DNA-Topology Simplification by Topoisomerases.

Andreas Hanke,Riccardo Ziraldo,Stephen D Levene

doi:10.3390/molecules26113375

Abstract

The topological properties of DNA molecules, supercoiling, knotting, and catenation, are intimately connected with essential biological processes, such as gene expression, replication, recombination, and chromosome segregation. Non-trivial DNA topologies present challenges to the molecular machines that process and maintain genomic information, for example, by creating unwanted DNA entanglements. At the same time, topological distortion can facilitate DNA-sequence recognition through localized duplex unwinding and longer-range loop-mediated interactions between the DNA sequences. Topoisomerases are a special class of essential enzymes that homeostatically manage DNA topology through the passage of DNA strands. The activities of these enzymes are generally investigated using circular DNA as a model system, in which case it is possible to directly assay the formation and relaxation of DNA supercoils and the formation/resolution of knots and catenanes. Some topoisomerases use ATP as an energy cofactor, whereas others act in an ATP-independent manner. The free energy of ATP hydrolysis can be used to drive negative and positive supercoiling or to specifically relax DNA topologies to levels below those that are expected at thermodynamic equilibrium. The latter activity, which is known as topology simplification, is thus far exclusively associated with type-II topoisomerases and it can be understood through insight into the detailed non-equilibrium behavior of type-II enzymes. We use a non-equilibrium topological-network approach, which stands in contrast to the equilibrium models that are conventionally used in the DNA-topology field, to gain insights into the rates that govern individual transitions between topological states. We anticipate that our quantitative approach will stimulate experimental work and the theoretical/computational modeling of topoisomerases and similar enzyme systems.

Highlights

IntroductionFor circular DNA molecules (or a piece of string with joined ends), the knot type K is a topological invariant in the sense that it is maintained through all of the conformational changes that occur in the absence of breaking both strands of the DNA (or cutting the string)
Figure 2B), we introduce a network of DNA topological states (K, ∆Lk), where the transitions between these states that are catalyzed by the enzyme are described by a chemical master equation (Section 2.1) [103]
We considered local, virtual deformations of the chain that was obtained by replacing the red segments that correspond to the G segment by the gray segments that are shown in Figure 6, and determined the knot type K for the virtually deformed chain using the Alexander and HOMFLY polynomials

Summary

Introduction

For circular DNA molecules (or a piece of string with joined ends), the knot type K is a topological invariant in the sense that it is maintained through all of the conformational changes that occur in the absence of breaking both strands of the DNA (or cutting the string). Most knots are chiral, which means that the knot and its mirror image form two topologically distinct enantiomorphic forms, whicha re referred to as right-handed and left-handed. The trefoil knot 3.1 is an example of a chiral knot, which occurs in the topologically distinct forms 3.1+ and 3.1−; one of these forms cannot be converted into the other without cutting the string forming the knot. By definition, topologically equivalent to its mirror image, i.e., the knot can be continuously deformed into its own mirror image. All of the torus knots, except the unknot 0.1, are chiral

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