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

石头-布-剪刀(RPS)描述了博弈论中的循环优势现象。在这样的游戏中，一个人可以从三种命名策略中选择一种，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。这种行为在自然界的蜥蜴种群中观察到，并导致了振荡。在这种情况下，总人口一直由其中一种战略主导，直到它被另一种战略取代。在对三个大肠杆菌菌株的实验中，观察到了模式的形成，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了有趣的时空现象，如螺旋波，这些现象尚未在实验中观察到。该计划的目的是在RPS实验系统中首次观测到这种螺旋波。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，以观察振荡和时空模式。DNA工具箱是一个创建生化反应网络的框架，在该网络中，模板指导的酶动态地建立DNA物种，这些DNA物种也被酶降解。杂交反应允许物种之间相互作用。通过合适的序列设计，可以产生三种自催化物种(岩石、布和剪刀)，它们相互循环地抑制。与上述岩石-布-剪刀系统相比，DNA工具箱的一个优势是完全控制许多关键参数，这些参数在活着的人群中很难控制。单一物种的生长速度可以通过改变模板浓度来调节，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都是可以改变的，这是图案形成过程中的一个基本参数。此外，分子系统可以很容易地并行化。我的初步结果显示，三个自催化物种的复制可以用三个荧光记者和单一物种的抑制特异性地监测。当整个系统完成后，许多问题不仅在理论上得到解决，而且在实验上也得到了解决。在什么情况下会发生振荡？对于外部扰动(例如，温度变化)，这些状态的稳定性如何？什么时候观察到时空模式，它们会受到怎样的影响？

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?