A practical algorithm for an important class of the Luria-Delbruck distribution

Qi Zheng

Texas A&M Uniersity School of Public Health

"A practical algorithm for an important class of the Luria-Delbruck distribution"

Since its invention by two trailblazing biologists in 1943, the Luria-Delbruck experiment has been a preferred tool for measuring microbial mutation rates in the laboratory. Practical algorithms for computing a variety of mutant distributions induced by the Luria-Delbruck experiment play a pivotal role in helping biologists obtain accurate estimates of mutation rates. This presentation focuses on an important type of the Luria-Delbruck distribution that simultaneously accommodates differential fitness between mutants and nonmutants and imperfect plating efficiency. This distribution was earnestly tackled in the 1990s, and important intermediate results were obtained. However, a workable algorithm remained an unachieved expectation at the time. In the 2010s, a clever contour integration approach was taken. An elegant algorithm relying on numerical integration was then devised. Illustrative testing examples showed remarkable performance of the integration-based algorithm. But real-world research problems can be far more challenging than artificial testing examples, and the integration-based method performed dishearteningly on some real-world examples. I here present an alternative algorithm that effectively exploits some properties of the hypergeometric function. Reliant on the hypergeometric function and simple arithmetic operations, the new algorithm may appear at first sight to be clumsy but computes the mutant distribution more accurately and efficiently. Examples are given to show the usefulness of the new algorithm in actual microbial mutation research.

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