CALCULATION OF MACROMOLECULAR FORCE CONSTANTS AND VIBRATIONAL PROPERTIES OF A SEMI-INFINITE STRAND OF THE DNA DOUBLE HELIX

BRYAN FERRELL PUTNAM, Purdue University

Abstract

In the first part of this work, a force constant refinement procedure is developed which is capable of assimilating all spectral data, refining large numbers of force constants simultaneously and predicting intramolecular interactions. The method is capable of giving in principle, perfect reproduction of all known spectral information. We show how the familiar least-squares refinement procedure is actually an approximation (appropriate in the small molecule limit) to this more general refinement procedure. We show how a systematic constraining of the zeroth order eigenvectors produces the stability needed to prevent divergences in large molecule refinements with their associated large number of independent force constant parameters. When all the constraints on the zeroth order vectors are released, the new method reduces to the standard least-squares procedure. In a later section, this new refinement procedure is utilized in a complete planar and nonplanar normal coordinate analysis of the pyrimidine base cytosine. Comparison with results on previous studies of the planar vibrations of the same molecule demonstrate that the new refinement procedure produces a quantitatively better fit to the observed spectrum. The new procedure leads to the development of a new torsional internal coordinates, leading to the prediction of two isolated low frequency (near 200 wavenumbers) cytosine torsional modes in the vicinity of where two such modes are believed to occur. In addition, we were able to describe the recently observed coalescence of the torsional and wagging motions of the cytosine amino group upon deuteration of the amino group. The deuterated cytosine spectrum was predicted quite well from a refinement to the cytosine spectrum alone, pointing out the predictive power of the new technique. In the second part of this work, a Green's function approach is used in contructing a dynamical model of a semi-infinite length of the DNA homopolymer B poly(dG)(.)poly(dC). Considerable attention is focused on the hydrogen bond stretching close to the terminus. A melting (or breathing) coordinate is defined as an average over the three linking hydrogen bond stretches in a base pair unit cell. A large amplitude in this coordinate would be expected to precede DNA strand melting. Adjacent to the cut, the contribution to the thermal mean square displacement amplitude of the melting coordinate is about a factor of two greater than for the same quantity far from the cut. We suggest that the thermal melting of a DNA double helical homopolymer may tend to start from an end (if one is available), and moves into the interior of the chain. We show how certain infinite chain modes with small breathing amplitude can develop breathing mode character near the terminus, and suggest that the same phenomenon may occur near other specific base pair sequences. Considerable attention is also fastened on the low microwave region from about 0 to 1.75 wavenumbers. Of great interest is the existence of narrow resonant modes in this frequency region. Particularly pronounced breathing resonances occur near .03 and .08 wavenumbers (about .9 and 2.4 GHz). Future work will involve determining how well these resonant melting modes couple to a microwave field, suggesting that disruption of the double helix could be induced.

Degree

Ph.D.

Subject Area

Biophysics

COinS