Electrophoresis in polyacrylamide gels provides a simple yet powerful means of analyzing the relative disposition of helical arms in branched nucleic acids. The electrophoretic mobility of DNA or RNA with a central discontinuity is determined by the angle subtended between the arms radiating from the branchpoint. In a multi-helical branchpoint, comparative gel electrophoresis can provide a relative measure of all the inter-helical angles and thus the shape and symmetry of the molecule. Using the long–short arm approach, the electrophoretic mobility of all the species with two helical arms that are longer than all others is compared. This can be done as a function of conditions, allowing the analysis of ion-dependent folding of branched DNA and RNA species. Notable successes for the technique include the four-way (Holliday) junction in DNA and helical junctions in functionally significant RNA species such as ribozymes. Many of these structures have subsequently been proved correct by crystallography or other methods, up to 10 years later in the case of the Holliday junction. Just as important, the technique has not failed to date. Comparative gel electrophoresis can provide a window on both fast and slow conformational equilibria such as conformer exchange in four-way DNA junctions. But perhaps the biggest test of the approach has been to deduce the structures of complexes of four-way DNA junctions with proteins. Two recent crystallographic structures show that the global structures were correctly deduced by electrophoresis, proving the worth of the method even in these rather complex systems. Comparative gel electrophoresis is a robust method for the analysis of branched nucleic acids and their complexes.

DNA topoisomerases are a diverse set of essential enzymes responsible for maintaining chromosomes in an appropriate topological state. Although they vary considerably in structure and mechanism, the partnership between topoisomerases and DNA has engendered commonalities in how these enzymes engage nucleic acid substrates and control DNA strand manipulations. All topoisomerases can harness the free energy stored in supercoiled DNA to drive their reactions; some further use the energy of ATP to alter the topology of DNA away from an enzyme-free equilibrium ground state. In the cell, topoisomerases regulate DNA supercoiling and unlink tangled nucleic acid strands to actively maintain chromosomes in a topological state commensurate with particular replicative and transcriptional needs. To carry out these reactions, topoisomerases rely on dynamic macromolecular contacts that alternate between associated and dissociated states throughout the catalytic cycle. In this review, we describe how structural and biochemical studies have furthered our understanding of DNA topoisomerases, with an emphasis on how these complex molecular machines use interfacial interactions to harness and constrain the energy required to manage DNA topology.