Turing's theory of morphogenesis of 1952 and the subsequent discovery of the crucial role of local self-enhancement and long-range inhibition

Self-Organization of Stem Cell Colonies and of Early Mammalian Embryos: Recent Experiments Shed New Light on the Role of Autonomy vs. External Instructions in Basic Body Plan Development

"Organoids", i.e., complex structures that can develop when pluripotent or multipotent stem cells are maintained in three-dimensional cultures, have become a new area of interest in stem cell research. Hopes have grown that when focussing experimentally on the mechanisms behind this type of in vitro morphogenesis, research aiming at tissue and organ replacements can be boosted. Processes leading to the formation of organoids in vitro are now often addressed as self-organization, a term referring to the formation of complex tissue architecture in groups of cells without depending on specific instruction provided by other cells or tissues. The present article focuses on recent reports using the term self-organization in the context of studies on embryogenesis, specifically addressing pattern formation processes in human blastocysts attaching in vitro, or in colonies of pluripotent stem cells ("gastruloids"). These morphogenetic processes are of particular interest because, during development in vivo, they lead to basic body plan formation and individuation. Since improved methodologies like those employed by the cited authors became available, early embryonic pattern formation/self-organization appears to evolve now as a research topic of its own. This review discusses concepts concerning the involved mechanisms, focussing on autonomy of basic body plan development vs. dependence on external signals, as possibly provided by implantation in the uterus, and it addresses biological differences between an early mammalian embryo, e.g., a morula, and a cluster of pluripotent stem cells. It is concluded that, apart from being of considerable biological interest, the described type of research needs to be contemplated carefully with regard to ethical implications when performed with human cells.

The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles

The single cell-centred approach emphasises ion channels as specific proteins that determine individual properties, disregarding their contribution to multicellular outcomes. We simulate the interplay between genetic and bioelectrical signals in non-excitable cells from the local single-cell level to the long range multicellular ensemble. The single-cell genetic regulation is based on mean-field kinetic equations involving the mRNA and protein concentrations. The transcription rate factor is assumed to depend on the absolute value of the cell potential, which is dictated by the voltage-gated cell ion channels and the intercellular gap junctions. The interplay between genetic and electrical signals may allow translating single-cell states into multicellular states which provide spatio-temporal information. The model results have clear implications for biological processes: (i) bioelectric signals can override slightly different genetic pre-patterns; (ii) ensembles of cells initially at the same potential can undergo an electrical regionalisation because of persistent genetic differences between adjacent spatial regions; and (iii) shifts in the normal cell electrical balance could trigger significant changes in the genetic regulation.

In vitro Reconstitution of a Membrane Switch Mechanism for the Polarity Protein LGL

Cell polarity arises from a combination of interactions between biological molecules, such as activation, inhibition, and positive or negative feedback between specific polarity units. Activation and inhibition often take place in the form of a membrane binding switch. Lethal giant larvae (LGL), a conserved regulator of cell polarity in animals, was suggested to function as such a switch. LGL localizes to both the cytoplasm and, asymmetrically, the membrane. However, the spatial regulation mechanism of LGL membrane localization has remained unclear. For systematic elucidation, we set out to reconstitute a minimal polarity unit using a model membrane, Caenorhabditis elegans LGL (LGL-1), and atypical protein kinase C (aPKC) supposed to activate the membrane switch. We identified a membrane binding sequence (MBS) in LGL-1 by a screen in vivo, reconstituted LGL-1 membrane binding in vitro, and successfully implemented the membrane switch by aPKC phosphorylation activity, detaching LGL from membranes. Upon membrane binding, LGL-1 MBS folds into an alpha-helix in which three regions can be identified: a positively charged patch, a switch area containing the three aPKC phosphorylation sites, and a hydrophobic area probably buried in the membrane. Phosphorylation by aPKC dramatically reduces the binding affinity of the LGL-1 MBS to negatively charged model membranes, inducing its detachment. Specific residues in the MBS are critical for LGL-1 function in C. elegans.

Toward Synthetic Spatial Patterns in Engineered Cell Populations with Chemotaxis

A major force shaping form and patterns in biology is based in the presence of amplification mechanisms able to generate ordered, large-scale spatial structures out of local interactions and random initial conditions. Turing patterns are one of the best known candidates for such ordering dynamics, and their existence has been proven in both chemical and physical systems. Their relevance in biology, although strongly supported by indirect evidence, is still under discussion. Extensive modeling approaches have stemmed from Turing's pioneering ideas, but further confirmation from experimental biology is required. An alternative possibility is to engineer cells so that self-organized patterns emerge from local communication. Here we propose a potential synthetic design based on the interaction between population density and a diffusing signal, including also directed motion in the form of chemotaxis. The feasibility of engineering such a system and its implications for developmental biology are also assessed.

Signaling Delays Preclude Defects in Lateral Inhibition Patterning

Lateral inhibition represents a well-studied example of biology's ability to self-organize multicellular spatial patterns with single-cell precision. Despite established biochemical mechanisms for lateral inhibition (e.g., Delta-Notch), it remains unclear how cell-cell signaling delays inherent to these mechanisms affect patterning outcomes. We investigate a compact model of lateral inhibition highlighting these delays and find, remarkably, that long delays can ensure defect-free patterning. This effect is underscored by an interplay with synchronous oscillations, cis interactions, and signaling strength. Our results suggest that signaling delays, though previously posited as a source of developmental defects, may in fact be a general regulatory knob for tuning developmental robustness.

Positional information and reaction-diffusion: two big ideas in developmental biology combine

One of the most fundamental questions in biology is that of biological pattern: how do the structures and shapes of organisms arise? Undoubtedly, the two most influential ideas in this area are those of Alan Turing's 'reaction-diffusion' and Lewis Wolpert's 'positional information'. Much has been written about these two concepts but some confusion still remains, in particular about the relationship between them. Here, we address this relationship and propose a scheme of three distinct ways in which these two ideas work together to shape biological form.

Villification in the mouse: Bmp signals control intestinal villus patterning

In the intestine, finger-like villi provide abundant surface area for nutrient absorption. During murine villus development, epithelial Hedgehog (Hh) signals promote aggregation of subepithelial mesenchymal clusters that drive villus emergence. Clusters arise first dorsally and proximally and spread over the entire intestine within 24 h, but the mechanism driving this pattern in the murine intestine is unknown. In chick, the driver of cluster pattern is tensile force from developing smooth muscle, which generates deep longitudinal epithelial folds that locally concentrate the Hh signal, promoting localized expression of cluster genes. By contrast, we show that in mouse, muscle-induced epithelial folding does not occur and artificial deformation of the epithelium does not determine the pattern of clusters or villi. In intestinal explants, modulation of Bmp signaling alters the spatial distribution of clusters and changes the pattern of emerging villi. Increasing Bmp signaling abolishes cluster formation, whereas inhibiting Bmp signaling leads to merged clusters. These dynamic changes in cluster pattern are faithfully simulated by a mathematical model of a Turing field in which an inhibitor of Bmp signaling acts as the Turing activator. In vivo, genetic interruption of Bmp signal reception in either epithelium or mesenchyme reveals that Bmp signaling in Hh-responsive mesenchymal cells controls cluster pattern. Thus, unlike in chick, the murine villus patterning system is independent of muscle-induced epithelial deformation. Rather, a complex cocktail of Bmps and Bmp signal modulators secreted from mesenchymal clusters determines the pattern of villi in a manner that mimics the spread of a self-organizing Turing field.

Patterning of the angiosperm female gametophyte through the prism of theoretical paradigms

The FG (female gametophyte) of flowering plants (angiosperms) is a simple highly polar structure composed of only a few cell types. The FG develops from a single cell through mitotic divisions to generate, depending on the species, four to 16 nuclei in a syncytium. These nuclei are then partitioned into three or four distinct cell types. The mechanisms underlying the specification of the nuclei in the FG has been a focus of research over the last decade. Nevertheless, we are far from understanding the patterning mechanisms that govern cell specification. Although some results were previously interpreted in terms of static positional information, several lines of evidence now show that local interactions are important. In the present article, we revisit the available data on developmental mutants and cell fate markers in the light of theoretical frameworks for biological patterning. We argue that a further dissection of the mechanisms may be impeded by the combinatorial and dynamical nature of developmental cues. However, accounting for these properties of developing systems is necessary to disentangle the diversity of the phenotypic manifestations of the underlying molecular interactions.

Forging patterns and making waves from biology to geology: a commentary on Turing (1952) 'The chemical basis of morphogenesis'

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, 'The chemical basis of morphogenesis', on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of 'Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Forging patterns and making waves from biology to geology: a commentary on Turing (1952) 'The chemical basis of morphogenesis'

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, 'The chemical basis of morphogenesis', on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of 'Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

A new mechanochemical model: coupled Ginzburg-Landau and Swift-Hohenberg equations in biological patterns of marine animals

In this work the skin coating of some vertebrate marine animals is modeled considering only dermis, epidermis and basal layers. The biological process takes into account: cellular diffusion of the epidermis, diffusion inhibition and long-range spatial interaction (nonlocal effect on diffusive dispersal) for cells of dermal tissue. The chemical and physical interactions between dermis and epidermis are represented by coupling quadratic terms and nonlinear terms additional. The model presents an interesting property associated with their gradient form: a connection between some physical, chemical and biological systems. The model equations proposed are solved with numerical methods to study the spatially stable emergent configurations. The spatiotemporal dynamic obtained of the numerical solution of these equations, present similarity with biological behaviors that have been found recently in the cellular movement of chromatophores (as contact-dependent depolarization and repulsion movement between melanophores, xanthophores and iridophores). The numerical solution of the model shows a great variety of beautiful patterns that are robust to changes of boundary condition. The resultant patterns are very similar to the pigmentation of some fish.

Symmetry breaking, germ layer specification and axial organisation in aggregates of mouse embryonic stem cells

Mouse embryonic stem cells (mESCs) are clonal populations derived from preimplantation mouse embryos that can be propagated in vitro and, when placed into blastocysts, contribute to all tissues of the embryo and integrate into the normal morphogenetic processes, i.e. they are pluripotent. However, although they can be steered to differentiate in vitro into all cell types of the organism, they cannot organise themselves into structures that resemble embryos. When aggregated into embryoid bodies they develop disorganised masses of different cell types with little spatial coherence. An exception to this rule is the emergence of retinas and anterior cortex-like structures under minimal culture conditions. These structures emerge from the cultures without any axial organisation. Here, we report that small aggregates of mESCs, of about 300 cells, self-organise into polarised structures that exhibit collective behaviours reminiscent of those that cells exhibit in early mouse embryos, including symmetry breaking, axial organisation, germ layer specification and cell behaviour, as well as axis elongation. The responses are signal specific and uncouple processes that in the embryo are tightly associated, such as specification of the anteroposterior axis and anterior neural development, or endoderm specification and axial elongation. We discuss the meaning and implications of these observations and the potential uses of these structures which, because of their behaviour, we suggest to call ‘gastruloids’.

Modelling from the experimental developmental biologists viewpoint

In this review we consider Reaction-Diffusion as the archetype of a model in developmental biology. We consider its history in relation to experimental work since it was first proposed in 1952 by Turing and revived in the 1970s by Meinhardt. We then discuss the most recent examples of experiments that address this model, including the challenges that remain in capturing the physico-chemical manifestation of the model mechanism in a real developmental system. Finally we discuss the model's current status and use in the experimental community.

Testing Turing's theory of morphogenesis in chemical cells

Alan Turing, in "The Chemical Basis of Morphogenesis" [Turing AM (1952) Philos Trans R Soc Lond 237(641):37-72], described how, in circular arrays of identical biological cells, diffusion can interact with chemical reactions to generate up to six periodic spatiotemporal chemical structures. Turing proposed that one of these structures, a stationary pattern with a chemically determined wavelength, is responsible for differentiation. We quantitatively test Turing's ideas in a cellular chemical system consisting of an emulsion of aqueous droplets containing the Belousov-Zhabotinsky oscillatory chemical reactants, dispersed in oil, and demonstrate that reaction-diffusion processes lead to chemical differentiation, which drives physical morphogenesis in chemical cells. We observe five of the six structures predicted by Turing. In 2D hexagonal arrays, a seventh structure emerges, incompatible with Turing's original model, which we explain by modifying the theory to include heterogeneity.

Cellular polarization: interaction between extrinsic bounded noises and the wave-pinning mechanism

Cell polarization (cued or uncued) is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the onset of cell polarity might arise by means of the well-known phenomenon of wave-pinning [Gamba et al., Proc. Natl. Acad. Sci. USA 102, 16927 (2005)]. A particularly simple and elegant deterministic model of cell polarization based on the wave-pinning mechanism has been proposed by Edelstein-Keshet and coworkers [Biophys. J. 94, 3684 (2008)]. This model consists of a small biomolecular network where an active membrane-bound factor interconverts into its inactive form that freely diffuses in the cell cytosol. However, biomolecular networks do communicate with other networks as well as with the external world. Thus, their dynamics must be considered as perturbed by extrinsic noises. These noises may have both a spatial and a temporal correlation, and in any case they must be bounded to preserve the biological meaningfulness of the perturbed parameters. Here we numerically show that the inclusion of external spatiotemporal bounded parametric perturbations in the above wave-pinning-based model of cellular polarization may sometimes destroy the polarized state. The polarization loss depends on both the extent of temporal and spatial correlations and on the kind of noise employed. For example, an increase of the spatial correlation of the noise induces an increase of the probability of cell polarization. However, if the noise is spatially homogeneous then the polarization is lost in the majority of cases. These phenomena are independent of the type of noise. Conversely, an increase of the temporal autocorrelation of the noise induces an effect that depends on the model of noise.

An adaptive neuromorphic model of ocular dominance map using floating gate 'synapse'

A novel analogue CMOS design of a cortical cell, that computes weighted sum of inputs, is presented. The cell's feedback regime exploits the adaptation dynamics of floating gate pFET 'synapse' to perform competitive learning amongst input weights as time-staggered winner take all. A learning rate parameter regulates adaptation time and a bias enforces resource limitation by restricting the number of input branches and winners in a competition. When learning ends, the cell's response favours one input pattern over others to exhibit feature selectivity. Embedded in a 2-D RC grid, these feature selective cells are capable of performing a symmetry breaking pattern formation, observed in some reaction-diffusion models of cortical feature map formation, e.g. ocular dominance. Close similarity with biological networks in terms of adaptability and long term memory indicates that the cell's design is ideally suited for analogue VLSI implementation of Self-Organizing Feature Map (SOFM) models of cortical feature maps.