Majority rule in complex mixtures

When living cells first appeared, structures formed via liquids separating into distinct regions, in a process known as "phase separation." In the same way that a vinaigrette (a mixture of vinegar and oil) separates into droplets if left to sit after stirring, phase separation created structures in the cell that evolved to become what are known in the cells alive today as "membraneless organelles." The researchers used a mathematical model for the complex interactions between the many different types of molecules in a mixture. Their model incorporates information on the composition, meaning the amount of each component of the mixture. They applied the laws of thermodynamics to identify if the liquid mixture will undergo phase separation and what kind of structures will be formed. In the past, due to the complexity of the problem, only uniform compositions could be studied, assuming an equal number of molecules of each type. The researchers from the University of Göttingen developed a more sophisticated method to take this into account and discovered that small imbalances in the composition -- that is, small deviations from a uniform composition -- can make a big difference via thermodynamic instabilities. This can lead to a small number of mixture components driving the formation of new phases.

"It's surprising that even very small imbalances in the composition can be strongly amplified. For simple interactions, entropy would be maximized by creating new phases of similar composition. But here, even if there is just 2% of one component in a mixture of 100 different molecules, that component can be present at a concentration of 70% in a droplet that is beginning to separate," comments lead author Filipe Thewes, PhD researcher at Göttingen University's Institute for Theoretical Physics. This amplification could provide a mechanism for cells to regulate phase separation and thus structure formation, simply by making small changes in their composition. Senior author Professor Peter Sollich, also at Göttingen University's Institute for Theoretical Physics, adds: "Because our mathematical approach can be applied generally to many different situations, these results offer exciting potential for applications in related models. For instance, this mechanism could be at work in a range of different fields -- from living cells to market economies or ecological networks with many species."