Links numbers

Dl A. Supercoiling. Supercoiling is a topological property of closed-circular DNA molecules. Circular DNA molecules can exist in various conformations differing in the number of times one strand of the helix crosses the other. These different isomeric conformations are called topoisomers and maybe characterized in terms of the linking number, Ek. A linear DNA molecule having Nbase pairs and h base pairs per turn of the helix, if joined end to end, has the following ... 

The linking difference can be considered in terms of changes in the twist, Tiv, and writh, Wr, of the molecule. Twist describes how the DNA strands are coHed around each other writh describes the coiling of the hehcal axis. The change in linking number is related to changes in twist and writh ... 

Electron micrographs of supercoiled DNA m vitro demonstrate that supercoiled molecules have a stmcture intermediate between Figures 4c and 4d, where changes in the linking number are accompanied by approximately a 75% change in Wr and a 25% change in Tw. This conformation is called plectonemic supercoiling. 

Table 3. Effect of Increasing Cross-Link Number and Length ...

Vulcanization changes the physical properties of rubbers. It increases viscosity, hardness, modulus, tensile strength, abrasion resistance, and decreases elongation at break, compression set and solubility in solvents. All those changes, except tensile strength, are proportional to the degree of cross-linking (number of crosslinks) in the rubber network. On the other hand, rubbers differ in their ease of vulcanization. Since cross-links form next to carbon-carbon double bonds. 

The basic parameter characterizing supercoiled DNA is the linking number (L). This is the number of times the two strands are intertwined, and, provided both strands remain covalently intact, L cannot change. In a relaxed circular... 

DNA duplex of 400 bp, L is 40 (assuming 10 bp per turn in B-DNA). The linking number for relaxed DNA is usually taken as the reference parameter and is written as Lq. L can be equated to the twist (T) and writhe (W) of the duplex, where twist is the number of helical turns and writhe is the number of supercoils ... 

The difference between the linking number of a DNA and the linking number of its relaxed form is AL AL = (L — To) - In our example with four negative supercoils, AL = 4. The superhelix density or specific linking difference... 

If the average number of contacts in the chain were constant during the reaction, the process would be a random one with the Poisson cross-links number distribution. The dispersion of such process is... 

Introduction the linking number paradox and DNA local helical periodicity on the histone surface... 

In spite of these progresses, and perhaps because of them, some early basic problems have not received all the attention they deserved, even if their solutions are likely to fill crucial gaps in our understanding of chromatin function. Among them, the so-called linking number paradox [6,7], previously reviewed by one of the authors [8], has raised heated debate in the past [9-11]. As will be shown below, this paradox is at the heart of nucleosome conformational dynamics within the context of chromatin superstructure. 

This problem first emerged from the necessity to reconcile topological and structural data of nucleosomes and chromatin. As soon as a minichromosome could be reconstituted from pure DNA and histones, the total reduction of the DNA linking number (Lk) was found to be equal to the number of nucleosomes, which was also true for the native Hl-bearing SV40 minichromosome [12]. On the other hand, the first low-resolution crystal of the core particle showed that DNA was wrapped with 1 3/4 turns of a left-handed superhelix. Assuming linker DNAs... 

Linker positive crossing provided an attractive explanation to the linking number paradox. Positive crossing would indeed partially or totally compensate for the internal negative crossing, so that the (ALkn) value associated with such closed positive nucleosomes would be close to zero. This explanation further required nucleosomes to spontaneously fluctuate to that conformation, rather than being... 

From this, the mean linking number of the topoisomer equilibrium distribution, at size N, is... 

Linking number (ALk ) and free energy (AG ) differences were derived from fitting of the three-state model to topoisomer relative amounts-versus-ALk data in Fig. 5. 

Prunell, A. (1998) A topological approach to nucleosome structure and dynamics. The linking number paradox and other issues. Biophys. J. 74, 2531-2544. 

Fuller, F.B. (1971) The writhing number of a space curve. Proc. Natl. Acad. Sci. USA 68, 815-819. Crick, F.H.C. (1976) Linking numbers and nucleosomes. Proc. Natl. Acad. Sci. USA 73,... 

De Lucia, F., Alilat, M., Sivolob, A., and Prunell, A. (1999) Nucleosome dynamics. III. Histone-tail dependent fluctuation of nucleosomes between open and closed DNA conformations implications for chromatin dynamics and the linking number paradox. A relaxation study of mononucleosomes on DNA minicircles. J. Mol. Biol. 285, 1101-1119. 

Norton, V.G., Imai, B.S., Yau, P., and Bradbury, E.M. (1989) Histone acetylation reduces nucleosome core particle linking number change. Cell 57, 449-457. 

Stein, A. (1980) DNA wrapping in nucleosomes. The linking number problem re-examined. Nucl. Acids Res. 8, 4803 820. 

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