D'Arcy W. Thompson's On Growth and Form: A landmark for the mathematical foundations of epigenetics

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.

The reversibility of cellular determination: An evolutive pattern of epigenetic plasticity

Until the middle of the 20th century, embryogenesis patterns were considered as based on a rigid, unidirectional ontogenetic development, whose nuclear programming yields an irreversibility feature for cellular determination. Further empirical pieces of evidence have provided new insights about a certain reversibility to cellular determination, finding new biomolecular mechanisms (nuclear reprogramming, dedifferentiation, transdifferentiation) which have clearly shown that such a reversibility exists, warranting a certain cellular plasticity inside cell cycle; moreover, they seem mainly ruled by epigenetic factors. In this framework, evolution can be viewed as a systemic transformation of the spatiotemporal epigenetic organization, and the maintenance of the stable final adult stage includes a possibility of dedifferentiation at the particular points of ontogenetic development leading to the achievement of the final stage though the alternate sets of epigenetic trajectories. This paper is aimed to briefly outline historically the main aspects which have led to define the mechanisms of cellular plasticity, highlighting the chief empirical facts supporting it and the related still unresolved problematic issues.

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.