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，它利用代数拓扑学的思想和方法来研究数据的基本几何结构。TDA中的工具通常对噪声具有很强的鲁棒性，并且很容易适用于高维输入，这使得它们特别适合于广泛的生物应用。在这种情况下经常出现的一个挑战是空间信息的结合。空间数据集通常是噪声的，现有的技术可能会被离群值和错误标签所误导。然而，最近关于支持TDA的统计框架的工作已经允许在这一方向上有希望的新的拓扑应用。例如，多参数持久性景观[1]已经成功地应用于空间组织数据的研究，这种方法在统计学上是合理的，并且不受人工制品的存在[2]的阻碍。单细胞测序是一个特别丰富的复杂生物信息的来源，产生大量单个细胞的基因表达数据。现代技术允许同时读取数百个基因，从而产生非常高维的、噪声很大的数据集。因此，TDA是这一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分析，并在合成数据上优于现有的几种方法[3]。然而，scTDA没有考虑细胞的空间分布，通常认为这是理解组织行为的关键因素[4]。现在有几种技术可以将空间信息与转录分析结合起来，包括SpatialDE[5]、trendsceek[6]和Spark[7]。然而，它们的特点通常是侧重于表达梯度，而不是识别细胞边界。这使得它们不适合其中稀疏单元的检测很重要的环境。此外，这些方法没有考虑到广泛的可用额外信息，如转录密度和核定位。基于scTDA的成功，并考虑到拓扑方法在空间数据分析中的潜力，我们认为TDA将为空间转录数据的分析提供一个理想的框架。我们将产生新的拓扑方法，解决现有技术中存在的问题。为了实现这项工作，我们将利用尖端的立体序列技术，该技术已经能够以前所未有的分辨率收集大量的空间转录信息[8]。该项目属于EPSRC数学生物学、生物信息学以及几何和拓扑学研究领域。

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.