On Haldane’s formulation of Luria and Delbrück’s mutation model

Two formulations of Luria and Delbrück’s mutation model have been in common use since the 1940s. While mathematicians focused their attention on the formulation of Lea and Coulson that assumes asynchronous cell growth, biologists found more appealing the formulation of Haldane that assumes synchronous cell growth. This article attempts to solve several outstanding issues for the latter formulation. First, it provides an exact, closed-form expression for the mutant distribution by correcting a minor error in the literature. Second, it presents a novel algorithm for computing the mutant distribution, which leads to novel methods for computing point and interval estimates of mutation rates based on the maximum likelihood principle. Third, it critically examines existing methods based on the mean number of mutants. Finally, it compares the two formulations to underline their strengths and shortcomings.