Self-organization in and on biological spheres

Three biological settings involving self-organization performed by the Turing-Child field inside a sphere and on its surface are considered. In the first setting the interior of a sphere made up of cells communicating via gap junctions is considered. It is suggested that the Turing-Child self-organization is the cause of radial polarization, the first differentiation of an early mammalian embryo. In the second setting, the Turing example of gastrulation of a hollow cellular sphere is considered. It is shown that Child's experimental patterns are predicted and explained by the Turing-Child theory. The third setting is the interior of a biological cell, and it is suggested that it is the self-organization of the Turing-Child field that causes the formation of the mitotic spindle.     

The Turing-Child energy field as a driver of early mammalian development

The equivalence of the early mammalian cells, of importance in assisted reproductive technologies (ART), is considered. It is suggested that this controversial topic can be settled by finding whether the cells are distinguished by the Turing-Child (TC) field, as expressed for example by patterns of mitochondrial activity. The division of the pronuclear embryo is driven by a symmetrical bipolar TC pattern whose experimental shape and chemical nature is predicted by TC theory. This bipolar pattern drives the subsequent cell divisions too, and according to present experimental results all cells are equivalent until compaction since they are not distinguished by the TC field in normal development. Interphase cells exhibit homogeneous mitochondrial activity, or perinuclear, or perinuclear and cortical activity, and these patterns too and the rotational symmetry observed are predicted by TC theory. The first differentiation, into an inner mass cell and the trophectoderm, as well as the formation of cell polarity in the trophectoderm are considered. It is suggested that these two events are driven by a peripheral spherical shell of high energy metabolism in the morula; such a shell is predicted by TC theory in a compacted multicellular sphere whose cells are connected by gap junctions. The experimental patterns of mitochondrial activity in unfertilized oocytes exhibit rotational symmetry or polarity. The shape and the chemical nature of these patterns also are predicted and explained by TC theory in a sphere. The change in the spatial pattern of mitochondrial activity with development is attributed to a change in the spatial pattern of mitochondrial activity and not to physical translocation of mitochondria. The experimental finding that these spatial patterns of mitochondrial activity are observed only in live and not in dead biological material is explained by the TC pattern being biology's unique and universal dissipative structure that requires ongoing specific biochemical reactions and energy dissipation.     

Symmetry breaking and convergent extension in early chordate development

The initiation of axis, polarity, cell differentiation, and gastrulation in the very early chordate development is due to the breaking of radial symmetry. It is believed that this occurs by an external signal. We suggest instead spontaneous symmetry breaking through the agency of the Turing-Child field. Increased size or decreased diffusivity, both brought about by mitotic activity, cause the spontaneous loss of stability of the homogeneous state and the evolution of the metabolic pattern during development. The polar metabolic pattern is the cause of polar gene expression, polar morphogenesis (gastrulation), and polar mitotic activity. The Turing-Child theory explains not only the spontaneous formation of the invagination in gastrulation but also the coherent cell movement observed in convergence and extension during gastrulation and neurulation. The theory is demonstrated with respect to experimental observations on the early development of fish, amphibian, and the chick. The theory can explain a multitude of experimental details. For example, it explains the splayed polar progression of reduction in the fish blastoderm. Reduction starts on that side of the blastoderm margin, which will initiate invagination several hours later. It progresses toward the blastoderm center and somewhat laterally from this future "dorsal lip". This is precisely as predicted by a Turing-Child system in a circle. And for a fish like zebrafish with a blastoderm that is slightly oval, reduction is observed to progress along the long axis of the ellipse, which is what Turing-Child theory predicts. In general the shape and the chemical nature of the experimental patterns are the same as predicted by the Turing couple (cAMP, ATP). Embryological polarity and convergent extension are based on polar eigenfunction and saddle-shaped eigenfunction, respectively.     

Morphological diversity of Pandorina morum (Mull.) Vory (Volvocaceae) colonies

Morphological variability of polyhedral colonies of green algae (Volvocaceae) were studied using some elements of combinative theory of polyhedron and the theory of diophantine equations. These colonies are considered as results of self-organization according to topological regularities of sphere dissection by convex polygons. It was shown that in three-dimensional Euclidean space for each colony of Pandorina morum (Müll.) Bory only three different forms are possible. One of them has no plane of symmetry and, thus, has two enantiomorphous varieties. It is suggested that frequency spectrum of forms can be used as potential indicator of environment pollution.     

Maternal-effect genes as the recording genes of Turing-Child patterns: sequential compartmentalization in Drosophila

The early embryo is often a two-dimensional surface. The fate map is the subdivision of this surface into regions which give rise to parts of the phenotype. It is shown for Drosophila that the fate map is generated by the spontaneous and sequential formation of Turing-Child (TC) eigenfunction patterns. These patterns are recorded by the maternal-effect genes. The addition of the nodal lines of the TC patterns yields the correct number, positions, sequences and symmetries of regional boundaries. A simplest nontrivial 'homeotic transformation' is suggested and explained. A single mutation converts a region in one end of the fate map to a mirror-symmetric image of a nonadjacent region in the other end of the fate map, and this is attributed to the geometry of the TC patterns. This geometry also determines the initial shape of the zygotic gene expression. The vision of William Bateson that biological form is shaped like Chladni's patterns in acoustics and music is justified. A similar sequence of TC patterns occurs in the normal development of all organisms, and it is suggested that artificial intervention which completes the full sequence of TC patterns can be useful in the context of regenerative medicine and this is illustrated with the sea urchin.     

Induction and the Turing-Child field in development

The central problem in biological development is the understanding of epigenesis. The dominant theory of development in the last 80 years that also purports to explain epigenesis is induction theory. It suggests that development is driven by sequential inductions where each "induction" (in one sense of the word induction) is effected by the action of an inducing part of the embryo on a responding part of the embryo. The theory stems from Spemann and Mangold (W.Roux' Arch.f.Entw.d.Organis.u.mikrosk.Anat.100 (1924) 599) who transplanted a tissue from the dorsal blastopore lip of Triturus into the ventral ectoderm of another gastrula and thus initiated and "induced" (in another sense of the word induction) gastrulation and embryogenesis in the ventral side of the host that became a double embryo (siamese twins). We explain this induction, i.e. the formation of the double embryo, according to the Child theory and the Turing-Gierer-Meinhardt theory when it is also assumed that cAMP and ATP are the Turing activator and inhibitor, respectively. Spemann and Mangold (W.Roux' Arch.f.Entw.d.Organis.u.mikrosk.Anat.100 (1924) 599) also suggested that the ingressing mesoderm induces the overlying ectoderm to form the neural plate and neural tube. This 'neural induction', the 'primary embryonic induction', became the cornerstone of induction theory, i.e. of the sequential induction concept referred to above. But we argue that the metabolic gradients that precede and accompany neurulation, as obtained by Child, also for Triturus, arise through a Turing self-organization if it is assumed that cAMP and ATP are the Turing morphogens, and these gradients are the cause and primary event of neurulation. Thus there is no need to invoke the 'neural induction'. It is argued that fundamental events such as gastrulation and also organ formation are caused by the Turing-Child field and not by sequential induction. Similar principles, such as bud formation caused by a radial metabolic pattern that transforms to a longitudinal pattern, govern the formation, for example, of the mouth and the gut. The formation and localization of bottle cells is explained according to the Child-Turing field and modern biochemistry. The chemical metabolic pre-pattern precedes, and causes, morphogenesis and differentiation as envisaged by Turing. The Spemann and Mangold (W.Roux' Arch.f.Entw.d.Organis.u.mikrosk.Anat.100 (1924) 599) transplantation experiment when performed on a sea urchin duplicates not only the phenotype but also the metabolic (reduction) pattern. These experimental results, by Horstadius, predicted by Child, follow from the Turing-Gierer-Meinhardt theory if it is assumed that cAMP and ATP are the Turing morphogens. If the transplantation is performed not onto the whole sea urchin but onto only a part of it, that manifests only a part of the metabolic pattern, then from the part a phenotypic whole underlain by a normal and a whole metabolic pattern can be rescued. These experimental results of Horstadius follow from Turing theory if cAMP and ATP are the Turing morphogens. Understanding how to transform a part into a whole can be valuable in regenerative medicine. Unspecific induction of a secondary amphibian embryo is similar to the induction of posterior structures at the anterior pole of an insect, and the "double abdomen" (and Kalthoff's experimental results) of the midge Smittia resulting from UV irradiation of the anterior pole, can be explained by Meinhardt theory of unspecific induction if ATP is the Turing morphogen. When not working on regeneration, Child investigated intact living organisms and his observation method was not disruptive to normal development, whereas workers in induction theory work with pieces and in general disrupt normal development. We conclude that the Turing-Child field causes all development and explains epigenesis. Sequential induction does not explain epigenesis and does not exist in normal development. But induction in the sense of a transplantation leading to double embryo or rescuing a whole phenotype from a part is of interest.     

Polarity and form regulation in development and reconstitution

In the literature, it is often assumed, for example with respect to Hydra, that several Turing systems coexist and it is also assumed that maintaining the polar profile, even when the system increases in size, is important for the polarity of the final phenotype. It is shown here that in reality there is only one Turing system, Child's system. To obtain a complete polar individual or organ, whether in reconstitution or development, it is essential that the complete succession of metabolic patterns occurs. Child's concepts of physiological dominance, subordination and isolation are interpreted in the light of Turing theory and in particular the Turing wavelength. It is emphasised, particularly by pointing to Child's metabolic patterns in coelenterates, both in development and in reconstitution, that it is the elongation that drives the succession polar metabolic pattern-->bipolar metabolic pattern, and this corresponds to the prediction of Turing theory supporting the thesis that Child's metabolic pattern is a Turing pattern. It is shown that if we assume that ATP is the Turing inhibitor then the many results of Child about the reduction of the scale of organisation with the decrease in the intensity of the energy metabolism correspond to the reduction of the Turing wavelength. The interplay between the Turing wavelength and the length of the form explains the conditions of reconstitution under which partial forms, wholes and form regulation are obtained. It is suggested that higher metabolism is responsible for both larger size and larger Turing wavelength thus securing form regulation. The results could be of importance in modern 'regenerative biology'. Heteromorphosis, i.e. animals with two heads (or two tails), one at each end, is explained by a bipolar Turing-Child metabolic pattern replacing a polar metabolic pattern. This can be brought about by chemical or by genetic means and indeed the prediction for Drosophila that the transition, wild type-->Bicaudal D, occurs because a polar Turing pattern is replaced by bipolar Turing pattern is confirmed, again if we accept that Child's metabolic pattern is the underlying Turing pattern. Child's experiments on Drosophila, including the requirement of critical length for metabolic polarity, are explained by Turing theory. Phenocopies and phenotypes are explained by the Turing-Child theory. It is shown that both Child's results about metabolic patterns and modern results for Hydra about gap junctions, 'endogeneous inhibitor' and gene expression, are correlated and explained by (cAMP, ATP) Turing theory. It is argued that the double-gradient hypothesis is incorrect in its original formulation and that it is Child's conception of succeeding metabolic patterns that is the correct one and that it corresponds to the prediction of the Turing theory.     

Self-organization in biological systems

Biological systems are considered that are capable of dynamic self-organization, i.e., spontaneous emergence of spatio-temporal order with the formation of various spatio-temporal patterns. A cell is involved in the organization of ontogenesis of all stages. Embryonic cells exhibit coordinated social behavior and generate ordered morphological patterns displaying variability and equifinality of development. Physical and topological patterns are essential for biological systems as an imperative that restricts and directs biological morphogenesis. Biological self-organization is directed and fixed by natural selection during which selection of the most sustainable, flexible, modular systems capable of adaptive self-organization occurs.     

Historical and conceptual background of self-organization by reactive processes

Order, form, pattern and organization are properties central to much living matter. The physicochemical processes by which an initially homogeneous solution of reacting chemicals or biochemicals might self-organize is hence a question of fundamental biological importance. In most cases, solutions of reacting chemicals in a test-tube do not self-organize. Because of this, for many years, it was not thought possible that reactive processes could result in self-organization. However, progressively over the last hundred years, it has been shown that this is not always the case, and under certain conditions, the combination of reaction with molecular diffusion can lead to macroscopic self-organization. In 'complex' systems comprised of populations of strongly coupled elements, new 'emergent' properties, such as self-organization, arise by way of the dynamics of the system. Self-organizing reaction-diffusion systems form a specific type of complex system. Here, I will give a personal overview of the conceptual and historical background to this approach with an emphasis on biological self-organization.     

Effects of prey refuges on a predator-prey model with a class of functional responses: The role of refuges

In this paper, the effects of refuges used by prey on a predator-prey interaction with a class of functional responses are studied by using the analytical approach. The refuges are considered as two types: a constant proportion of prey and a fixed number of prey using refuges. We will evaluate the effects with regard to the local stability of the interior equilibrium point, the values of the equilibrium density and the long-term dynamics of the interacting populations. The results show that the effects of refuges used by prey increase the equilibrium density of prey population while decrease that of predators. It is also proved that the effects of refuges can stabilize the interior equilibrium point of the considered model, and destabilize it under a very restricted set of conditions which is disagreement with previous results in this field.     

Some permeability properties of isolated rat liver cell mitochondria

The rates of penetration of various solutes into isolated rat liver mitochondria have been studied. Sodium, potassium, and sucrose were observed to enter the mitochondria until an equilibrium concentration was reached. The diffusion of these solutes, after the first few minutes, followed the predicted diffusion curve for solutes entering a particle with a rate-limiting membrane and instantaneous mixing in the interior. Reasons for deviations from the predicted equation during the first few minutes of diffusion are suggested. The data show that at pH 7.4 sodium and potassium enter more rapidly than sucrose. I¹³¹-labelled albumin was found to enter very slowly, if at all. Increasing the pH from 7.4 reduced the rate at which sodium ion penetrated the mitochondria. The rate of diffusion of sucrose into mitochondria was considerably slower than diffusion of sucrose into a sphere of water of the same size. Sodium ion was not found to be concentrated in vitro against an external concentration gradient as has been reported by other investigators. It is concluded that the rate of diffusion of solutes between the external medium and the interior of mitochondria is probably restricted and controlled by a mitochondrial membrane exhibiting passive permeability characteristics.     

Systems biology and the origins of life? Part I. Are biochemical networks possible ancestors of living systems? Reproduction,identity and sensitivity to signals of biochemical networks

The set of these two theoretical papers offers an alternative to the hypothesis of a primordial RNA-world. The basic idea of these papers is to consider that the first prebiotic systems could have been networks of catalysed reactions encapsulated by a membrane. In order to test this hypothesis it was attempted to list the main obligatory features of living systems and see whether encapsulated biochemical networks could possibly display these features. The traits of living systems are the following: the ability they have to reproduce; the fact they possess an identity; the fact that biological events should be considered in the context of a history; the fact that living systems are able to evolve by selection of alterations of their structure and self-organization. The aim of these two papers is precisely to show that encapsulated biochemical networks can possess these properties and can be considered good candidates for the first prebiotic systems. In the present paper it is shown that if the proteinoids are not very specific catalysts and if some of the reactions of the network are autocatalytic whereas others are not, the resulting system does not reach a steady-state and tends to duplicate. In the same line, these biochemical networks possess an identity, viz. an information, defined from the probability of occurrence of these nodes. Moreover interaction of two ligands can increase, or decrease, this information. In the first case, the system is defined as emergent, in the second case it is considered integrated. Another property of living systems is that their behaviour is defined in the context of a time-arrow. For instance, they are able to sense whether the intensity of a signal is reached after an increase, or a decrease. This property can be mimicked by a simple physico-chemical system made up of the diffusion of a ligand followed by its chemical transformation catalysed by a proteinoid displaying inhibition by excess substrate. Under these conditions the system reacts differently depending on whether the same ligand concentration is reached after an increase or a decrease.     

Interaction between two conducting spheres in weakly ionized collisional plasma

Charging of two conducting spheres in a weakly ionized collisional plasma flow is considered. The spheres are arranged along the flow, and the plasma is assumed to consist of two ion species with the charges equal in magnitude but opposite in sign. The problem is analyzed with allowance for the external electric field, charging of the spheres due to the sedimentation of plasma ions on them, the fields of the sphere charges, the space charge field, and the processes of recombination and molecular diffusion. The interaction between the spheres and plasma is studied by numerically solving a time-dependent problem in a bispherical coordinate system by the finite difference method. The steady-state values of the sphere charges and the distributions of the space charge and ion densities in the ambient plasma are found as functions of the plasma parameters and the distance between the spheres. The electrostatic forces acting on the spheres are determined, and the effects of the external field, the space charge fields, and the fields of the sphere charges are comparatively analyzed. It is shown that, for the considered plasma parameters, the main electrostatic effect in the interaction between two spheres is their mutual approach in the external field due to the difference in their charges (one sphere catches up with the other). Due to the friction force with the neutral gas, this mutual approach is much slower than all other processes in the system. For widely spaced spheres, the results coincide with the solution obtained previously for a solitary sphere.     

A model of myoglobin self-organization

The self-organization of helical regions of myoglobin into a compact tertiary structure is considered on the basis of the hypothesis on the step-wise mechanism of self-organization of protein molecules. It is assumed that the self-organization begins with the formation of “ centers of crystallization ” and proceeds with the growth of one such center or by a sequential collapse of two or more grown centers.Different pathways of self-organization of myoglobin are considered; the most favourable structures corresponding to the greatest number of dehydrated bulky hydroptiobic groups and to all the strongly hydrophilic groups exposed to water are selected at every stage of the given pathway and the others are neglected. One of the two most favourable structures obtained in such a way coincides in rough resolution with the native tertiary structure of protein.     

Application of theoretical group methods in the modeling of complex systems

It has been shown that theoretical group methods can be applied in studies of complex physical and biological systems in which the phenomenon of self-organization takes place. The problem of calculating the parameters of climatic sensitivity with allowance for the cyclone-anticyclone structure of the atmosphere optically dense in the infrared region is considered as an example.     

“Our standpoint different from common...” (Scientific heritage of Alexander Gurwitsch)

The work of prominent Russian biologist Alexander Gavrilovich Gurwitsch (1874–1954) on the theory of organism development are reviewed. Alexander Gurwitsch introduced the concept of embryonic (morphogenetic, biological, and cellular) field and proposed several revisions of it from 1912 to 1944. Although neither of them can be considered as a final theory of development, his the persistent search for the invariant law that allows the shape (spatial structure) to be proposed for each next developmental stage from the previous shape is of imperishable methodological interest. Alexander Gurwitsch anticipated many ideas of the future theory of self-organization. His theoretical constructions are explicit and experiment-oriented but absolutely not esoteric. They represent a highly important and original contribution to theoretical biology and are an essential step to further development of the ontogenetic theory.     

"Our standpoint different from common ..." (scientific heritage of Alexander Gurwitsch)

The work of prominent Russian biologist Alexander Gavrilovich Gurwitsch (1874-1954) on the theory of organism development are reviewed. Alexander Gurwitsch introduced the concept of embryonic (morphogenetic, biological, and cellular) field and proposed several revisions of it from 1912 to 1944. Although neither of them can be considered as a final theory of development, his the persistent search for the invariant law that allows the shape (spatial structure) to be proposed for each next developmental stage from the previous shape is of imperishable methodological interest. Alexander Gurwitsch anticipated many ideas of the future theory of self-organization. His theoretical constructions are explicit and experiment-oriented but absolutely not esoteric. They represent a highly important and original contribution to theoretical biology and are an essential step to further development of the ontogenetic theory.     

The mechanical behaviour of cell membranes as a possible physical origin of cell polarity

The mechanical behaviour of a closed layered membrane enclosing a structureless interior is considered. The shape of such an object in flaccid conditions is determined theoretically by assuming that it corresponds to the minimum value of the membrane bending energy. The symmetry breaking properties of this system are revealed. It is suggested that a continuous transition from an axisymmetrical shape involving mirror symmetry with regard to the equatorial plane of the object to the shape with polar asymmetry could be the primary event in establishing cell polarity.     

Life Began When Evolution Began: A Lipidic Vesicle-Based Scenario

The research on the origin of life, as such, seems to have reached an impasse as a clear and universal scientific definition of life is probably impossible. On the contrary, the research on the origin of evolution may provide a clue. But it is necessary to identify the minimum requirements that allowed evolution to emerge on early Earth. The classical approach, the ‘RNA world hypothesis’ is one way, but an alternative based on nonlinear dynamics dealing with far-from-equilibrium self-organization and dissipative structures can also be proposed. The conditions on early Earth, near deep-sea hydrothermal sites, were favorable to the emergence of dissipative structures such as vesicles with bilayer membranes composed of a mixture of amphiphilic and hydrophobic molecules. Experimentally these vesicles are able to self-reproduce but not to evolve. A plausible scenario for the emergence of a positive feedback process giving them the capability of evolving on early Earth is suggested. The possibilities offered by such a process are described in regard to specific characteristics of extant biological organisms and leads for future research in the field are suggested.     

Biological diversity and cultural heritage

In this paper some examples of the development of communities of microorganisms and plants on historic buildings and montiments are shown. When the building stones differ from the surrounding natural substrata, an increase in the biological diversity of the area is produced. In some cases, monuments can come to constitute a true refuge for a few species when the natural habitat is threatened. It is suggested that biological diversity, when it does not represent a threat for the cultural heritage, should be considered worthy of preservation.