In the past decade, experimental developments in the field of transcriptomics have enabledresearchers to measure gene expression at the level of single cells, leading to a great increasein...Show moreIn the past decade, experimental developments in the field of transcriptomics have enabledresearchers to measure gene expression at the level of single cells, leading to a great increasein measurement resolution. Clustering the cells according to their gene expression profilescan aid the discovery of novel cell types. Unfortunately, it is often difficult to tell whetherthe established clusters are homogeneous or if sub-clustering might be possible. Recently,a new clusterability measure has been developed that aims to quantify the heterogeneityof gene expression within clusters. The so-calledSIGnal Measurement Angle(SIGMA)is based on a result from random matrix theory which states that the singular values ofa random matrix follow a known probability distribution. Singular values that stronglydeviate from this distribution are likely to be caused by deterministic sources of variability,such as differences between cell types. However, the heterogeneity may also be causedby unwanted technical sources of variance, such as batch effects, which arise when datafrom several experiments are combined. Various methods exist for batch effect correction,but it is yet unclear whether they reduce batch effects to the extent that their effect onSIGMA is sufficiently eliminated. In this thesis, we compared the efficacy of three differentbatch correction methods (fastMNN, Harmony, and Seurat) on simulated data and on twoempirical data sets. Their effectiveness was evaluated with several batch mixing metricsas well as by inspecting the singular values and vectors of the batch-corrected expressionmatrices. In conclusion, both fastMNN and Harmony worked well in most cases, but withunbalanced data sets (i.e., when one or more cell types were absent in one of the batches), itbecame increasingly difficult to decide whether singular values were batch effect-associated,because in those cases the batch effect also contained biological heterogeneity.Show less
In this thesis, we analyze and evaluate a phenomenological model for cell differentiation based on Hill-function type interaction kinetics. This is an extension of a model formulated by Dr. Sui...Show moreIn this thesis, we analyze and evaluate a phenomenological model for cell differentiation based on Hill-function type interaction kinetics. This is an extension of a model formulated by Dr. Sui Huang that has been proposed by Dr. Stefan Semrau to explain the observations of retinoic-acid driven mouse embryonic stem cells differentiation. Thereby, our main goal in this thesis is to evaluate the proposition that the model suffices as a conceptual mechanism of the performed experiments. Towards this end, we investigate how Frege’s theory of judgment can be used along with Kant’s theory of judgment to provide a systematic evaluation of phenomenological mathematical models.Show less
