Biomathematics Emphasis Program at San Diego State University

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### Investigating Site-specific Recombination of Bacteriophage Lambda Using Biochemical and Mathematical Approaches

#### Department of Biology§, and Department of Mathematics and Statistics%, San Diego State University

Bacteriophage lambda is one of a large class of temperate phages that establishes lysogeny by inserting its genome into that of its host, E. coli, and becoming a prophage. When the DNA of lysogenic bacteria is damaged, essentially all prophages excise and return to the lytic cycle to produce new phage particles. Both integration into and excision from the chromosome of the host entail a site-specific recombination event, performed by a phage-encoded recombinase named Integrase. The decisions to integrate or to excise appear to be largely irreversible: once the decision is made, the phage would compromise its ability to survive if it does not complete the reaction. The recombination reaction proceeds through a pseudo-symmetric intermediate called a Holliday junction. The recombining DNA substrates (which we collectively refer to as A) undergo one round of catalytic events – DNA cleavage, strand exchange, and ligation – to generate the first Holliday junction isomer (B). This initial Holliday junction isomerizes to a different conformation, which we call C. Finally, the C Holliday junction isomer undergoes another round of catalytic events to generate the substrates, which we collectively refer to as E. Whether the Holliday junction is in the B or C conformation appears to determine whether the reaction proceeds forward to products E or backwards to regenerate substrates A. Ultimately, we would like to understand how the Integrase protein accomplishes Holliday junction isomerization at the molecular level, and what features regulate this event. To address this goal, we are combining biochemical assays with mathematical modeling approaches to determine the equilibrium constants of each of the reaction steps. We monitor recombination by using radiolabeled substrates and measure the rates of the complete recombination reaction. We have isolated the Holliday junction intermediates, re-load them with proteins, and monitor the second round of catalytic events or the reverse of the first round of catalytic events. We have also used two Holliday junction isomers whose conformation is biased towards either the B or the C conformation. We assumed that the catalytic events that convert B to A and C to E are not affected by the biased conformation of the B or C Holliday junctions. Therefore, by comparing the reaction rates of the B -> A and C -> E using the different Holliday junction substrates, we extracted the equilibrium constants and obtained a ratio of the C:B isomers for the different biased Holliday junctions. In addition, we are trying to optimize conditions for the separation of the different Holliday junction isomers complexed with proteins, in order to simplify and to extend our analysis.