Effect of Excluded Volume on Topological Properties of Circular DNA

Abstract

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.

The abundance of unknots in various models of polymer loops

“…In other words, using professional parlance of the field, what is the probability that random loop is a trivial knot (unknot) Most of what we know about these "probabilistic topology" questions is learned from computer simulations. In particular, it has been observed by many authors over the last 3 decades [15,16,17,18,19] that the trivial knot probability depends on the length of the loop, decaying exponentially with the number of segments in the loop, N :…”

“…First, the constant's value was invariably found to be quite large, around 300 for all examined models of "thin" loops with no excluded volume, or no self-avoidance [15,16,17,23,24]. Second, it is known that knots are dramatically suppressed for "thick" self-avoiding polymers, which means that N 0 rapidly increases with the radius of self-avoidance [17,19]. The latter issue is also closely connected to the probabilities of knots in lattice models, where the non-zero effective self-avoidance parameter is automatically set by the lattice geometry.…”

Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical self-avoiding polygons

“…Here we note that another algorithm is discussed in Ref. [6] for the model of cylindrical SAPs, where self-avoiding polygons of impenetrable cylinders with N < 100 are constructed in association with knotted DNAs [19,20].…”

“…We call them cylindrical self-avoiding polygons or cylindrical SAPs, for short. The cylinder radius r can be related to the stiffness of some stiff polymers such as DNAs [6,14].…”

“…Furthermore, some dynamical or thermodynamical properties of ring polymers under topological constraints could also be nontrivial. In fact, various computer simulations of ring polymers with fixed topology were performed by several groups [1,2,3,4,5,6,7,8,9,10,11,12]. However, there are still many unsolved problems related to the topological effect, such as the average size of a knotted ring polymer in solution.…”