Trajectory Inference approaches for multimodal SDEs with applications in developmental biology

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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?