Water-mediated correlations in DNA-enzyme interactions

Abstract

In this paper we consider dipole-mediated correlations between DNA and enzymes in the context of their water environment. Such correlations emerge from electric dipole-dipole interactions between aromatic ring structures in DNA and in enzymes. We show that there are matching collective modes between DNA and enzyme dipole fields, and that a dynamic time-averaged polarization vanishes in the water dipole field only if either DNA, enzyme, or both are absent from the sample. This persistent field may serve as the electromagnetic image that, in popular colloquialisms about DNA biochemistry, allows enzymes to "scan" or "read" the double helix. Topologically nontrivial configurations in the coherent ground state requiring clamplike enzyme behavior on the DNA may stem, ultimately, from spontaneously broken gauge symmetries.

FIG. 1. Mediating wave fields or quanta in subatomic and biological physics

(A) Electron-electron correlations are mediated by photons in quantum field theory. (B) Analogously, long-range correlations in the molecular water field between DNA and enzymes may be mediated by dipole waves. Note that these are schematic renderings, neither drawn to scale nor representative of the actual orientations of water molecules.

FIG. 2. Aromatic amino acid network in EcoRI

Tryptophan (blue), tyrosine (purple), and phenylalanine (green) form dipole networks in EcoRI, shown here bound to its double-stranded DNA substrate, with A:T (yellow) and C:G (orange) base pairs highlighted. Other amino acids (gray) are displayed in the context of their secondary structures within the enzyme. Image of EcoRI (PDB ID: 1CKQ) at 1.85 Å resolution created with PyMOL.

FIG. 3. Aromatic amino acid network in Taq DNA polymerase

Tryptophan (blue), tyrosine (purple), and phenylalanine (green) form dipole networks in Taq polymerase, shown here bound to a blunt-ended duplex DNA in the polymerase active-site cleft, with A:T (yellow) and C:G (orange) base pairs highlighted. Other amino acids (gray) are displayed in the context of their secondary structures within the enzyme. Image of Taq polymerase (PDB ID: 1TAU) at 3.0 Å resolution created with PyMOL.

FIG. 4. Orientation geometries and molecular centers of aromatic ring structures in amino acids

(A) Indole ring in tryptophan. (B) Phenol ring in tyrosine. (C) Benzene ring in phenylalanine. The positive z-axis is directed out of the page.

FIG. 5. Collective dipole oscillations in aromatic amino acid networks of DNA-interacting enzymes

Collective normal-mode solutions to networks of aromatic dipoles in EcoRI (5a) and Taq (5b) are within the energy range of the collective dipole modes of DNA bounded by its relevant protein clamps. These states are precisely those for which the number operator $n_s=a_s^{†}{a}_s$ acts in the diagonalized form of Eq. (6), analogous to Eq. (1) for DNA, to produce a zero eigenvalue, thus identifying them with zero-point modes that exist independent of external excitations and arise from the ground state of the enzyme aromatic network. Data for the collective modes (arranged along the abscissa axis according to increasing energy) are presented in units of eV on the ordinate axis.