Essential Genes Are Enriched in Semantic Error-Protected Coding Sequences: A Communication-Theoretic Analysis of the Genetic Code

The genetic code is commonly described as a redundant mapping from nucleotide triplets to amino acids, but this redundancy does not make all nucleotide substitutions equivalent. A physical mutation rate at the DNA level may translate into silent changes, conservative amino-acid substitutions, severe missense events, or nonsense mutations. Here, we develop a communication-theoretic framework to quantify how nucleotide-level errors are transformed into semantic degradation of protein-coding information. Single-nucleotide substitutions were modelled as an error channel with variable transition/transversion structure, and their effects were weighted using a normalized physicochemical distance between amino acids, with nonsense mutations assigned maximal cost. This allowed the definition of codon-level semantic cost, sequence-level degradation, and synonymous-codon protection scores. The framework first confirmed that the standard genetic code reduces expected semantic cost relative to randomized genetic-code baselines. At fixed nucleotide substitution probability, semantic degradation depended strongly on the transition/transversion spectrum, showing that physical error rate and genetic-information degradation are not equivalent quantities. The model was then applied to real coding sequences from the RefSeq Escherichia coli K-12 MG1655 assembly. Gene-level analysis revealed substantial heterogeneity in semantic vulnerability across CDS, driven by codon composition, synonymous-codon choice, nonsense susceptibility, and sequence length. Protein-preserving synonymous null models were used to separate amino-acid-composition effects from codon-choice effects. Relative to uniformly chosen synonymous alternatives, real E. coli CDS showed lower semantic substitution cost, increased silent-error protection, and reduced nonsense vulnerability. Much of this signal was explained by genome-wide codon-usage bias, but a subset of genes remained locally protected or locally vulnerable after controlling for global codon usage. Importantly, high-confidence essential genes were enriched among locally protected CDS and depleted among locally vulnerable CDS. This association remained robust across essentiality definitions, mutation-channel assumptions, multivariate controls, and random-label permutation tests. These results support a layered view of genetic-information robustness: the standard genetic code provides a primary semantic-protection layer, organism-wide codon usage provides a secondary modulation, and gene-specific synonymous choice introduces local heterogeneity associated with functional constraint. The proposed framework links mutation-channel parameters to interpretable measures of semantic degradation and provides a quantitative bridge between molecular error processes, codon usage, and gene essentiality.