A reaction-diffusion theory of morphogenesis with inherent pattern invariance under scale variations

Self-organization of developing embryo using scale-invariant approach

BACKGROUND

Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.

METHODS

In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.

RESULTS AND CONCLUSION

The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.

Quantitative analysis of streptococcal exoprotein flow to the host receptor--exact basis for therapy of tumors and Alzheimer's disease

The basis of a bacterial pathogenic process consists in the change of a certain host structure to a completely different one. This is accomplished by binding of a bacterial protein product to the host structure. Streptococcal NAD+-nucleosidase was explored as to its binding to the host receptor represented by beef heart extract. The bacterial product was found to bind to the host structure until the available host structure was fully saturated. The similarity of the above flows of macromolecules with some models of morphogenesis indicates the existence of diseases associated with the flow of a protein to the undesirable site in the organism. In such a case therapy with low-molar-mass substances is wrong in principle.

Pattern formation in a Turing's type model with minimal reactional complexity

Turing's original reaction network is systematically studied, particularly in what concerns: (a) Its ability to produce patterns in a predictable way. (b) The feasibility of its concentration-independent sink term. Despite the widely accepted view that Turing's original model presents some inherent inability to produce regular structures, the pattern formation properties of this model are found to obey the predictions of the corresponding Linear Stability Analysis in the one-dimension and in 'small' two-dimensional systems. An 'Enzymatic' variation of the original Turing's Model is introduced, where the unrealistic sink term is substituted by an enzymatic degradation. It seems that reaction networks of this type can inspire a promising search for chemical or biochemical experimental systems with pattern formation properties, even in the absence of high non-linearities. It is pointed out that temporal oscillations, impossible for the original Turing's Model, are stable and persistent in its Enzymatic variation.

What is the status of reaction-diffusion theory thirty-four years after turing?

Physicochemical explanations of phenomena are divisible into three classes: structure, equilibrium and kinetics. For the phenomena of biological development, many physical scientists have the preconception that the explanations must turn out to be principally kinetic. In this class of theory, reaction-diffusion is by far the most extensively developed, and is worthy of attention both for its own sake and because many of its features well exemplify the nature of the broader field of kinetic theory. Reaction-diffusion should be thought of as a class, rather than a species, of theory. This review addresses three aspects: first, the general nature of the two-morphogen interaction as first proposed by Turing and incorporated in many later models; second, the specifics of these later models and their probable relative scope; third, the current state of attempts to identify the chemical nature of morphogens. It is concluded that reaction-diffusion in particular, and kinetic theory in general, are now slowly emerging from the almost total neglect by biologists which reaction-diffusion suffered for its first 20 years.