Presented here is a genome sequence of an individual human. It was produced from ∼32 million random DNA fragments, sequenced by Sanger dideoxy technology and assembled into 4,528 scaffolds, comprising 2,810 million bases (Mb) of contiguous sequence with approximately 7.5-fold coverage for any given region. We developed a modified version of the Celera assembler to facilitate the identification and comparison of alternate alleles within this individual diploid genome. Comparison of this genome and the National Center for Biotechnology Information human reference assembly revealed more than 4.1 million DNA variants, encompassing 12.3 Mb. These variants (of which 1,288,319 were novel) included 3,213,401 single nucleotide polymorphisms (SNPs), 53,823 block substitutions (2–206 bp), 292,102 heterozygous insertion/deletion events (indels)(1–571 bp), 559,473 homozygous indels (1–82,711 bp), 90 inversions, as well as numerous segmental duplications and copy number variation regions. Non-SNP DNA variation accounts for 22% of all events identified in the donor, however they involve 74% of all variant bases. This suggests an important role for non-SNP genetic alterations in defining the diploid genome structure. Moreover, 44% of genes were heterozygous for one or more variants. Using a novel haplotype assembly strategy, we were able to span 1.5 Gb of genome sequence in segments >200 kb, providing further precision to the diploid nature of the genome. These data depict a definitive molecular portrait of a diploid human genome that provides a starting point for future genome comparisons and enables an era of individualized genomic information.

/pdf/the-diploid-genome-sequence-of-an-individual-human-2asexwsaju.pdf

The Diploid Genome Sequence of an Individual Human

PART I: FOUNDATIONS 1. Introduction to Fixed-Parameter Algorithms 2. Preliminaries and Agreements 3. Parameterized Complexity Theory - A Primer 4. Vertex Cover - An Illustrative Example 5. The Art of Problem Parameterization 6. Summary and Concluding Remarks PART II: ALGORITHMIC METHODS 7. Data Reduction and Problem Kernels 8. Depth-Bounded Search Trees 9. Dynamic Programming 10. Tree Decompositions of Graphs 11. Further Advanced Techniques 12. Summary and Concluding Remarks PART III: SOME THEORY, SOME CASE STUDIES 13. Parameterized Complexity Theory 14. Connections to Approximation Algorithms 15. Selected Case Studies 16. Zukunftsmusik References Index

Invitation to fixed-parameter algorithms

Although genotyping errors affect most data and can markedly influence the biological conclusions of a study, they are too often neglected. Errors have various causes, but their occurrence and effect can be limited by considering these causes in the production and analysis of the data. Procedures that have been developed for dealing with errors in linkage studies, forensic analyses and non-invasive genotyping should be applied more broadly to any genetic study. We propose a protocol for estimating error rates and recommend that these measures be systemically reported to attest the reliability of published genotyping studies.

Genotyping errors: causes, consequences and solutions.

In this age of modern era, the use of internet must be maximized. Yeah, internet will help us very much not only for important thing but also for daily activities. Many people now, from any level can use internet. The sources of internet connection can also be enjoyed in many places. As one of the benefits is to get the on-line analysis of human genetic linkage book, as the world window, as many people suggest.

Analysis of human genetic linkage

In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight; there exist metric spaces where any tree embedding must have distortion Ω(log n)-distortion. This problem lies at the heart of numerous approximation and online algorithms including ones for group Steiner tree, metric labeling, buy-at-bulk network design and metrical task system. Our result improves the performance guarantees for all of these problems.

/pdf/a-tight-bound-on-approximating-arbitrary-metrics-by-tree-2ori42r02g.pdf

A tight bound on approximating arbitrary metrics by tree metrics

With the consensus human genome sequenced and many other sequencing projects at varying stages of completion, greater attention is being paid to the genetic differences among individuals and the abilities of those differences to predict phenotypes. A significant obstacle to such work is the difficulty and expense of determining haplotypes - sets of variants genetically linked because of their proximity on the genome - for large numbers of individuals for use in association studies. This paper presents some algorithmic considerations in a new approach for haplotype determination: inferring haplotypes from localised polymorphism data gathered from short genome 'fragments.' Formalised models of the biological system under consideration are examined, given a variety of assumptions about the goal of the problem and the character of optimal solutions. Some theoretical results and algorithms for handling haplotype assembly given the different models are then sketched. The primary conclusion is that some important simplified variants of the problem yield tractable problems while more general variants tend to be intractable in the worst case.

/pdf/algorithmic-strategies-for-the-single-nucleotide-3y2wtwglke.pdf

Algorithmic strategies for the single nucleotide polymorphism haplotype assembly problem

Single nucleotide polymorphisms (SNPs) are the most frequent form of human genetic variation. They are of fundamental importance for a variety of applications including medical diagnostic and drug design. They also provide the highest-resolution genomic fingerprint for tracking disease genes. This paper is devoted to algorithmic problems related to computational SNPs validation based on genome assembly of diploid organisms. In diploid genomes, there are two copies of each chromosome. A description of the SNPs sequence information from one of the two chromosomes is called SNPs haplotype. The basic problem addressed here is the Haplotyping, i.e., given a set of SNPs prospects inferred from the assembly alignment of a genomic region of a chromosome, find the maximally consistent pair of SNPs haplotypes by removing data "errors" related to DNA sequencing errors, repeats, and paralogous recruitment. In this paper, we introduce several versions of the problem from a computational point of view. We show that the general SNPs Haplotyping Problem is NP-hard for mate-pairs assembly data, and design polynomial time algorithms for fragment assembly data.We give a network-flow based polynomial algorithm for the Minimum Fragment Removal Problem, and we show that the Minimum SNPs Removal problem amounts to finding the largest independent set in a weakly triangulated graph.

https://www.brown.edu/Research/Istrail_Lab/papers/snpproblems.pdf

SNPs Problems, Complexity, and Algorithms

Given an undirected graph with nonnegative costs on the edges, the routing cost of any of its spanning trees is the sum over all pairs of vertices of the cost of the path between the pair in the tree. Finding a spanning tree of minimum routing cost is NP-hard, even when the costs obey the triangle inequality. We show that the general case is in fact reducible to the metric case and present a polynomial-time approximation scheme valid for both versions of the problem. In particular, we show how to build a spanning tree of an n-vertex weighted graph with routing cost at most (1 +) of the minimum in time O(n O( 1 ) ). Besides the obvious connection to network design, trees with small routing cost also nd application in the construction of good multiple sequence alignments in computational biology. The communication cost spanning tree problem is a generalization of the minimum routing cost tree problem where the routing costs of dierent pairs are weighted by dierent requirement amounts. We observe that a randomized O(logn log logn)-approximation for this problem follows directly from a recent result of Bartal, where n is the number of nodes in a metric graph. This also yields the same approximation for the generalized sum-of-pairs alignment problem in computational biology.

https://www.csie.ntu.edu.tw/~kmchao/papers/2000_SICOMP.pdf

A polynomial time approximation scheme for minimum routing cost spanning trees

Protein structure comparison is a fundamental problem for structural genomics, with applications to drug design, fold prediction, protein clustering, and evolutionary studies. Despite its importance, there are very few rigorous methods and widely accepted similarity measures known for this problem. In this paper we describe the last few years of developments on the study of an emerging measure, the contact map overlap (CMO), for protein structure comparison. A contact map is a list of pairs of residues which lie in three-dimensional proximity in the protein's native fold. Although this measure is in principle computationally hard to optimize, we show how it can in fact be computed with great accuracy for related proteins by integer linear programming techniques. These methods have the advantage of providing certificates of near-optimality by means of upper bounds to the optimal alignment value. We also illustrate effective heuristics, such as local search and genetic algorithms. We were able to obtain for...

1001 optimal PDB structure alignments: integer programming methods for finding the maximum contact map overlap.

Dense genetic linkage maps have been constructed for the human and mouse genomes, with average densities of 2.9 cM and 0.35 cM, respectively. These genetic maps are crucial for mapping both Mendelian and complex traits and are useful in clinical genetic diagnosis. Current maps are largely comprised of abundant, easily assayed, and highly polymorphic PCR-based microsatellite markers, primarily dinucleotide (CA)n repeats. One key limitation of these length polymorphisms is the PCR stutter (or slippage) artifact that introduces additional stutter bands. With two (or more) closely spaced alleles, the stutter bands overlap, and it is difficult to accurately determine the correct alleles; this stutter phenomenon has all but precluded full automation, since a human must visually inspect the allele data. We describe here novel deconvolution methods for accurate genotyping that mathematically remove PCR stutter artifact from microsatellite markers. These methods overcome the manual interpretation bottleneck and thereby enable full automation of genetic map construction and use. New functionalities, including the pooling of DNAs and the pooling of markers, are described that may greatly reduce the associated experimentation requirements.

Giuseppe Lancia

Papers

Algorithmic strategies for the single nucleotide polymorphism haplotype assembly problem

SNPs Problems, Complexity, and Algorithms

A polynomial time approximation scheme for minimum routing cost spanning trees

1001 optimal PDB structure alignments: integer programming methods for finding the maximum contact map overlap.

Toward fully automated genotyping: genotyping microsatellite markers by deconvolution.