Joint work with Rasika M Harshey, Section of Molecular Genetics and Microbiology, University of Texas at Austin, Austin, TX 78712. Important DNA transactions in biological systems, replication, transcription, recombination etc., often require the assembly of complex protein machines at specific DNA sites. Within these higher order assemblies, the DNA often follows a defined path, generating a fixed number of duplex crossings characteristic of individual systems. In the absence of crystal structure data, it is well nigh impossible to decipher the DNA topology organized by a particular protein machine. A ‘difference topology’ method, based on site-specific recombination, can be employed to derive this information indirectly. The rationale of the analysis is outlined below. Simple members of the tyrosine family site-specific recombinases, Flp and Cre, mediate DNA exchange by arranging their target sites in an antiparallel fashion and introducing no DNA crossing during recombination. Flp and Cre are therefore useful in sealing off DNA domains by recombination and preserving the DNA crossings between two sites introduced by another recombinase or transposase protein or a multi-protein complex. The crossings can be displayed and counted as knot crossings or catenane crossings by suitable analytical methods. Knots result when Flp or Cre mediates inversion between a pair of head-to-head sites; catenanes are formed when the recombinase mediates deletion between head-to-tail sites. For a matched pair of inversion and deletion substrates, the crossing numbers between the knot and catenane products will differ by one, and the smaller number will represent the DNA crossings present in the ‘unknown synapse’ being analyzed. The extra node is imposed by the requirement that Flp or Cre recombination sites have to be arranged in antiparallel geometry. In the case of a system with multiple site interactions, these can be broken down into a series of pairwise interactions, and the crossings between each pair analyzed independently. They may then be summed to arrive at the composite interactions among all of the sites. The difference topology method can also be useful in revealing the topological changes during the maturation of dynamic DNA-protein assemblies. Furthermore, in cases where identical protein monomers associate with several copies of a consensus DNA site, it can help define the interactions between individual protein subunits and their cognate sites that mould the final architecture of a DNA-protein complex.