As the DNA in our genome comprises about three billion base-pairs, with each base-pair separated by a third of a nanometer – its total length is about a meter – of all which residing within a compact form knows as chromatin. At first guess, one might think the DNA to be a wound up like a ball of yarn, but chromatin turns out to be a more complex structure, DNA being organized into hierarchical series of superhelices. Counting the right-handed double-helix as the first stage in the hierarchical ordering, the second consists of 147 base-pairs wound around the outside of nucleosomes as a left-handed toroidal-superhelix containing one and three-quarter turns. Each nucleosome contains two pairs each of four different histones, small positively charged basic proteins called H2A, H2B, H3 and H4 spatially related by two-fold symmetry. Adjacent nucleosomes remain connected together by linker DNA, additional DNA (variable in length, but generally between 5- to 60 base-pairs) that exists between nucleosomes, resulting in the formation of an extended 100 Angstrom fiber. In the presence of an additional histone (H1), DNA is known to undergo a still higher level of compaction, organizing itself into a solenoidal super helical structure having a diameter of about 300 Angstroms. This 300 Angstrom fiber can readily be seen by electron microscopy and, almost certainly, the unraveling of its structure foreshadows still further complex structural features of chromatin to be discovered in future years. In order for DNA to be organized into this hierarchical series of superhelices, there must be a source of flexibility in DNA structure that allows this to happen.Earlier, the author put forward a kinked model to understand how DNA is organized within the nucleosome. The model assumed nucleosome DNA to be in its B- form, separated by ‘mixed-puckered kinks’ every 10 base-pairs. Ink this book, he presents a modification to this model; this being necessary to explain important additional experimental information uncovered several years after the model was proposed. The modified model proposed that if there were an equal probability of both 10 base-pars of B- DNA or 11 base-pairs of A- DNA existing within any given segment of the left-handed toroidal super helical structure – these being connected together by ‘mixed-puckered kinks’ – then a population of such aperiodic structures can be expected to give rise to the periodic cutting-patterns observed experimentally. This would be true for naked DNA molecules immobilized on a calcium-phosphate crystalline surface as well, provided they also formed left-handed toroidal superhelices under these conditions.
In both cases, probability considerations predict cutting patters to be symmetrically distributed around integral multiples of 10.5 base-pairs along DNA, the relative magnitudes of the surroundings peaks in these patterns being governed by the binomial distribution – the proof of which is presented in this book.
