Programmable pattern formation in systems of communicating subunits

During the last funding period, we studied physical principles underlying the spatial organization of localised catalytic particles. This general issue arises in biological and synthetic systems across different length scales, from enzyme complexes to metabolically coupled cells. To obtain physical design principles, we employed different theoretical approaches, ranging from computational solution of reaction-diffusion equations with fixed reaction centers to analytical optimization within a Lagrangian formulation and variational calculus. Leveraging these approaches, we identified design principles for metabolic microcompartments and for regulating reaction fluxes via enzyme localization, identified a criterion for the optimal distribution of enzymes, and clarified the physics of two general trade-offs in the arrangement of catalytic particles.

We also started a second line of investigation, which we intend to fully develop in the current funding period. Here, we are focused on the question of how systems consisting of communicating subunits (referred to as 'cells’), with fixed spatial arrangements, can form different patterns in a programmable way. Experimentally, such systems can be on the molecular scale, e.g. based on DNA or RNA nanotechnology as developed in A02 (Simmel), or on the scale of cell-sized compartments, as studied e.g. by the Schwille group (A09). For our theoretical investigation, we assume that the 'cells’ have two or more internal states, and are able to perform simple local information-processing operations, the effects of which can be described in the framework of cellular automata models. Within this framework, we explore the general issue of controlling pattern formation processes in cellular systems. Our initial work was limited to a specific scenario, where a small number of local “organizer” subunits steers the patterning process of the entire system. We found that a small fraction of update rules indeed enables complete programmability of pattern formation in one-dimensional arrays. We will now systematically explore different scenarios for controlling pattern formation in one- and two-dimensional systems, where (at least some of) the patterning information is generated in a distributed way, without organizer cells. More specifically, we will study (i) pattern formation with asynchronous cell updates, (ii) the dynamics of irregularly arranged cells, (iii) the interplay of global and local signaling, (iv) the evolution of pattern formation rules, and (v) coupled pattern formation and growth/death of cells. In collaboration with the Simmel group (A03), we will work on the device physics of 'DNA robot arm’ systems, with the goal to implement programmable pattern formation on the scale of macromolecules.