The problem of pattern formationThe 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?
Gradient formationA 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.
Pattern regenerationAn important feature of many developing systems is their ability to regenerate lost parts. For instance, in the freshwater polyp Hydra, after removal of a head a new head regenerates. Pattern regulation is a property of the activator-inhibitor system. As shown in the simulation above, with the removal of the activated region, also the inhibitor-producing cells are removed. The remnant inhibitor decays until a new maximum is formed via autocatalysis. Regeneration is only one of the most extreme manifestations of the self-regulation, an important component to make development error-tolerant and reproducible.
Example for an equation with pattern formation propertiesIn the models, equations are used that describe the concentration changes per time unit. These depend on the production, removal and exchange rates with neighboring cells (diffusion) and a small baseline (activator independent) production rate. The latter is required to initiate the reaction, for instance during regeneration or during oscillations. A typical equation for an interaction of an activator (a) and an inhibitor (h) is given below:
Other molecular realizationsThe activator-inhibitor mechanism is, of course, only an example, and other realizations are possible as well. The inhibition may not result from an inhibitor but from the depletion of a co-factor that is produced everywhere and which is consumed in the autocatalytic reaction. The autocatalysis can consist of a chain of reaction in which many molecules are involved. An example for an indirect autocatalysis is the mutual inhibition of two substances: the increase in the production of one substance leads to a reduction of the second, and thus to a further increase of the first, as if the first system would be autocatalytic.
This paper introduces the concepts of autocatalysis and lateral inhibition underlying the generation of spatial concentration patterns. It derives mathematical criteria for non-linear interactions required for pattern generation, providing a method for designing molecular models. One of the simplest and most widely used example is bimolecular activation in conjunction with monomolecular inhibition. Striking features of developmental regulation can be accounted for along these lines.
The paper reviews models and mechanisms of biological pattern formation with emphasis on the roles of autocatalysis and lateral inhibition. In particular, it contains a demonstration that these two features are mathematically necessary for the simplest two-factor systems, and that they can be generalized, to a considerable extent, to apply to multicomponent systems of pattern formation.
In the book, many models of biological pattern formation are discussed. Since it was definitely written before the molecular tools became available, the mechanisms proposed on the basis of modeling where clear predictions. Several mechanism central in biological pattern formation have been meanwhile confirmed.