Prime Times: The Distribution of Singularities in Hydrophobic Free Energy of Proteins

摘要

The hyperbolic dynamics of the hydrophobic free energy of amino acid side chains serve as the mechanism of generation, storage, and delivery of the small surface tension-like hydrophobic free energy of the macromolecule-solvent interface which proteins use for their functions. We describe a hidden thermodynamic symmetry, enthalpy-entropy compensation, as dominating the hydrophobic free energy of protein function. Trigonometric transformation of this two dimensional phase space yields hydrophobic modes that scale time as complex low-order primes which can be recovered as universal singularities in the power spectra of critically nonlinear, two-parameter maps of hydrophobic free energy. A universal exponent describes the scaling and yields a universal power law for the protein's enthalpy-entropy distribution.