Gene expression in all biological cells is tightly regulated by the binding of transcription factors and by epigenetic modifications of the DNA. Importantly, gene expression and cell differentiation or cell reprogramming are triggered by suitable stimuli in a stochastic manner. Here, atomistic biomolecular simulations and coarse-grained Brownian dynamics simulations will be used to study the binding processes governing gene expression in the E.coli pap operon that is being studied experimentally in project C1. A second part of the project involves stochastic dynamics simulations to model state transitions of the gene-regulatory network centered on the pluripotency factors Oct4, Nanog and Sox2. In collaboration with project C2, we will characterize how dynamic changes of transcription factor concentrations and DNA methylation levels affect cell differentiation during the development of the early mouse embryo until the 32-cell stage.