A potential connection between physico-chemical properties of mRNAs and cognate proteins, with implications concerning both the origin of the genetic code and mRNA-protein interactions, is unexplored. We compare pyrimidine content of naturally occurring mRNA coding sequences with the propensity of cognate protein sequences to interact with pyrimidines. The latter is captured by polar requirement, a measure of solubility of amino acids in aqueous solutions of pyridines, heterocycles closely related to pyrimidines. We find that the higher the pyrimidine content of an mRNA, the stronger the average propensity of its cognate protein's amino acids to interact with pyridines. Moreover, window-averaged pyrimidine profiles of individual mRNAs strongly mirror polar-requirement profiles of cognate protein sequences. For example, 4953 human proteins exhibit a correlation between the two with |R| > 0.8. In other words, pyrimidine-rich mRNA regions quantitatively correspond to regions in cognate proteins containing residues soluble in pyrimidine mimetics and vice versa. Finally, by studying randomized genetic code variants we show that the universal genetic code is highly optimized to preserve these correlations. Overall, our findings redefine the stereo-chemical hypothesis concerning code's origin and provide evidence of direct complementary interactions between mRNAs and cognate proteins before development of ribosomal decoding, but also presently, especially if both are unstructured.