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

Fast and accurate construction of ultra-dense consensus genetic maps using evolution strategy optimization

Our aim was to develop a fast and accurate algorithm for constructing consensus genetic maps for chip-based SNP genotyping data with a high proportion of shared markers between mapping populations. Chip-based genotyping of SNP markers allows producing high-density genetic maps with a relatively standardized set of marker loci for different mapping populations. The availability of a standard high-throughput mapping platform simplifies consensus analysis by ignoring unique markers at the stage of consensus mapping thereby reducing mathematical complicity of the problem and in turn analyzing bigger size mapping data using global optimization criteria instead of local ones. Our three-phase analytical scheme includes automatic selection of ~100-300 of the most informative (resolvable by recombination) markers per linkage group, building a stable skeletal marker order for each data set and its verification using jackknife re-sampling, and consensus mapping analysis based on global optimization criterion. A novel Evolution Strategy optimization algorithm with a global optimization criterion presented in this paper is able to generate high quality, ultra-dense consensus maps, with many thousands of markers per genome. This algorithm utilizes "potentially good orders" in the initial solution and in the new mutation procedures that generate trial solutions, enabling to obtain a consensus order in reasonable time. The developed algorithm, tested on a wide range of simulated data and real world data (Arabidopsis), outperformed two tested state-of-the-art algorithms by mapping accuracy and computation time.

ALLMAPS: robust scaffold ordering based on multiple maps

The ordering and orientation of genomic scaffolds to reconstruct chromosomes is an essential step during de novo genome assembly. Because this process utilizes various mapping techniques that each provides an independent line of evidence, a combination of multiple maps can improve the accuracy of the resulting chromosomal assemblies. We present ALLMAPS, a method capable of computing a scaffold ordering that maximizes colinearity across a collection of maps. ALLMAPS is robust against common mapping errors, and generates sequences that are maximally concordant with the input maps. ALLMAPS is a useful tool in building high-quality genome assemblies. ALLMAPS is available at: https://github.com/tanghaibao/jcvi/wiki/ALLMAPS.

Reliable Radiation Hybrid Maps: An Efficient Scalable Clustering-Based Approach

The process of mapping markers from radiation hybrid mapping (RHM) experiments is equivalent to the traveling salesman problem and, thereby, has combinatorial complexity. As an additional problem, experiments typically result in some unreliable markers that reduce the overall quality of the map. We propose a clustering approach for addressing both problems efficiently by eliminating unreliable markers without the need for mapping the complete set of markers. Traditional approaches for eliminating markers use resampling of the full data set, which has an even higher computational complexity than the original mapping problem. In contrast, the proposed approach uses a divide-and-conquer strategy to construct framework maps based on clusters that exclude unreliable markers. Clusters are ordered using parallel processing and are then combined to form the complete map. We present three algorithms that explore the trade-off between the number of markers included in the map and placement accuracy. Using an RHM data set of the human genome, we compare the framework maps from our proposed approaches with published physical maps and with the results of using the Carthagene tool. Overall, our approaches have a very low computational complexity and produce solid framework maps with good chromosome coverage and high agreement with the physical map marker order.

Two-phase analysis in consensus genetic mapping

Numerous mapping projects conducted on different species have generated an abundance of mapping data. Consequently, many multilocus maps have been constructed using diverse mapping populations and marker sets for the same organism. The quality of maps varies broadly among populations, marker sets, and software used, necessitating efforts to integrate the mapping information and generate consensus maps. The problem of consensus genetic mapping (MCGM) is by far more challenging compared with genetic mapping based on a single dataset, which by itself is also cumbersome. The additional complications introduced by consensus analysis include inter-population differences in recombination rate and exchange distribution along chromosomes; variations in dominance of the employed markers; and use of different subsets of markers in different labs. Hence, it is necessary to handle arbitrary patterns of shared sets of markers and different level of mapping data quality. In this article, we introduce a two-phase approach for solving MCGM. In phase 1, for each dataset, multilocus ordering is performed combined with iterative jackknife resampling to evaluate the stability of marker orders. In this phase, the ordering problem is reduced to the well-known traveling salesperson problem (TSP). Namely, for each dataset, we look for order that gives minimum sum of recombination distances between adjacent markers. In phase 2, the optimal consensus order of shared markers is selected from the set of allowed orders and gives the minimal sum of total lengths of nonconflicting maps of the chromosome. This criterion may be used in different modifications to take into account the variation in quality of the original data (population size, marker quality, etc.). In the foregoing formulation, consensus mapping is considered as a specific version of TSP that can be referred to as “synchronized TSP.” The conflicts detected after phase 1 are resolved using either a heuristic algorithm over the entire chromosome or an exact/heuristic algorithm applied subsequently to the revealed small non-overlapping regions with conflicts separated by non-conflicting regions. The proposed approach was tested on a wide range of simulated data and real datasets from maize.

Accurate construction of consensus genetic maps via integer linear programming

We study the problem of merging genetic maps, when the individual genetic maps are given as directed acyclic graphs. The computational problem is to build a consensus map, which is a directed graph that includes and is consistent with all (or, the vast majority of) the markers in the input maps. However, when markers in the individual maps have ordering conflicts, the resulting consensus map will contain cycles. Here, we formulate the problem of resolving cycles in the context of a parsimonious paradigm that takes into account two types of errors that may be present in the input maps, namely, local reshuffles and global displacements. The resulting combinatorial optimization problem is, in turn, expressed as an integer linear program. A fast approximation algorithm is proposed, and an additional speedup heuristic is developed. Our algorithms were implemented in a software tool named MERGEMAP which is freely available for academic use. An extensive set of experiments shows that MERGEMAP consistently outperforms JOINMAP, which is the most popular tool currently available for this task, both in terms of accuracy and running time. MERGEMAP is available for download at http://www.cs.ucr.edu/~yonghui/mgmap.html.

LTC: a novel algorithm to improve the efficiency of contig assembly for physical mapping in complex genomes

Background

Physical maps are the substrate of genome sequencing and map-based cloning and their construction relies on the accurate assembly of BAC clones into large contigs that are then anchored to genetic maps with molecular markers. High Information Content Fingerprinting has become the method of choice for large and repetitive genomes such as those of maize, barley, and wheat. However, the high level of repeated DNA present in these genomes requires the application of very stringent criteria to ensure a reliable assembly with the FingerPrinted Contig (FPC) software, which often results in short contig lengths (of 3-5 clones before merging) as well as an unreliable assembly in some difficult regions. Difficulties can originate from a non-linear topological structure of clone overlaps, low power of clone ordering algorithms, and the absence of tools to identify sources of gaps in Minimal Tiling Paths (MTPs).

Results

To address these problems, we propose a novel approach that: (i) reduces the rate of false connections and Q-clones by using a new cutoff calculation method; (ii) obtains reliable clusters robust to the exclusion of single clone or clone overlap; (iii) explores the topological contig structure by considering contigs as networks of clones connected by significant overlaps; (iv) performs iterative clone clustering combined with ordering and order verification using re-sampling methods; and (v) uses global optimization methods for clone ordering and Band Map construction. The elements of this new analytical framework called Linear Topological Contig (LTC) were applied on datasets used previously for the construction of the physical map of wheat chromosome 3B with FPC. The performance of LTC vs. FPC was compared also on the simulated BAC libraries based on the known genome sequences for chromosome 1 of rice and chromosome 1 of maize.

Conclusions

The results show that compared to other methods, LTC enables the construction of highly reliable and longer contigs (5-12 clones before merging), the detection of "weak" connections in contigs and their "repair", and the elongation of contigs obtained by other assembly methods.