Multilocus consensus genetic maps (MCGM): formulation, algorithms, and results

In process of creating genetic maps different labs/research groups obtain overlapping parts of the map. Merging these parts into one integrative map is based on looking for maximum shared marker orders among the maps. Really, not all shared markers of such maps have consensus order that obstructs building of the integrative maps. In this paper we propose a new approach to build verified multilocus consensus genetic maps in which shared markers always are integrated in stable consensus order. The approach is based on combined analysis of initial mapping data rather than manipulating with previously constructed maps. We show that more effective and reliable solutions may be obtained based on "synchronized ordering" facilitated by cycles of "re-sampling-->ordering-->removing unstable markers". The proposed formulation of consensus genetic mapping can be considered as a version of traveling salesperson problem (TSP) that we refer to as synchronized-TSP. From the viewpoint of optimization, synchronized-TSP belongs to discrete constrained optimization problems. Earlier we developed new powerful and fast guided evolution strategy algorithms for some types of discrete constrained optimization. These algorithms were used here as a basis for solving more challenging problems of consensual marker ordering.

A fast and scalable radiation hybrid map construction and integration strategy

This paper describes a fast and scalable strategy for constructing a radiation hybrid (RH) map from data on different RH panels. The maps on each panel are then integrated to produce a single RH map for the genome. Recurring problems in using maps from several sources are that the maps use different markers, the maps do not place the overlapping markers in same order, and the objective functions for map quality are incomparable. We use methods from combinatorial optimization to develop a strategy that addresses these issues. We show that by the standard objective functions of obligate chromosome breaks and maximum likelihood, software for the traveling salesman problem produces RH maps with better quality much more quickly than using software specifically tailored for RH mapping. We use known algorithms for the longest common subsequence problem as part of our map integration strategy. We demonstrate our methods by reconstructing and integrating maps for markers typed on the Genebridge 4 (GB4) and the Stanford G3 panels publicly available from the RH database. We compare map quality of our integrated map with published maps for GB4 panel and G3 panel by considering whether markers occur in the same order on a map and in DNA sequence contigs submitted to GenBank. We find that all of the maps are inconsistent with the sequence data for at least 50% of the contigs, but our integrated maps are more consistent. The map integration strategy not only scales to multiple RH maps but also to any maps that have comparable criteria for measuring map quality. Our software improves on current technology for doing RH mapping in areas of computation time and algorithms for considering a large number of markers for mapping. The essential impediments to producing dense high-quality RH maps are data quality and panel size, not computation.