The Biological Radio Amplitude and Frequency Modulation in the Protein Backbone, with Cross-Substrate Confirmation in Exoplanet Spacings

**The Biological Radio: Amplitude and Frequency Modulation in the Protein Backbone, with Cross-Substrate Confirmation in Exoplanet Spacings**

David Coates. Independent Researcher, Reynoldsburg, Ohio, United States.

The binary-alloy decomposition (Anderson 1958) of the protein backbone under the Perez P1/P2 amino-acid partition yields two algebraically independent information channels: amplitude modulation (AM, inter-class mass contrast) and frequency modulation (FM, spatial residue pattern). The system operates in narrowband FM at quarter-modulation AM depth (μ = 0.245).

Pathogenic missense mutations preferentially cross the P1/P2 class boundary, disrupting the AM channel (UniProt OR = 1.471, N = 73,055; ClinVar OR = 1.416, N = 431,890; both p < 10⁻¹⁵). The effect survives Grantham physicochemical distance stratification (mean stratified OR = 1.424) and is replicated across two independent databases. Within-class P1→P1 substitutions are specifically protective (OR = 0.791, p = 3.7 × 10⁻²⁸), a partition-specific effect independent of physicochemistry. The replicated enrichment (OR ≈ 1.414) matches √2 = σ₂ − 1 to 0.15%, where σ₂ = 1 + √2 is the silver mean at the parabolic boundary k = 2 of the SL(2,ℝ) transfer-matrix framework — the operating point where the two channels project equally (Θ = cos 45°).

Three predictions of the narrowband regime are confirmed: flat population-level cardinality sweep (Carson's Rule), one dominant sideband pair at the α-helix period (Bessel truncation), and gain-dependent mirror-breaking between protein families (N = 100 per family, CIs non-overlapping). Channel independence is demonstrated: thermal adaptation in bacteria shifts AM but not FM.

The FM channel generalises beyond biology. In exoplanet orbital spacings (N = 360 ratio-of-ratio pairs from 236 multi-planet systems), shuffling planet order within systems destroys 31% of modulation structure (p < 10⁻⁴), confirming that sequential ordering carries real frequency information. Both substrates cluster at the parabolic boundary k ≈ 2 (36% of exoplanet consecutive ratios), with a gain mirror at k ≈ 3.5 separating structured from scattered regimes (CV ratio 17×). The pronic trace identity (trace = 2 + 1/L) places the modulation depth μ = 1/4 and coupling constant g = 1/6 as reciprocal components of threads at L = 12 and L = 42 on the pronic ladder.

The paper distinguishes pre-committed predictions from post-hoc observations in an evidential-status table, and reports six corrections or retractions from the research programme. All analysis uses publicly available data (UniProt Swiss-Prot, NCBI ClinVar, NASA Exoplanet Archive). Code deposited alongside.

In memory of Shirley..