DISSERTATION ABSTRACT.    

In site-specific recombination experiments on circular DNA substrate, two 2-string tangles are formed. The pair of DNA segments that are bound to the enzyme forms one of the tangles, the other consists of the unbound DNA. The local effect of recombination can be seen as tangle surgery. One round of recombination is expressed by a system of two tangle equations. Further rounds (processive recombination) yield a series of simultaneous tangle equations that often yield analytic solutions.
Gin is the site-specific recombination system of bacteriophage Mu. It mediates the inversion of the G-segment of the phage genome resulting in the expression of alternate sets of tail fibre genes whose products determine the host range of the phage. In the model for the enzymatic action proposed by Kanaar et al [Cell 62 (1990), 353-366], wild-type Gin is specific for a synaptic complex where the enzyme binds two negative supercoils (the tangle (-2,0)), and each round of recombination adds a positive supercoil (R=(+1)) between the recombination sites. Tangle analysis of Gin data proves that, under certain mathematical and biological assumptions, the biological model is correct.
On the other hand, Gin is a highly specific recombinase that requires for its action the presence of three accessory factors: the protein Fis, an enhancer sequence that contains the binding sites for Fis, and negatively supercoiled DNA substrate. A mutant of Gin that requires neither Fis nor negative supercoiling has been utilized to better understand Gin’s specificity to the initial (-2,0) tangle and the roles of Fis and supercoiling in recombination [Crisona et al, J Mol Biol 243,3 (1994),pp.437-457)]. Tangle analysis of Mutant Gin data proves that the products observed do not fit in a single recombination scheme. This enzyme uses a variety of different synaptic complexes, and all of these are of the form (-n,0) for a positive integer n.
The last part of our work deals with the Xer system from Escherichia coli. Xer is an Int-like site-specific recombinase that changes the topology of circular DNA by resolving dimeric molecules (unlinking pairs of DNA circles), thus allowing segregation at cell division. Colloms et al [Cell 88(1997), 855-864] found that Xer recombination on unknotted DNA substrates with two sites in direct repeat produces a right-handed 4-crossing torus link with anti-parallel sites. Later, in Bath et al [J. Mol. Biol. (1999) 289,873-883], 6-crossing and the 8-crossing right-handed torus DNA links with anti-parallel psi sites were created by Int recombination and then used as substrates for Xer. Electrophoretic analysis of the products shows that they migrate as DNA knots or links with 7 and 9 crossings, respectively. The tangle model is used to analyze knotted and linked products of Xer recombination. Under certain assumptions, all possible Xer mechanisms on both the unknotted and the 6-crossing torus link substrates are elucidated. The results find very few other possible mechanisms in addition to the ones proposed by Colloms and Bath.  Some of these mechanisms can be rejected on biological grounds. The ultimate goal is to design an experiment which will uniquely characterize Xer binding and mechanism.

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