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

石头剪刀布（RPS）描述了博弈论中的循环优势现象。在这种游戏中，玩家可以从三种相互竞争的命名策略中选择一种：石头赢剪刀，剪刀赢布，布赢石头。这种行为在自然界的蜥蜴种群中被观察到，并导致了振荡。在这种情况下，总人数由一种策略占主导地位，直到它被下一种策略所取代。在三种大肠杆菌菌株的实验中，观察到模式的形成，但没有振荡。然而，在实验可用的系统和理论预测之间存在着巨大的差距。对具有周期性优势的系统的模拟显示出有趣的时空现象，如螺旋波，这些现象尚未在实验中观察到。该项目旨在首次在实验RPS系统中观察到这种螺旋波。为了实现这一目标，我想使用dna工具箱——一种分子编程语言——来创建一个体外RPS游戏来观察振荡和时空模式。DNA工具箱是一个用于创建生化反应网络的框架，其中模板定向酶动态构建DNA物种，这些物种也被酶解降解。杂交反应允许物种相互作用。通过适当的序列设计，可以创建三种自催化物质（石头、布、剪刀），它们循环地相互抑制。与上面描述的石头剪刀布系统相比，dna工具箱的一个优点是可以完全控制许多关键参数，而这些参数在活体种群中很难控制。单个物种的生长速度可以通过改变其模板浓度来调节，而酶浓度或温度的变化对系统具有全局影响。此外，每个单一物种的扩散系数可以改变，这是模式形成的重要参数。此外，分子系统可以很容易地并行化。我的初步结果显示，三种自催化物种的复制可以通过三个荧光报告器和单个物种的抑制来特异性地监测。当整个系统完成后，许多问题不仅在理论上可以解决，而且在实验上也可以解决。振荡在什么条件下发生？这些状态对外部扰动（例如温度变化）有多稳定？何时观察到时空模式？它们如何受到影响？

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?