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

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.

Gap junctional signaling in pattern regulation: Physiological network connectivity instructs growth and form

Gap junctions (GJs) are aqueous channels that allow cells to communicate via physiological signals directly. The role of gap junctional connectivity in determining single-cell functions has long been recognized. However, GJs have another important role: the regulation of large-scale anatomical pattern. GJs are not only versatile computational elements that allow cells to control which small molecule signals they receive and emit, but also establish connectivity patterns within large groups of cells. By dynamically regulating the topology of bioelectric networks in vivo, GJs underlie the ability of many tissues to implement complex morphogenesis. Here, a review of recent data on patterning roles of GJs in growth of the zebrafish fin, the establishment of left-right patterning, the developmental dysregulation known as cancer, and the control of large-scale head-tail polarity, and head shape in planarian regeneration has been reported. A perspective in which GJs are not only molecular features functioning in single cells, but also enable global neural-like dynamics in non-neural somatic tissues has been proposed. This view suggests a rich program of future work which capitalizes on the rapid advances in the biophysics of GJs to exploit GJ-mediated global dynamics for applications in birth defects, regenerative medicine, and morphogenetic bioengineering. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 77: 643-673, 2017.

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.

Metabolic Field (Schrodinger); an explanatory platform for biology: Based on lecture at Trinity College, Dublin, Ireland, July 18, 2012

Metabolism represents the nexus of fundamental physical forces, which while present in all structure and function require new explanatory emergent principles, which, so far, cannot be predicted or derived solely from description of chemistry and physics. Metabolism is essentially concerned with the transduction of energy flows with respect to time, space, and matter. Language models and metaphors contribute to construction of scientific explanation within biology. The concept of a metabolic field yields a deeper, broader, more quantitative integrated theoretical framework leading to novel predictive models of systems biology.

Endogenous electric fields as guiding cue for cell migration

This review covers two topics: (1) "membrane potential of low magnitude and related electric fields (bioelectricity)" and (2) "cell migration under the guiding cue of electric fields (EF)."Membrane potentials for this "bioelectricity" arise from the segregation of charges by special molecular machines (pumps, transporters, ion channels) situated within the plasma membrane of each cell type (including eukaryotic non-neural animal cells). The arising patterns of ion gradients direct many cell- and molecular biological processes such as embryogenesis, wound healing, regeneration. Furthermore, EF are important as guiding cues for cell migration and are often overriding chemical or topographic cues. In osteoblasts, for instance, the directional information of EF is captured by charged transporters on the cell membrane and transferred into signaling mechanisms that modulate the cytoskeleton and motor proteins. This results in a persistent directional migration along an EF guiding cue. As an outlook, we discuss questions concerning the fluctuation of EF and the frequencies and mapping of the "electric" interior of the cell. Another exciting topic for further research is the modeling of field concepts for such distant, non-chemical cellular interactions.

Morphogenetic fields in embryogenesis, regeneration, and cancer: non-local control of complex patterning

Establishment of shape during embryonic development, and the maintenance of shape against injury or tumorigenesis, requires constant coordination of cell behaviors toward the patterning needs of the host organism. Molecular cell biology and genetics have made great strides in understanding the mechanisms that regulate cell function. However, generalized rational control of shape is still largely beyond our current capabilities. Significant instructive signals function at long range to provide positional information and other cues to regulate organism-wide systems properties like anatomical polarity and size control. Is complex morphogenesis best understood as the emergent property of local cell interactions, or as the outcome of a computational process that is guided by a physically encoded map or template of the final goal state? Here I review recent data and molecular mechanisms relevant to morphogenetic fields: large-scale systems of physical properties that have been proposed to store patterning information during embryogenesis, regenerative repair, and cancer suppression that ultimately controls anatomy. Placing special emphasis on the role of endogenous bioelectric signals as an important component of the morphogenetic field, I speculate on novel approaches for the computational modeling and control of these fields with applications to synthetic biology, regenerative medicine, and evolutionary developmental biology.