Nicholas P. Timms
Submitted: December 2025 : Published: 18th February, 2026
Abstract
The “Unified theory of phonon in solids” (2025) recently resolved a long-standing controversy in condensed matter physics regarding the relationship between the Boson Peak (BP) and the Van Hove Singularity (VHS). By modeling solids as elastic continua embedded with local “scatterers,” this theory demonstrated that these vibrational anomalies are governed by a unified phase diagram defined by two parameters: the scatterer size and the phonon mean free path. This paper translates this physical model into a quantitative framework for biological systems. We map the abstract parameters of the unified theory onto biophysical structures: protein backbone vibrations serve as the “phonons,” structural heterogeneities (such as active sites and hydration shells) act as “scatterers”, and the efficiency of allosteric communication is defined by the mean free path. Using this mapping, we propose two novel mechanisms for high-level biological function. First, we hypothesize that allosteric regulation is a resonance-induced phase transition where effector binding “tunes” the protein into a “coexistence” regime, inducing localized phonon softening at distal active sites. Second, we propose a “Vibrational Vise” model for enzyme catalysis, where substrate binding creates a scattering resonance that drives mechanical instability (negative sound velocity), effectively using focused vibrational energy to perform work on the substrate. Validated against a “master curve” of heat capacity data from 143 diverse solids, this unified model provides a testable physical basis for reframing proteins as tunable resonant systems. We conclude by outlining specific inelastic neutron and X-ray scattering experiments designed to map the functional phase diagrams of proteins during catalysis and regulation.
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