Efficient and Accurate Construction of Genetic Linkage Maps from the Minimum Spanning Tree of a Graph

Genetic linkage maps are cornerstones of a wide spectrum of biotechnology applications, including map-assisted breeding, association genetics, and map-assisted gene cloning. During the past several years, the adoption of high-throughput genotyping technologies has been paralleled by a substantial increase in the density and diversity of genetic markers. New genetic mapping algorithms are needed in order to efficiently process these large datasets and accurately construct high-density genetic maps. In this paper, we introduce a novel algorithm to order markers on a genetic linkage map. Our method is based on a simple yet fundamental mathematical property that we prove under rather general assumptions. The validity of this property allows one to determine efficiently the correct order of markers by computing the minimum spanning tree of an associated graph. Our empirical studies obtained on genotyping data for three mapping populations of barley (Hordeum vulgare), as well as extensive simulations on synthetic data, show that our algorithm consistently outperforms the best available methods in the literature, particularly when the input data are noisy or incomplete. The software implementing our algorithm is available in the public domain as a web tool under the name MSTmap

The Imprinted Gene DIO3 Is a Candidate Gene for Litter Size in Pigs

Genomic imprinting is an important epigenetic phenomenon, which on the phenotypic level can be detected by the difference between the two heterozygote classes of a gene. Imprinted genes are important in both the development of the placenta and the embryo, and we hypothesized that imprinted genes might be involved in female fertility traits. We therefore performed an association study for imprinted genes related to female fertility traits in two commercial pig populations. For this purpose, 309 SNPs in fifteen evolutionary conserved imprinted regions were genotyped on 689 and 1050 pigs from the two pig populations. A single SNP association study was used to detect additive, dominant and imprinting effects related to four reproduction traits; total number of piglets born, the number of piglets born alive, the total weight of the piglets born and the total weight of the piglets born alive. Several SNPs showed significant () additive and dominant effects and one SNP showed a significant imprinting effect. The SNP with a significant imprinting effect is closely linked to DIO3, a gene involved in thyroid metabolism. The imprinting effect of this SNP explained approximately 1.6% of the phenotypic variance, which corresponded to approximately 15.5% of the additive genetic variance. In the other population, the imprinting effect of this QTL was not significant (), but had a similar effect as in the first population. The results of this study indicate a possible association between the imprinted gene DIO3 and female fertility traits in pigs

A Large Maize (Zea mays L.) SNP Genotyping Array: Development and Germplasm Genotyping, and Genetic Mapping to Compare with the B73 Reference Genome

SNP genotyping arrays have been useful for many applications that require a large number of molecular markers such as high-density genetic mapping, genome-wide association studies (GWAS), and genomic selection. We report the establishment of a large maize SNP array and its use for diversity analysis and high density linkage mapping. The markers, taken from more than 800,000 SNPs, were selected to be preferentially located in genes and evenly distributed across the genome. The array was tested with a set of maize germplasm including North American and European inbred lines, parent/F1 combinations, and distantly related teosinte material. A total of 49,585 markers, including 33,417 within 17,520 different genes and 16,168 outside genes, were of good quality for genotyping, with an average failure rate of 4% and rates up to 8% in specific germplasm. To demonstrate this array's use in genetic mapping and for the independent validation of the B73 sequence assembly, two intermated maize recombinant inbred line populations – IBM (B73×Mo17) and LHRF (F2×F252) – were genotyped to establish two high density linkage maps with 20,913 and 14,524 markers respectively. 172 mapped markers were absent in the current B73 assembly and their placement can be used for future improvements of the B73 reference sequence. Colinearity of the genetic and physical maps was mostly conserved with some exceptions that suggest errors in the B73 assembly. Five major regions containing non-colinearities were identified on chromosomes 2, 3, 6, 7 and 9, and are supported by both independent genetic maps. Four additional non-colinear regions were found on the LHRF map only; they may be due to a lower density of IBM markers in those regions or to true structural rearrangements between lines. Given the array's high quality, it will be a valuable resource for maize genetics and many aspects of maize breeding

Mapping quantitative trait loci (QTL) in sheep. I. A new male framework linkage map and QTL for growth rate and body weight

A male sheep linkage map comprising 191 microsatellites was generated from a single family of 510 Awassi-Merino backcross progeny. Except for ovine chromosomes 1, 2, 10 and 17, all other chromosomes yielded a LOD score difference greater than 3.0 between the best and second-best map order. The map is on average 11% longer than the Sheep Linkage Map v4.7 male-specific map. This map was employed in quantitative trait loci (QTL) analyses on body-weight and growth-rate traits between birth and 98 weeks of age. A custom maximum likelihood program was developed to map QTL in half-sib families for non-inbred strains (QTL-MLE) and is freely available on request. The new analysis package offers the advantage of enabling QTL × fixed effect interactions to be included in the model. Fifty-four putative QTL were identified on nine chromosomes. Significant QTL with sex-specific effects (i.e. QTL × sex interaction) in the range of 0.4 to 0.7 SD were found on ovine chromosomes 1, 3, 6, 11, 21, 23, 24 and 26

Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth “Dialogue for Reverse Engineering Assessments and Methods” (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on “Systems Genetics” proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics

Russian Doll Search with Tree Decomposition

Optimization in graphical models is an important problem which has been studied in many AI frameworks such as weighted CSP, maximum satisfiability or probabilistic networks. By identifying conditionally independent subproblems, which are solved independently and whose optimum is cached, recent Branch and Bound algorithms offer better asymptotic time complexity. But the locality of bounds induced by decomposition often hampers the practical effects of this result because subproblems are often uselessly solved to optimality. Following the Russian Doll Search (RDS) algorithm, a possible approach to overcome this weakness is to (inductively) solve a relaxation of each subproblem to strengthen bounds. The algorithm obtained generalizes both RDS and treedecomposition based algorithms such as BTD or AND-OR Branch and Bound. We study its efficiency on different problems, closing a very hard frequency assignment instance which has been open for more than 10 years.

TagSNP selection using Weighted CSP and Russian Doll Search with Tree Decomposition

Abstract. The TagSNP problem is a specific form of compression problem arising in genetics. Given a very large set of SNP (genomic positions where polymorphism is observed in a given population), the aim is to select a smallest subset of SNPs which represents the complete set of tagSNP reliably. This is possible because strong correlations existing between neighboring SNPs. Typically, besides minimizing the tagSNP set size (mostly for economical reasons), one also seek a maximally informative subset for the given size, generating different secondary criteria. This problem, which is also closely related to a set covering problem, can be simply described as a weighted CSP. We report here our experiments with human tag SNP data using a recently designed WCSP algorithm combining the “Russian Doll Search ” algorithm with local consistency for cost functions and an active exploitation of the problem structure, through a tree decomposition of the problem

Modeling and parameter identification of the batch lactic acid production process from wheat flour

The application of white biotechnological processes to produce biopolymers has been increasing recently. In this study, a mathematical model describing the lactic acid production from wheat flour using lactic acid bacteria is presented. The model considers the kinetics degradation of maltose into glucose and the inhibitor effect of substrate and product at the simultaneous saccharification and fermentation step. The identification procedure developed to determine model parameters is described. Experimental data from batch fermentation experiments in a pilot fermenter under different conditions are used to fit and validate the model