A short tutorial on the Janus-faced logic of differentiation waves and differentiation trees and their evolution

Butterfly pupal wing tissue with an eyespot organizer

Butterfly wing eyespots are developmentally determined at the early pupal stage, when prospective eyespot focal cells underneath the pupal cuticle focal spot function as eyespot organizers in the pupal wing tissue. Here, we performed light microscopy and transmission electron microscopy (TEM) to describe cellular structures of pupal wing tissue with an eyespot organizer immediately after pupation using the Blue Pansy butterfly Junonia orithya. The pupal forewing dorsal epidermis was a pseudostratified monolayer of vertically elongated epidermal cells. The apical portion of the cells adhered laterally to one another, but their medial and basal portions were thinner than the apical portion and were tilted to enclose cells at the center, forming a cellular cluster. The cellular cluster at the organizer was relatively large laterally and vertically. The apical portion of the cells and its corresponding cuticle at the organizer were thicker than those in the surroundings. The innermost cuticle layer was being synthesized, indicating high cuticle synthesis and secretion activity of the cells. At the medial and basal portions of the dorsal epidermis, there were many intracellular and extracellular vacuole-like globules, most likely containing extracellular matrix molecules. Some of the basal processes from epidermal cells extended to form protrusions of the basement membrane, which was often attended by hemocytes. These results suggest that the butterfly eyespot organizer is composed of a single or a few cellular clusters that secrete more cuticle than surrounding clusters, supporting the pupal cuticle hypothesis that cuticle formation is critical for eyespot color pattern determination in butterflies.

The indispensable role of time in autonomous development

Advances in single-cell analysis have led to a picture of development largely in agreement with Waddington's eponymous epigenetic landscape, in which a cell's fate is determined by its basin of attraction in a high-dimensional gene-expression space. Yet conceptual gaps remain as to how a single progenitor can simultaneously generate multiple endpoints, and why time should be required of the process at all. We propose a theoretical model based on the Hamiltonian mechanics of n-dimensional rotational motion, which resolves these paradoxes. We derive the result that systems which become different from themselves over time must initially move in a direction not towards their ultimate endpoints, and propose that this process of resolving ambiguity can be quantified (in an information-theoretic sense) by the volume subtended in gene-expression space by the trajectories taken by the system towards its endpoints. We discuss the implications of this theory for the analysis of single-cell gene-expression data in studies of development.

Antibody-Mediated Protein Knockdown Reveals Distal-less Functions for Eyespots and Parafocal Elements in Butterfly Wing Color Pattern Development

One of the important genes for eyespot development in butterfly wings is Distal-less. Its function has been evaluated via several methods, including CRISPR/Cas9 genome editing. However, functional inhibition may be performed at the right time at the right place using a different method. Here, we used a novel protein delivery method for pupal wing tissues in vivo to inactivate a target protein, Distal-less, with a polyclonal anti-Distal-less antibody using the blue pansy butterfly Junonia orithya. We first demonstrated that various antibodies including the anti-Distal-less antibody were delivered to wing epithelial cells in vivo in this species. Treatment with the anti-Distal-less antibody reduced eyespot size, confirming the positive role of Distal-less in eyespot development. The treatment eliminated or deformed a parafocal element, suggesting a positive role of Distal-less in the development of the parafocal element. This result also suggested the integrity of an eyespot and its corresponding parafocal element as the border symmetry system. Taken together, these findings demonstrate that the antibody-mediated protein knockdown method is a useful tool for functional assays of proteins, such as Distal-less, expressed in pupal wing tissues, and that Distal-less functions for eyespots and parafocal elements in butterfly wing color pattern development.

The Molecular Basis of Differentiation Wave Activity in Embryogenesis

As development varies greatly across the tree of life, it may seem difficult to suggest a model that proposes a single mechanism for understanding collective cell behaviors and the coordination of tissue formation. Here we propose a mechanism called differentiation waves, which unify many disparate results involving developmental systems from across the tree of life. We demonstrate how a relatively simple model of differentiation proceeds not from function-related molecular mechanisms, but from so-called differentiation waves. A phenotypic model of differentiation waves is introduced, and its relation to molecular mechanisms is proposed. These waves contribute to a differentiation tree, which is an alternate way of viewing cell lineage and local action of the molecular factors. We construct a model of differentiation wave-related molecular mechanisms (genome, epigenome, and proteome) based on bioinformatic data from the nematode Caenorhabditis elegans. To validate this approach across different modes of development, we evaluate protein expression across different types of development by comparing Caenorhabditis elegans with several model organisms: fruit flies (Drosophila melanogaster), yeast (Saccharomyces cerevisiae), and mouse (Mus musculus). Inspired by gene regulatory networks, two Models of Interactive Contributions (fully-connected MICs and ordered MICs) are used to suggest potential genomic contributions to differentiation wave-related proteins. This, in turn, provides a framework for understanding differentiation and development.

Socket Array Irregularities and Wing Membrane Distortions at the Eyespot Foci of Butterfly Wings Suggest Mechanical Signals for Color Pattern Determination

Eyespot foci on butterfly wings function as organizers of eyespot color patterns during development. Despite their importance, focal structures have not been examined in detail. Here, we microscopically examined scales, sockets, and the wing membrane in the butterfly eyespot foci of both expanded and unexpanded wings using the Blue Pansy butterfly Junonia orithya. Images from a high-resolution light microscope revealed that, although not always, eyespot foci had scales with disordered planar polarity. Scanning electron microscopy (SEM) images after scale removal revealed that the sockets were irregularly positioned and that the wing membrane was physically distorted as if the focal site were mechanically squeezed from the surroundings. Focal areas without eyespots also had socket array irregularities, but less frequently and less severely. Physical damage in the background area induced ectopic patterns with socket array irregularities and wing membrane distortions, similar to natural eyespot foci. These results suggest that either the process of determining an eyespot focus or the function of an eyespot organizer may be associated with wing-wide mechanics that physically disrupt socket cells, scale cells, and the wing membrane, supporting the physical distortion hypothesis of the induction model for color pattern determination in butterfly wings.

Macroevolution, differentiation trees, and the growth of coding systems

An open process of evolution of multicellular organisms is based on the rearrangement and growth of the program of differentiation that underlies biological morphogenesis. The maintenance of the final (adult) stable non-equilibrium state (stasis) of a developmental system determines the direction of the evolutionary process. This state is achieved via the sequence of differentiation events representable as differentiation trees. A special type of morphogenetic code, acting as a metacode governing gene expression, may include electromechanical signals appearing as differentiation waves. The excessive energy due to the incorporation of mitochondria in eukaryotic cells resulted not only in more active metabolism but also in establishing the differentiation code for interconnecting cells and forming tissues, which fueled the evolutionary process. The "invention" of "continuing differentiation" distinguishes multicellular eukaryotes from other organisms. The Janus-faced control, involving both top-down control by differentiation waves and bottom-up control via the mechanical consequences of cell differentiations, underlies the process of morphogenesis and results in the achievement of functional stable final states. Duplications of branches of the differentiation tree may be the basis for continuing differentiation and macroevolution, analogous to gene duplication permitting divergence of genes. Metamorphoses, if they are proven to be fusions of disparate species, may be classified according to the topology of fusions of two differentiation trees. In the process of unfolding of morphogenetic structures, microevolution can be defined as changes of the differentiation tree that preserve topology of the tree, while macroevolution represents any change that alters the topology of the differentiation tree.

Closing the loop on morphogenesis: a mathematical model of morphogenesis by closed-loop reaction-diffusion

Morphogenesis, the establishment and repair of emergent complex anatomy by groups of cells, is a fascinating and biomedically-relevant problem. One of its most fascinating aspects is that a developing embryo can reliably recover from disturbances, such as splitting into twins. While this reliability implies some type of goal-seeking error minimization over a morphogenic field, there are many gaps with respect to detailed, constructive models of such a process. A common way to achieve reliability is negative feedback, which requires characterizing the existing body shape to create an error signal-but measuring properties of a shape may not be simple. We show how cells communicating in a wave-like pattern could analyze properties of the current body shape. We then describe a closed-loop negative-feedback system for creating reaction-diffusion (RD) patterns with high reliability. Specifically, we use a wave to count the number of peaks in a RD pattern, letting us use a negative-feedback controller to create a pattern with N repetitions, where N can be altered over a wide range. Furthermore, the individual repetitions of the RD pattern can be easily stretched or shrunk under genetic control to create, e.g., some morphological features larger than others. This work contributes to the exciting effort of understanding design principles of morphological computation, which can be used to understand evolved developmental mechanisms, manipulate them in regenerative-medicine settings, or engineer novel synthetic morphology constructs with desired robust behavior.

Overcoming the limits of natural computation in biological evolution toward the maximization of system efficiency

The goal-directedness of biological evolution is realized via the anticipatory achievement of the final state of the system that corresponds to the condition of its perfection in self-maintenance and in adaptability. In the course of individual development, a biological system maximizes its power via synergistic effects and becomes able to perform external work most efficiently. In this state, defined as stasis, robust self-maintaining configurations act as attractors resistant to external and internal perturbations. This corresponds to the local energy–time constraints that most efficiently fit the integral optimization of the whole system. In evolution, major evolutionary transitions that establish new states of stasis are achieved via codepoiesis, a process in which the undecided statements of existing coding systems form the basis for the evolutionary unfolding of the system by assigning new values to them. The genetic fixation of this macroevolutionary process leads to new programmes of individual development representing the process of natural computation. The phenomenon of complexification in evolution represents a metasystem transition that results in maximization of a system’s power and in the ability to increase external work performed by the system.

Étienne Geoffroy Saint-Hilaire as a predecessor of the epigenetic concept of evolution

The contribution of Étienne Geoffroy Saint-Hilaire (1772-1844) to evolutionary biology is reviewed in commemoration of his 250th birthday. Geoffroy's views on saltational changes during embryogenesis of animals characterize him as a predecessor of the epigenetic concept of evolution, which is now developing in the frames of the extended evolutionary synthesis or evo-devo. While Lamarck distinguished between the two modes of evolution, one within the same level of organization and the other characterized by the transition to a more complex organization, Geoffroy Saint-Hilaire attempted to explain the second mode by the changes in embryogenesis triggered by environmental influences. In this regard, he placed the phenomenon of complexification in the centre of the evolutionary context. Geoffroy Saint-Hilaire can be considered also as an early predecessor of the cell theory. His ideas about the unique plan of structure for animal species and of the fundamental connections that establish the homology of anatomical parts represent an important contribution to the evolutionary concept.

The drawbridge of nature: Evolutionary complexification as a generation and novel interpretation of coding systems

The phenomenon of evolutionary complexification corresponds to the generation of new coding systems (defined as а codepoiesis by Marcello Barbieri). The whole process of generating novel coding statements that substantiate organizational complexification leads to an expansion of the system that incorporates externality to support newly generated complex structures. During complexifying evolution, the values are assigned to the previously unproven statements via their encoding by using new codes or rearranging the old ones. In this perspective, living systems during evolution continuously realize the proof of Gödel's theorem. In the real physical world, this realization is grounded in the irreversible reduction of the fundamental uncertainty appearing in the self-referential process of internal measurement performed by living systems. It leads to the formation of reflexive loops that establish novel interrelations between the biosystem and the external world and provide a possibility of active anticipatory transformation of externality. We propose a metamathematical framework that can account for the underlying logic of codepoiesis, outline the basic principles of the generation of new coding systems, and describe main codepoietic events in the course of progressive biological evolution. The evolutionary complexification is viewed as a metasystem transition that results in the increase of external work by the system based on the division of labor between its components.