GRAM and genfragII: solving and testing the single-digest, partially ordered restriction map problem

GRAM (Genomic Restriction map AsseMbly) takes as input single-digest restriction fragments for a set of overlapping clones and outputs one or more plausible partially ordered restriction maps. For each restriction map, GRAM shows the corresponding alignment of the input clone fragments. Due to the error and uncertainty in experimental data, this problem is computationally difficult to solve; therefore, the principle objective in the design of GRAM is to facilitate man-machine collaborative problem solving. GRAM quickly approximates a solution, as follows. (i) A clustering algorithm determines a probable set of restriction fragments. (ii) An assembly algorithm permutes the set of restriction fragments such that the maximal number of clone fragments are contiguous. The output of the GRAM algorithm is displayed for the user to query and edit. This paper describes the stochastic assembly algorithm and shows how it works with the interactive graphics to support man-machine problem solving. In order to test and verify the performance of GRAM, we have developed a program called genfragII to simulate the digestion of clones and fragments; this program is described and results are presented. GRAM is also being used for a number of genome mapping projects.