Manifold Based Optimization for Single-Cell 3D Genome Reconstruction
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{"title"=>"Manifold Based Optimization for Single-Cell 3D Genome Reconstruction", "type"=>"journal", "authors"=>[{"first_name"=>"Jonas", "last_name"=>"Paulsen", "scopus_author_id"=>"55511750900"}, {"first_name"=>"Odin", "last_name"=>"Gramstad", "scopus_author_id"=>"19933243100"}, {"first_name"=>"Philippe", "last_name"=>"Collas", "scopus_author_id"=>"7006637846"}], "year"=>2015, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"84940746185", "isbn"=>"10.1371/journal.pcbi.1004396", "scopus"=>"2-s2.0-84940746185", "pui"=>"605889641", "pmid"=>"26262780", "issn"=>"15537358", "doi"=>"10.1371/journal.pcbi.1004396"}, "id"=>"ac05b65b-b68b-37c3-bfab-a28fa464393e", "abstract"=>"The three-dimensional (3D) structure of the genome is important for orchestration of gene expression and cell differentiation. While mapping genomes in 3D has for a long time been elusive, recent adaptations of high-throughput sequencing to chromosome conformation capture (3C) techniques, allows for genome-wide structural characterization for the first time. However, reconstruction of \"consensus\" 3D genomes from 3C-based data is a challenging problem, since the data are aggregated over millions of cells. Recent single-cell adaptations to the 3C-technique, however, allow for non-aggregated structural assessment of genome structure, but data suffer from sparse and noisy interaction sampling. We present a manifold based optimization (MBO) approach for the reconstruction of 3D genome structure from chromosomal contact data. We show that MBO is able to reconstruct 3D structures based on the chromosomal contacts, imposing fewer structural violations than comparable methods. Additionally, MBO is suitable for efficient high-throughput reconstruction of large systems, such as entire genomes, allowing for comparative studies of genomic structure across cell-lines and different species.", "link"=>"http://www.mendeley.com/research/manifold-based-optimization-singlecell-3d-genome-reconstruction", "reader_count"=>44, "reader_count_by_academic_status"=>{"Unspecified"=>3, "Professor > Associate Professor"=>1, "Researcher"=>8, "Student > Ph. D. Student"=>12, "Student > Postgraduate"=>1, "Student > Master"=>10, "Student > Bachelor"=>3, "Lecturer"=>1, "Professor"=>5}, "reader_count_by_user_role"=>{"Unspecified"=>3, "Professor > Associate Professor"=>1, "Researcher"=>8, "Student > Ph. D. Student"=>12, "Student > Postgraduate"=>1, "Student > Master"=>10, "Student > Bachelor"=>3, "Lecturer"=>1, "Professor"=>5}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Biochemistry, Genetics and Molecular Biology"=>8, "Mathematics"=>3, "Agricultural and Biological Sciences"=>18, "Medicine and Dentistry"=>1, "Physics and Astronomy"=>2, "Computer Science"=>8}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>18}, "Computer Science"=>{"Computer Science"=>8}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>8}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>4}}, "reader_count_by_country"=>{"United Kingdom"=>2, "Lithuania"=>1, "Spain"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2208674"], "description"=>"<p>A: Original chromosomal contact map (<i>C</i><sub><i>ij</i></sub>) based on chromosome X from cell 1. A blue dot indicates the presence of an observed interaction in the single-cell Hi-C data set. B: Distance matrix (<i>D</i><sub><i>ij</i></sub>) consisting of Euclidean distances (in <i>μ</i>m) corresponding to the contact map to the left after running the shortest-path algorithm. C: Corresponding weight matrix (<i>H</i><sub><i>ij</i></sub>), containing numbers between 0 and 1 giving the weight for each of the distances in the Euclidean distance matrix to the left. See the <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004396#sec008\" target=\"_blank\">Methods</a> section for details.</p>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508138, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004396.g001", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Example_of_generation_of_distance_and_weight_matrices_for_the_optimization_procedure_/1508138", "title"=>"Example of generation of distance and weight matrices for the optimization procedure.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-08-11 03:33:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/2208683"], "description"=>"<p>(1–Spearman rank correlation) between the original and reconstructed distances in a single structure of chromosome X from [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004396#pcbi.1004396.ref018\" target=\"_blank\">18</a>], for the different models (CMDS, ChromSDE and MBO) using different noise levels (<i>σ</i>) and ratios of missing distances. <i>σ</i> = 0 corresponds to the case where no noise was added to the distance matrix, whereas <i>σ</i> = 0.1, 0.5 and 1.0, corresponds to cases where increasing levels of Gaussian noise has been added. On the horizontal axis, different levels of missing distances are shown, spanning from 0 (no missing distances) to 0.95 (95% of distances have been removed).</p>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508140, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004396.g002", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_3D_genome_reconstruction_comparisons_for_the_different_algorithms_/1508140", "title"=>"3D genome reconstruction comparisons for the different algorithms.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-08-11 03:33:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/2208685"], "description"=>"<p>A: Original chromosome X structure from [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004396#pcbi.1004396.ref018\" target=\"_blank\">18</a>], resampled at 600 kbp. B-F: Reconstructed 3D structures of chromosome X, with different ratios of observed distance information (20%, 10%, 5%, 2% and 1%, respectively). Information about the RMSD (in nm) and 1 − <i>ρ</i>, compared to the original structure (A) is given below each of the structures in A-F. G: Ratio of observed values as a function of the number of bins <i>n</i>, i.e. the size of the structure being reconstructed. The structures in B-F are highlighted (orange dots), and compared to an estimated curve showing the minimum ratio of observed values for complete reconstruction ([1-<i>ρ</i>]<1e-10; blue curve) or partial reconstruction ([1-<i>ρ</i>]<0.1; black curve). All data from [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004396#pcbi.1004396.ref018\" target=\"_blank\">18</a>] are shown as gray circles, and the X chromosome data sets from cell 1 and cell 2 are highlighted in green.</p>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508142, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004396.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Reconstruction_of_chromosome_X_at_different_levels_of_observed_information_/1508142", "title"=>"Reconstruction of chromosome X at different levels of observed information.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-08-11 03:33:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/2208686"], "description"=>"<p>Computational time (in seconds) for reconstructing a single chromosome structure using three different algorithms CMDS (dark blue), ChromSDE (green), and the MBO algorithm (red) presented here. For comparison, the shortest path algorithm (light blue) is also shown. The computational time is shown as a function of structure size <i>n</i>, i.e. the number of bins in the structure.</p>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508143, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004396.g004", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Computational_time_evaluations_for_the_different_algorithms_/1508143", "title"=>"Computational time evaluations for the different algorithms.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-08-11 03:33:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/2208690"], "description"=>"<p>A: Original contact map. Blue dot indicates the presence of a contact in the single-cell Hi-C data set for chromosome X (cell 1). B: Contact map obtained after 3D reconstruction using MBO, based on the contact map (in A) and then re-calculating the contacts. C: Reconstructed contact map, as in B, but using CMDS. D: Reconstructed 3D structure using MBO, corresponding to the contact map in B. E: Reconstructed 3D structure using CMDS, corresponding to the contact map in C. Each bead in D and E has a diameter of 150 nm. Lines represent connected beads with missing bead position information.</p>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508147, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004396.g005", "stats"=>{"downloads"=>1, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Contact_map_reconstruction_comparison_between_MBO_and_CMDS_/1508147", "title"=>"Contact map reconstruction comparison between MBO and CMDS.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-08-11 03:33:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/2208693"], "description"=>"<p>Consistency of the structures obtained from reconstructing all chromosomes for cell 1 (left) and 2 (right) using MBO (blue) and CMDS (red). A: Reconstruction accuracy, given as the percent correct contacts when comparing original and reconstructed contacts maps for different chromosomes. B: Distance violation, given as the occurrence (in percent) of regions in the structures that are below the minimum distance (at 30 nm). C: Connectivity violation, given as the occurrence (in percent) of consecutive regions in the structures that are further away than the maximum distance (200 nm). Blue bars indicate the performance of MBO, while red bars indicate the performance of CMDS.</p>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508150, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004396.g006", "stats"=>{"downloads"=>2, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Consistency_comparison_of_reconstructed_3D_genome_models_based_on_MBO_and_CMDS_/1508150", "title"=>"Consistency comparison of reconstructed 3D genome models based on MBO and CMDS.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-08-11 03:33:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/2208694"], "description"=>"<p>The heatmap shows clustered RMSD values between 100 independent optimizations with random initial configurations prior to using MBO on chromosome X. The dendrogram above shows the result of the hierarchical clustering based on the RMSD values. At the bottom, 5 example structures from each cluster are shown.</p>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508151, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004396.g007", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Clustering_of_chromosome_X_structural_models_/1508151", "title"=>"Clustering of chromosome X structural models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-08-11 03:33:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/2208698", "https://ndownloader.figshare.com/files/2208699", "https://ndownloader.figshare.com/files/2208700", "https://ndownloader.figshare.com/files/2208701", "https://ndownloader.figshare.com/files/2208702", "https://ndownloader.figshare.com/files/2208703", "https://ndownloader.figshare.com/files/2208704", "https://ndownloader.figshare.com/files/2208705", "https://ndownloader.figshare.com/files/2208706"], "description"=>"<div><p>The three-dimensional (3D) structure of the genome is important for orchestration of gene expression and cell differentiation. While mapping genomes in 3D has for a long time been elusive, recent adaptations of high-throughput sequencing to chromosome conformation capture (3C) techniques, allows for genome-wide structural characterization for the first time. However, reconstruction of \"consensus\" 3D genomes from 3C-based data is a challenging problem, since the data are aggregated over millions of cells. Recent single-cell adaptations to the 3C-technique, however, allow for non-aggregated structural assessment of genome structure, but data suffer from sparse and noisy interaction sampling. We present a manifold based optimization (MBO) approach for the reconstruction of 3D genome structure from chromosomal contact data. We show that MBO is able to reconstruct 3D structures based on the chromosomal contacts, imposing fewer structural violations than comparable methods. Additionally, MBO is suitable for efficient high-throughput reconstruction of large systems, such as entire genomes, allowing for comparative studies of genomic structure across cell-lines and different species.</p></div>", "links"=>[], "tags"=>["3 D structures", "genomic structure", "3 D genomes", "genome structure", "mapping genomes", "mbo", "reconstruction", "3 D genome structure", "chromosome conformation", "gene expression", "chromosomal contact data", "chromosomal contacts", "interaction sampling", "3 D", "Cell differentiation"], "article_id"=>1508155, "categories"=>["Uncategorised"], "users"=>["Jonas Paulsen", "Odin Gramstad", "Philippe Collas"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1004396.s001", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s002", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s003", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s004", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s005", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s006", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s007", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s008", "https://dx.doi.org/10.1371/journal.pcbi.1004396.s009"], "stats"=>{"downloads"=>13, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Manifold_Based_Optimization_for_Single_Cell_3D_Genome_Reconstruction_/1508155", "title"=>"Manifold Based Optimization for Single-Cell 3D Genome Reconstruction", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-08-11 03:33:30"}

PMC Usage Stats | Further Information

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{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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