Cell populations are heterogeneous in terms of, e.g, cell age, cell cycle state, and protein abundance [1, 2]. This heterogeneity is ubiquitous, even in clonal population, and influences cell fate decisions [2, 3], such as cell death/proliferation [4–7]. Thus, to ultimately understand and control the behavior of populations, the key sources of cell-to-cell variability have to be unraveled. Unfortunately, this is challenging due to experimental constraints. Most experimental systems and measurement devices only allow for the simultaneous assessment of a few cellular properties on a single cell basis. This prohibits the purely experimental analysis of processes which depend on many different cellular properties. Spencer et al. [5] have shown that the experimental limitations can be overcome partially using mathematical models.

To mathematically describe heterogeneous populations, agent-based models are used most frequently. Each agent provides a mechanistic description of the signal transduction within individual cells and thus of its behavior. In such a framework, variability can be modeled by either stochastic [8–10] or deterministic [4, 5, 11] differences among individual cells. The source of the former is the stochasticity of biochemical reactions, while the latter may arise from genetic and epigenetic differences, environmental heterogeneity, or slow dynamic processes (such as the cell cycle).

We focus on the deterministic differences among cells — also called extrinsic factors [12] — in populations of non-interacting cells. Those differences are commonly modeled by differential parameter values and initial conditions [5, 13]. Several methods exist to infer the distribution of parameters and initial conditions from experimental data [13–15] and to obtain quantitative, mechanistic models for cell populations. Unfortunately, the resulting agent-based models are in general highly complex. This complexity prevents the analysis of these models using common tools for dynamical systems [16], such as sensitivity and bifurcation analysis. To the best of our knowledge, for models of heterogeneous cell populations, no structured analysis approach is available. To study population models and to facilitate a model-driven analysis of the heterogeneity, highly flexible methods are required which do not rely on an analytical analysis.

In this work, we propose two methods to fill this gap and to facilitate the analysis of population models. These methods — *parallel-coordinates plots*[17] and *support vector (SV) machines*[18–20] — are tools widely used for the analysis of high-dimensional datasets. We outline how these tools can also be used to analyze complex models of heterogeneous cell populations, particularly addressing the question: "Which parameters cause the heterogeneity of the population's response?". Thereby, we extend our previous work [21] and consider qualitative heterogeneity among cells, in the context of cell fate decisions, as well as quantitative heterogeneity, such as the delay of a decision process.

We show that parallel-coordinates plots provide an easy tool to obtain a qualitative understanding of the system, whereas SV machines allow for assessing the performance of marker combinations quantitatively. Good markers are thereby defined as single cell parameters that facilitate a good prediction of the cell fate decision or the quantitative property under consideration of the individual cell. Furthermore, we show how the combination of parallel-coordinates plots and SV machines enables an in-depth analysis of complex models using exploration techniques.

The article is structured as follows: In the section "Methods", the considered system class and problem are described in mathematical terms, the general idea is discussed, and the application of parallel-coordinates plots and SV machines is outlined. In the section "Results", we provide an exemplary application of our method to a model of the caspase cascade. The article is summarized in the section "Discussion".