Abstract Cancer cell lines differ greatly in their sensitivity to anticancer drugs as a result of different oncogenic drivers and drug resistance mechanisms operating in each cell line. Although many of these mechanisms have been discovered, it remains a challenge to understand how they interact to render an individual cell line sensitive or resistant to a particular drug. To better understand this variability, we profiled a panel of 30 breast cancer cell lines in the absence of drugs for their mutations, copy number aberrations, mRNA, protein expression and protein phosphorylation, and for response to seven different kinase inhibitors. We then constructed a knowledge-based, Bayesian computational model that integrates these data types and estimates the relative contribution of various drug sensitivity mechanisms. The resulting model of regulatory signaling explained the majority of the variability observed in drug response. The model also identified cell lines with an unexplained response, and for these we searched for novel explanatory factors. Among others, we found that 4E-BP1 protein expression, and not just the extent of phosphorylation, was a determinant of mTOR inhibitor sensitivity. We validated this finding experimentally and found that overexpression of 4E-BP1 in cell lines that normally possess low levels of this protein is sufficient to increase mTOR inhibitor sensitivity. Taken together, our work demonstrates that combining experimental characterization with integrative modeling can be used to systematically test and extend our understanding of the variability in anticancer drug response. Significance: By estimating how different oncogenic mutations and drug resistance mechanisms affect the response of cancer cells to kinase inhibitors, we can better understand and ultimately predict response to these anticancer drugs. Graphical Abstract: http://cancerres.aacrjournals.org/content/canres/78/15/4396/F1.large.jpg. Cancer Res; 78(15); 4396–410. ©2018 AACR.