deviation from topological equilibrium for relaxation predicted by the model agrees with our experimental results and provides an explanation for the puzzling observation that type II topoisomerases are much better at decatenation and unknotting than relaxation (10,13,14).The ability of type II topoisomerases to directionally simplify DNA topology is in accord with their physiological role in DNA replication and chromosome segregation (25). Every turn of the double helix that is replicated introduces a positive supercoil or catenane link into topologically constrained DNA, which must be faithfully and rapidly removed by topoisomerases. However, given the high intracellular DNA concentration (26) and the presence of DNA condensing agents, the topoisomerases might instead be expected to ensnarl chromosomes (27). Our discovery that type II topoisomerases untangle DNA molecules against the thermal drive may help solve this problem. Biochem. 65, 635 (1996). 8. L. F. Liu, C.-C. Liu, B. M. Alberts, Cell 19, 697 (1980). 9. J.-i. Kato, H. Suzuki, H. Ikeda, J. Biol. Chem. 267, 25676 (1992). 10. H. Peng and K. J. Marians, ibid. 268, 24481 (1993). 11. M. A. Krasnow and N. R. Cozzarelli, ibid. 257, 2687 (1982. 12. To obtain mixtures with twice the equilibrium amount of heterodimeric catenanes, we cyclized P4 DNA (4 g/ml) in the presence of pAB4 DNA (100 g/ml). To obtain mixtures with no heterodimeric catenanes, we cyclized P4 DNA in the absence of pAB4. After cyclization, the concentration of DNA substrates in both mixtures was adjusted to 2 g/ml for P4 DNA and 50 g/ml for pAB4 DNA. The reaction mixtures also contained 20 mM tris-Cl (pH 7.8), 10 mM MgCl 2 , 1 mM dithiothreitol, bovine serum albumin (50 g/ml), 1 mM ATP, and either 80 mM potassium acetate for E. coli topoisosomerases III and IV and bacteriophage T2 topo II or 200 mM potassium acetate for eukaryotic topo II, so that each enzyme was assayed under its optimal ionic conditions. The reactions were carried out at 30°C for 60 min, quenched by adding 20 mM EDTA, 0.5% SDS, and 100 g/ml proteinase K, and incubated for an additional 60 min at 30°C. Because topo III requires single-stranded regions of DNA for optimal activity, this enzyme was assayed on pAB4 DNA containing a 25-nucleotidelong gap generated by exonuclease III from E. coli. 13. J. Roca and J. C. Wang, Genes Cells 1, 17 (1996). 14. C. J. Ullsperger and N. R. Cozzarelli, J. Biol. Chem. 271, 31549 (1996 REFERENCES AND NOTES ___________________________