Non Equilibrium Physics of Single-Cell Genomics

The self-organisation of cells into complex tissues relies on the tight regulation of molecular processes governing their behaviour. Understanding these processes is a central questions in cell biology. In recent years, technological breakthroughs in single-cell sequencing experiments have enabled us to probe these processes with unprecedented molecular detail. However, biological function relies on collective processes on the mesoscopic and macroscopic scale, which do not necessarily obey the rules that govern it on the microscopic scale. Insights from these experiments on how collective processes determine cellular behaviour consequently remain severely limited. Methods from nonequilibrium statistical physics provide a rigorous framework to connect microscopic measurements to their mesoscopic or macroscopic consequences. In this thesis, by combining for the first time the possibilities of single-cell technologies and tools from nonequilbrium statistical physics, we develop theoretical frameworks that overcome these conceptual limitations. In particular, we derive a theory that maps measurements along the linear sequence of the DNA to mesoscopic processes in space and time in the cell nucleus. We demonstrate this approach in the context of the establishment of chemical modifications of the DNA (DNA methylation) during early embryonic development. Drawing on sequencing experiments both in vitro and in vivo, we find that the embryonic DNA methylome is established through the interplay between DNA methylation and 30-40 nm dynamic chromatin condensates. This interplay gives rise to hallmark scaling behaviour with an exponent of 5/2 in the time evolution of embryonic DNA methylation and time dependent, scale-free connected correlation functions, both of which are predicted by our theory. Using this theory, we successfully identify regions of the DNA that carry DNA methylation patterns anticipating cellular symmetry breaking in vivo. The primary layer determining cell identity is gene expression. However, read-outs of gene-expression profiling experiments are dominated by systematic technical noise and they do not provide “stochiometric” measurements that allow experimental data to be predicted by theories. Here, by developing effective spin glass methods, we show that the macroscopic propagation of fluctuations in the concentration of mRNA molecules gives direct information on the physical mechanisms governing cell states, independent of technical bias. We find that gene expression fluctuations may exhibit glassy behaviour such that they are long-lived and carry biological information. We demonstrate the biological relevance of glassy fluctuations by analysing single-cell RNA sequencing experiments of mouse neurogenesis. Taken together, we overcome important conceptual limitations of emerging technologies in biology and pioneer the application of methods from stochastic processes, spin glasses, field and renormalization group theories to single-cell genomics