[This page in a printer-friendly PDF version]

The problem of pattern formation

The generation of the complex structure of a higher organism within each life cycle is one of the most fascinating aspects of biology. The similarity of identical twins underlines of how reproducible this process can be when the genetic information is the same. Reference to the genes, however, does not provide on its own an explanation for the generation of spatial structures since with each cell division both daughter cells obtain, as the rule, the same genetic information. This leads to the question of how different parts of the developing organism can become different from each other. How can patterns emerge in an initially more or less structure-less system? How can different genetic information be activated at different positions?
Although many eggs have pronounced asymmetries, the final pattern cannot already be present in the egg in a hidden form. At early stages, many embryos can be fragmented into two parts and each part forms a complete organism. The sea urchin embryo at the 16-cell stage is an example. Thus, the structures must arise during development. Basic concepts for the underlying mechanisms have been derived from experiments involving perturbations of normal development.
We have used such observations to develop specific models for different developmental situations. By computer simulation we have shown that the regulatory features of the models correspond closely to the experimental observations. More recently, the new tools of molecular biology have opened the opportunity to clone genes and isolate molecules involved. In this way, several of these models have obtained direct support.

In his pioneering paper, Alan Turing [1] has shown in 1952 that pattern formation is possible by the interaction of two substances with different diffusion rates. We found that the crucial condition for pattern formation is local self-enhancement and long-range inhibition. A possible reaction consists of an activator (green) that has a strong feedback on its own productions rate. It controls also the production of its long ranging antagonist, the inhibitor. (In reality, more molecules could be involved to realize these positive and negative feedback loops.). A small elevation above a homogeneous steady state has a strong feedback on its further increase such that the deviation becomes more and more pronounced. The concomitantly produced inhibitor diffuses into the surroundings of this incipient maximum and regulates down the activation there. Random fluctuations in the ability to perform the reaction (blue squares) are sufficient for pattern initiation. Eventually, a stable pattern is formed in which the activator maximum is in balance with the surrounding cloud of inhibition. The antagonistic effect can also result from a depletion of a component that is required for the self-enhancing reaction (Gierer and Meinhardt, 1972 , [PDF] ; Gierer, 1981, [PDF] Meinhardt, 1982 [book-remake PDF]; 2003pattern7). Pattern formation is not a privilege of living systems. High sand dunes are formed although the sand is permanently redistributed by the blowing wind. Sharply contoured rivers are formed by erosion although the rain is more or less homogeneously distributed over a particular region. These and many other cases of inorganic pattern formation depend on the same principle.

Gradient formation

A pattern emerges whenever the size of the field becomes larger than the range of the activator. In fields with a size comparable to the activator range, the high activator concentration can be formed at one end of the field only. This is a very important aspect for the understanding of pattern formation in an early embryo: one side of the embryo becomes different from the other although the genetic information is the same in all cells. Activator maxima are assumed to act as organizing regions. The graded activator and/or inhibitor distribution can activate different genetic information in different parts of the tissue leading to an ordered sequence of structures in space (see Gene activation). Thus, the system is able to generate "positional information". In larger fields, several maxima and thus periodic structures can emerge.