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

The binary-alloy decomposition (Anderson 1958) splits the protein backbone into two independent information channels: amplitude modulation (AM, compositional 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 amino-acid class boundary (OR = 1.471, p < 10⁻¹⁵, N = 73,055 UniProt variants), disrupting the dominant power channel. This effect persists after Grantham physicochemical distance stratification (mean stratified OR = 1.424). Within-class P1→P1 substitutions are specifically protective (OR = 0.791, p = 3.7 × 10⁻²⁸), independent of physicochemistry.

The modulation depth (1/4) and coupling constant (1/6) are identified as reciprocal components of pronic threads at L = 12 and L = 42 on the pronic trace ladder (trace = 2 + 1/L). The enrichment factor 3/2 matches M₆/ℓ₆ = 63/42, the Mersenne-to-complement ratio at the sixth node of the intersection lattice. The FM channel generalises to exoplanet orbital spacings (shuffle test p < 10⁻⁴, 236 multi-planet systems), with both substrates clustering at the parabolic boundary k ≈ 2. Five earlier claims are corrected or retracted. Code and data sources included.

Pathogenic missense mutations in the human proteome are 47% more likely to cross the P1/P2 amino-acid class boundary than benign polymorphisms (OR = 1.471, p < 10−15, N = 73,055 UniProt variants). This effect persists after stratifying by Grantham physicochemical distance (mean stratified OR = 1.424), ruling out radical-substitution bias. Among class-preserving mutations, P1→P1 substitutions are 21% more tolerated than P2→P2 (OR = 0.791, p = 3.7 × 10−28), a partition-specific effect independent of physicochemistry. 

These findings are predicted by a transfer-matrix decomposition of the protein backbone into two algebraically independent channels: amplitude modulation (AM, inter-class mass contrast) and frequency modulation (FM, spatial residue pattern). The system operates in narrowband FM (β ≪ 1) at quarter-modulation AM depth (µ = 0.245), a regime in which the AM channel carries the dominant signal power and is therefore most costly to disrupt. 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). The theoretical backbone is the pronic trace identity: for any consecutive pair (a, a+1), eigenvalues a/(a+1) and (a+1)/a have trace 2 + 1/L where L = a(a+1). The modulation depth µ = 1/4 and the coupling constant g = 1/6 are reciprocal components of pronic threads at L = 12 and L = 42 respectively. The enrichment magnitude OR ≈ 3/2 matches M6/ℓ6 = 63/42, the Mersenne-to-complement ratio at the sixth node of the intersection lattice, where Θ = J6/ℓ6 = 1/2. In exoplanet systems (N = 360 ratio-of-ratio pairs, 236 systems), the FM channel is independently confirmed: shuffling planet order within systems destroys 31% of modulation structure (p < 10−4 ). The population clusters at the parabolic boundary k ≈ 2 (36% of consecutive ratios). Five earlier claims from the research programme are corrected or retracted.

Below is a 3d model for visual interpretation.

Immersive 3d model, Mutation, Trace Map and AM/FM