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Abstract Background Protein kinases are a large family of druggable proteins that are genomically and proteomically altered in many human cancers. Kinase-targeted drugs are emerging as promising avenues for personalized medicine because of the differential response shown by altered kinases to drug treatment in patients and cell-based assays. However, an incomplete understanding of the relationships connecting genome, proteome and drug sensitivity profiles present a major bottleneck in targeting kinases for personalized medicine. Results In this study, we propose a multi-component Quantitative Structure–Mutation–Activity Relationship Tests (QSMART) model and neural networks framework for providing explainable models of protein kinase inhibition and drug response ( $$\hbox {IC}_{50}$$ IC 50 ) profiles in cell lines. Using non-small cell lung cancer as a case study, we show that interaction terms that capture associations between drugs, pathways, and mutant kinases quantitatively contribute to the response of two EGFR inhibitors (afatinib and lapatinib). In particular, protein–protein interactions associated with the JNK apoptotic pathway, associations between lung development and axon extension, and interaction terms connecting drug substructures and the volume/charge of mutant residues at specific structural locations contribute significantly to the observed $$\hbox {IC}_{50}$$ IC 50 values in cell-based assays. Conclusions By integrating multi-omics data in the QSMART model, we not only predict drug responses in cancer cell lines with high accuracy but also identify features and explainable interaction terms contributing to the accuracy. Although we have tested our multi-component explainable framework on protein kinase inhibitors, it can be extended across the proteome to investigate the complex relationships connecting genotypes and drug sensitivity profiles.