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Vinograd, 1976). As we stated above, relaxed SV40 has a linking number, Lk0, of approximately 500. Therefore minichromosomal SV40 has Lk = 475.

We can now answer an important question: Is the number of base pairs per turn, the helical repeat, unchanged from the 10.5 of relaxed DNA, when DNA is wrapped on the nucleosome? The answer must be negative because of the relationship Lk = SLk + F. Thus, we can theoretically determine that because Lk = 475 and SLk = -45, F must be 520. However, we have seen above that F for relaxed SV40 is equal to Lk0 =  500. Because F = 520, the average helical repeat for minichromosomal SV40 equals 5,250/520 = 10.10. In this analysis, we have made a great many simplifications, but it is noteworthy that this number is in remarkably good agreement with the number 10.17 that is obtained by nuclease digestion experiments. The answer to the question is thus negative.

To summarize, we have found a fundamental relationship Lk = SLk + Ffor three quantities that are directly accessible to experiment, Lk by electrophoresis, SLk by X-ray diffraction, and F by digestion. If two of the three are known, one can use the relationship to predict and therefore verify the experimental evidence for finding the third. This gives a powerful use of differential topology in the field of molecular biology.

References

Bauer, W.R., 1978, ''Structure and reactions of closed duplex DNA," Annu. Rev. Biophys. Bioeng. 7, 287-313.

Bauer, W.R., F.H.C. Crick, and J.H. White, 1980, "Supercoiled DNA," Scientific American 243, 118-133.

Boles, T.C., J.H. White, and N.R. Cozzarelli, 1990, "Structure of plectonemically supercoiled DNA," Journal of Molecular Biology 213, 931-951.

Drew, H.R., and A.A. Travers, 1985, "DNA bending and its relation to nucleosome positioning," Journal of Molecular Biology 186, 773-790.

Finch, J.T., L.C. Lutter, D. Rhodes, R.S. Brown, B. Rushton, M. Levitt, and A. Klug, 1977, "Structure of nucleosome core particles of chromatin," Nature 269, 29-36.

Finch, J.T., R.S. Brown, D. Rhodes, T. Richmond, B. Rushton, L.C. Lutter, and A. Klug, 1981, "X-ray diffraction study of a new crystal form of the nucleosome core showing higher resolution," Journal of Molecular Biology 145, 757-770.



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