A molecular rock-paper-scissors game and the formation of spatiotemporal patterns

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Rock-paper-scissors (RPS) describes the phenomenon of cyclic dominance in game theory. In such a game an individual can chose one of the three name-giving strategies, which can outcompete each other: rock beats scissors, scissors beat paper, paper beats rock.Such a behavior was observed in nature in lizard populations and lead to oscillations. In this case, the total population was dominated by one of the strategies until it was replaced by the next one. In experiments with three E. coli strains the formation of patterns was observed, but no oscillations. However, there is a huge gap between the experimentally available systems and theoretical predictions. Simulations of systems with cyclical dominance show intriguing spatiotemporal phenomena, such as spiral waves, which have not yet been observed experimentally. The proposed project aims to observe such spiral waves for the first time in an experimental RPS system. To achieve this, I want to use the DNA-toolbox - a molecular programming language - to create an in vitro RPS game to observe oscillations and spatiotemporal patterns. The DNA-Toolbox is a framework for the creation of biochemical reaction networks in which template directed enzymes dynamically build up DNA species, which are also degraded enzimatically. Hybridization reactions allow the species to interact with each other. With a suitable sequence design three autocatalytic species (rock, paper, scissors) can be created, which inhibit each other cyclically. An advantage of the DNA-toolbox compared to the rock-paper-scissors systems described above is the full control of many key parameters that are very hard to control with living populations. Growth rates of single species can be tuned by changing their template concentration, whereas changes of the enzyme concentrations or the temperature have a global effect on the system. Furthermore, the diffusion coefficient of every single species can be changed, which is an essential parameter in pattern formation. Furthermore, molecular systems can be easily parallelized.My preliminary results show three autocatalytic species whose replication can be monitored specifically with three fluorescence-reporters and the inhibition of single species. When the full system is completed, many questions cannot only be addressed theoretically, but also experimentally. Under which conditions do oscillations occur? How stable are those states against external perturbations (e.g. a temperature change)? When are spatiotemporal patterns observed and how can they be influenced?