LMU physicists have developed a model to describe how reaction-diffusion networks develop “foams”.

For numerous fundamental processes of life, the formation of certain protein patterns is essential. Protein pattern formation controlled by molecular switches is – like many processes in nature – far removed from a state of equilibrium. For such non-equilibrium processes, a general theory is lacking that predicts the spatial structure of the patterns. A team led by LMU biophysicist Professor Erwin Frey has developed a new concept describing how equilibrium-like laws can nonetheless arise from such processes driven far from equilibrium. In this way, the researchers have substantially expanded our understanding of pattern formation in systems in which multiple components interact.

The new concept is based on the fact that interfacial tensions control the structure of a system close to thermal equilibrium by ensuring that the contact area between two phases is minimized. In liquids, such interfacial tensions cause bubbles and foams to form. In reaction-diffusion systems, however, there are no mechanical interactions of the proteins, and thus no mechanical surface tensions like there are in liquids – and yet foam-like networks form all the same. At these “Turing foams,” as the researchers call them, chemical reaction-diffusion flows generate an effective interfacial tension that determines the structure of the network.

The researchers managed to develop structural and dynamic laws based on this mechanism which mirror the structure formation in these systems. The decisive difference to foams in fluid is as follows: Far from a state of equilibrium, the otherwise endless coarsening of the foam bubbles can stop and the structure “freezes” on a finite scale – creating a lasting pattern.

“We observe precisely this behavior in experiments with the bacterial Min protein system – which controls symmetric cell division in many bacteria – and explain it through the laws we derived,” says Henrik Weyer, first author of the study. Frey concludes, “Our work shows that universal rules for many-body systems can be derived from distinct microscopic mechanisms – rules that not only explain biological patterns, but also open up new paths for the design of synthetic active matter.”