Loss C. Analysis of Single-Cell Data. ODE Constrained Mixture Modeling and Approximate Bayesian Computation

New York: Springer, 2016. - 102 p.Investigating cellular heterogeneity is of great importance for a holistic understanding of biological processes and is therefore a focus of systems biology. This task requires sophisticated models of single-cell data, which in turn need parameter estimation approaches that are able to fit these models to given measurement data.
The first part of this thesis focuses on using ODE constrained mixture models (ODEMMs) for the analysis of single-cell snapshot data. With these models subpopulations can be identified and even the source of differences between subpopulations can be detected. We investigate the method’s applicability to the study of the alteration of subpopulation response by the cellular environment with novel data of NGF-induced Erk signaling, a process relevant in pain sensitization. We enhance the method by providing a mechanistic description of the variability of the subpopulations using moment equations. In addition, we propose ODE-MMs for the analysis of multivariate measurements, which accounts for correlations among the measurands. Applying our method to artificial data of a conversion process and to real multivariate data for NGF-induced phosphorylation of Erk enables an improved insight into the underlying system.
In the second part of this thesis, we study stochastic dynamics of individuals cells that are modeled with continuous time Markov chains (CTMCs). We introduce a likelihoodfree approximate Bayesian computation (ABC) approach for single-cell time-lapse data. This method uses multivariate statistics on the distribution of single-cell trajectories. We evaluate our method for samples of a bivariate normal distribution and for artificial equilibrium and non-equilibrium single-cell time-series of a one-stage model of gene expression. In addition, we assess our method by applying it to data generated with parameter variability and to tree-structured time-series data. A comparison with an existing method using statistics reveals an improved parameter identifiability using multivariate statistics.
In summary, this thesis introduces two novel approaches for the analysis of multivariate data that can be used to study cellular heterogeneity based on single-cell data.