So far our discussion has been rather formal, and the model which we had been able to solve referred to A-Life systems. Let us now make a brief review the known relationships between the spatially developing embryo, its differentiating cells, and their genetically identical nuclei. It seems that above discussed self-organization phenomena may provide a physico-chemical basis for the understanding of real biological morphogenesis. Taking into account the simplicity and universalism of the model, the obtained results may bring in evidence that there is a small biological specificness of the early embryo morphogenesis and that the prevalence of physical specificness of this process does exist (Cf. Newman, Comper, 1990). In other words, revealed moduses of the model behavior are the simplest ones that are occurring in the framework of the simplest hypotheses about the interaction of the morphogen patterns and the epithelia movements, and just these moduses are realized in the early development.
These conclusions in the below paragraphs will hopefully help to illustrate the ways of verification the models developed. Also it will help to give some further insight into the motivation for that models.
The homeobox-containing genes products have at least some of the required properties to pretend to real morphogen roles. The homeobox-containing (HOX) network is a family of genes that is providing a wealth of information on the processes of axial patterning in invertebrate and vertebrate embryos. The HOX genes are believed to function during embryogenesis in a variety of structures. There is considerable evidence that their products are small chromatin-binding proteins, at least some of which are transcriptional regulators. They have large upstream regulatory regions that respond to multiple inputs, including self-activation. The importance of co-operativity in transcriptional control, especially dimer formation, is well established (Jackle et al., 1992), and co-operativity is an essential part of any reaction-diffusion model.
It is experimentally well established that a single gene may be activated by different combinations of other gene products. In turn, the gene own product may itself be involved in quite different molecular combinations of activating or repressing elements on the promoter for other genes. In the corresponding theoretical framework, highly non-linear off-on control is a central feature of multistability in gene networks (See Hunding and Engelhardt, 1995).
Well studied cases of gene activation such as cascade of Drosophila segmentation genes give remarkable examples of non-linear co-operative kinetic equations with self-activation loops (See Edgar et al., 1989; Lacalli, 1990; Jackle et al., 1992; Hunding, 1993). Primary embryonic pattern formation is thought to be similarly accomplished by the coupling of short-range gene self-activation process with a long-range repression by the diffusing product of another gene(Meinhardt, 1994). In general, set of equations describing self-activation and cross-regulations of the genes by their products could display non-linear behavior formally mirrored by Brusselator system, for instance.
It is well known that a Turing-like pattern-forming mechanism should be sought in low molecular weight components that could diffuse rapidly enough. However, it is important to realize that for many model systems, the higher the cooperativity, the easier it is to get Turing structures with effective diffusion rates which do not differ from each other. Thus the usual requirement of approximately an order of magnitude spread between the two effective diffusion rates is relaxed, and a trend towards higher Hill numbers would greatly facilitate the formation of a Turing structure (Hunding and Engelhardt, 1995).
Over the years there have been a large number of different proposals concerning the nature of elusive "morphogen". Almost invariably, the morphogen has been seen as an agent in a Turing-like reaction-diffusion scheme. In such a view, the diffusible morphogen is most easily envisioned as a small biochemical easily diffusing from cell to cell, e.g. via the gap junctions.
More general, diffusion of a substance may be replaced by the transport of cell- communicating substances through gap junctions among cells. In the mathematical formulation of Turing-like models, it may not necessary be a substance that diffuses (Hunding, 1993). It could just as well be some cell state that is induced from one cell to its neighbors. If this process is fast enough to let all cells in the region communicate with each other as a speed that could keep the essential growth process in check in a concerted global mode (as in Turing's mechanism), it could mimics a diffusion term of "canonical" RD systems.
The Edelman's (1988) idea about place-dependent dynamic regulatory loop that ranges from the gene to layers, and back to control the expression of the same or a different gene is shared by Richard Gordon with co-authors (reviewed in Bjorklund and Gordon, 1993).
According to Richard Gordon, competent blastula/gastrula cells at each critical (bifurcation) point of developmental pathway has prepared an "unstable initial state" in the nucleus, consisting of pair of master gene regulatory proteins. Each protein is likely the product of a homeobox gene. Enhancement of either master protein will result in a gene cascade specific to one master protein but not the other. One gene cascade would result in one pathway, while the other would trigger the other way.
The cells will remain competent until they receive their signal, which is initiated by mechanics. Apical microtubule/microfilament ring typical for many morphogenetically active epithelial cells has interpret as biomechanically instable cell organelle, so called cell state splitter (Bjorklund and Gordon, 1993).
The cell state splitter is presumed to start out in a mechanically metastable state. After the cell state splitter resolves its mechanical instability, the nucleus receives a one-bit signal telling it which of the two possible events occurred in the cell. The reaction of the nucleus to this commitment signal is to activate one of the two prepared gene cascades. The cell state splitter is essentially both a sensory organelle for testing mechanical environment and a signaling apparatus to contact other cells. It is by the interaction of the cell state splitter with the whole tissue that the nucleus is able to direct differentiation.
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