Maxwell demon and topology simplification by type II topoisomerases

Type II topoisomerases catalyze the strand passage reaction between DNA segments changing topology of circular molecules. According to the generally accepted model type II topoisomerases bind one DNA segment, Gsegment, make a transient brake there to allow passage of another segment, T-segment, and then reseal the brake. The second segment is just one randomly caught by the complex and can belong to the same or another DNA molecule. Thus the enzymes convert real DNA molecules into phantom chains that freely pass through themselves and have to generate the equilibrium distribution of topological states, that is the equilibrium fractions of knotted and linked circular DNAs. It was found recently by Rybenkov et al. (1) that the actual picture is more complex, however. The steady state fractions of knotted and catenated circular DNAs produced by type II topoisomerases are up to two orders lower than at thermodynamic equilibrium. Although this property of the enzymes has very clear biological meaning, it was not easy to understand how do they manage to simplify the DNA topology. Topology of circular chain(s) is the global property and cannot be determined by small, in comparison with the DNA coil, enzyme. It was suggested in (1) that the topoisomerases bind an extra DNA segment before catching the T-segment that passes through the enzyme gate. Forming a clamp by the first two segments affects the random selection of the T-segment and thus changes the steady state distribution of topological states. This model has essential problems, however. To make unlinking efficient the model requires sliding of the protein clamp along the DNA to trap a catenane or knot node in a small loop, thereby facilitating removal of topological links from the molecule. Although the energy of ATP hydrolysis is consumed during the reaction, it is very difficult to imagine how the loop trapping can occur. Here we will suggest much more simple model which better corresponds to available experimental data We will present quantitative analysis of the model based on computer simulations. This analysis shows that the model is able to provide great simplification of DNA topology observed experimentally.