Simplification of Topology by Type II Topoisomerases and Kinetic Proofreading model

Topoisomerases are enzymes that have evolved to solve the topological problems associated with DNA manipulation in the cell, such as in transcription, replication, packing and unpacking of DNA. Since these enzymes are essential for the correct functioning of the cell they are important drug targets. People study topoisomerases from many different perspectives: protein structure, detailed atomic level mechanisms of how they work, single molecular experiments, effects of mutations on enzyme function, etc. However, the first question I have as a beginner is what topoisomerases do. I would also like to imagine at least one physically plausible mechanism capable to account for the observed functions. I will discuss a relatively recent experimental paper by Rybenkov et. al.(1997). [1], revealing unexpected abilities of various type II topoisomerases, and theoretical papers by Yan, et al. [2],[3] giving a possible explanation. There are two types of topoisomerases (topos). Type I topos cut one of the two DNA strands, rotate it at 360 degrees around the other and reseal it. Type II topos cut both strands, pass another double stranded DNA segment through the gap and reseal the broken strands. Further very important distinction is between “passive” topoisomerases which simply catalyze passage of DNA strands through each other helping the DNA molecules to relax toward topological thermal equilibrium, and “active” topoisomerases which fight to establish a different distribution of topological species. Topoisomerases that do not hydrolyze ATP necessarily belong to the “passive” class because otherwise they would play a role of Maxwell demons. From physical point of view these topos convert a real DNA chain into a phantom chain which can pass through itself. Gyrases (type II) use ATP hydrolysis to introduce negative supercoiling in DNA. Reverse gyrases (type I topos present in some thermophilic organisms) use ATP to positively supercoil. However, there are type II topoisomerases that use ATP but still do not supercoil. Instead they relax supercoiled DNA just as the “passive” topos do. Though there is no thermodynamic problem with that one, can ask why cells waste ATP for something that can be done passively (for ex. gyrases can relax supercoiling even in the absence of ATP)? The only available answer before Rybenkov, et al. paper (1997) was that ATP is used only to somehow accelerate the relaxation. The finding of the paper is that some type II topoisomerases can drastically