Morphogenesis as a macroscopic self-organizing process

Biological thermodynamics: Ervin Bauer and the unification of life sciences and physics

Biological systems operate toward the maximization of their self-maintenance and adaptability. This is achieved through the establishment of robust self-maintaining configurations acting as attractors resistant to external and internal perturbations. Ervin Bauer (1890-1938) was the first who formulated this essential thermodynamic constraint in the operation of biological systems, which he defined as the stable non-equilibrium state. The latter appears as the basic attractor relative to which biological organization is established. The stable non-equilibrium state represents a generalized cell energy status corresponding to efficient spatiotemporal organization of the fluxes of matter and energy and constantly reproducing the conditions of self-maintenance of metabolism and controlling the rates of major metabolic fluxes that follow thermodynamically and kinetically defined computational principles. This state is realized in the autopoietic structures having closed loops of causation based on the operation of biological codes. The principle of thermodynamic buffering determines the conditions for optimization of the fluxes of load and consumption in metabolism establishing the conditions of metabolic stable non-equilibrium. In developing and evolving biological systems, the principle of stable non-equilibrium is transformed into the principle of increasing external work, which is grounded in the hyper-restorative non-equilibrium dynamics. Bauer's concept of the stable non-equilibrium state puts thermodynamics into the frames of the internal biological causality governing self-maintenance and development of living systems. It can be defined as a relational theory of biological thermodynamics since the standard to which it refers represents the actual biological function rather than the abstract state of thermodynamic equilibrium.

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.

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.

Mechanosensation Mediates Long-Range Spatial Decision-Making in an Aneural Organism

The unicellular protist Physarum polycephalum is an important emerging model for understanding how aneural organisms process information toward adaptive behavior. Here, it is revealed that Physarum can use mechanosensation to reliably make decisions about distant objects in its environment, preferentially growing in the direction of heavier, substrate-deforming, but chemically inert masses. This long-range sensing is abolished by gentle rhythmic mechanical disruption, changing substrate stiffness, or the addition of an inhibitor of mechanosensitive transient receptor potential channels. Additionally, it is demonstrated that Physarum does not respond to the absolute magnitude of strain. Computational modeling reveales that Physarum may perform this calculation by sensing the fraction of its perimeter that is distorted above a threshold substrate strain-a fundamentally novel method of mechanosensation. Using its body as both a distributed sensor array and computational substrate, this aneural organism leverages its unique morphology to make long-range decisions. Together, these data identify a surprising behavioral preference relying on biomechanical features and quantitatively characterize how the Physarum exploits physics to adaptively regulate its growth and shape.

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.

On the problem of biological form

Embryonic development, which inspired the first theories of biological form, was eventually excluded from the conceptual framework of the Modern Synthesis as irrelevant. A major question during the last decades has centred on understanding whether new advances in developmental biology are compatible with the standard view or whether they compel a new theory. Here, I argue that the answer to this question depends on which concept of morphogenesis is held. Morphogenesis can be conceived as (1) a chemically driven or (2) a mechanically driven process. According to the first option, genetic regulatory networks drive morphogenesis. According to the second, morphogenesis results from an invariant tendency of embryonic tissues to restore changes in mechanical stress. While chemically driven morphogenesis allows an extension of the standard view, mechanically driven morphogenesis would deeply transform it. Which of these hypotheses has wider explanatory power is unknown. At present, the problem of biological form remains unsolved.

Endogenous Bioelectrics in Development, Cancer, and Regeneration: Drugs and Bioelectronic Devices as Electroceuticals for Regenerative Medicine

A major frontier in the post-genomic era is the investigation of the control of coordinated growth and three-dimensional form. Dynamic remodeling of complex organs in regulative embryogenesis, regeneration, and cancer reveals that cells and tissues make decisions that implement complex anatomical outcomes. It is now essential to understand not only the genetics that specifies cellular hardware but also the physiological software that implements tissue-level plasticity and robust morphogenesis. Here, we review recent discoveries about the endogenous mechanisms of bioelectrical communication among non-neural cells that enables them to cooperate in vivo. We discuss important advances in bioelectronics, as well as computational and pharmacological tools that are enabling the taming of biophysical controls toward applications in regenerative medicine and synthetic bioengineering.

Time and Life in the Relational Universe: Prolegomena to an Integral Paradigm of Natural Philosophy

Relational ideas for our description of the natural world can be traced to the concept of Anaxagoras on the multiplicity of basic particles, later called “homoiomeroi” by Aristotle, that constitute the Universe and have the same nature as the whole world. Leibniz viewed the Universe as an infinite set of embodied logical essences called monads, which possess inner view, compute their own programs and perform mathematical transformations of their qualities, independently of all other monads. In this paradigm, space appears as a relational order of co-existences and time as a relational order of sequences. The relational paradigm was recognized in physics as a dependence of the spatiotemporal structure and its actualization on the observer. In the foundations of mathematics, the basic logical principles are united with the basic geometrical principles that are generic to the unfolding of internal logic. These principles appear as universal topological structures (“geometric atoms”) shaping the world. The decision-making system performs internal quantum reduction which is described by external observers via the probability function. In biology, individual systems operate as separate relational domains. The wave function superposition is restricted within a single domain and does not expand outside it, which corresponds to the statement of Leibniz that “monads have no windows”.

Local and global dynamics in collective movements of embryonic cells

Several important morphogenetic processes belong to the category of collective cell movements (CCM), by which we mean coordinated rearrangements of many neighboring cells. The causes of the dynamic order established during CCM are still unclear. We performed statistical studies of rates and angular orientations of cell rearrangements in two kinds of embryonic tissues, which we categorized as "committed" (in the sense of being capable of autonomous CCM) as opposed to "naïve" tissues, which are those that require external forces in order to exhibit full scale CCM. In addition, we distinguished two types of cell rearrangements: first, those in which mutual cell-cell shifts characterizing the local dynamics (LD); and, second, those which moved in reference to common external coordinates (global dynamics, GD). We observed that in most cases LD rates deviated from normal distributions and do so by creating excesses of extensively converging and moderately diverging cells. In contrast, GD was characterized by nearly random behavior of slowly moving cells, combined with increased angular focusing of the fast cells trajectories as well as bimodal distribution of cell rates. When committed tissues were opposed by external mechanical forces, then they tended to preserve the inherent CCM patterns. On the other hand, the naïve ones reacted by creating two orthogonal cells flows, one of these coinciding with the force direction. We consider CCM as a self-organizing process based on feedbacks between converging and diverging cell shifts, which is able to focus the trajectories imposed by external forces.

Two ways for interpreting Driesch's law: "Positional information" and morphogenetic fields

The late Lev V. Beloussov wrote a 2005 textbook The Foundations of General Embryology which is available in Russian. In 2003 he prepared an excellent, annotated translation of the part of his manuscript for this book on distinguishing positional information models from morphogenetic field models of embryogenesis, which is reproduced here verbatim. He concluded: "…the PI [positional information] concept has no predictive value, and cannot be thus regarded as a scientific theory".

On symmetries, resonances and photonic crystals in morphogenesis

Biological symmetries, theories of the morphogenetic field, resonant interactions and the role of photons in morphogenetic processes represented the main fields of interest of Lev Beloussov and his followers. This review article includes some results of our study on the important role of resonances and photonic crystals in genetic informatics. Mathematical formalisms of differential Riemannian geometry and tensor analysis are used for modeling inherited curved surfaces in biomorphology and for understanding conformal bio-symmetries connected with the networks of curvature lines of surfaces. Notions of a morpho-resonance field as one of variants of morphogenetic fields are discussed. The connection of the golden section with the Fibonacci matrix of growth used in morphogenetic models of phyllotaxis is shown. Photonic crystals are considered as important participants of organisation of molecular-genetic informatics.

A general framework dedicated to computational morphogenesis Part I - Constitutive equations

In order to understand living organisms, considerable experimental efforts and resources have been devoted to correlate genes and their expressions with cell, tissue, organ and whole organisms' phenotypes. This data driven approach to knowledge discovery has led to many breakthrough in our understanding of healthy and diseased states, and is paving the way to improve the diagnosis and treatment of diseases. Complementary to this data-driven approach, computational models of biological systems based on first principles have been developed in order to deepen our understanding of the multi-scale dynamics that drives normal and pathological biological functions. In this paper we describe the biological, physical and mathematical concepts that led to the design of a Computational Morphogenesis (CM) platform baptized Generic Modeling and Simulating Platform (GMSP). Its role is to generate realistic 3D multi-scale biological tissues from virtual stem cells and the intended target applications include in virtuo studies of normal and abnormal tissue (re)generation as well as the development of complex diseases such as carcinogenesis. At all space-scales of interest, biological agents interact with each other via biochemical, bioelectrical, and mechanical fields that operate in concert during embryogenesis, growth and adult life. The spatio-temporal dependencies of these fields can be modeled by physics-based constitutive equations that we propose to examine in relation to the landmark biological events that occur during embryogenesis.

Re-membering the body: applications of computational neuroscience to the top-down control of regeneration of limbs and other complex organs

A major goal of regenerative medicine and bioengineering is the regeneration of complex organs, such as limbs, and the capability to create artificial constructs (so-called biobots) with defined morphologies and robust self-repair capabilities. Developmental biology presents remarkable examples of systems that self-assemble and regenerate complex structures toward their correct shape despite significant perturbations. A fundamental challenge is to translate progress in molecular genetics into control of large-scale organismal anatomy, and the field is still searching for an appropriate theoretical paradigm for facilitating control of pattern homeostasis. However, computational neuroscience provides many examples in which cell networks - brains - store memories (e.g., of geometric configurations, rules, and patterns) and coordinate their activity towards proximal and distant goals. In this Perspective, we propose that programming large-scale morphogenesis requires exploiting the information processing by which cellular structures work toward specific shapes. In non-neural cells, as in the brain, bioelectric signaling implements information processing, decision-making, and memory in regulating pattern and its remodeling. Thus, approaches used in computational neuroscience to understand goal-seeking neural systems offer a toolbox of techniques to model and control regenerative pattern formation. Here, we review recent data on developmental bioelectricity as a regulator of patterning, and propose that target morphology could be encoded within tissues as a kind of memory, using the same molecular mechanisms and algorithms so successfully exploited by the brain. We highlight the next steps of an unconventional research program, which may allow top-down control of growth and form for numerous applications in regenerative medicine and synthetic bioengineering.

Targeting mitochondria for cancer treatment - two types of mitochondrial dysfunction

Two basic types of cancers were identified – those with the mitochondrial dysfunction in cancer cells (the Warburg effect) or in fibroblasts supplying energy rich metabolites to a cancer cell with functional mitochondria (the reverse Warburg effect). Inner membrane potential of the functional and dysfunctional mitochondria measured by fluorescent dyes (e.g. by Rhodamine 123) displays low and high values (apparent potential), respectively, which is in contrast to the level of oxidative metabolism. Mitochondrial dysfunction (full function) results in reduced (high) oxidative metabolism, low (high) real membrane potential, a simple layer (two layers) of transported protons around mitochondria, and high (low) damping of microtubule electric polar vibrations. Crucial modifications are caused by ordered water layer (exclusion zone). For the high oxidative metabolism one proton layer is at the mitochondrial membrane and the other at the outer rim of the ordered water layer. High and low damping of electric polar vibrations results in decreased and increased electromagnetic activity in cancer cells with the normal and the reverse Warburg effect, respectively. Due to nonlinear properties the electromagnetic frequency spectra of cancer cells and transformed fibroblasts are shifted in directions corresponding to their power deviations resulting in disturbances of interactions and escape from tissue control. The cancer cells and fibroblasts of the reverse Warburg effect tumors display frequency shifts in mutually opposite directions resulting in early generalization. High oxidative metabolism conditions high aggressiveness. Mitochondrial dysfunction, a gate to malignancy along the cancer transformation pathway, forms a narrow neck which could be convenient for cancer treatment.

Bending and twisting the embryonic heart: a computational model for c-looping based on realistic geometry

The morphogenetic process of cardiac looping transforms the straight heart tube into a curved tube that resembles the shape of the future four-chambered heart. Although great progress has been made in identifying the molecular and genetic factors involved in looping, the physical mechanisms that drive this process have remained poorly understood. Recent work, however, has shed new light on this complicated problem. After briefly reviewing the current state of knowledge, we propose a relatively comprehensive hypothesis for the mechanics of the first phase of looping, termed c-looping, as the straight heart tube deforms into a c-shaped tube. According to this hypothesis, differential hypertrophic growth in the myocardium supplies the main forces that cause the heart tube to bend ventrally, while regional growth and cytoskeletal contraction in the omphalomesenteric veins (primitive atria) and compressive loads exerted by the splanchnopleuric membrane drive rightward torsion. A computational model based on realistic embryonic heart geometry is used to test the physical plausibility of this hypothesis. The behavior of the model is in reasonable agreement with available experimental data from control and perturbed embryos, offering support for our hypothesis. The results also suggest, however, that several other mechanisms contribute secondarily to normal looping, and we speculate that these mechanisms play backup roles when looping is perturbed. Finally, some outstanding questions are discussed for future study.

Generic oscillation patterns of the developing systems and their role in the origin and evolution of ontogeny

The role of generic oscillation patterns in embryonic development on a macroscopic scale is discussed in terms of active shell model. These self-oscillations include periodic changes in both the mean shape of the shell surface and its spatial variance. They lead to origination of a universal oscillatory contour in the form of a non-linear dependence of the average rudiment's curvature upon the curvature variance. The alternation of high and low levels of the variance makes it possible to pursue the developmental dynamics irrespective to the spatiotemporal order of development and characters subject to selection and genetic control. Spatially homogeneous and heterogeneous states can alternate in both time and space being the parametric modifications of the same self-organization dynamics, which is a precondition of transforming of the oscillations into spatial differences between the parts of the embryo and then into successive stages of their formation. This process can be explained as a "retrograde developmental evolution", which means the late evolutionary appearance of the earlier developmental stages. The developing system progressively retreats from the initial self-organization threshold replacing the self-oscillatory dynamics by a linear succession of stages in which the earlier developmental stages appear in the evolution after the later ones. It follows that ontogeny is neither the cause, nor the effect of phylogeny: the phenotype development can be subject to directional change under the constancy of the phenotype itself and, vice versa, the developmental evolution can generate new phenotypes in the absence of the external environmental trends of their evolution.

A linear-encoding model explains the variability of the target morphology in regeneration

A fundamental assumption of today's molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This 'inverse problem' is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila, hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering.

Epithelial machines of morphogenesis and their potential application in organ assembly and tissue engineering

Sheets of embryonic epithelial cells coordinate their efforts to create diverse tissue structures such as pits, grooves, tubes, and capsules that lead to organ formation. Such cells can use a number of cell behaviors including contractility, proliferation, and directed movement to create these structures. By contrast, tissue engineers and researchers in regenerative medicine seeking to produce organs for repair or replacement therapy can combine cells with synthetic polymeric scaffolds. Tissue engineers try to achieve these goals by shaping scaffold geometry in such a way that cells embedded within these scaffold self-assemble to form a tissue, for instance aligning to synthetic fibers, and assembling native extracellular matrix to form the desired tissue-like structure. Although self-assembly is a dominant process that guides tissue assembly both within the embryo and within artificial tissue constructs, we know little about these critical processes. Here, we compare and contrast strategies of tissue assembly used by embryos to those used by engineers during epithelial morphogenesis and highlight opportunities for future applications of developmental biology in the field of tissue engineering.

Morphogenesis of active shells

We consider the active shell as a single-cell or epithelial sheet surface that, sharing basic properties of stretched elastic shells, is capable of active planar movement owing to recruiting of the new surface elements. As model examples of their morphogenesis, we consider the growth and differentiation of single-cell hairs (trichomes) in plants of the genus Draba, and the epiboly and formation of the dorsoventral polarity in loach. The essential feature of the active shell behavior at both cellular and supracellular levels is regular deviating from the spatially homogeneous form, which is a primary cause of originating of the active mechanical stresses inside the shell in addition to its passive stretching by the intrinsic forces. Analyzing the quantitative morphological data, we derive the equations in which the temporal self-oscillations and spatial differentiation are distinguishable only at the parametric level depending on the proportion of active to passive stresses. In contrast to the ordinary activator-inhibitor systems, the self-oscillation dynamics is principally non-local and, consequently, one-parametric, the shell surface curvature being an analog of the inhibitor, while its spatial variance being an analog of the activator of shaping. Analyzing variability and evolution of the hair cell branching, we argue that the linear ontogeny (succession of the developmental stages) is a secondary evolutionary phenomenon originating from cyclic self-organizing algorithms of the active shell shaping.

Topological singularities and symmetry breaking in development

The review presents a topological interpretation of some morphogenetic events through the use of well-known mathematical concepts and theorems. Spatial organization of the biological fields is analyzable in topological terms. Topological singularities inevitably emerging in biological morphogenesis are retained and transformed during pattern formation. It is the topological language that can provide strict and adequate description of various phenomena in developmental and evolutionary transformations. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. A topological inevitability of some developmental events through the use of classical topological concepts is discussed. This methodology reveals a topological imperative as a certain set of topological rules that constrains and directs embryogenesis. A breaking of spatial symmetry of preexisting pattern plays a critical role in biological morphogenesis in development and evolution.

Morphogenetic origin of natural variation

We studied individual pathways of gastrulation in two related amphibian species making an emphasis on the developmental dynamics of normal variation in the geometry of gastrulation movements. Analyzing the variation dynamics, we show that the linear succession of developmental stages is a secondary phenomenon disguising self-oscillations that lie at the heart of the dorsal blastopore lip morphogenesis. Characteristic features of the equations derived to describe the oscillations are, first, their dependence only on the movement geometry and, second, including of the dynamics of spatial variance directly into the movement equations, making it clear that the reasons for variability of morphogenesis are the same that for morphogenesis itself. The equations describing morphogenetic oscillations are mathematically similar to those describing natural selection in that the system tends to minimize its variance, individual or within-individual one, but the spatially uniform state turns to be unstable. Comparing of the dynamics of natural developmental variation in gastrulation in two frog species shows that, depending on the mechanics and geometry mass cell movements, different types of gastrulation movements have different proportions of the between- to within-individual differences, which strongly influences the choice of characters subject to evolution. Instead of being a source of constraints imposed on externally guided evolutionary trends, morphogenesis becomes a driving force of the adaptively silent, but directional evolution of the developing systems, which seems to be the only possible way of originating of the evolutionary novelties, both in evolution and ontogeny of the biological structures.