Improved inference of mutation rates - II. Generalization of the Luria-Delbruck distribution for realistic cell-cycle time distributions

In the first paper of this series (Kepler and Oprea, Theor. Popul. Biol. 20 01) we found a continuum approximation of the Luria-Delbruck distribution i n terms of a scaled variable related to the proportion of mutants in the cu lture. Here we show that the Luria-Delbruck distribution is inaccurate when realistic division processes are being considered due to the non-Markovian character of the cell cycle. We derive the expectation of the proportion o f mutants in the culture for arbitrary cell-cycle time distributions. We th en introduce a two-parameter generalization of the continuum Luria-Delbruck distribution for two of the more commonly used cell-cycle time distributio ns: gamma and shifted exponential. We obtain the generalized distribution b y defining a map from the actual parameters to "effective" parameters. The effective mutation rate is obtained analytically, while the effective popul ation size is obtained by fitting simulation data. Our simulations show tha t the second parameter depend mostly on the coefficient of variation of the cell-cycle time distribution. (C) 2001 Academic Press.