V. K. Saxena

Vibrational Local Modes in DNA Polymer

Where the translational symmetry of a long polymer chain is interrupted, characteristic vibrations of the molecule are possible in which only those atoms at or relatively near the defect site partake of the motion. This contrasts with the more common vibrational states in which the motion propagates along the chain as a sound wave. Examples of readily producible local defects include broken bonds, missing atoms or groups, and extra links as are found, e.g., in thymine dimers. For each different defect, the spectrum of local mode frequencies is characteristic of its structure. Hence the local modes give direct information about the nature of the defect and can serve as a diagnostic signature of the polymer chain lesion. We have developed and are using algorithms and fortran code to predict the existence and nature of local modes based on their atomic structures. We have studied examples of different defects and found their eigen-frequencies and eigenvectors. For the simplest case of a broken hydrogen bond in a single A-T unit in a long homopolymer dA.dT chain, we display stereo views of the vibrating unit side-by-side with the undisturbed molecule for the three local modes occurring below 300 cm-1 in frequency.

Atomic motions and high frequency cutoff in biological macromolecules

Abstract We point out that the structure of a class of biological macromolecules permits a reduction of the complete atomic dynamical description into motions of subunits consisting of mutually rigidly bound atomic subgroups with relatively weak, flexible joints connecting them. As an example performing an analysis of the DNA normal mode vibrations, we find a distinct bifurcation of the phonon frequency spectrum into two regions. Below a sharp cutoff at about 380 cm −1 the vibrations consist nearly entirely of simple translations and rotations of the subgroups, and are thus potentially capable of metabolic involvement. Above the cutoff, a subunit as a whole is essentially stationary, showing internal vibration only.

Plasmon Interpretation of 25 cm−1 Mode in DNA

An extension of the effective field approach for the normal mode dynamics of dissolved DNA polymers has been applied to study the vibrational modes of DNA-hydration sheath-counterion system, to include the effect of site bound counterions on the system dynamics. An alternative interpretation has been suggested for a 25 cm-1 mode recently observed in DNA samples and interpreted earlier as an interhelical mode. Analysing the eigenvectors this mode is found to possess a large electric dipole moment with longitudinal collective oscillations of the system. These characteristics identify this mode as a collective plasmon mode. Possible physical reasons for the existence of this character have been presented.

Low-Frequency Parametrization of Hydrogen Bonding

Abstract We review the model of the hydrogen bond developed by Lippincott and Schroeder and discuss the frequency range in which it is valid, specifically in the optical and near infrared range. We then show why and how to modify the Lippincott and Schroeder formulae to apply to the far infrared and lower ranges. The contrasts between the old and modified systems, particularly with respect to the effective force constants are worked out and plotted for an example.

Closed form solution for localized modes on a polymer chain with a defect

Abstract The problem of localized vibration modes on a polymer chain with a symmetry breaking defect is formulated as a finite sum of exponentially decaying waves on the polymer. Applying a set of similarity and unitary transformations and using the singular value decomposition technique, the size of the problem is reduced to relatively small dimensions as compared to the large size of the original set of equations for propagating modes on the chain. A modification of the polynomial eigenvalue problem converts the algebraic system to a simple eigenvalue problem which may be diagonalized to give eigenvectors of different decaying waves for an expansion set to describe general localized excitations. Application of proper boundary conditions at the site of broken symmetry leads to determination of the frequencies of the localized modes and corresponding eigenvector expansion. Possible applications of the algorithm to various defect problems on a polymer chain are discussed and some preliminary result on a particular defect are presented.