Pattern formation in discrete cell tissues under long range filopodia-based direct cell to cell contact

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Coupling dynamics of 2D Notch-Delta signalling

Understanding pattern formation driven by cell-cell interactions has been a significant theme in cellular biology for many years. In particular, due to their implications within many biological contexts, lateral-inhibition mechanisms present in the Notch-Delta signalling pathway led to an extensive discussion between biologists and mathematicians. Deterministic and stochastic models have been developed as a consequence of this discussion, some of which address long-range signalling by considering cell protrusions reaching non-neighbouring cells. The dynamics of such signalling systems reveal intricate properties of the coupling terms involved in these models. In this work, we investigate the advantages and drawbacks of a single-parameter long-range signalling model across diverse scenarios. By employing linear and multi-scale analyses, we discover that pattern selection is not only partially explained but also depends on nonlinear effects that extend beyond the scope of these analytical techniques.

The present and future of Turing models in developmental biology

The Turing model (or reaction-diffusion model), first published in 1952, is a mathematical model that can account for autonomy in the morphogenesis of organisms. Although initially controversial, the model has gradually gained wider acceptance among experimental embryologists due to the accumulation of experimental data to support it. More recently, this model and others based on it have been used not only to explain biological phenomena conceptually but also as working hypotheses for molecular-level experiments and as internal components of more-complex 3D models. In this Spotlight, I will provide a personal perspective from an experimental biologist on some of the recent developments of the Turing model.

Dynamic switching of lateral inhibition spatial patterns

Hes genes are transcriptional repressors activated by Notch. In the developing mouse neural tissue, HES5 expression oscillates in neural progenitors (Manning et al. 2019 Nat. Commun.10, 1–19 (doi:10.1038/s41467-019-10734-8)) and is spatially organized in small clusters of cells with synchronized expression (microclusters). Furthermore, these microclusters are arranged with a spatial periodicity of three–four cells in the dorso-ventral axis and show regular switching between HES5 high/low expression on a longer time scale and larger amplitude than individual temporal oscillators (Biga et al. 2021 Mol. Syst. Biol.17, e9902 (doi:10.15252/msb.20209902)). However, our initial computational modelling of coupled HES5 could not explain these features of the experimental data. In this study, we provide theoretical results that address these issues with biologically pertinent additions. Here, we report that extending Notch signalling to non-neighbouring progenitor cells is sufficient to generate spatial periodicity of the correct size. In addition, introducing a regular perturbation of Notch signalling by the emerging differentiating cells induces a temporal switching in the spatial pattern, which is longer than an individual cell’s periodicity. Thus, with these two new mechanisms, a computational model delivers outputs that closely resemble the complex tissue-level HES5 dynamics. Finally, we predict that such dynamic patterning spreads out differentiation events in space, complementing our previous findings whereby the local synchronization controls the rate of differentiation.

Studies of Turing pattern formation in zebrafish skin

Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell-cell interactions have been observed to satisfy the 'short-range activation and long-range inhibition' prerequisites for Turing pattern formation, numerous individual reactions were not envisioned based on the classical reaction-diffusion model. For example, in real skin, it is not an alteration in concentrations of chemicals, but autonomous migration and proliferation of pigment cells that establish patterns, and cell-cell interactions are mediated via direct contact through cell protrusions. Therefore, the classical reaction-diffusion mechanism cannot be used as it is for modelling skin pattern formation. Various studies are underway to adapt mathematical models to the experimental findings on research into skin patterns, and the purpose of this review is to organize and present them. These novel theoretical methods could be applied to autonomous pattern formation phenomena other than skin patterns. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Mechano-regulated cell-cell signaling in the context of cardiovascular tissue engineering

Cardiovascular tissue engineering (CVTE) aims to create living tissues, with the ability to grow and remodel, as replacements for diseased blood vessels and heart valves. Despite promising results, the (long-term) functionality of these engineered tissues still needs improvement to reach broad clinical application. The functionality of native tissues is ensured by their specific mechanical properties directly arising from tissue organization. We therefore hypothesize that establishing a native-like tissue organization is vital to overcome the limitations of current CVTE approaches. To achieve this aim, a better understanding of the growth and remodeling (G&R) mechanisms of cardiovascular tissues is necessary. Cells are the main mediators of tissue G&R, and their behavior is strongly influenced by both mechanical stimuli and cell-cell signaling. An increasing number of signaling pathways has also been identified as mechanosensitive. As such, they may have a key underlying role in regulating the G&R of tissues in response to mechanical stimuli. A more detailed understanding of mechano-regulated cell-cell signaling may thus be crucial to advance CVTE, as it could inspire new methods to control tissue G&R and improve the organization and functionality of engineered tissues, thereby accelerating clinical translation. In this review, we discuss the organization and biomechanics of native cardiovascular tissues; recent CVTE studies emphasizing the obtained engineered tissue organization; and the interplay between mechanical stimuli, cell behavior, and cell-cell signaling. In addition, we review past contributions of computational models in understanding and predicting mechano-regulated tissue G&R and cell-cell signaling to highlight their potential role in future CVTE strategies.

Improving the understanding of cytoneme-mediated morphogen gradients by in silico modeling

Morphogen gradients are crucial for the development of organisms. The biochemical properties of many morphogens prevent their extracellular free diffusion, indicating the need of an active mechanism for transport. The involvement of filopodial structures (cytonemes) has been proposed for morphogen signaling. Here, we describe an in silico model based on the main general features of cytoneme-meditated gradient formation and its implementation into Cytomorph, an open software tool. We have tested the spatial and temporal adaptability of our model quantifying Hedgehog (Hh) gradient formation in two Drosophila tissues. Cytomorph is able to reproduce the gradient and explain the different scaling between the two epithelia. After experimental validation, we studied the predicted impact of a range of features such as length, size, density, dynamics and contact behavior of cytonemes on Hh morphogen distribution. Our results illustrate Cytomorph as an adaptive tool to test different morphogen gradients and to generate hypotheses that are difficult to study experimentally.

Graded distribution of signaling molecules (morphogens) is crucial for the development of organisms. Signaling membrane protrusions, called Cytonemes, have been experimentally demonstrated to be involved in morphogen transport and reception. Here, we have developed an in silico model for gradient formation based on key features of cytoneme mediated signaling. We have also implemented the model into an open software tool we named Cytomorph, and validated it by comparing its simulations with experimental data obtained from Hedgehog morphogen distribution. Finally, we have generated in silico predictions for the impact of different cytoneme features such as length, size, density, dynamics and contact behavior. Our results show that Cytomorph is an adaptive tool that can facilitate the study of other cytoneme-dependent morphogen gradients, besides being able to generate hypotheses about aspects that remain elusive to experimental approaches.

Role of cell polarity dynamics and motility in pattern formation due to contact-dependent signalling

A key challenge in biology is to understand how spatio-temporal patterns and structures arise during the development of an organism. An initial aggregate of spatially uniform cells develops and forms the differentiated structures of a fully developed organism. On the one hand, contact-dependent cell-cell signalling is responsible for generating a large number of complex, self-organized, spatial patterns in the distribution of the signalling molecules. On the other hand, the motility of cells coupled with their polarity can independently lead to collective motion patterns that depend on mechanical parameters influencing tissue deformation, such as cellular elasticity, cell-cell adhesion and active forces generated by actin and myosin dynamics. Although modelling efforts have, thus far, treated cell motility and cell-cell signalling separately, experiments in recent years suggest that these processes could be tightly coupled. Hence, in this paper, we study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signalling molecules. Such signalling interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusional contacts. We present a vertex model which accounts for contact-dependent signalling between adjacent cells and between non-adjacent neighbours through long protrusional contacts that occur along the orientation of cell polarization. We observe a rich variety of spatiotemporal patterns of signalling molecules that is influenced by polarity dynamics of the cells, relative strengths of adjacent and non-adjacent signalling interactions, range of polarized interaction, signalling activation threshold, relative time scales of signalling and polarity orientation, and cell motility. Though our results are developed in the context of Delta-Notch signalling, they are sufficiently general and can be extended to other contact dependent morpho-mechanical dynamics.

Cytonemes in development

Cell-cell communication is essential during the development of multicellular organisms. Specialized cell protrusions called cytonemes have been identified to exchange signals between cells that are vital for tissue development. Cytonemes can carry signalling components between distant cells and thus regulate the activity levels of the corresponding signalling pathways across entire tissues. This review summarizes the key findings on the formation and function of cytonemes in tissue development.

Emergence of form in embryogenesis

The development of form in an embryo is the result of a series of topological and informational symmetry breakings. We introduce the vector-reaction-diffusion-drift (VRDD) system where the limit cycle of spatial dynamics is morphogen concentrations with Dirac delta-type distributions. This is fundamentally different from the Turing reaction-diffusion system, as VRDD generates system-wide broken symmetry. We developed 'fundamental forms' from spherical blastula with a single organizing axis (rotational symmetry), double axis (mirror symmetry) and triple axis (no symmetry operator in three dimensions). We then introduced dynamics for cell differentiation, where genetic regulatory states are modelled as a finite-state machine (FSM). The state switching of an FSM is based on local morphogen concentrations as epigenetic information that changes dynamically. We grow complicated forms hierarchically in spatial subdomains using the FSM model coupled with the VRDD system. Using our integrated simulation model with four layers (topological, physical, chemical and regulatory), we generated life-like forms such as hydra. Genotype-phenotype mapping was investigated with continuous and jump mutations. Our study can have applications in morphogenetic engineering, soft robotics and biomimetic design.

Cell-cell adhesion interface: orthogonal and parallel forces from contraction, protrusion, and retraction

The epithelial lateral membrane plays a central role in the integration of intercellular signals and, by doing so, is a principal determinant in the emerging properties of epithelial tissues. Mechanical force, when applied to the lateral cell-cell interface, can modulate the strength of adhesion and influence intercellular dynamics. Yet the relationship between mechanical force and epithelial cell behavior is complex and not completely understood. This commentary aims to provide an investigative look at the usage of cellular forces at the epithelial cell-cell adhesion interface.

Modeling the Notch Response

NOTCH signaling regulates developmental processes in all tissues and all organisms across the animal kingdom. It is often involved in coordinating the differentiation of neighboring cells into different cell types. As our knowledge on the structural, molecular and cellular properties of the NOTCH pathway expands, there is a greater need for quantitative methodologies to get a better understanding of the processes controlled by NOTCH signaling. In recent years, theoretical and computational approaches to NOTCH signaling and NOTCH mediated patterning are gaining popularity. Mathematical models of NOTCH mediated patterning provide insight into complex and counterintuitive behaviors and can help generate predictions that can guide experiments. In this chapter, we review the recent advances in modeling NOTCH mediated patterning processes. We discuss new modeling approaches to lateral inhibition patterning that take into account cis-interactions between NOTCH receptors and ligands, signaling through long cellular protrusions, cell division processes, and coupling to external signals. We also describe models of somitogenesis, where NOTCH signaling is used for synchronizing cellular oscillations. We then discuss modeling approaches that consider the effect of cell morphology on NOTCH signaling and NOTCH mediated patterning. Finally, we consider models of boundary formation and how they are influenced by the combinatorial action of multiple ligands. Together, these topics cover the main advances in the field of modeling the NOTCH response.

Perspectives on Intra- and Intercellular Trafficking of Hedgehog for Tissue Patterning

Intercellular communication is a fundamental process for correct tissue development. The mechanism of this process involves, among other things, the production and secretion of signaling molecules by specialized cell types and the capability of these signals to reach the target cells in order to trigger specific responses. Hedgehog (Hh) is one of the best-studied signaling pathways because of its importance during morphogenesis in many organisms. The Hh protein acts as a morphogen, activating its targets at a distance in a concentration-dependent manner. Post-translational modifications of Hh lead to a molecule covalently bond to two lipid moieties. These lipid modifications confer Hh high affinity to lipidic membranes, and intense studies have been carried out to explain its release into the extracellular matrix. This work reviews Hh molecule maturation, the intracellular recycling needed for its secretion and the proposed carriers to explain Hh transportation to the receiving cells. Special focus is placed on the role of specialized filopodia, also named cytonemes, in morphogen transport and gradient formation.

A new mechanism for spatial pattern formation via lateral and protrusion-mediated lateral signalling

Tissue organization and patterning are critical during development when genetically identical cells take on different fates. Lateral signalling plays an important role in this process by helping to generate self-organized spatial patterns in an otherwise uniform collection of cells. Recent data suggest that lateral signalling can be mediated both by junctional contacts between neighbouring cells and via cellular protrusions that allow non-neighbouring cells to interact with one another at a distance. However, it remains unclear precisely how signalling mediated by these distinct types of cell-cell contact can physically contribute to the generation of complex patterns without the assistance of diffusible morphogens or pre-patterns. To explore this question, in this work we develop a model of lateral signalling based on a single receptor/ligand pair as exemplified by Notch and Delta. We show that allowing the signalling kinetics to differ at junctional versus protrusion-mediated contacts, an assumption inspired by recent data which show that the cleavage of Notch in several systems requires both Delta binding and the application of mechanical force, permits individual cells to act to promote both lateral activation and lateral inhibition. Strikingly, under this model, in which Delta can sequester Notch, a variety of patterns resembling those typical of reaction-diffusion systems is observed, together with more unusual patterns that arise when we consider changes in signalling kinetics, and in the length and distribution of protrusions. Importantly, these patterns are self-organizing-so that local interactions drive tissue-scale patterning. Together, these data show that protrusions can, in principle, generate different types of patterns in addition to contributing to long-range signalling and to pattern refinement.