The vertebrate limb: An evolving complex of self-organizing systems

Form, function, mind: What doesn't compute (and what might)

The applicability of computational and dynamical systems models to organisms is scrutinized, using examples from developmental biology and cognition. Developmental morphogenesis is dependent on the inherent material properties of developing animal (metazoan) tissues, a non-computational modality, but cell differentiation, which utilizes chromatin-based revisable memory banks and program-like function-calling, via the developmental gene co-expression system unique to the metazoans, has a quasi-computational basis. Multi-attractor dynamical models are argued to be misapplied to global properties of development, and it is suggested that along with computationalism, classic forms of dynamicism are similarly unsuitable to accounting for cognitive phenomena. Proposals are made for treating brains and other nervous tissues as novel forms of excitable matter with inherent properties which enable the intensification of cell-based basal cognition capabilities present throughout the tree of life. Finally, some connections are drawn between the viewpoint described here and active inference models of cognition, such as the Free Energy Principle.

Perspectives on Principles of Cellular Behavior from the Biophysics of Protists

Cells are the fundamental unit of biological organization. Although it may be easy to think of them as little more than the simple building blocks of complex organisms such as animals, single cells are capable of behaviors of remarkable apparent sophistication. This is abundantly clear when considering the diversity of form and function among the microbial eukaryotes, the protists. How might we navigate this diversity in the search for general principles of cellular behavior? Here, we review cases in which the intensive study of protists from the perspective of cellular biophysics has driven insight into broad biological questions of morphogenesis, navigation and motility, and decision making. We argue that applying such approaches to questions of evolutionary cell biology presents rich, emerging opportunities. Integrating and expanding biophysical studies across protist diversity, exploiting the unique characteristics of each organism, will enrich our understanding of general underlying principles.

A two-galectin network establishes mesenchymal condensation phenotype in limb development

Previous work showed that Gal-1A and Gal-8, two proteins belonging to the galactoside-binding galectin family, are the earliest determinants of the patterning of the skeletal elements of embryonic chicken limbs, and further, that their experimentally determined interactions in the embryonic limb bud can be interpreted via a reaction-diffusion-adhesion (2GL: two galectin plus ligands) model. Here, we use an ordinary differential equation-based approach to analyze the intrinsic switching modality of the 2GL network and characterize the network behavior independent of the diffusive and adhesive arms of the patterning mechanism. We identify two states: where the concentrations of both the galectins are respectively, negligible, and very high. This bistable switch-like system arises via a saddle-node bifurcation from a monostable state. For the case of mass-action production terms, we provide an explicit Lyapunov function for the system, which shows that it has no periodic solutions. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time, without any intermediate states. We test these predictions in experiments performed with high density cultures of chick limb mesenchymal cells and observe that cells inside precartilage protocondensations express Gal-1A at a much higher rate than those outside, for which it was negligible. The Gal-1A and -8-based patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell states with different developmental (chondrogenic vs. non-chondrogenic) fates. When incorporated into an adhesion and diffusion-enabled framework this system can generate a spatially patterned limb skeleton.

Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations

This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of “order from fluctuations” is a key component of Turing’s theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between “inelegant” examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and “elegant” ones expressible in equations like Turing’s: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing’s ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.

Spatial waves and temporal oscillations in vertebrate limb development

The mesenchymal tissue of the developing vertebrate limb bud is an excitable medium that sustains both spatial and temporal periodic phenomena. The first of these is the outcome of general Turing-type reaction-diffusion dynamics that generate spatial standing waves of cell condensations. These condensations are transformed into the nodules and rods of the cartilaginous, and eventually (in most species) the bony, endoskeleton. In the second, temporal periodicity results from intracellular regulatory dynamics that generate oscillations in the expression of one or more gene whose products modulate the spatial patterning system. Here we review experimental evidence from the chicken embryo, interpreted by a set of mathematical and computational models, that the spatial wave-forming system is based on two glycan-binding proteins, galectin-1A and galectin-8 in interaction with each other and the cells that produce them, and that the temporal oscillation occurs in the expression of the transcriptional coregulator Hes1. The multicellular synchronization of the Hes1 oscillation across the limb bud serves to coordinate the biochemical states of the mesenchymal cells globally, thereby refining and sharpening the spatial pattern. Significantly, the wave-forming reaction-diffusion-based mechanism itself, unlike most Turing-type systems, does not contain an oscillatory core, and may have evolved to this condition as it came to incorporate the cell-matrix adhesion module that enabled its pattern-forming capability.

Differential cellular responses to adhesive interactions with galectin-8- and fibronectin-coated substrates

The mechanisms underlying the cellular response to extracellular matrices (ECMs) that consist of multiple adhesive ligands are still poorly understood. Here, we address this topic by monitoring specific cellular responses to two different extracellular adhesion molecules - the main integrin ligand fibronectin and galectin-8, a lectin that binds β-galactoside residues  - as well as to mixtures of the two proteins. Compared with cell spreading on fibronectin, cell spreading on galectin-8-coated substrates resulted in increased projected cell area, more-pronounced extension of filopodia and, yet, the inability to form focal adhesions and stress fibers. These differences can be partially reversed by experimental manipulations of small G-proteins of the Rho family and their downstream targets, such as formins, the Arp2/3 complex and Rho kinase. We also show that the physical adhesion of cells to galectin-8 was stronger than adhesion to fibronectin. Notably, galectin-8 and fibronectin differently regulate cell spreading and focal adhesion formation, yet act synergistically to upregulate the number and length of filopodia. The physiological significance of the coherent cellular response to a molecularly complex matrix is discussed. This article has an associated First Person interview with the first author of the paper.

Making and shaping endochondral and intramembranous bones

Skeletal elements have a diverse range of shapes and sizes specialized to their various roles including protecting internal organs, locomotion, feeding, hearing, and vocalization. The precise positioning, size, and shape of skeletal elements is therefore critical for their function. During embryonic development, bone forms by endochondral or intramembranous ossification and can arise from the paraxial and lateral plate mesoderm or neural crest. This review describes inductive mechanisms to position and pattern bones within the developing embryo, compares and contrasts the intrinsic vs extrinsic mechanisms of endochondral and intramembranous skeletal development, and details known cellular processes that precisely determine skeletal shape and size. Key cellular mechanisms are employed at distinct stages of ossification, many of which occur in response to mechanical cues (eg, joint formation) or preempting future load‐bearing requirements. Rapid shape changes occur during cellular condensation and template establishment. Specialized cellular behaviors, such as chondrocyte hypertrophy in endochondral bone and secondary cartilage on intramembranous bones, also dramatically change template shape. Once ossification is complete, bone shape undergoes functional adaptation through (re)modeling. We also highlight how alterations in these cellular processes contribute to evolutionary change and how differences in the embryonic origin of bones can influence postnatal bone repair.

Compares and contrasts Endochondral and intramembranous bone development

Reviews embryonic origins of different bones

Describes the cellular and molecular mechanisms of positioning skeletal elements.

Describes mechanisms of skeletal growth with a focus on the generation of skeletal shape

Multiscale modeling of vertebrate limb development

We review the current state of mathematical modeling of cartilage pattern formation in vertebrate limbs. We place emphasis on several reaction-diffusion type models that have been proposed in the last few years. These models are grounded in more detailed knowledge of the relevant regulatory processes than previous ones but generally refer to different molecular aspects of these processes. Considering these models in light of comparative phylogenomics permits framing of hypotheses on the evolutionary order of appearance of the respective mechanisms and their roles in the fin-to-limb transition. This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models Developmental Biology > Developmental Processes in Health and Disease Analytical and Computational Methods > Analytical Methods.

Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models

The phenomenon of chondrogenic pattern formation in the vertebrate limb is one of the best studied examples of organogenesis. Many different models, mathematical as well as conceptual, have been proposed for it in the last fifty years or so. In this review, we give a brief overview of the fundamental biological background, then describe in detail several models which aim to describe qualitatively and quantitatively the corresponding biological phenomena. We concentrate on several new models that have been proposed in recent years, taking into account recent experimental progress. The major mathematical tools in these approaches are ordinary and partial differential equations. Moreover, we discuss models with non-local flux terms used to account for cell-cell adhesion forces and a structured population model with diffusion. We also include a detailed list of gene products and potential morphogens which have been identified to play a role in the process of limb formation and its growth.

Embryo-Based Large Fragment Knock-in in Mammals: Why, How and What's Next

Endonuclease-mediated genome editing technologies, most notably CRISPR/Cas9, have revolutionized animal genetics by allowing for precise genome editing directly through embryo manipulations. As endonuclease-mediated model generation became commonplace, large fragment knock-in remained one of the most challenging types of genetic modification. Due to their unique value in biological and biomedical research, however, a diverse range of technological innovations have been developed to achieve efficient large fragment knock-in in mammalian animal model generation, with a particular focus on mice. Here, we first discuss some examples that illustrate the importance of large fragment knock-in animal models and then detail a subset of the recent technological advancements that have allowed for efficient large fragment knock-in. Finally, we envision the future development of even larger fragment knock-ins performed in even larger animal models, the next step in expanding the potential of large fragment knock-in in animal models.

Inherency of Form and Function in Animal Development and Evolution

I discuss recent work on the origins of morphology and cell-type diversification in Metazoa – collectively the animals – and propose a scenario for how these two properties became integrated, with the help of a third set of processes, cellular pattern formation, into the developmental programs seen in present-day metazoans. Inherent propensities to generate familiar forms and cell types, in essence a parts kit for the animals, are exhibited by present-day organisms and were likely more prominent in primitive ones. The structural motifs of animal bodies and organs, e.g., multilayered, hollow, elongated and segmented tissues, internal and external appendages, branched tubes, and modular endoskeletons, can be accounted for by the properties of mesoscale masses of metazoan cells. These material properties, in turn, resulted from the recruitment of “generic” physical forces and mechanisms – adhesion, contraction, polarity, chemical oscillation, diffusion – by toolkit molecules that were partly conserved from unicellular holozoan antecedents and partly novel, distributed in the different metazoan phyla in a fashion correlated with morphological complexity. The specialized functions of the terminally differentiated cell types in animals, e.g., contraction, excitability, barrier function, detoxification, excretion, were already present in ancestral unicellular organisms. These functions were implemented in metazoan differentiation in some cases using the same transcription factors as in single-celled ancestors, although controlled by regulatory mechanisms that were hybrids between earlier-evolved processes and regulatory innovations, such as enhancers. Cellular pattern formation, mediated by released morphogens interacting with biochemically responsive and excitable tissues, drew on inherent self-organizing processes in proto-metazoans to transform clusters of holozoan cells into animal embryos and organs.