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In this thesis, we studied models and parameter estimation methods for single-cell data that are able to account for cellular heterogeneity. We developed two methods, ODE-MMs with MEs for multivariate measurements (Chapter 3) and ABC SMC using multivariate test statistics (Chapter 4). While ODE-MMs have merely been used for single-cell snapshot data, the latter method, ABC SMC with multivariate statistics, can be applied to single-cell time-lapse data.

The focus of this chapter is to assess, improve and extend ODE constrained mixture modeling (ODE-MM) (Hasenauer et al., 2014b), a method for studying dynamics and structures of subpopulations. In Section 3.1, we introduce the underlying method and formulate the problems that are subsequently addressed in the following sections. In Section 3.2, we apply ODE-MMs to novel single-cell snapshot data for NGF-induced Erk signaling.

In the previous chapter we focused on modeling and parameter estimation for single-cell snapshot data. We provided and assessed a method, which not only considers the mean behavior of the cell population, but also the second order moments. In this chapter we go one step further in the direction of treating cells as individuals by modeling single-cell time-lapse data with continuous time Markov chains (CTMCs) (Gillespie, 2007).