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

剪刀石头布（RPS）描述了博弈论中的循环优势现象。在这样一个游戏中，个体可以选择三种命名策略中的一种，这三种策略可以相互竞争：石头击败剪刀，剪刀击败布，布击败石头。在这种情况下，总种群被其中一个策略所支配，直到它被下一个策略所取代。在实验中，三个E.大肠杆菌菌株的模式的形成，但没有观察到振荡。然而，实验可用的系统和理论预测之间存在巨大差距。对具有周期性优势的系统的模拟显示了有趣的时空现象，例如螺旋波，这在实验中还没有观察到。该项目旨在首次在实验性RPS系统中观察这种螺旋波。为了实现这一点，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-PCR是一种用于创建生物化学反应网络的框架，其中模板指导的酶动态地构建DNA种类，这些种类也被酶降解。杂交反应允许物种彼此相互作用。通过合适的序列设计，可以产生三种自催化物质（石头、剪刀、布），它们循环地相互抑制。与上述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，而这些参数在活体中很难控制。单个物种的生长速率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，这是一个重要的参数，在图案形成。此外，分子系统可以很容易地parallelized.My初步的结果显示，三个自催化物种的复制可以监测特异性与三个荧光报告和抑制的单一物种。当整个系统完成后，许多问题不仅可以在理论上解决，而且可以在实验上解决。在什么条件下会发生振荡？这些状态对于外部扰动（例如温度变化）的稳定性如何？何时观察到时空模式，如何影响它们？

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?