During cell differentiation, progenitor cells integrate signals from their environment that guide their development into specialized phenotypes. The ways by which cells respond to complex signal combinations remain difficult to analyze and model. To gain additional insight into signal integration, we systematically mapped the response of CD4 + T cells to a large number of input cytokine combinations that drive their differentiation. We find that, in response to varied input combinations, cells differentiate into a continuum of cell fates as opposed to a limited number of discrete phenotypes. Input cytokines hierarchically influence the cell population, with TGFβ being most dominant followed by IL-6 and IL-4. Mathematical modeling explains these results using additive signal integration within hierarchical groups of input cytokine combinations and correctly predicts cell population response to new input conditions. These findings suggest that complex cellular responses can be effectively described using a segmented linear approach, providing a framework for prediction of cellular responses to new cytokine combinations and doses, with implications to fine-tuned immunotherapies.C ell differentiation is controlled by complex gene regulatory networks that determine the expression of a large number of genes in response to external stimuli. CD4 + T cells, central regulators of immune responses, can differentiate into a number of phenotypes (or cell states), each defined by the expression of a panel of genes, such as lineage-specifying transcription factors (TFs) and cytokines (1). Differentiation outcome depends on a number of factors, including strength of antigen stimulation (2, 3), interactions with antigen presenting cells, and the signaling environment defined by secreted cytokines (1). By applying specific cytokine signals, it is possible to direct antigen-activated T cells toward differentiation into a number of specific phenotypes. Although the molecular interactions and regulatory networks that govern the differentiation process are being revealed at increasing resolution (4, 5), understanding the logic of operation of these complex networks and developing predictive mathematical models for cellular responses remain a challenge.Mathematical models that describe complex cellular processes are difficult to construct because of a lack of complete information about the underlying networks of molecular interactions and in particular, missing quantitative data regarding the parameters of biochemical interactions within these networks. Alternatively, a "black box" approach can be used, constructing a model of the system by analyzing its response to different input conditions (Fig. 1A). This technique enables study of complex systems in a simplified manner, because its implementation merely requires measurable inputs and outputs, without quantifying the response of each component inside the box. Approaches based on this concept are highly useful for describing engineered systems and were also applied for studying som...