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Despite the great importance of nucleic acid–protein interactions in the cell, our understanding of their physico-chemical basis remains incomplete. In order to address this challenge, we have for the first time determined potentials of mean force and the associated absolute binding free energies between all standard RNA/DNA nucleobases and amino-acid sidechain analogs in high- and low-dielectric environments using molecular dynamics simulations and umbrella sampling. A comparison against a limited set of available experimental values for analogous systems attests to the quality of the computational approach and the force field used. Overall, our analysis provides a microscopic picture behind nucleobase/sidechain interaction preferences and creates a unified framework for understanding and sculpting nucleic acid–protein interactions in different contexts. Here, we use this framework to demonstrate a strong relationship between nucleobase density profiles of mRNAs and nucleobase affinity profiles of their cognate proteins and critically analyze a recent hypothesis that the two may be capable of direct, complementary interactions.