We study several simple models for optical mapping and explore their power and limitations when applied to the construction of maps of clones (e.g., lambdas, cosmids, BACs and YACs). We provide precise lower and upper bounds on the number of clone molecules needed to create the correct map of the clone. Our probabilistic analysis shows that as the number of clone molecules is increased in the optical mapping data, the probability of successful computation of the map jumps from 0 to 1 for fairly small number of molecules (for typical values of the parameterS, the transition point is around 70 molecules). These observations have been independently verified with extensive tests, with both in vitro and in silico data.

In addition, we compare our results with those derived by Karp and Shamir in a recent paper. We hope that this paper clarifies certain misconceptions and explains why the model proposed in Anantharaman et al. (1997) has proven so powerful.