There is some degree of homology in the kinase domain and I suppose that's why some TKIs of the VEGFR family also work on other closely related receptor tyrosine kinases like Kit and PDGFR. Apparently, most tumours can escape from the inhibition of any single kinase by the compensatory activation of other kinase/s and by mutations in the kinase domain so, developing multi-kinase inhibitors make sense (and combos as well). Off-target drug effects could result from non-specific interactions of the TKI with additional target and/or indirect cross-talk between the targeted pathway and other pathways in the signaling network. These effects are hard to predict and there are computational models and cell assays to try assessing the possible responses that will occur in vivo and design safer and effective drugs, but as we can see, they are far from being perfect.
Here's is one approach to predict the sensitivity of a new drug or drug combinations based on known kinase inhibitor targets
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