Topological data analysis for spatial transcriptomics

拓扑数据分析（TDA）是一个相对较新的数学领域，它使用代数拓扑的思想和技术来研究数据的底层几何。TDA中的工具通常具有很强的抗噪声稳健性，并且易于适用于高维输入，使其特别适合用于各种生物应用。在这方面经常出现的一个挑战是空间信息的结合。空间数据集通常是嘈杂的，现有的技术可能被异常值和错误标记误导。然而，最近关于支持TDA的统计框架的工作已经允许在这个方向上有希望的新拓扑应用。例如，多参数持续性景观[1]已经成功地应用于研究空间组织数据，这种方法在统计上是合理的，并且不受人工制品[2]的影响。单细胞测序是复杂生物信息的一个特别丰富的来源，为大量的单个细胞产生基因表达数据。现代技术允许同时读取数百个基因，产生非常高维，嘈杂的数据集。因此，TDA是该领域研究的自然选择。事实上，scTDA方法使用TDA的技术来执行无监督的时间转录组分析，并且在合成数据方面优于几种现有的方法。然而，scTDA并不能解释细胞的空间分布，人们普遍认为这是理解组织行为的关键因素。目前已有几种将空间信息与转录组学分析相结合的技术，包括SpatialDE[5]、trendsceek[6]和SPARK[7]。然而，它们通常的特点是关注表达梯度而不是细胞边界的识别。这使得它们不适用于检测稀疏细胞很重要的环境。此外，这些方法无法解释广泛的其他可用信息，如转录本密度和核定位。基于scTDA的成功，并考虑到空间数据分析的拓扑方法的潜力，我们提出TDA将为空间转录组数据分析提供一个理想的框架。我们将产生新的拓扑方法，以解决现有技术中存在的问题。为了实现这项工作，我们将利用尖端的Stereo-Seq技术，该技术能够以前所未有的分辨率收集大量的空间转录组信息。该项目属于EPSRC数学生物学、生物信息学、几何和拓扑研究领域。

Topological data analysis (TDA) is a relatively new field of mathematics which uses ideas and techniques from algebraic topology to study the underlying geometry of data. Tools in TDA typically feature strong robustness to noise and are readily applicable to high-dimensional inputs, making them particularly suitable for use in a wide variety of biological applications.One challenge which arises frequently in this context is the incorporation of spatial information. Spatial data sets are often noisy, and existing techniques can be misled by outliers and mislabelling. However, recent work on the statistical frameworks underpinning TDA has allowed for promising new topological applications in this direction. For example, multiparameter persistence landscapes [1] have been successfully applied to study spatial tissue data in a way which is both statistically sound and unhindered by the presence of artefacts [2].Single-cell sequencing is a particularly rich source of complex biological information, producing gene expression data for large numbers of individual cells. Modern technology allows for hundreds of genes to be read simultaneously, producing very high-dimensional, noisy data sets. TDA is therefore a natural choice for study in this area. Indeed, the scTDA methodology uses techniques from TDA to perform unsupervised temporal transcriptomic analysis, and outperforms several existing methodologies on synthetic data [3]. However, scTDA does not account for the spatial distribution of cells, and it is generally understood that this is a critical factor in understanding tissue behaviour [4].Several techniques now exist for incorporating spatial information with transcriptomic analysis, including SpatialDE [5], trendsceek [6], and SPARK [7]. However, they are generally characterised by a focus on expression gradients rather than identification of cell boundaries. This makes them unsuitable for contexts in which the detection of sparse cells is important. Further, these methods fail to account for a wide range of additional available information, such as transcript density and nuclear localisation.Building on the success of scTDA, and given the demonstrated potential of topological methods for analysis of spatial data, we propose that TDA would provide an ideal framework for the analysis of spatial transcriptomic data. We will produce novel topological methodologies which address the issues present in existing techniques. To enable this work, we will make use of the cutting-edge Stereo-Seq technology, which has enabled the collection of vast amounts of spatial transcriptomic information at unprecedented resolutions [8].This project falls within the EPSRC Mathematical Biology, Biological Informatics, and Geometry and Topology research areas.