SynopsisA normal coordinate analysis has been performed for the polyribonucleotides poly(rU) and poly(rA). The polymers are assumed to be 11-fold infinite helical structures in the A conformation. The hydrogen atoms have been rigidly attached to the appropriate atoms in order to reduce the dimension of the problem. The potential energy is defined in terms of a valence force field initially and a model for the inclusion of nonbonded interactions has been presented. A method for factoring the secular equation for infinite helical polymers in Cartesian coordinates is presented. All of the general features of polyribonucleotide spectra have been reproduced and, in many cases, good quantitative agreement between observed and calculated frequencies is obtained. More specific assignments are offered for some of the observed lines.

We have applied the method of vibrational mode softening to investigate conformation changes (i.e., changes in three-dimensional structure) in double-helical DNA. Conformation changes of these macromolecules are analogous to displacive phase changes in crystalline solids. We have calculated a mode softening which would drive the double helix from its B conformation to its A conformation. The mode is not softened by temperature change, but rather by changes in the macromolecular environment which mimics the conditions which cause the conformation change experimentally,The DNA double helix can take on several conformations. 1 When dissolved in water or in gels at high humidity (much water of hydration) it is found in the B conformation. Upon drying the gel in an atmosphere of less than 92% relative humidity, it converts to the A conformation. RNA on the other hand is found only in A-type conformations. It has been suggested that DNA switches to A conformation locally when transcribing RNA in vivo and that this conformation change is an important switching mechanism in the biological function of nucleic acid. 2 We have carried on extensive theoretical investigations of the lattice dynamics of DNA and RNA helices. 3 These calculations were made using valence and Urey-Bradley force fields which were 7 I. S. Sokoknikoff andR. M. Redheffer, Mathematics of Physics and Modern Engineering man, Phhs. Rev. B 12, 4434 (1975), 12 P. C. Arnett and 3. H. Yun, Appl. Phys. Lett. 26, 94 (1975). 13 H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975).obtained, by various authors, by refinement from the observed spectra of the constituent parts of nucleic acid. The calculations were done for artificial homopolymer DNA in which all the base units in a single helix were the same. Two such double-helical DNA compounds exist-poly(dA)* poly(dT) and poly (dG) • poly (dC)-where the bases are adenine, thymine, guanine, and cytosine, respectively. These homopolymer duplexes are available and a considerable amount of experimental ir and Raman analysis has been done for all the occurring conformations. A comparison of our theoretical lines with those observed shows quite good agreement for those regions of the spectrum where data exist. 3 In our calculations for both poly (dG)-poly (dC) and poly(dA)-poly(dT) the lowest-lying optical mode is one in which the two single helices move up and down relative to each other along the double-helix axis. It is this mode which softens in our calculations.The eigenvector of the mode that softens agrees very well with the description of the B to A conformation change. The B conformation has the bases of the helix perpendicular to the helix axes. In the A conformation, the bases are tilted from the perpendicular. The soft mode in which the two helices displace relative to each other along the axis does lead to such a tilting of the bases.In doing our calculations for the soft mode, weWe show that a soft mode arises when the vibrational modes of double-helical DNA are perturbed by increasing the electrost...

SynopsisThe eigenvalues and eigenvectors of I I-fold double-helical poly(rU).poly(rA) have been calculated. The vibrational potential energy of the double-helical sl ruclure is init.ially considered to be a suni of the vibrational potential energy of the single-helicnl struct,ures poly(rU) and poly(rA). Coupling between the single helices is introduced by including a stret,ch force ccnstant, for each hydrogen bond between the uracil and adenine base residues. In addition, a model is presented for nonhonded interart ions between nearest neighbor base pairs, which is consistent. with :t previous model for surh interactions in the single helices. Because of t.he simple st.ruct.ural rela( ionship between t he uncoupled single helices and the double helix we are able to rxst the secular equation for poly(rU).poly(rA) in a form suitable for the use of perturbation thenry tising the previously calculated normal modes for the single helices as the unperturbed modes. Perturbation theory was found t.o be inapplicable for the region of the spectrim 5 4 6 0 mi-'. In this region an exact, Green function technique is used to calciilate the strongly coupled modes.The stretching mot.ions of the hydrogen bonds in the region of the spectrim <450 rni-' have been plotted as bar graphs for each mode.We explicitly display one aspect. of t hese double-helicd normal modes.

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SynopsisWe have investigated the B to A conformation change of DNA double helices by a new method "soft-mode analysis." We find theoretically that a mode does soften when the vibration normal modes are perturbed by increasing the electrostatic interaction between the unbalanced charges on atoms in the double helix. The same mode also softens for enhanced van der Waals interactions. The mode softening indicates the onset of conformation change. The enhancing of the electrostatic and van der Waals interaction mimic the effect of decreasing the polar nature of the solvent or water of hydration associated with the B conformation DNA. We discuss qualitatively the concept of soft modes and their relation to conformation change as well as their applicabilityto macromolecules. We discuss previous work in which the normal vibrational modes have been calculated. We also discuss the displacement which comes from the soft mode and show that it correlates very well with that expected for the B to A conformation charge.