Many critical processes in the cell involve direct binding between RNAs and proteins, making it imperative to fully understand the physicochemical principles behind such interactions at the atomistic level. Here, we use molecular dynamics simulations and 15 μs of sampling to study the behavior of amino acids and amino acid sidechain analogs in high-concentration aqueous solutions of standard RNA nucleobases. Structural and energetic analysis of simulated systems allows us to derive interaction propensity scales for different amino acid/nucleobase combinations. The derived scales closely match and greatly extend the available experimental data, providing a comprehensive foundation for studying RNA–protein interactions in different contexts. By using these scales, we demonstrate a statistically significant connection between nucleobase composition of human mRNA coding sequences and nucleobase interaction propensities of their cognate protein sequences. For example, pyrimidine density profiles of mRNAs match uracil-propensity profiles of their cognate proteins with a median Pearson correlation coefficient of R = −0.70. Our results provide support for the recently proposed hypotheses that mRNAs and their cognate proteins may be physicochemically complementary to each other and bind, especially if unstructured, with the complementarity level being negatively influenced by mRNA adenine content. Finally, we utilize the derived scales to refine the complementarity hypothesis and closely examine its physicochemical underpinnings.