Charting the molecular structure of complex tissues using spatial covariance tensors

近十年来分子生物学的发展使得研究组织中单细胞的许多特性成为可能，例如它们的遗传信息（遗传学）、细胞中的工作拷贝（转录组学）和它们的蛋白质设备（蛋白质组学）。例如，这些“组学”可以用来描述所有人类细胞的特征，并将它们分组为细胞类型，就像国际人类细胞图谱项目已经完成的那样。这些结果为更好地了解健康组织和疾病以及设计治疗方法提供了基础。直到最近，要分析的组织必须溶解到分离的细胞中，以便获得分离细胞的分子图谱。然而，在这个过程中，人们失去了关于细胞之间空间关系的信息，而这对组织的生长、结构和功能至关重要。事实上，在某些疾病，如自身免疫性疾病和癌症中，细胞之间的局部通信故障或误导起着潜在的重要作用。最近，越来越多的实验方法被开发，使组学在完整组织内的细胞。通过空间关系，得到的数据包含了全新的信息质量，应该最有效地利用这些信息来充分发挥其潜力。然而，目前用于分析这些数据的方法远不如用于分析没有空间成分的纯单细胞数据的方法发达。在这个项目中，这些分析将采用一个看似完全不同的科学领域的方法：晶格量子场论，理论物理学的一个子领域。在那里，具有空间依赖性的数据已经司空见惯了几十年，并且已经开发了许多最佳利用它们的方法。这两个地区的数据有一个重要的共同点：空间相关性构成了观测现象的基础。在晶格量子场论中，这些是基本粒子的状态，在空间分辨组学中，这些是细胞的状态或程序，它们对细胞的边界施加影响，从而至关重要地决定了组织的整体外观。为了破译这些空间细胞程序，本项目将侧重于将单细胞协方差矩阵扩展到空间协方差张量，包括其计算，建模和分析。此外，还将开发一种方法来模拟空间解析组学数据，以测试数据分析方法，并帮助设计实验，例如上述地图集项目。

Developments in molecular biology during the last decade made it possible to investigate many properties of single cells in tissues, e.g. their genetic information (genetics), its working copies in the cells (transcriptomics) and their protein equipment (proteomics). These "omics" can be used e.g. to characterize all human cells and to group them into cell types, like it is already being done in the international Human Cell Atlas project. The results serve as basis for a better understanding of healthy tissues and diseases as well as for devising treatments. Until recently, the tissue to be analysed had to be dissolved into separated cells in order to acquire the molecular profiles of isolated cells. However, in this process one loses information about the spatial relationships between cells, which are of paramount importance for growth, structure, and function of tissues. In fact, there are also certain diseases like auto-immune diseases and cancer, in which malfunctioning or mislead local communication between cells plays a potentially important role. Recently, experimental methods are increasingly being developed which enable omics on cells within the intact tissue. With the spatial relationships, the resulting data contain a brand-new quality of information, which should be utilized most efficiently to leverage its full potential. However, the methods for the analysis of these data are at the moment far less developed than for pure single cell data without spatial component. In this project, methods from a seemingly completely different field of science shall be recruited for these analyses: from lattice quantum field theory, a subdomain of theoretical physics. There, data with spatial dependencies have been commonplace for decades and many methods to make optimal use of them have been developed there. The data from both areas have an important aspect in common: spatial correlations constitute the basis of the observed phenomena. In lattice quantum field theory these are states of elementary particles and in spatially resolved omics these are states or programs of cells which exert influence across the boundaries of cells and thereby crucially determine the overall appearance of a tissue. To decipher these spatial cell programs, this project will focus on the extension of single cell covariance matrices to spatial covariance tensors, including their computation, modelling and analysis. Complementarily, a method will be developed to simulate spatially resolved omics data for testing data-analytic methods and to aid the design of experiments e.g. for the above-mentioned atlas projects.