Time-varying causal inference from phosphoproteomic measurements in macrophage cells

Cellular signaling circuitry in eukaryotes can be studied by analyzing the regulation of protein phosphorylation and its impact on downstream mechanisms leading to a phenotype. A primary role of phosphorylation is to act as a switch to turn "on" or "off" a protein activity or a cellular pathway. Specifically, protein phosphorylation is a major leit motif for transducing molecular signals inside the cell. Errors in transferring cellular information can alter the normal function and may lead to diseases such as cancer; an accurate reconstruction of the "true" signaling network is essential for understanding the molecular machinery involved in normal and pathological function. In this study, we have developed a novel framework for time-dependent reconstruction of signaling networks involved in the activation of macrophage cells leading to an inflammatory response. Several signaling pathways have been identified in macrophage cells, but the time-varying causal relationship that can produce a dynamic directed graph of these molecules has not been explored in detail. Here, we use the notion of Granger causality, and apply a vector autoregressive model to phosphoprotein time-course data in RAW 264.7 macrophage cells. Through the reconstruction of the phosphoprotein network, we were able to estimate the directionality and the dynamics of information flow. Significant interactions were selected through statistical hypothesis testing ( t-test) of the coefficients of a linear model and were used to reconstruct the phosphoprotein signaling network. Our approach results in a three-stage phosphoprotein network that represents the evolution of the causal interactions in the intracellular signaling pathways.