Pattern formation in active matter and biology: bacterial mixtures and vegetation

Abstract

The emergence of complex biological functions depends on the spontaneous formation of spatio temporal patterns between agents such as cells, plants, and animals. In the first part of this project, we will investigate the collective behavior of binary mixtures of bacterial cells and how they undergo cooperative or competitive pattern formation. We will focus on phenomena similar to so-called ""motility-induced phase separation"" found in collections of active (i.e., motile) particles like bacterial fluids, where persistent motion takes the role of ""attractive forces"" in generating agglomeration. It is known that, compared with systems of identical particles, the phenomenology of passive (i.e., nonmotile) mixtures is much richer. The study of bacterial mixtures is therefore of great relevance as different bacterial species and strains frequently coexist in nature. This project aims to discover new features that appear only for mixtures, e.g., the slow approach to stationary segregation incrowded environments, for which there are no results. Our research questions will beans wered via a combination of theoretical methods, simulations, and collaboration with experimentalists. Initially, we will consider reciprocal mixtures where both types of bacteria have the same motility properties, i.e., the same self-propulsion speeds and reorientation rates. As found in Biology, we will consider the scenario where the motility properties of each type are affected reciprocally by the presence of the other type. These ""quorum-sensing"" interactions can be achieved and tuned in the lab by genetically modifying each type's biochemical signalling; in doing so, their motility properties will depend on the concentration of highly-diffusive molecules produced exclusively by the other type. With this mechanism, it was shown that co-localization (or anti-localization) of the bacterial types emerges. Nonetheless, several questions remain open. One example is the environmental coupling that arises for bacterial mixtures compartmentalized in spatial niches. Another question is whether bacterial types, say, A and B, can regulate their motilities such that A moves at higherself-propulsion speed in the presence of B while B moves at lower self-propulsion speed in the presence of A, effectively leading to a phenomenon preliminarily dubbed ""type chasing"". Finally, we will consider mixtures of bacteria with different motilities. Answering these questions will provide important steps towards avoiding the pathogenic formation of bacterial agglomerates found in medical contamination. Secondly, we will investigate the minimal ecological requirements for the formation of vegetation patterns. Particularly, we will study the structural effects of rainfall spatial gradients (as at the border of deserts) and their seasonal temporal variability. These features are expected to generate the coexistence of distinct patterns. A similar behavior occurs during the phase separation of thermodynamic fluids, where abrupt environmental changes are known to generate secondary domains on a matrix of evolving primary structures. Later in the dynamics, all domains merge together as the system approaches thermodynamic equilibrium. For vegetation patterns, however, thermodynamic equilibrium is absent, meaning that primary and secondary ""domains"" coexist indefinitely. The implications of such primary-secondary domain coupling will be analyzed. Our results will be compared with image analysis from available satellite data. This project is designed to bring outstanding advances to the lively fields of active matter and theoretical ecology. It involves a synergy of interests as well as theoretical and experimental expertises. The proposal is physically relevant, viable, and presentes great potential for applications. (AU)