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We have performed computer simulations of closed polymer chains with allowance for the excluded volume effects within the framework of the free-joint model. The probability of knot formation, the linking probability of a pair of chains and the variance in the writhing number proved to be significantly affected by the excluded volume effects. This is true even for DNA with completely screened charges for which the b/d ratio (where b is the Kuhn statistical length and d is the diameter of the double helix) is as large as 50. Allowance for the electrostatic repulsion (change of the DNA effective diameter d) further increases the effects. The most dramatic dependence on d is found for the probability of knot formation. The data on the dependence of the variance of writhing, mean value of (WR)2, on d indicate that the DNA superhelix energy should be significantly ionic strength-dependent. Special calculations have shown that the free-joint model underestimates the mean value of (Wr)2 value by about 20% as compared with the wormlike model.

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