Modeling DNA Shuffling

In vitro evolution is a new, important laboratory method to evolve molecules with desired properties. It has been used in a variety of biological studies and drug development. In this paper, we study one important mutagenesis method used in in vitro evolution experiments called DNA shuffling. We construct a mathematical model for DNA shuffling and study the properties of molecules after DNA shuffling experiments based on this model. The model for DNA shuffling consists of two parts. First we apply the Lander-Waterman model for physical mapping by fingerprinting random clones to model the distribution of regions that can be reassembled through DNA shuffling. Then we present a model for recombination between different DNA species with different mutations. We compare our theoretical results with experimental data. Finally we propose novel applications of the theoretical results to the optimal design of DNA shuffling experiments and to physical mapping using DNA shuffling.