Topological Phase Transitions and Foraging in the Slime Mold Physarum polycephalum

真正的粘菌多头绒泡菌是一种含有多个核的阿米巴原虫。它的大小可以达到一平方米，通常作为一种觅食策略，它会形成一个延伸的运输网络。觅食单位的结构和动态取决于环境条件和相应的生活期。多头绒泡菌运输网络已被证明具有解决复杂任务的能力，如在路径长度和效率方面解决迷宫求解和网络优化。此外，这些网络似乎在探索其环境时表现出一定的学习能力。这种新出现的行为是如何从基本的细胞过程发展而来的，在很大程度上是未知的。我们设计了实验和理论分析，以弥合生物体的行为与其有效软物质机械的局部动力学之间的差距。简而言之，我们通过剪切来破坏原质体，以产生不相连的微原质(MPS)，当它们被放置在二维琼脂基质上的斑块时，它们努力重新结合。在营养丰富的情况下，这些MPS会在渗流过程中直接融合成一个扩展的网络。相比之下，在特定的饥饿条件下，MPS首先结合成卫星，卫星从原始补丁辐射出去。随后，这些卫星开发出无数个洞，并过渡到一个网络。在这两种情况下，生物体的最终状态是相同的。这两条路径都涉及一系列的拓扑转换，其中节点和链接的数量以一种特有的方式变化。这项提议的目的是描述这些过程的静态和动态。将使用图论和标度分析中的元素来描述相应过渡附近和更远的原虫网络结构。全球网络动态将由主方程建模。我们将根据营养历史、初始密度、营养含量和基质硬度进行实验。疟原虫由外部或内部静脉组成，作为(蠕动的)营养和化学信号以及一般细胞物质的运输管道。我们的目标是揭示静脉内胞液流动与网络的几何和拓扑的相互作用。这需要概述全球网络结构和细胞骨架组织的微观细节，包括静脉内的流动模式。配备了环境室的电动变焦显微镜可以在高时间分辨率下以交替放大进行长时间观察。它将使我们能够将协调觅食行为的全球网络结构和动力学与局部细胞内相互作用联系起来。

The true slime mold Physarum polycephalum grows as an amoeboid plasmodium containing multiple nuclei. It can reach a size up to square meters and usually forms an extended transport network as a foraging strategy. The structure and dynamics of foraging units are dependent on environmental conditions and corresponding life stage. Physarum polycephalum transportation networks have been shown to possess the ability to solve complex tasks like maze solving and network optimization in terms of path length and efficiency. In addition, these networks appear to exhibit certain learning capabilities while exploring their environment. It is largely unknown how this emergent behavior develops from basic cellular processes. We have designed experiments and theoretical analyses in order to bridge the gap between the behavior of the organism and the local dynamics of its effective soft matter machinery. Briefly, we disrupt a plasmodium by shear to create disconnected microplasmodia (MPs), which strive to reunite when placed in patches on a 2-dimensional agar substrate. Given abundant nutrients, these MPs fuse in a percolation transition directly into an extended network. In contrast, under specific starvation conditions MPs combine first into satellites, which radiate away from the original patch. Subsequently, these satellites develop numerous holes and transition into a network. The final state of the organism in both scenarios is the same. Both pathways involve a sequence of topological transitions where the number of nodes and links changes in a characteristic way. It is the aim of this proposal to describe the statics and dynamics of these processes. The plasmodium network structure in the vicinity of the respective transitions and beyond will be characterized using elements from graph theory and scaling analysis. Global network dynamics will be modeled by a Master equation. We will perform experiments as a function of nutrient history, initial density, nutrient content and substrate stiffness. The plasmodium is comprised of external or internal veins serving as (peristaltic) transport pipelines for nutrients and chemical signals as well as general cellular material. We aim to unravel the reciprocal interaction of cytosolic flow within veins with geometry and topology of the network. This requires an overview of global network structure and microscopic details of cytoskeletal organization including flow patterns within veins. A motorized zoom microscope equipped with an environmental chamber allows prolonged observation at high temporal resolution with alternating magnification. It will enable us to link global network structure and dynamics orchestrating foraging behavior to local intra cellular interactions.