symmetry breaks during organogenesis.

Many organs develop through branching morphogenesis, but whether the underlying mechanisms are shared is unknown. Here, the authors show that a ligand-receptor based Turing mechanisms, similar to that observed in lung development, likely underlies branching morphogenesis of the kidney.

Scalable population-level modelling of biological cells incorporating mechanics and kinetics in continuous time

The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this detailed knowledge of the individual cell to be able to explain at the population level how cells interact and respond with each other and their environment. In particular, the goal is to understand how organisms develop, maintain and repair functional tissues and organs. In this paper, we propose a novel computational framework for modelling populations of interacting cells. Our framework incorporates mechanistic, constitutive descriptions of biomechanical properties of the cell population, and uses a coarse-graining approach to derive individual rate laws that enable propagation of the population through time. Thanks to its multiscale nature, the resulting simulation algorithm is extremely scalable and highly efficient. As highlighted in our computational examples, the framework is also very flexible and may straightforwardly be coupled with continuous-time descriptions of biochemical signalling within, and between, individual cells.

Simulation of Morphogen and Tissue Dynamics

Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modeling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focuses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and growing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretization as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.

Mechanocellular models of epithelial morphogenesis

Embryonic epithelia achieve complex morphogenetic movements, including in-plane reshaping, bending and folding, through the coordinated action and rearrangement of individual cells. Technical advances in molecular and live-imaging studies of epithelial dynamics provide a very real opportunity to understand how cell-level processes facilitate these large-scale tissue rearrangements. However, the large datasets that we are now able to generate require careful interpretation. In combination with experimental approaches, computational modelling allows us to challenge and refine our current understanding of epithelial morphogenesis and to explore experimentally intractable questions. To this end, a variety of cell-based modelling approaches have been developed to describe cell-cell mechanical interactions, ranging from vertex and 'finite-element' models that approximate each cell geometrically by a polygon representing the cell's membrane, to immersed boundary and subcellular element models that allow for more arbitrary cell shapes. Here, we review how these models have been used to provide insights into epithelial morphogenesis and describe how such models could help future efforts to decipher the forces and mechanical and biochemical feedbacks that guide cell and tissue-level behaviour. In addition, we discuss current challenges associated with using computational models of morphogenetic processes in a quantitative and predictive way.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Comparing individual-based approaches to modelling the self-organization of multicellular tissues

The coordinated behaviour of populations of cells plays a central role in tissue growth and renewal. Cells react to their microenvironment by modulating processes such as movement, growth and proliferation, and signalling. Alongside experimental studies, computational models offer a useful means by which to investigate these processes. To this end a variety of cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended shapes. However, it remains unclear how these approaches compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. Here, we exploit the availability of an implementation of five popular cell-based modelling approaches within a consistent computational framework, Chaste (http://www.cs.ox.ac.uk/chaste). This framework allows one to easily change constitutive assumptions within these models. In each case we provide full details of all technical aspects of our model implementations. We compare model implementations using four case studies, chosen to reflect the key cellular processes of proliferation, adhesion, and short- and long-range signalling. These case studies demonstrate the applicability of each model and provide a guide for model usage.

A cell-based computational model of early embryogenesis coupling mechanical behaviour and gene regulation

The study of multicellular development is grounded in two complementary domains: cell biomechanics, which examines how physical forces shape the embryo, and genetic regulation and molecular signalling, which concern how cells determine their states and behaviours. Integrating both sides into a unified framework is crucial to fully understand the self-organized dynamics of morphogenesis. Here we introduce MecaGen, an integrative modelling platform enabling the hypothesis-driven simulation of these dual processes via the coupling between mechanical and chemical variables. Our approach relies upon a minimal 'cell behaviour ontology' comprising mesenchymal and epithelial cells and their associated behaviours. MecaGen enables the specification and control of complex collective movements in 3D space through a biologically relevant gene regulatory network and parameter space exploration. Three case studies investigating pattern formation, epithelial differentiation and tissue tectonics in zebrafish early embryogenesis, the latter with quantitative comparison to live imaging data, demonstrate the validity and usefulness of our framework.