500 Naturwissenschaften und Mathematik
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This is the invited evening lecture of the biannual workshop on hydroid development of 1999. Its topic is the role of hydra as a rather puristic model for the de-novo generation of spatial patterns in development, and our work in this field. Emphasis is placed not only on experimental studies, but also on theoretical analysis, because the understanding of spatial order requires a systems approach involving the combination of knowledge on molecules, cells and tissues with mathematical analysis, laws and facts.
Physical principles underlying biological pattern formation are discussed. In particular, the combination of local self-enhancement and long-range (“lateral”) inhibition (Gierer and Meinhardt, 1972) accounts for de-novo pattern formation, and for striking features of developmental regulation such as induction, spacing and proportion regulation of centers of activation in tissues and cells. Part I explains physical principles of spatial organisation in biological development. Part II demonstrates in mathematical terms that and how short-range activation and long-range inhibition are conditions for the generation of spatial concentration patterns. The conditions can be expressed in terms of ranges, rates and orders of reactions. These conditions, in turn, can also be derived by analysis of dynamic instabilities by means of Fourier waves, showing the neither obvious nor trivial relation between the latter approach and the theory based primarily on autocatalysis and lateral inhibition.
Aggregates of previously isolated cells of Hydra are capable, under suitable solvant conditions, of regeneration forming complete animals. In a first stage, ecto- and endodermal cells sort out, producing the bilayered hollow structure characteristic of Hydra tissue; thereafter, heads are formed (even if the original cell preparation contained no head cells), eventually leading to the separation of normal animals with head, body column and foot. Hydra appears to be the highest type of organism that allows for regeneration of the entire structure from random cell aggregates. The system is particularly useful for studying cell interactions, tissue polarity, pattern formation, and cell differentiation.
The generation of viral mutants in vitro was demonstrated by treatment of the isolated RNA of Tobacco Mosaic Virus by nitrous acid. This agent causes deaminations converting cytosine into uracil, and adenine into hypoxanthine. Our assay for mutagenesis was the production of local lesions on a tobacco variety on which the untreated strain produces systemic infections only. A variety of different mutants are generated in this way. Quantitative analysis of the kinetics of mutagenesis leads to the conclusion that alteration of a single out of the 6000 nucleotides of the viral RNA is sufficient for causing a mutation.
Within the sedimentation diagram of infective RNA preparations isolated from Tobacco Mosaic Virus, undegraded molecules form a sharp peak with a molecular weight corresponding to the total RNA content of the virus particle. Degradation kinetics by ribonuclease is of the linear, single-target type, indicating that the RNA is single-stranded. The intact RNA of a virus particle thus forms one big single-stranded molecule. Quantitative evaluation of the effect degradation by RNA-ase on the infectivity of the RNA shows that the integrity of the entire molecule is required for its biological activity.
Aside from the increasing, impressive evidence on chemical identification of graded molecules involved, it is the capability of axons for approaching the target position from different aspects in a two-dimensional field which is per se a strong indication for the involvement of gradients. Targeting requires, in the target field, counter-graded effects, either by antagonistic gradients, or by a single gradient in each dimension exerting attractive effects at low, reverting to inhibitory (repulsive) effects at high concentrations. A further requirement for mapping is the modulation of the counter-graded effects by components of the growth cone itself which depends on the origin of the corresponding axon.Transduction and processing of graded signals in the navigating growth cones are proposed to be strongly enhanced by intra-growth-cone pattern formation. The concept also encompasses regulatory and branching processes including the formation of the terminal arbors.