Nearest neighbor frequencies

RNA has four kinds of bases along its polyribose-phosphate backbone and Tanaka assumes that only uracil is photochemically active, the other three bases being equivalently inert. In order to specify the statistical nature of the base sequence, the base composition and nearest neighbor frequencies are used, both of these being experimentally available quantities in many cases. If one assumes the sequence to be stationary, then ptt andpt, the probabilities that an arbitrarily given site is a uracil or an inert (photochemically) base, respectively, and the conditional probabilities, e.g., puu, suffice to represent the sequence. Because of the relations governing these probabilties, viz. 

Although the general trend follows the expected probabihties, there are wide deviations from the expected numbers. Such deviations are common, and are attributable to the variations in the G C content of the DNAs and the variable nearest-neighbor frequencies of the bases. 

Nearest neighbor frequency the fi-equeniy with which a given pair of bases are immediately adjacent in the sequence of a polynucleotide chain. Since there are 4 bases, there arc 16 possible pairs of nearest neighbors. Although it is now possible to determine the sequence of DNA, the parameter still gives useful information about the structure of the molecide. 

Larsen, B., Smidsrod, O., Haug, A., and Painter, T. (1969) Determiation by a kinetic method of the nearest neighbor frequencies in a fragment of alginic acid. Acta Chem. Scand., 23, 2375-2388. 

The double helix structure not only takes into account the equalities A = T and G = C, but also predicts sequence homologies. Thus, a sequence ApG will face CpT on the other strand. But ApT will be paired with ApT. This important aspect of the DNA helix is the basis of Korn-berg s nearest neighbor frequency experiment, which is probably the most important proof of the opposite polarity of the two strands (Section 4.2.3). 

If the incorporation fractions in Table 4.2 are weighted for the compositions obtained, the nearest neighbor frequencies in Table 4.3 can be derived. 

Table 4.2 Nearest Neighbor Frequency Experiment with M. phlei DNA ... 

Table 4.3 Nearest Neighbor Frequencies of M. phfei DMA Obtained from the Data in Table 4.2 ...

An LVM is a vibration of a light impurity atom that does not propagate in the lattice. The atom motions are confined primarily to the impurity itself and its nearest neighbors, with rapidly decaying vibrational amplitude for more distant host atoms. Usually, the lighter the impurity, the higher the frequency of the vibration and the more localized the mode. 

Fig. 3. (a) Partially resolved nuclear hyperfine structure in the p.SR spectrum for Mu in GaAs in an applied field of 0.3 T. The structure occurs in the line corresponding to 0 = 90° and Ms = —1/2. (b) Theoretical frequency spectrum obtained by exact diagonalization of the spin Hamiltonian using the nuclear hyperfine and electric quadrupole parameters in Table I for the nearest-neighbor Ga and As on the Mu symmetry axis. Both Ga isotopes, 69Ga and 71Ga, were taken into account. From Kiefl et al. (1987). 

Fig. 7. The /iSR frequency spectrum in Si with a field of 23.5 mT applied along a (100) crystalline direction. The small satellite lines, indicated by arrows, are caused by Mu centers that have one nearest-neighbor 29Si on the (111) symmetry axis, whereas the strong main lines result from centers with no nearest-neighbor 29Si. From Kiefl et al. (1988b).

Fig. 8. The yuLCR spectra for Mu in silicon with H ( 110). The resonances occur at a field where a muon transition frequency of Mu is matched to that of a 29Si neighbor. The /xLCR in (a) is due to the nearest-neighbor 29Si on the Mu symmetry axis and those in (b) to the six next-nearest 29Si neighbors off the symmetry axis (the high-field line arises from the nearest neighbors). From Kiefl et al. (1989b).

Fig. 9. The magnetic field dependence of the /xSR frequencies in Si with the field aligned along the (100) direction. The solid (dashed) curves are predicted if none (one) of the nearest-neighbor nuclei on the symmetry axis is 29Si. From Kiel et al. (1988b). 

In Eq. (6.1) 1 is the unit operator, there is one state /> associated with each lattice site, and l and l A A = 1, 2, 3, 4) label a molecule and its nearest neighbors in the tetrahedral lattice. Weare and Alben show also that the theorem remains valid when small distortions away from tetrahedrality exist, hence it can be used to describe a random amorphous solid derived from a tetrahedral parent lattice. Basically, the density of states of the amorphous solid is a somewhat washed out version of that of the parent lattice. The general shape of the frequency spectrum is not much altered by the inclusion of a non zero bond-bending force constant provided the ratio of it to the bond stretching force constant is small relative to unity. 

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