Cellular circuits sense the environment, process signals, and compute decisions using networks of interacting proteins. Emerging high-dimensional single-cell technologies such as mass cytometry can measure dozens of protein epitopes simultaneously in millions of individual cells. With thousands of individual cells, each providing a point of data on co-occurring protein states, it is possible to infer and quantify the functional forms of the relationships between proteins. However, in practice these underlying relationships are typically obscured by statistical limitations of the data, hence rendering the analysis and interpretation of single-cell data challenging. We developed computational methods, tailored to single-cell data, to more completely define the function and strength of signaling relationships.

Quantitative characterization of T cell signaling. (A) The pCD3ζ-pSLP76 signaling interaction shown as (I) a scatterplot, (II) a kernel density estimate, and (III) by using a conditional DREVI method. (IV) Shape features are extracted and quantified. (B) DREVI plots of a signaling cascade downstream of TCR show the time-varying nature of edge shapes and strengths. (C) Edge strengths are quantified by use of conditional DREMI.

We demonstrate the utility of our methods using single-cell data collected from T cells. Although T cell subpopulations are phenotypically delineated into several cell subsets—such as regulatory, effector, and memory—and are thought to have similarly wired signaling networks, their responses to activation differ in ways that are not understood.

We used mass cytometry to measure the abundance of 20 internal and surface protein epitopes, at 13 time points, after two different types of TCR activation in T cells of B6 mice—resulting in more than 2 million data points. To study TCR signaling, we developed conditional-Density Resampled Estimate of Mutual Information (DREMI) to quantify the strengths of the influence that a protein X has on protein Y, and conditional-Density Rescaled Visualization (DREVI) to visualize and characterize the edge-response function underlying their molecular interaction. A key conceptual shift in DREMI and DREVI is our use of the conditional probability of Y | X rather than the joint probability of X and Y. We show that the consensus Y-response for each value of X is much easier to identify in the conditional density estimate, especially when the joint density is concentrated in a narrow range, which is typical of such data (Fig. 1A).

We used DREMI to characterize the rapid dynamics of signaling interactions upon TCR activation (Fig. 1B) and show that the strength of signal transfer peaks in canonical pathway order (Fig. 1C). We compared edges in naive and antigen-exposed CD4⁺ T cells and identified differential signal transmission along a key signaling cascade that starts at pCD3ζ and continues through pSLP76, pERK, and pS6. At each stage in this cascade, more information (higher DREMI) is transferred downstream from one protein to another, over a longer time period, in naïve cells than in antigen-exposed cells. We validated our characterization in mice lacking the extracellular-regulated mitogen-activated protein kinase (ERK2), demonstrating stronger influence of pERK on pS6 in naive cells, as predicted.

DREMI solves a challenging problem: quantifying the strength of the underlying complex relationships between proteins from noisy data. Our approach reveals how signaling is fine-tuned between T cell subpopulations: The differences we identified between naïve and antigen-exposed T cells suggest that naïve cells more sensitively transmit upstream signaling …