Selforganization, The Engines

This site presents parts of the text and illustrations for a soon to be published book presenting a new paradigm of biological origins based on the self-organization of the membrane of the germ plasm.
It has been accepted as a plausible account of evolution and development by prominent evolutionary biologists.

AUTHOR'S NOTE

The Engines of Evolution is the publication of a controversial new theory of evolution, purporting to solve the 2000-year old problem of the origin of living forms. It has been accepted as plausible by prominent scientists, yet is condemned by many as a threat to the established dogma of biology.

Biodiversity is the study of how species differ, by describing the adult forms of complex animals and plants. But nature may be better understood by the study of what species have in common. The nineteenth century morphologists sought the ancestor of form in the early stages of simple animals. Haeckel famously noted that the earlier the stage of the embryo, the more it resembles the embryos of more distantly related species. What then is the absolute zero of embryogenesis, the one form common to all life, the elementary particle of biology? Goethe called it the Urform.

This is about the discovery of the Urform, the product of a ten-year search. The book demonstrates graphically that the gamut of living forms may be accurately simulated by the deformation of a single, simple structure, the dynamic toroidal surface, exemplified by the smoke-ring. Since the germ plasm, predecessor of the egg, is a dynamic torus, as is the egg membrane, the blastula (E. Davidson, 2 Nov. 2007, Science), the embryo, the larva, and the adult, then it is plausible that this is the solution to the mystery of morphogenesis and evolution.

THE DYNAMIC TORUS
A Genetic Algorithm for Organic Form

Life of the individual begins not with the egg, but with its predecessor, the miniscule, wandering, amoeboid blob which August Weismann named the Immortal Germ Plasm.

This essay proposes that the origin and evolution of the complex body is directed not by a code in the DNA, but rather by the structural pattern of the early cell membrane. The model is demonstrated by a topological algorithm showing the sequence from one cell to the complex body driven by the predictable deformations of a toroidal surface by mechanical forces implicit in its growth.

It is well established that the membrane of the germ plasm is a dynamic torus, like an elongated smoke ring in slow motion. So is its successor the egg cell, and in turn, the embryo and the adult of all animal and plant species.

Protoplasm forms a membrane of protein molecules which are oriented axially during eons of toroidal streaming. The molecules are transversely cross-linked forming a gridded membrane.

The inflation of a large, central spherical nucleus stretches the tubular membrane forming a sphere, geodesically subdivided in rectangular elements. The swollen nucleus splits in two, tearing the toroidal membrane in half, each half easily regenerating the whole by adding protein to the streaming morphogenetic field.

The universal toroidality of living form can be accounted for if morphogenesis preserves the patterned membrane of the early tissue. The means for this conservation of form is the morphogenetic field, the properties of which can account for the encoding and “downloading“ of the species form.

The torus is to life what the hexagon is to snowflakes. Bodyform is ruled by the rules of topological geometry, which govern shapes on the surface of a torus.

This proposed hypothetical construction may be simply demonstrated by use of graphic mechanical analysis, and by inflatable toroidal model structures. The generally unfamiliar tubular torus balloon has remarkable, counter-intuitive properties in forming surprising structural configurations and movement under mechanical forces. Tension between the outer and inner surfaces of the torus produces axial segmentation of the outer surface, as well as deep transverse folds along one side. In life these folds can part at the midline, and swing outward in the shape of jointed limbs and mouth parts.

Radial phyla are simulated by the simple, symmetrical axial compression by tension of the inner tubular canal. The forms of the different bilateral phyla result from the mechanical failure patterns, which occur under axial bending. An elongated, tubular torus can generate the form of uniformly segmented worms. The ovoidal torus forms the tripartite insect body. A more spherical ovoid results in the crustacean and vertebrate forms.

Premise: Living form is an implicit property of protoplasm, encoded in its recipe. Morphogenesis is protoplasmic crystallography. There is only one form in nature, the deformed tubular torus.

THE MULTI-TORUS
Least Common Denominator of Complex Form

In 1993, Jockusch and Dress published their finding that the embryonic tissue is in the form of a torus within a torus. They called this the “Multi-Torus.” In November of 2007 Eric Davidson published the discovery that genetic expression in the sea urchin embryo is in the form of a “Dynamic Torus.” The multi-torus can originate as the outcome of the delamination of a toroidal bilayer, the form of the germ plasm, predecessor of the egg. The study of biological form can be well illuminated by this remarkable topological phenomenon capable of simulating the forms which occur in animals and plants.

The dynamic toroidal surface is exemplified by the smoke ring which is a ring torus composed of streaming laminations. The elongated tubular torus exhibits surprisingly different forms and behavior. The outer surface, under tension, is that of a regular tubular balloon. An internal canal passes from end to end, of star-shaped cross-section, the result of the compression of the tubular surface as it is forced to assume a minimal volume contained by the enclosing surface, like turning a sleeve inside out. The pattern can range from flat, like an empty fire-hose, to star patterns comprising three or more arms formed of two tightly clinging membranes surmounted by a tight circular tubule, which permits the containment and flow of fluid, separate from the interior volume. Radial animals and plants are of this cross-section.

The streaming toroidal membrane is subject to the continual change of lateral pressure from compression to tension as it passes from outside to inside. This process may be expected to engrain a longitudinal and circumferential pattern, subdividing the surface into quadrilateral segments. The membrane is robust enough to preserve the pattern under the compression of the internal passage, reconstituting it on emerging at the other end. The deformation of this pattern establishes the phyletic bodyplan. Bending of the axis causes arc-shaped wrinkles in the outside ventral surface, morphological predecessors of limbs.

The delamination of a single toroidal surface creates the multi-torus of two or more concentric tori. The tense internal canal of the outer torus passes through the inner canal of the inner torus constraining mutual rotation. Rotation results in the indentation of the outer membrane of the inner torus and can cause it to part, as in cell division.

The worm, insect, crustacean and vertebrate body forms are determined by the topological exigencies inherent in the growth from a cylindrical, ellipsoidal, or spherical egg. The larval and adult bodies derive separately from the outer and inner toroidal membranes, respectively.

The elongated insect egg develops by the linear invagination of the ventral side caused by the lateral pressure of dorsal overgrowth.

The curled, segmented body of the crustacean is delaminated from the surface of its round egg and embryo.

The round vertebrate egg produces an embryo subject to an additional step consisting of the rotation of the inner torus within the stationary outer torus. The rotation causes the centric cable to press upon the dorsal surface, causing a deep groove which seals over, encapsulating the cable within. Ventral wrinkles form the limbs, the scapula detaches from the midline, forming the neck, the pelvis from the lumbar vertebrae. The individual quadrilateral elements of the bilayer surface roll axially, forming bones, each encapsulated in a tube of muscle. Concurrently the internal cables drag the outer torus behind it, turning it inside-out as its covers the inner body with the skin.

The flower is simulated by the cylindrically constrained expansion of a multi-toroidal tube.

THE STEPS IN TOROIDAL TOPOLOGY WHICH ACCOUNT FOR THE PHYLETIC FORMS

The following is a sequence of developmental complexity of phyla meant to suggest a sequence of evolutionary development. Over time, the predictable stages of an ever expanding toroidal membrane become mechanically sustainable in embryology. Evolutionary history is the recapitulation of these stages.Ontogeny recapitulates phylogeny, but only at the earliest stages.

The locomotive amoeboid germ plasm assumes the form of a dynamic tubular toroidal membrane. This delaminates, forming a tubular torus within a torus. This is the body form of unsegmented worms.

Tension in the inner canal surface causes the axial segmentation of the outer surface, creating the form of segmented worms.

Tension causes the tube to turn partly, or fully inside out, creating the body form of radial animals.

Interior tension causes the segmented tube to bend axially, causing the ventral side to crimp, forming tubular, transverse folds, which bend transversely in a zigzag pattern. This is the body form of insects.

The introduction of a large spherical nucleus causes the pattern of the bent segmented form to become compressed against its surface. This produces the body form of crustaceans.

The morphogenesis of vertebrates includes an additional step, wherein the inner torus rotates with respect to the outer torus. The interior canal of the outer torus remains tense, as a taut cable passing through the interior of the inner rotating torus. The cable causes the transverse wrinkles in the ventral surface to arch anteriorly, while on the dorsal side it presses a furrow into the midline in which it becomes sealed. Concurrently the outer torus membrane is pulled inside-out over the inner body, forming a patterned skin.

Plants are formed by the expansion of the multi-torus within the constraint of a vertical outer cylinder. Extrusive growth from both ends forms shoots and roots. Flower parts are formed from the constraining cylinder as it splits axially.

GLOSSARY FOR A PROPOSED SOLUTION TO THE PROBLEM OF COMPLEX ORGANIC DESIGN

Origin: Protoplasm generates an enveloping, dynamic toroidal membrane.

Morphogenesis: The body shape originates in the deformation of the self-organized geometric pattern of the toroidal membrane of the germ plasm, predecessor of the egg. The toroidal surface becomes subdivided in rectangular plates which deform tectonically with the streaming of the surface. The inflation of a central nuclear sphere stretches the torus to form a geodesically subdivided sphere, with circular holes due to tension at the center of the component rectangular elements. The embryo is produced by the deformation of this figure during gastrulation.

Phylogenesis: Tension in the inner toroidal canal surface can deform the patterned membrane either by the compression, or by the bending of the axis, producing radial or bilateral forms.

All life is a version of one or the other of these two possible deformations. Biodiversity is the result of changes in the proportions of an otherwise immutable body plan.

Development: The embryo materializes chemically by the tensorial energy of the surface stress pattern. Developing like a photographic plate, the image is initiated by mechanical stress upon the deformed membrane along the lines of the stress pattern, out of materials synthesized by the genome, in timed, measured doses. Like a freezing stream, development bars flow which continues intersticially after the dynamic membrane becomes static cellular tissue.

Regeneration: The germ plasm lives eternally in its ability to grow, divide and regenerate itself by the properties of the morphogenetic field engrained in its surface over eons of toroidal streaming.

Inheritance: The immortal germ plasm is a universally totipotent morphogenetic field, the heritable element of form.

The Life Cycle: The immortal germ plasm periodically splits in two. Each half may regenerate, or else one half may dwell in the mortal body formed by the cellular subdivision of the other.

Evolution: Embryonic development is independent of the environment. Shapes and movements occur epigenetically in predictable mechanical sequence.

THE GEOMETRY AND MECHANICS OF SELF-ORGANIZATION
Genome, Body and Shell–Helix, Torus and Sphere: The Triple Code of Life

The following demonstrates by the methods of geometry and topology that the general form of multi-cellular animals is the simple, topologically predictable result of the expansion of a toroidal surface within a sphere.

The attached serially animated illustrations show that the concurrent expansion of a torus within a sphere leads to a single terminal configuration – that of a bisected, double-walled, hemispheric shell enclosing a segmented tube with paired opposing appendages. This is also a description of the general body plan of the bilateral animals.

A property of protoplasm is the generation of lipids. These molecules enclose protoplasm in a spherical, elastic membrane. A second spherical membrane is generated interior to the first. As the surfaces expand, the constraint of a spherical shell causes the surface of the inner sphere to expand inwardly, forming an interior canal, thus producing the configuration of a torus within a sphere. The growth of the torus causes axial deformation of the constraining sphere and forces the rotation of its polar axis to the horizontal.

Further tension causes the incursion of the ventral half of the horizontal, segmented spheroid into the dorsal half, forming a double-walled dome, entrapping and compressing the toroidal body between its walls. The bending of the tubular toroidal body axis causes it to arch and to crimp as does a tubular circus balloon, forming internal folds. The axial extension of the elongating torus deforms the posterior of the enclosing ellipsoid shell, causing it to part along the segmental boundaries, resulting in the typical head-tail configuration of the bilateral body. Dorsal-ventral compression causes the extrusion of the internal folds as paired, tubular, transverse appendages.

The embryo is thereby shaped by the mutual morphological influence of body and shell as both expand. This list summarizes the hypothetical steps of embryogenesis by self-organization, depicted in the serial animations:

1 - 2	The self-generation of a sphere within a sphere.
3 - 4	The axial and meridianal segmentation along a vertical polar axis of the outer sphere.
5	The internally directed expansion of the inner sphere, forming a horizontal, axially extended torus.
6	The rotation of the vertical axis of the sphere to the horizontal.
7	The invasion of the ventral hemisphere of the segmented sphere into the dorsal hemisphere.
8 - 9	The bending and crimping of the toroidal surface.
10	The dorsal-ventral compression of the toroidal tube causing the extrusion of paired appendages.
11 - 13	The anterior-posterior partition of the shell, and the loss of the posterior section.

THE PHENOMENA OF SELF-ORGANIZATION

The question immediately arises: If these simple mechanically-driven steps are the process used by nature to create the living body, why has it not been observed and reported by Aristotle, or by Leewenhoek in the seventeenth century? How come no mathematician ever discovered the algorithm by which the phlyetic forms can be generated by the topological deformation of a sphere?

As to the inability to observe the steps described in this model, the answer lies in the difficulty in the microscopic observation of the steps of early embryogenesis as well as the complexity of comparative embryology. Few conclusions can be drawn by the contemporary practice which focuses on merely five laboratory animal species. In fact, animal embryology occurs in a staggering variety of forms. Nearly a hundred different types of gastrulation are reported in nineteenth century literature.

The focus of modern biology is biodiversity, the way species and individuals differ. The study is of the adult form of animals. Haeckel, von Baer, Goethe, and the nineteenth century developmental biologists sought the origin of form in the way species are alike. Goethe sought a single Urform and Urpflanze from which all living form is derived. The answer was sought in the stages of embryological development.

A coherent train of mechanical events is interrupted by the intrusion of cleavage in the midst of the embryological sequence – the sudden subdivision of the egg into hundreds of cells. The theory that cellular subdivision is irrelevant to morphology clarifies the topological sequence that shapes the embryo. It is the basis of the once-prevalent organismal theory of development, which dismisses the role of the individual cells as mere bricks. Replaced in the 1930s by current developmental cell differentiation.

Vertebrate gastrulation is generally seen as the formation of a cup from a sphere. Arthropod gastrulation is the rolling of a tube. The well-studied sea urchin embryology is congruent in all its steps with the depicted model of radial phyla.

The phenomenon called condensation is held responsible for the loss of steps in the embryological sequence, interrupting its train of events. Ontogeny and Phylogeny, the 1976 landmark work of Stephen Jay Gould, is a summation of the complex embryological phenomena such as heterochrony and condensation which account for evolution. The full sequence of embryology consists of the integration of its parts, the defective embryological sequences of many individual species. For the history of organicism, see Crystals, Fabrics and Fields by Donna Haraway (1976).

In the diversity of morphological paths of embryogenesis, those events of embryology that are universal are listed here to be compared with the hypothetical events of the subject model. There seem to be no apparent inconsistencies nor the absence of any necessary conditions.

1   The origin of the egg cell in a motile, toroidal amoeba within a spherical envelope.
2   The introduction of a spherical nucleus producing a polar spherical egg cell.
3   The self-organized segmentation along the polar axis, including an apical polar cap.
4   The rotation of the polar axis to the horizontal upon fertilization.
5   Subdivision into a syncytium of interconnected, or separate, cells by various means.
6   Gastrulation: the entry of part of the surface of the egg cell membrane into the interior.
7   Organogenesis: the appearance of the embryonic form.

THE BODY

The geometric deformations that produce the form of the shell were described in the previous chapter. The deformations of the toroidal surface contained within the shell are described in the following pages. These propose the mechanical origin of the paired appendages common to bilateral animals which serve as sense organs, limbs, wings and mouthparts. They are seen as the result of dorsal-ventral compression of the toroidal figure which causes the extrusion of internal folds and tubes.

The homuncular structure is a simple topological configuration consisting of a torus within a sphere. To visualize its shapes and behavior is nearly impossible without real models. The principle is demonstrated using models consisting of fluid-filled toroidal balloons made of plastic film. These automatically assume the general configuration of the phyla by simple manipulations, beyond the control of the operator, like the bending and folding of a tubular latex balloon, or plastic drinking straw. Mechanical drawings describe these and extrapolate the further transformations which may be predicted mechanically. The surprising ability of this unusual topological artifact to simulate life forms suggests that Nature herself uses this very process.

THE MECHANICAL ORIGINS OF THE BILATERAL BODY FORM

EXPERIMENTING WITH FORM

The recent conclusions as to the toroidal nature of the embryonic tissue (Belousov, Krauss, Presnov, Jockusch and Dress) led to the investigation of the morphological properties of the amoeboid pseudopod, for which purpose toroidal balloons of latex rubber, polyvinylchloride and other elastomeric sheet materials were fabricated in varying sizes and proportions (plate 1). Use was made of small (10 cm) toroidal balloons made as water toys, widely commercially available. These were filled with air, water, glycerine, honey, and other fluids of varying viscosity. A 20 cm balloon, filled with water, and then submerged in water, was observed to assume a series of distorted configurations which bear resemblance to various developmental forms of animal and plant species by simple manual manipulation of the hydrostatic pressure in the parts of the structure. Schematic drawings were made of extrapolations to predict mechanical failure patterns which could not be experimentally reproduced and recorded. These drawings are observed to corroborate the concordance of the model with the adult forms of the appended organs of the species suggested in the experiment.

PSEUDOPODAL STREAMING

Observations of artificial pseudopod models demonstrate that slow toroidal streaming of a bendable, elastic membrane causes axial wrinkles with tubular borders to form in the interior surfaces which subdivide the figure radially, as the surface is condensed in the incurrent vortex funnel by self-organized folds (plate 3). These form due to the lateral forces produced as the cylindrical surface enters the reduced volume of the interior. Toroidal streaming may generate any number of tube vortices distributed radially at the perimeter of the inner vortex, depending on simple physical parameters such as the thickness and elasticity of the sheet. Observation of the internal tubules in the plastic models may be enhanced by submerging in a colored fluid, such as fluorescent stain, coffee, or red wine, allowing it to enter the interior folds.

The form assumed by a membrane-bound colloidal fluid is exemplified in the phenomenon of organic amoeboid locomotion, well known to be the result of toroidal streaming, and understood as a sol-gel inter-phase phenomenon. The transparency of moving fluid surfaces makes observation vague, resulting in varying interpretation of what is seen. Amoeboid locomotion is simulated by the gravity descent on an inclined plane by a model toroidal balloon (plate 1, fig. 1).

This paragraph presents an idealized model of pseudopodal locomotion based on the classic descriptions of the phenomenon: The protoplasm mass generates an enveloping membrane. A weakness in the wall results in a circular port from which the newly formed membrane radiates as it emerges, causing a domed cylindrical tube to project from the surface. Sol state material exits the port, immediately to undergo gelation, producing more membrane which radiates to flow backwards over the body, re-entering at the posterior port.

While it has not been clearly observed, it is theorized that the behavior of the membrane as it is compressed laterally on entering the interior space will wrinkle in a radial pattern like the one formed when a coat-sleeve is turned inside out. In the mechanical models the pattern produces radial segmentation and forms pinched-off tubes from the distal borders of the axial segment walls which envelop the tubular figure from posterior to anterior.

The tubular toroidal balloon is observed to be subject to three types of mechanical failure under axial tension and bending torque. The first of these is an observed pattern of circumferential undulations which segment the surface axially (plate 1, fig. 3). The second is failure by small, infolded bands on the concave curve of the bend (plate 1, fig 4). The third failure is the subdivision of the tube in a small number of large folds, the familiar bending maneuver of a tubular balloon (plate 1, fig. 5). A bending torque on the axis produces a series of quantified stages of folded forms, rather than a continuously variable bend. This phenomenon is familiar to anyone who has manipulated a tubular balloon where axial torque produces a succession of separated stages of equilibrium rather than a smooth bend.

Anterior-posterior tension in the inner tubular surface of the toroidal tube can cause the axis to bend and fold in a pattern of quantified subdivision of the length of the tube. The interior folds of the bend is observed (plate 6, fig. 3) to be in the form of lunettes, in the shape of the sector of a circle, comprising two tightly adhering surfaces bordered at the top rim by a thin, straight horizontal tube, the predictable folding pattern of an elastic sheet. In the tubular balloon the sectors remain erect, that is, perpendicular to the axis, while in the toroidal balloon the interior structure forces them to lie flat by the pressure imposed by two tubes on either side of the midline (plate 1, fig. 5). These can hold the tissue firmly in place as opposing lateral forces tear the figure apart at the midline, generating the topological configurations resembling limb primordia.

The transverse midline parting of the lunette is accompanied by the stretching of the bilayer membrane causing its segmentation into separate rectangles resulting from the subdivision of the external surface of the toroidal tube before infolding as lunettes. The differential in growth rate of the two layers causes the separated rectangles to curl axially, forming a seamed tube, and then to extend cuffs at each end, each of which splits medially, forming the configuration of the archetypal long bone.

The shape of any of the bones of the vertebrate skeleton may be synthesized by the deformation of a rectangular bilayer sheet of unequal growth rates.

The pressure of a pair of interior tubes on either side of the midline can cause the fault which locates the zigzag bends that characterize vertebrate and arthropodal limbs (plates 6, 8), and also the bars which occur as one of the elements in the patterning of butterfly wings (plate 9b).

It is noted that the axial deformation of a tubular balloon results in the folding rather than the bending of the tube. The folds occur in quantified instantaneous sequences with no intermediate forms perceptible. This quantification of toroidal form implies a limited number of morphological niches, with no in between stages.

Bilateral animals generate two, three, four, or five pairs of lunette folds in the ventral hemisphere (plate 10). These result in paired limbs and mouthparts (plate 8, fig. 1 – 4). In insects, two large lunettes occur which extend into the dorsal hemisphere forming wings (plate 9b). In lepidopterans these are so large that they extend, super-imposed, over the paired limb primordia which impress a pattern on the wing primordia which results in the wing spots. The compressive force of the pairs of internal axial tube structures on either side impresses the side bar pattern. The scalloped edge arises as the two halves of the wing primordia are bisected and stretched apart at the midline (plates 9a, 9b).

Anterior–posterior tension in the outer tube produces circumferential undulation along the length of the figure (plates 1, 10a). These mimic axial segmentation, universal in animal form (On Growth and Form, Thompson, 1942).

The streaming of an inflated toroidal surface produces a unique terminal structure, counter-intuitive in shape and behavior, and difficult to conceive without the experience of personally handling a model artificial pseudopod.