Self-organization in and on biological spheres

The generation of the flower by self-organisation

The essence of the Turing-Child theory (Schiffmann, 1991, 2017) is the direct and spontaneous conversion of chemical energy into simultaneous differentiation and morphogenesis, and all localised biological work and localised entropy-reducing processes. This is done via the identification of the Turing instability with cAMP and ATP being the Turing morphogens that mutually fulfil the five Turing inequalities. A flower model like the ABC model is derived from experiments with mutations. But what actually generates the model in real development? That is, how do genes of class A come to be expressed in the sepal and petal whorls, genes of class B in the petal and stamen whorls, and genes of class C in the stamen and carpel whorls. We suggest that the generation of the ABC model occurs via sequential compartmentalisation by Turing-Child eigenfunction patterns similar to the one occurring in Drosophila (Schiffmann, 2012). We also suggest a similar mechanism for the generation of the dorso-lateral-ventral polarity and bilateral symmetry. A mechanism for the generation of the regular location of the floral organs is also suggested. The symmetry and regularity of flowers, which are the source of their attraction and beauty, stem from the symmetry and regularity of the Turing-Child eigenfunctions. The central problem in developmental biology is the endless regress. This endless regress is halted by the Turing-Child pre-patterns and this is illustrated on a central example in flower generation. Both the shape and the chemistry - the steady-state rate of ATP synthesis and hydrolysis - of the Turing-Child pre-patterns are exactly what is required. Art and science meet in flower formation.

Emergent structures in reaction-advection-diffusion systems on a sphere

We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

The non-equilibrium basis of Turing Instability and localised biological work

Turing's theory for biological pattern formation is based on the instability of the homogeneous state, which occurs if certain key criteria are met. The problem of how chemical energy is converted to localised biological work requires one to understand not only the basis of localised power generation, but also the age-old puzzle of how organisms decrease their entropy; these problems can only be solved by the identification of the Turing Instability. At the heart of this is how natural selection, not chemistry, has fashioned the large non-equilibrium overall affinity (ΔG is a large negative quantity) for the oxidation of the fuel molecules. Natural selection has also resulted in the homeostasis at non-equilibrium values of the hydrolysis of molecules like ATP, GTP, which are the energy links between the overall oxidation of the fuel and biological work. The conditions for such homeostasis are central requirements for the Turing Instability and are the essence of being alive. The Turing-Child (TC) patterns are the spontaneous primary spatial cause not only of localised biological work in multicellular systems (especially those in patterning and development) but also of intracellular patterns including the mitotic spindle and the contractile ring. The Turing picture comprises the nonuniform distribution of the concentrations of the Turing morphogens, cAMP and ATP, and the Child picture is the resulting nonuniform distribution of the metabolic rate and of power. The TC pattern is shaped as the dominant eigenfunction in the combination of eigenfunctions which provides the spatial pattern of the Turing morphogens. The TC patterns and the bifurcation parameter manifest quantisation and symmetry as in music and in applications of quantum mechanics. The notion of correlation diagrams is also introduced.

Cardiac Mechanoperception: A Life-Long Story from Early Beats to Aging and Failure

The life-long story of the heart starts concomitantly with primary differentiation events occurring in multipotent progenitors located in the so-called heart tube. This initially tubular structure starts a looping process, which leads to formation of the final four-chambered heart with a primary contribution of geometric and position-associated cell sensing. While this establishes the correct patterning of the final cardiac structure, it also provides feedbacks to fundamental cellular machineries controlling proliferation and differentiation, thus ensuring a coordinated restriction of cell growth and a myocyte terminal differentiation. Novel evidences provided by embryological and cell engineering studies have clarified the relevance of mechanics-supported position sensing for the correct recognition of cell fate inside developing embryos and multicellular aggregates. One of the main components of this pathway, the Hippo-dependent signal transduction machinery, is responsible for cell mechanics intracellular transduction with important consequences for gene transcription and cell growth control. Being the Hippo pathway also directly connected to stress responses and altered metabolism, it is tempting to speculate that permanent alterations of mechanosensing may account for modifying self-renewal control in tissue homeostasis. In the present contribution, we translate these concepts to the aging process and the failing of the human heart, two pathophysiologic conditions that are strongly affected by stress responses and altered metabolism.

On a model of pattern regeneration based on cell memory

We present here a new model of the cellular dynamics that enable regeneration of complex biological morphologies. Biological cell structures are considered as an ensemble of mathematical points on the plane. Each cell produces a signal which propagates in space and is received by other cells. The total signal received by each cell forms a signal distribution defined on the cell structure. This distribution characterizes the geometry of the cell structure. If a part of this structure is removed, the remaining cells have two signals. They keep the value of the signal which they had before the amputation (memory), and they receive a new signal produced after the amputation. Regeneration of the cell structure is stimulated by the difference between the old and the new signals. It is stopped when the two signals coincide. The algorithm of regeneration contains certain rules which are essential for its functioning, being the first quantitative model of cellular memory that implements regeneration of complex patterns to a specific target morphology. Correct regeneration depends on the form and the size of the cell structure, as well as on some parameters of regeneration.

What are melanocytes really doing all day long...?

Everyone knows and seems to agree that melanocytes are there to generate melanin - an intriguing, but underestimated multipurpose molecule that is capable of doing far more than providing pigment and UV protection to skin (1). What about the cell that generates melanin, then? Is this dendritic, neural crest-derived cell still serving useful (or even important) functions when no-one looks at the pigmentation of our skin and its appendages and when there is essentially no UV exposure? In other words, what do epidermal and hair follicle melanocytes do in their spare time - at night, under your bedcover? How much of the full portfolio of physiological melanocyte functions in mammalian skin has really been elucidated already? Does the presence or absence of melanocytes matter for normal epidermal and/or hair follicle functions (beyond pigmentation and UV protection), and for skin immune responses? Do melanocytes even deserve as much credit for UV protection as conventional wisdom attributes to them? In which interactions do these promiscuous cells engage with their immediate epithelial environment and who is controlling whom? What lessons might be distilled from looking at lower vertebrate melanophores and at extracutaneous melanocytes in the endeavour to reveal the 'secret identity' of melanocytes? The current Controversies feature explores these far too infrequently posed, biologically and clinically important questions. Complementing a companion viewpoint essay on malignant melanocytes (2), this critical re-examination of melanocyte biology provides a cornucopia of old, but under-appreciated concepts and novel ideas on the slowly emerging complexity of physiological melanocyte functions, and delineates important, thought-provoking questions that remain to be definitively answered by future research.