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A mathematical model for nonrandom generalized transduction is proposed and analyzed. The model takes into account the finite number of transducing particle classes for any given marker. The equations for estimation of the distance between markers from contransduction frequency data are derived and standard errors of the estimates are given. The obtained relationships depend significantly on the number of classes of transducing fragments. The model was applied to estimate the number of transducing fragment classes for a given marker in transduction with phage P22 of Salmonella typhimurium. It was found that the literature data on frequencies of contransduction in crosses with mutual substitution of selective and nonselective markers can be rationalized most accurately by assuming that the mean number of classes is equal to 2. An improved method for analysis of cotransduction data is proposed on the basis of our model and the results of calculation. The method relies on solving a set of algebraic equations for cotransduction frequencies of markers located within one phage length. The method allows a relatively precise determination of distances between markers, positions of transducing particle ends and deletion or insertion lengths. The approach is applied to the trp-cysB-pyrF and aroC-hisT-purF-dhuA regions of the Salmonella typhimurium chromosome.

A QUANTITATIVE MODEL FOR NONRANDOM GENERALIZED TRANSDUCTION, APPLIED TO THE PHAGE P22–SALMONELLA TYPHIMURIUM SYSTEM