Analysis and Control of Cellular Ensembles

An ensemble system is a collection of nearly identical dynamical systems which admit a certain degree of heterogeneity, and which are subject to the restriction that they may only be manipulated or observed as a whole. This thesis presents analysis and control methods for cellular ensembles by considering reduced 1-dimensional dynamics of biological processes in high-dimensional single-cell data and models.

To be more specific, we address the quest for real-time analysis of biological processes within single-cell data by introducing the measure-preserving map of pseudotime into real-time, in short MAPiT. MAPiT enables the reconstruction of temporal and spatial dynamics from single-cell snapshot experiments. In addition, we propose a PDE-constrained learning algorithm which allows for efficient inference of changes in cell cycle progression from time series single-cell snapshot data. The second part of this thesis, is devoted to controlling a heterogeneous cell population, in the sense, that we aim at achieving a desired distribution of cellular oscillators on their periodic orbit. A systems theoretic approach to the ensemble control problem provides novel necessary and sufficient conditions for the control of phase distributions in terms of the Fourier coefficients of the phase response curve.

This thesis establishes a connection between the previously separate areas of single cell analysis and ensemble control. Our holistic view opens new perspectives for theoretic concepts in basic research and therapeutic strategies in precision medicine.