Mean-field branching process and PCR reaction (Q2749129)

The author considers Sun and Waterman's branching process model of DNA mutations during PCR reactions. Since exact expressions cannot be obtained in the model, Sun and Waterman used a mean-field approximation. The present article shows theoretically that the approximate values fit the exact values well for a wide range of parameters. Explicit bounds are derived for the biases, in law and in mean, that the mean-field approximation induces in the random number of mutations of a DNA molecule. The bounds involve the initial number of molecules, the number of PCR cycles, the efficiency rate and the mutation rate. The domain in which the approximation fits well includes mutation rates observed in many actual PCR reactions.