Moving forward moving backward: directional sorting of chemotactic cells due to size and adhesion differences

Engineering tools for quantifying and manipulating forces in epithelia

The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.

Unraveling the effect of intra- and intercellular processes on acetaminophen-induced liver injury

In high dosages, acetaminophen (APAP) can cause severe liver damage, but susceptibility to liver failure varies across individuals and is influenced by factors such as health status. Because APAP-induced liver injury and recovery is regulated by an intricate system of intra- and extracellular molecular signaling, we here aim to quantify the importance of specific modules in determining the outcome after an APAP insult and of potential targets for therapies that mitigate adversity. For this purpose, we integrated hepatocellular acetaminophen metabolism, DNA damage response induction and cell fate into a multiscale mechanistic liver lobule model which involves various cell types, such as hepatocytes, residential Kupffer cells and macrophages. Our model simulations show that zonal differences in metabolism and detoxification efficiency are essential determinants of necrotic damage. Moreover, the extent of senescence, which is regulated by intracellular processes and triggered by extracellular signaling, influences the potential to recover. In silico therapies at early and late time points after APAP insult indicated that prevention of necrotic damage is most beneficial for recovery, whereas interference with regulation of senescence promotes regeneration in a less pronounced way.

Second-order agent-based models of emergent behaviour of Dictyostelium discoideum and their inspiration for swarm robotics

By studying and modelling the behaviour of Dictyostelium discoideum, we aim at deriving mechanisms useful for engineering collective artificial intelligence systems. This paper discusses a selection of agent-based models reproducing second-order behaviour of Dictyostelium discoideum, occurring during the migration phase; their corresponding biological illustrations; and how we used them as an inspiration for transposing this behaviour into swarms of Kilobots. For the models, we focus on: (1) the transition phase from first- to second-order emergent behaviour; (2) slugs’ uniform distribution around a light source; and (3) the relationship between slugs’ speed and length occurring during the migration phase of the life cycle of D. discoideum. Results show the impact of the length of the slug on its speed and the effect of ammonia on the distribution of slugs. Our computational results show similar behaviour to our biological experiments, using Ax2(ka) strain. For swarm robotics experiments, we focus on the transition phase, slugs’ chaining, merging and moving away from each other.

Alternating regimes of motion in a model with cell-cell interactions

Cellular movement is a complex dynamic process, resulting from the interaction of multiple elements at the intra- and extracellular levels. This epiphenomenon presents a variety of behaviors, which can include normal and anomalous diffusion or collective migration. In some cases, cells can get neighborhood information through chemical or mechanical cues. A unified understanding about how such information can influence the dynamics of cell movement is still lacking. In order to improve our comprehension of cell migration we have considered a cellular Potts model where cells move actively in the direction of a driving field. The intensity of this driving field is constant, while its orientation can evolve according to two alternative dynamics based on the Ornstein-Uhlenbeck process. In one case, the next orientation of the driving field depends on the previous direction of the field. In the other case, the direction update considers the mean orientation performed by the cell in previous steps. Thus, the latter update rule mimics the ability of cells to perceive the environment, avoiding obstacles and thus increasing the cellular displacement. Different cell densities are considered to reveal the effect of cell-cell interactions. Our results indicate that both dynamics introduce temporal and spatial correlations in cell velocity in a friction-coefficient and cell-density-dependent manner. Furthermore, we observe alternating regimes in the mean-square displacement, with normal and anomalous diffusion. The crossovers between diffusive and directed motion regimes are strongly affected by both the driving field dynamics and cell-cell interactions. In this sense, when cell polarization update grants information about the previous cellular displacement, the duration of the diffusive regime decreases, particularly in high-density cultures.

From energy to cellular forces in the Cellular Potts Model: An algorithmic approach

Single and collective cell dynamics, cell shape changes, and cell migration can be conveniently represented by the Cellular Potts Model, a computational platform based on minimization of a Hamiltonian. Using the fact that a force field is easily derived from a scalar energy (F = −∇H), we develop a simple algorithm to associate effective forces with cell shapes in the CPM. We predict the traction forces exerted by single cells of various shapes and sizes on a 2D substrate. While CPM forces are specified directly from the Hamiltonian on the cell perimeter, we approximate the force field inside the cell domain using interpolation, and refine the results with smoothing. Predicted forces compare favorably with experimentally measured cellular traction forces. We show that a CPM model with internal signaling (such as Rho-GTPase-related contractility) can be associated with retraction-protrusion forces that accompany cell shape changes and migration. We adapt the computations to multicellular systems, showing, for example, the forces that a pair of swirling cells exert on one another, demonstrating that our algorithm works equally well for interacting cells. Finally, we show forces exerted by cells on one another in classic cell-sorting experiments.

Cells exert forces on their surroundings and on one another. In simulations of cell shape using the Cellular Potts Model (CPM), the dynamics of deforming cell shapes is traditionally represented by an energy-minimization method. We use this CPM energy, the Hamiltonian, to derive and visualize the corresponding forces exerted by the cells. We use the fact that force is the negative gradient of energy to assign forces to the CPM cell edges, and then extend the results to approximate interior forces by interpolation. We show that this method works for single as well as multiple interacting model cells, both static and motile. Finally, we show favorable comparison between predicted forces and real forces measured experimentally.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?

D'Arcy Thompson's 'on Growth and form': From soap bubbles to tissue self-organization

Tissues are thought to behave like fluids with a given surface tension. Differences in tissue surface tension (TST) have been proposed to trigger cell sorting and tissue envelopment. D'Arcy Thompson in his seminal book 'On Growth and Form' has introduced this concept of differential TST as a key physical mechanism dictating tissue formation and organization within the developing organism. Over the past century, many studies have picked up the concept of differential TST and analyzed the role and cell biological basis of TST in development, underlining the importance and influence of this concept in developmental biology.

The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics

BACKGROUND

The biophysical characteristics of cells determine their shape in isolation and when packed within tissues. Cells can form regular or irregular epithelial structures, round up and form clusters, or deform and attach to substrates. The acquired shape of cells and tissues is a consequence of (i) internal cytoskeletal processes, such as actin polymerisation and cortical myosin contraction, (ii) adhesion molecules within the cell membrane that interact with substrates and neighbouring cells, and (iii) processes that regulate cell volume. Although these processes seem relatively simple, when combined they unleash a rich variety of cellular behaviour that is not readily understandable outside a theoretical framework.

METHODS

We perform a mathematical analysis of a commonly used class of model formalisms that describe cell surface mechanics using an energy-based approach. Predictions are then confirmed through comparison with the computational outcomes of a Vertex model and 2D and 3D simulations of the Cellular Potts model.

RESULTS

The analytical study reveals the complete possible spectrum of single cell behaviour and tissue packing in both 2D and 3D, by taking the typical core elements of cell surface mechanics into account: adhesion, cortical tension and volume conservation. We show that from an energy-based description, forces and tensions can be derived, as well as the prediction of cell behaviour and tissue packing, providing an intuitive and biologically relevant mapping between modelling parameters and experiments.

CONCLUSIONS

The quantitative cellular behaviours and biological insights agree between the analytical study and the diverse computational model formalisms, including the Cellular Potts model. This illustrates the generality of energy-based approaches for cell surface mechanics and highlights how meaningful and quantitative comparisons between models can be established. Moreover, the mathematical analysis reveals direct links between known biophysical properties and specific parameter settings within the Cellular Potts model.

Computational modeling reveals that a combination of chemotaxis and differential adhesion leads to robust cell sorting during tissue patterning

Robust tissue patterning is crucial to many processes during development. The "French Flag" model of patterning, whereby naïve cells in a gradient of diffusible morphogen signal adopt different fates due to exposure to different amounts of morphogen concentration, has been the most widely proposed model for tissue patterning. However, recently, using time-lapse experiments, cell sorting has been found to be an alternative model for tissue patterning in the zebrafish neural tube. But it remains unclear what the sorting mechanism is. In this article, we used computational modeling to show that two mechanisms, chemotaxis and differential adhesion, are needed for robust cell sorting. We assessed the performance of each of the two mechanisms by quantifying the fraction of correct sorting, the fraction of stable clusters formed after correct sorting, the time needed to achieve correct sorting, and the size variations of the cells having different fates. We found that chemotaxis and differential adhesion confer different advantages to the sorting process. Chemotaxis leads to high fraction of correct sorting as individual cells will either migrate towards or away from the source depending on its cell type. However after the cells have sorted correctly, there is no interaction among cells of the same type to stabilize the sorted boundaries, leading to cell clusters that are unstable. On the other hand, differential adhesion results in low fraction of correct clusters that are more stable. In the absence of morphogen gradient noise, a combination of both chemotaxis and differential adhesion yields cell sorting that is both accurate and robust. However, in the presence of gradient noise, the simple combination of chemotaxis and differential adhesion is insufficient for cell sorting; instead, chemotaxis coupled with delayed differential adhesion is required to yield optimal sorting.

Skin stem cell hypotheses and long term clone survival--explored using agent-based modelling

Epithelial renewal in skin is achieved by the constant turnover and differentiation of keratinocytes. Three popular hypotheses have been proposed to explain basal keratinocyte regeneration and epidermal homeostasis: 1) asymmetric division (stem-transit amplifying cell); 2) populational asymmetry (progenitor cell with stochastic fate); and 3) populational asymmetry with stem cells. In this study, we investigated lineage dynamics using these hypotheses with a 3D agent-based model of the epidermis. The model simulated the growth and maintenance of the epidermis over three years. The offspring of each proliferative cell was traced. While all lineages were preserved in asymmetric division, the vast majority were lost when assuming populational asymmetry. The third hypothesis provided the most reliable mechanism for self-renewal by preserving genetic heterogeneity in quiescent stem cells, and also inherent mechanisms for skin ageing and the accumulation of genetic mutation.

Chemotactic migration of T cells towards dendritic cells promotes the detection of rare antigens

In many immunological processes chemoattraction is thought to play a role in guiding cells to their sites of action. However, based on in vivo two-photon microscopy experiments in the absence of cognate antigen, T cell migration in lymph nodes (LNs) has been roughly described as a random walk. Although it has been shown that dendritic cells (DCs) carrying cognate antigen in some circumstances attract T cells chemotactically, it is currently still unclear whether chemoattraction of T cells towards DCs helps or hampers scanning. Chemoattraction towards DCs could on the one hand help T cells to rapidly find DCs. On the other hand, it could be deleterious if DCs become shielded by a multitude of attracted yet non-specific T cells. Results from a recent simulation study suggested that the deleterious effect dominates. We re-addressed the question whether T cell chemoattraction towards DCs is expected to promote or hamper the detection of rare antigens using the Cellular Potts Model, a formalism that allows for dynamic, flexible cellular shapes and cell migration. Our simulations show that chemoattraction of T cells enhances the DC scanning efficiency, leading to an increased probability that rare antigen-specific T cells find DCs carrying cognate antigen. Desensitization of T cells after contact with a DC further improves the scanning efficiency, yielding an almost threefold enhancement compared to random migration. Moreover, the chemotaxis-driven migration still roughly appears as a random walk, hence fine-tuned analysis of cell tracks will be required to detect chemotaxis within microscopy data.

Multi-scale modeling in morphogenesis: a critical analysis of the cellular Potts model

Cellular Potts models (CPMs) are used as a modeling framework to elucidate mechanisms of biological development. They allow a spatial resolution below the cellular scale and are applied particularly when problems are studied where multiple spatial and temporal scales are involved. Despite the increasing usage of CPMs in theoretical biology, this model class has received little attention from mathematical theory. To narrow this gap, the CPMs are subjected to a theoretical study here. It is asked to which extent the updating rules establish an appropriate dynamical model of intercellular interactions and what the principal behavior at different time scales characterizes. It is shown that the longtime behavior of a CPM is degenerate in the sense that the cells consecutively die out, independent of the specific interdependence structure that characterizes the model. While CPMs are naturally defined on finite, spatially bounded lattices, possible extensions to spatially unbounded systems are explored to assess to which extent spatio-temporal limit procedures can be applied to describe the emergent behavior at the tissue scale. To elucidate the mechanistic structure of CPMs, the model class is integrated into a general multiscale framework. It is shown that the central role of the surface fluctuations, which subsume several cellular and intercellular factors, entails substantial limitations for a CPM's exploitation both as a mechanistic and as a phenomenological model.

Gastrulation: making and shaping germ layers

Gastrulation is a fundamental phase of animal embryogenesis during which germ layers are specified, rearranged, and shaped into a body plan with organ rudiments. Gastrulation involves four evolutionarily conserved morphogenetic movements, each of which results in a specific morphologic transformation. During emboly, mesodermal and endodermal cells become internalized beneath the ectoderm. Epibolic movements spread and thin germ layers. Convergence movements narrow germ layers dorsoventrally, while concurrent extension movements elongate them anteroposteriorly. Each gastrulation movement can be achieved by single or multiple motile cell behaviors, including cell shape changes, directed migration, planar and radial intercalations, and cell divisions. Recent studies delineate cyclical and ratchet-like behaviors of the actomyosin cytoskeleton as a common mechanism underlying various gastrulation cell behaviors. Gastrulation movements are guided by differential cell adhesion, chemotaxis, chemokinesis, and planar polarity. Coordination of gastrulation movements with embryonic polarity involves regulation by anteroposterior and dorsoventral patterning systems of planar polarity signaling, expression of chemokines, and cell adhesion molecules.

Study on multicellular systems using a phase field model

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell. The dynamics of each cell is based on the criteria for minimizing the surface area and retaining a certain volume. The effects of cell adhesion and excluded volume are also taken into account. The proposed model can be used to find the position of the membrane and/or the cortex of each cell without the need to adopt extra variables. This model is suitable for numerical simulations of a system having a large number of cells. The two-dimensional results of cell division, cell adhesion, rearrangement of a cell cluster, chemotaxis, and cell sorting as well as the three-dimensional results of cell clusters on the substrate are presented.

Multiobjective optimization based-approach for discovering novel cancer therapies

Solid tumors must recruit new blood vessels for growth and maintenance. Discovering drugs that block tumor-induced development of new blood vessels (angiogenesis) is an important approach in cancer treatment. The complexity of angiogenesis presents both challenges and opportunities for cancer therapies. Intuitive approaches, such as blocking VegF activity, have yielded important therapies. But there maybe opportunities to alter nonintuitive targets either alone or in combination. This paper describes the development of a high-fidelity simulation of angiogenesis and uses this as the basis for a parallel search-based approach for the discovery of novel potential cancer treatments that inhibit blood vessel growth. Discovering new therapies is viewed as a multiobjective combinatorial optimization over two competing objectives: minimizing the estimated cost of practically developing the intervention while minimizing the simulated oxygen provided to the tumor by angiogenesis. Results show the effectiveness of the search process by finding interventions that are currently in use, and more interestingly, discovering potential new approaches that are nonintuitive yet effective.

Cortical forces in cell shape changes and tissue morphogenesis

Cortical forces drive a variety of cell shape changes and cell movements during tissue morphogenesis. While the molecular components underlying these forces have been largely identified, how they assemble and spatially and temporally organize at cell surfaces to promote cell shape changes in developing tissues are open questions. We present here different key aspects of cortical forces: their physical nature, some rules governing their emergence, and how their deployment at cell surfaces drives important morphogenetic movements in epithelia. We review a wide range of literature combining genetic/molecular, biophysical and modeling approaches, which explore essential features of cortical force generation and transmission in tissues.

Computational model of cell positioning: directed and collective migration in the intestinal crypt epithelium

The epithelium of the intestinal crypt is a dynamic tissue undergoing constant regeneration through cell growth, cell division, cell differentiation and apoptosis. How the epithelial cells maintain correct positioning and how they migrate in a directed and collective fashion are still not well understood. In this paper, we developed a computational model to elucidate these processes. We show that differential adhesion between epithelial cells, caused by the differential activation of EphB receptors and ephrinB ligands along the crypt axis, is necessary to regulate cell positioning. Differential cell adhesion has been proposed previously to guide cell movement and cause cell sorting in biological tissues. The proliferative cells and the differentiated post-mitotic cells do not intermingle as long as differential adhesion is maintained. We also show that, without differential adhesion, Paneth cells are randomly distributed throughout the intestinal crypt. In addition, our model suggests that, with differential adhesion, cells migrate more rapidly as they approach the top of the intestinal crypt. Finally, by calculating the spatial correlation function of the cell velocities, we observe that differential adhesion results in the differentiated epithelial cells moving in a coordinated manner, where correlated velocities are maintained at large distances, suggesting that differential adhesion regulates coordinated migration of cells in tissues.

Forming patterns in development without morphogen gradients: scattered differentiation and sorting out

Few mechanisms provide alternatives to morphogen gradients for producing spatial patterns of cells in development. One possibility is based on the sorting out of cells that initially differentiate in a salt and pepper mixture and then physically move to create coherent tissues. Here, we describe the evidence suggesting this is the major mode of patterning in Dictyostelium. In addition, we discuss whether convergent evolution could have produced a conceptually similar mechanism in other organisms.

Image analysis of time-lapse movies--a precision control guided approach to correct motion artefacts

In long-term time-lapse studies of cell migration, it is often important to distinguish active movement of individual cells from global tissue motion caused, for instance, by morphogenetic changes, or due to artefacts. We have developed a method to define and correct global movements. This is realized by the sequential morphing of image sequences to the initial image based on the position of immobile reference objects. Technically, the approach is implemented in ImageJ, using the plugin UnwarpJ. We describe an efficient way to select parameter settings such as to optimize image correction. To this end, we implemented a strict statistical control that allows to quantify image registration quality. We document this approach using a time-lapse sequence of migrating interneurons in slice cultures of the developing cerebellum.

A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems

A three-dimensional mathematical model is used to determine the effects of adhesion and cell signalling on cell movements during the aggregation and slug stages of Dictyostelium discoideum (Dd) and to visualize cell sorting. The building blocks of the model are individual deformable ellipsoidal cells, where movement depends on internal parameter state (cell size and stiffness) and on external cues from the neighboring cells, extracellular matrix, and chemical signals. Cell movement and deformation are calculated from equations of motion using the total force acting on each cell, ensuring that forces are balanced. The simulations show that the sorting patterns of prestalk and prespore cells, emerging during the slug stage, depend critically on the type of cell adhesion and not just on chemotactic differences between cells. This occurs because cell size and stiffness can prevent the otherwise faster cells from passing the slower cells. The patterns are distinctively different when the prestalk cells are more or less adhesive than the prespore cells. These simulations suggest that sorting is not solely due to differential chemotaxis, and that differences in both adhesion strength and type between different cell types play a very significant role, both in Dictyostelium and other systems.

Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment

The CompuCell3D modeling environment provides a convenient platform for biofilm simulations using the Glazier-Graner-Hogeweg (GGH) model, a cell-oriented framework designed to simulate growth and pattern formation due to biological cells' behaviors. We show how to develop such a simulation, based on the hybrid (continuum-discrete) model of Picioreanu, van Loosdrecht, and Heijnen (PLH), simulate the growth of a single-species bacterial biofilm, and study the roles of cell-cell and cell-field interactions in determining biofilm morphology. In our simulations, which generalize the PLH model by treating cells as spatially extended, deformable bodies, differential adhesion between cells, and their competition for a substrate (nutrient), suffice to produce a fingering instability that generates the finger shapes of biofilms. Our results agree with most features of the PLH model, although our inclusion of cell adhesion, which is difficult to implement using other modeling approaches, results in slightly different patterns. Our simulations thus provide the groundwork for simulations of medically and industrially important multispecies biofilms.

Cell and biomolecular mechanics in silico

Recent developments in computational cell and biomolecular mechanics have provided valuable insights into the mechanical properties of cells, subcellular components and biomolecules, while simultaneously complementing new experimental techniques used for deciphering the structure-function paradigm in living cells. These computational approaches have direct implications in understanding the state of human health and the progress of disease and can therefore aid immensely in the diagnosis and treatment of diseases. We provide an overview of the computational approaches that are currently used in understanding various aspects of cell and bimolecular mechanics. Our emphasis is on state-of-the-art techniques and the progress made in addressing key challenges in biomechanics.

Cell adhesion and cortex contractility determine cell patterning in the Drosophila retina

Because of the resemblance of many epithelial tissues to densely packed soap bubbles, it has been suggested that surface minimization, which drives soap bubble packing, could be governing cell packing as well. We test this by modeling the shape of the cells in a Drosophila retina ommatidium. We use the observed configurations and shapes in wild-type flies, as well as in flies with different numbers of cells per ommatidia, and mutants with cells where E- or N-cadherin is either deleted or misexpressed. We find that surface minimization is insufficient to model the experimentally observed shapes and packing of the cells based on their cadherin expression. We then consider a model in which adhesion leads to a surface increase, balanced by cell cortex contraction. Using the experimentally observed distributions of E- and N-cadherin, we simulate the packing and cell shapes in the wild-type eye. Furthermore, by changing only the corresponding parameters, this model can describe the mutants with different numbers of cells or changes in cadherin expression.

Differential adhesion in morphogenesis: a modern view

The spreading of one embryonic tissue over another, the sorting out of their cells when intermixed and the formation of intertissue boundaries respected by the motile border cells all have counterparts in the behavior of immiscible liquids. The 'differential adhesion hypothesis' (DAH) explains these liquid-like tissue behaviors as consequences of the generation of tissue surface and interfacial tensions arising from the adhesion energies between motile cells. The experimental verification of the DAH, the recent computational models simulating adhesion-mediated morphogenesis, and the evidence concerning the role of differential adhesion in a number of morphodynamic events, including teleost epiboly, the specification of boundaries between rhombomeres in the developing vertebrate hindbrain, epithelial-mesenchymal transitions in embryos, and malignant invasion are reviewed here.

Patterns of mesenchymal condensation in a multiscale, discrete stochastic model

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.

The development of an organism from embryo to adult includes processes of pattern formation that involve the interactions over space and time of independent cells to form multicellular structures. Computational models permit exploration of possible alternative mechanisms that reproduce biological patterns and thereby provide hypotheses for empirical testing. In this article, we describe a biologically motivated discrete stochastic model that shows that the patterns of spots and stripes of tightly packed cells observed in cultures derived from the embryonic vertebrate limb can occur by a mechanism that uses only cell–cell signaling via diffusible molecules (morphogens) and cell substratum adhesion (haptotaxis). Moreover, similar-looking patterns can arise both from stable stationary dynamics and unstable transient dynamics of the same underlying core molecular–genetic mechanism. Simulations also show that spot and stripe patterns (which also correspond to the nodules and bars of the developing limb skeleton in vivo) are close in parameter space and can be generated in multiple ways with single-parameter variations. An important implication is that some developmental processes do not require a strict progression from one stable dynamic regime to another, but can occur by a succession of transient dynamic regimes tuned (e.g., by natural selection) to achieve a particular morphological outcome.