Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Models for regeneration: reconciling pattern formation and growth
Hans Meinhardt

Last modified: 2014-06-09


Development of higher organisms requires a long chain of pattern-forming reactions. These reactions have inherently strong self-regulatory features, contributing to make development to such a robust process. Many regeneration phenomena can be regarded as an extreme case of self-regulation after a perturbation. The restorations of primary body axes are classical examples. Tissue growth is a challenging problem since with increasing distances the communication via diffusion or related mechanisms becomes less and less efficient. Moreover, pattern-forming reactions have the tendency to switch into symmetric and periodic patterns during growth. However, multiple organizer formation would be a catastrophe for a developing organism, leading to malformations like Siamese twinning. It will be shown that different organisms found different solution to allow growth without formation of supernumerary organizing regions and to maintain nevertheless the possibility to regenerate. In the freshwater polyp Hydra a long-lasting feedback of the pattern on the ability to generate this pattern keeps only a part of the organism competent. Planarians, needing regeneration for asexual reproduction, use the wounds to restrict organizer regeneration to the appropriate positions and time points. In insect limbs and many other systems, cells respond to morphogenetic signals by a stepwise, irreversible and unidirectional change in their determination: cells maintain their once obtained differentiation even if the signals fade away due to growth. However, if regeneration is enforced, rebuilding the signal can reactivate the unidirectional change in the remaining tissue. All these mechanisms allow stretching the size window in which regeneration is possible. Due to this size problem, regeneration is usually observed only in small animals or at early developmental stages in which the systems are small. It will be shown that growth to even larger sizes requires switching off the pattern-forming reaction. This is an important safety mechanism to avoid malformation due to the spontaneous formation of supernumerary organizers. This step, however, is usually connected with a loss of the ability to regenerate. The size problem is proposed to be severe barrier to achieve regeneration in larger systems. The models to be presented are formulated as sets of partial differential equations; simulations will demonstrate that the models are able to account for the observed dynamical behaviour.