Diversity of extreme environments, phylogeny, and life styles of prokaryotes are reflected in nucleotide compositions of their genomes and amino acid compositions of their proteomes [1]. Despite significant efforts, causal relationship between these compositions remains unresolved. While the genetic code inherently bridges the realms of nucleic and amino acids, the rules of the mutual adjustment of nucleotide and amino acid compositions has not yet been established. We discovered a fundamental tradeoff [2], which analytically describes mutual adjustment of compositions and its effect on the mutational biases. The tradeoff is determined by the interplay between the genetic code, optimization of the codon entropy, and demands on the structure and stability of nucleic acids and proteins. In particular, an increase of the purine load in genomes with low GC content changes the balance between two major determinants of the double-stranded DNA stability: base pairing and base stacking interactions. Simulations yield an increasing proportion of nonsynonymous mutations in genomes with low GC. Corresponding amino acid substitutions result, however, mostly in changes into chemically similar amino acids. As a result, stability of the nucleic acids is maintained, while stability of the encoded proteins is not compromised. The tradeoff is a unifying property of all prokaryotes regardless of differences in their phylogenies, life styles, and extreme environments. It provides a foundation for the work of natural selection and underlies mutational biases characteristic for genomes with skewed GC compositions.