Formation of biological patterns by pulsed signals

• Alan Turing first described how regular patterns found in living things, such as the stripes of zebras, appear.
• A collaborative study between IFISC and Princeton University proposes an alternative mechanism to explain this pattern formation.

Understanding how regular shapes (patterns) are generated in nature is a key question, as they have a major influence on the functionality, resilience and properties of organisms and their aggregations. Structures as diverse as the patterns on an insect shell, the stripes on a zebra or bacterial cultures have been the subject of analysis for decades, mainly with the intention of understanding how they are generated.

A recent study in which Eduardo Colombo, from Princeton University in the United States, and Cristóbal López and Emilio Hernández-García, from IFISC (UIB-CSIC), have collaborated, has identified a new mechanism of pattern formation in biological contexts. The work, published in Physical Review Letters, proposes a mathematical model in which these patterns emerge from the interaction of organisms that communicate through the intermittent emission of noxious signals.

In the 1950s, the British mathematician Alan Turing found a very general mechanism capable of explaining some of the patterns found in nature. However, this mechanism was not necessarily linked to life activity, so it has been equally applied to understand other structures that appear spontaneously in inert systems, such as chemical reactions, optical and mechanical devices, etc. In essence, the Turing process consists of competition between a substance that tends to multiply, and which in turn generates another substance capable of eliminating the first one in an inefficient way, but having greater mobility and therefore occupying places where the first substance has not yet arrived. After 70 years of research, hundreds of physical, chemical and biological systems have been identified that can be explained by the Turing process with some variations.

The new mechanism proposed in this study also requires two types of substances, one of which is capable of eliminating the other, which produces it. The novelty of the model lies in the fact that the production of this second substance is carried out in a pulsed, intermittent manner. It is also necessary that the substance produced propagates through space in a certain way, for example as liquids propagate in porous media. In such situations, in cases where the Turing mechanism is not able to generate structures, and the substances would be distributed homogeneously in space, the intermittent production destabilises the homogeneous distribution and the substances are grouped together to form periodic fringe-like structures.

The proposed mechanism may be of relevance in patterns where the interaction between elements occurs in very short pulses compared to reaction processes. This category would include patterns found in chemistry or ecology, such as in bacterial cultures where bacteria may intermittently secrete toxins.  

Colombo, Eduardo H.; Lopez, Cristobal; Hernandez-Garcia, Emilio. Physical Review Letters 130, 058401 (1-5) (2023). DOI: 10.1103/PhysRevLett.130.058401