Trajectory Inference approaches for multimodal SDEs with applications in developmental biology

这项工作的目的是描述各种生物有机体中细胞分化的机制。最初，干细胞不是专门的，并且具有非常相似的遗传特征。在发育的最初阶段，这些细胞开始分裂，数量增加，同时变得更加专业化，开始致力于不同的命运。例如，在哺乳动物中，在第一个多能状态之后，细胞可以成为滋养外胚层-这是形成外部胎盘的细胞-或者它们留在卵子的内部并成为内部细胞团（ICM）的一部分。虽然滋养外胚层不再改变它们的类型和特征，但在ICM中，细胞会做出另一个二元决定，即成为上胚层细胞或原始内胚层细胞等。直至形成生物体内的所有组织和器官。他们选择某种类型的细胞是由遗传信号驱动的，也就是说，某些基因的表达或抑制指导他们的选择。在生物界，有一些与某些发育决定相关的基因的知识，但可能还有其他未知的基因参与其中，这些基因可以帮助解释和预测决策。有各种实验来研究胚胎中的发育现象，收集的数据是研究中每个细胞的基因表达谱。在目前的技术中，有：FACS：它允许收集数百个细胞的有限数量的基因（5-10）。一旦基因被测量，细胞就会被杀死，所以我们不会随着时间的推移跟踪相同的细胞，而是进行类似的重复实验，并在不同的发育时间点测量基因。单细胞RNA测序（scRNAseq）：允许随着时间的推移为有限数量的细胞收集数百至数千个基因。高维且嘈杂。我的合作者收集了这两种技术的数据，我的导师发表了关于应用于FACS数据的拟议建模方法的论文。然而，该实验室正试图使用scRNAseq进行更多的工作和发表，因为这是该领域的新尖端技术。还有一些来自其他小组的已发表的作品，它们都具有scRNAseq和FACS数据，这些数据是可用的，并且可以用于应用我们的技术。数据挑战：由于可以检索的数据量，目前对最新方法（scRNAseq）有很多兴趣。然而，拥有如此多的基因意味着在试图检测真正驱动决策的因素时会有很多噪音和混淆。如何区分相关基因和不相关基因？在现有的几种降维技术中，可以采用哪种降维技术？

The purpose of the work is to describe the mechanisms of cells differentiation in various biological organisms.Originally, stem cells are not specialised and share very similar genetic characteristics. At the very first stages of development, these cells start dividing, they increase in number and at the same time become more specialised, starting to commit to a different fate. For example in mammals, after the first pluripotent state, cells can either become trophectoderms -which are cells forming the outer placenta- or they stay in the inner part of the egg and become part of the Inner Cellular Mass (ICM). While the trophectoderms will not change their type and characteristics anymore, in the ICM there is another binary decision that cells make as of becoming Epiblasts or Primitive Endoderm cells, etc... until forming all tissues and apparatuses in the organisms. Their choice of committing to a certain type of cell is driven by the genetic signals, that is, the expression or inhibition of certain genes which guide them in their choice. There is knowledge, in the biology community, of genes which are relevant for some developmental decisions but there might be other unknown genes involved which could help explain and predict the decision-making. There are various experiments to study developmental phenomena in embryos and the data that are collected are the gene expression profile for each cell in the study. Among current techniques there are: FACS: which allows to collect a limited number of genes (5-10) for hundreds of cells. Once the genes are measured, the cells are killed, so we don't track the same cells over time but rather carry out similar repeated experiments and measure the genes at different developmental time points. Single-cell RNA sequencing (scRNAseq): allows to collect hundreds to thousands of genes for a limited number of cells, over time. High-dimensional and noisy. My collaborators have data collected with both techniques and my supervisor has published papers on the proposed modelling approach applied to FACS data. However, the lab is trying to work and publish more using scRNAseq as this is the new cutting-edge technique in the field. There are also a number of published works from other groups both with scRNAseq and FACS data which are available and could be used to apply our techniques. Data challenge: there is currently a lot of interest towards the newest method (scRNAseq)because of the amount of data that can be retrieved. However, having so many genes means there is a lot of noise and confounding when trying to detect what really drives the decision-making. How to distinguish between relevant and irrelevant genes? What dimensionality reduction technique can be employed among several available ones?