Symmetry breaking and convergent extension in early chordate 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.

Axial elongation of caudalized human organoids mimics aspects of neural tube development

Axial elongation of the neural tube is crucial during mammalian embryogenesis for anterior-posterior body axis establishment and subsequent spinal cord development, but these processes cannot be interrogated directly in humans as they occur post-implantation. Here, we report an organoid model of neural tube extension derived from human pluripotent stem cell (hPSC) aggregates that have been caudalized with Wnt agonism, enabling them to recapitulate aspects of the morphological and temporal gene expression patterns of neural tube development. Elongating organoids consist largely of neuroepithelial compartments and contain TBXT+SOX2+ neuro-mesodermal progenitors in addition to PAX6+NES+ neural progenitors. A critical threshold of Wnt agonism stimulated singular axial extensions while maintaining multiple cell lineages, such that organoids displayed regionalized anterior-to-posterior HOX gene expression with hindbrain (HOXB1) regions spatially distinct from brachial (HOXC6) and thoracic (HOXB9) regions. CRISPR interference-mediated silencing of TBXT, a Wnt pathway target, increased neuroepithelial compartmentalization, abrogated HOX expression and disrupted uniaxial elongation. Together, these results demonstrate the potent capacity of caudalized hPSC organoids to undergo axial elongation in a manner that can be used to dissect the cellular organization and patterning decisions that dictate early human nervous system development.

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.

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.

Turing-Child field underlies spatial periodicity in Drosophila and planarians

The regular spatial periodicity manifested in Drosophila gene expression has been considered as a test case for the involvement of a Turing system in biology. It was expected--if such involvement exists--to find a spatially periodic protein distribution where the proteins are Turing morphogens. The failure to find such a periodic distribution of Turing proteins, and the experimental findings of the involvement of different combinations of regulatory proteins and different binding sites for the different stripes of a periodic gene expression, has resulted in the dismissal of the involvement of a Turing system in Drosophila periodicity and segmentation. But if one is willing to allow a Turing system in the level of post-translational modification of proteins instead of in the protein level, one can explain the regular spatial periodicity of gene expression. The source of the spatial periodicity of gene expression does not lie in the regulatory proteins, but in the spatially periodic post-translational modification of these broadly distributed upstream regulatory proteins. The post-translational modification provides the missing spatial information for the regular pattern of 14 stripes. We report that such a field with segmental spatial periodicity that can affect downstream proteins and modify them post-translationally and periodically has been observed. This is the Turing-Child (TC) field. We explain the recent observation in Drosophila of phosphorylated transcription factor distributed with segmental periodicity, the disappearance of the spatially periodic gene expression when the regulatory protein loses its normal ability to be phosphorylated, and the spatially periodic segmental groove formation. Just as the reduction of Turing wavelength causes the appearance of 14 stripes in Drosophila so it causes the appearance of bipolar 2-headed Planaria.

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.