Applying methods from statistical physics and information theory to high-dimensional single cell omics data to establish a distribution biology framework
The aim of this project is to develop a widely applicable framework tailored for the molecular characterisation of single cells. Recently, single-cell techniques have made huge advancements, enabling comprehensive analysis of the transcriptome, genome and the protein level at single-cell resolution (Moignard 2013; Shi 2012; Yoon 2011). While these technical achievements are now used for characterising cellular heterogeneity, a systematic approach interpreting and using the resulting high-dimensional data for identifying biological principles of development and pathogenesis is lacking. The proposed subproject aims to address this challenge by further developing our statistical analysis framework and to complement this with a mechanistic mathematical framework based on distribution dynamics to identify CTs within complex systems. For this aim, the student will first use extant data and test different statistical methods to characterise different cell states and the transition between them. The resulting multi-dimensional distributions will then be used to parameterise methods from Statistical Physics (e.g. Fokker-Planck equations) to obtain a firm mathematical description (Risken 1989). The resulting partial differential equations often cannot be solved analytically, but can be simulated numerically. By combining simulations, biological constraints and mathematical approximations, the project will then generate a reduced mechanistic model that emphasises the principles of systems heterogeneity and its role in system transitions. The subproject will also have extensive exchange with the nonequilibrium thermodynamics project of the Esposito group (see below) for theoretical developments. The target disciplines of the PhD candidate to be hired for this project are applied mathematics and statistical physics.