UC Irvine

This thesis uses mathematical models to study the dynamics of biological systems under the single cell level. In the first chapter we study a minimal gene regulatory network permissive of multi-lineage mesenchymal stem cell differentiation into four cell fates. We present a continuous model that is able to describe the cell fate transitions that occur during differentiation, and analyze its dynamics with tools from multistability, bifurcation, and cell fate landscape analysis, and via stochastic simulation. In the second chapter we adapt a classical self-organizing-map approach to single-cell gene expression data, such as those based on qPCR and RNA-seq. In this method, a cellular state map (CSM) is derived and employed to identify cellular states inherited in a population of measured single cells. Cells located in the same basin of the CSM are considered as in one cellular state while barriers between the basins provide information on transitions among the cellular states. Consequently, paths of cellular state transitions (e.g. differentiation) and a temporal ordering of the measured single cells are obtained. In the third chapter on the basis of the functional mapping assays of primary visual cortex, we conducted a quantitative assessment of both excitatory and inhibitory synaptic laminar connections to excitatory cells at single cell resolution, establishing precise layer-by-layer synaptic wiring diagrams of excitatory and inhibitory neurons in the visual cortex inferred by the mathematical model. In the fourth chapter we constructed a multi-scale mathematical model integrating the gene regulatory network and cell lineage to study the functions of key genes in controlling mouse embryonic epidermis development. In the fifth chapter we studied the selections of models when prior information is provided to infer the gene regulatory network combining the expression data and ChIP-seq data.