## Using the Wu Formula to estimate physical distance from cotransduction frequency

When two genetic markers are packaged onto a single generalized transducing fragment, they can be cotransduced into a recipient cell. Typically the phenotype of one genetic marker is selected, and transductants that inherited this marker will be screened for inheritance of the second, unselected genetic marker. The cotransduction frequency is the ratio of transductants that co-inherited both markers divided by the total number of transductants.

The Wu formula can be used to estimate the correlation between cotransduction frequency and the physical distance between two genetic markers. The idea is simple -- the closer together two markers are the more frequently they will be co-inherited by generalized transduction; if two markers are too far apart to be packaged in the same transducing particle then they will never be co-inherited by generalized transduction. Thus, the mathematical relationship between cotransduction frequency and physical distance will depend upon size of the DNA that the phage can package into a phage head (L in the equation shown below). For example, phage P22 can package about 48 Kb of DNA into a phage head, and phage P1 can package about 100 Kb of DNA into a phage head. However, the co-transduction frequency and distance is not a simple linear relationship. The Wu equation and some examples are shown below.

Because there are hot spots and cold spots for genetic recombination, the physical distance predicted by the Wu formula is not precise, but it is often quite close to the true physical distance determined by DNA sequencing.

The Wu formula assumes that the genetic markers are point mutations and that the region transduced is the same size in the donor and recipient. However, cotransduction is often done with insertion mutations (e.g. transposons encoding antibiotic resistance). Insertions or deletions in the donor DNA will affect the co-transduction frequency because it will effectively alter the amount of flanking homologous DNA that can be packaged in the phage head. To correct for this, a modification of the Wu formula was described by Sanderson and Roth:

REFERENCES:

• Sanderson K and Roth J. 1988. Linkage map of Salmonella typhimurium, edition VII. Microbiol. Rev. 52: 485-532.
• Wu TT. 1966. A model for three-point analysis of random general transduction. Genetics 54: 405-410. (This paper describes the mathematical relationship ... readers should be prepared for some heavy duty math.)
• Wu TT. 1990. Citation Classic. Current Contents 33(22): 21. (An interesting short historical perspective on how Wu came up with the formula.)