Identifiability and sensitivity analysis of heterogeneous cell population models

Abstract

In this thesis, we introduce novel concepts to the modeling and analysis of heterogeneous cell populations. Heterogeneous cell populations can be interpreted as large populations of structurally identical cells with heterogeneous parameters and initial conditions. They appear in biological systems such as tissues of higher organisms or colonies of microorganisms. A well-known approach for the modeling of heterogeneous cell populations is the so called density-based approach, in which the state of a heterogeneous cell population is given by the probability density of the cell states. The evolution of the probability densities is in this approach given in terms of a partial differential equation. We extend this approach via a measure theoretical consideration, which exploits the probabilistic nature of the problem. The result of this novel ansatz is a framework in which the evolution of densities is described by operators. One of the key tasks in the analysis of heterogeneous cell population models is parameter estimation. For heterogeneous cell populations we want to estimate the probability density of parameters and initial conditions. However, to be able to perform parameter estimation, one always needs specific identifiability properties of a system. We formulate for the first time the concept of structural identifiability of a heterogeneous cell population model. It is revealed that this concept is closely related to observability of the corresponding single cell model. The connection between both concepts is studied and illuminated in a concrete example. The second emphasis of this thesis is the implementation of sensitivity analysis to the class of heterogeneous cell population models. Here we study sensitivity with respect to variations or misspecifications in the probability density of parameters and initial conditions.