Three-dimensional reconstruction of single-cell chromosome structure using recurrence plots

Single-cell analysis of the three-dimensional (3D) chromosome structure can reveal cell-to-cell variability in genome activities. Here, we propose to apply recurrence plots, a mathematical method of nonlinear time series analysis, to reconstruct the 3D chromosome structure of a single cell based on information of chromosomal contacts from genome-wide chromosome conformation capture (Hi-C) data. This recurrence plot-based reconstruction (RPR) method enables rapid reconstruction of a unique structure in single cells, even from incomplete Hi-C information.

[1]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[2]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[3]  J. Gower.  Some distance properties of latent root and vector methods used in multivariate analysis , 1966 .

[4]  M. Levandowsky,et al.  Distance between Sets , 1971, Nature.

[5]  O. Rössler.  An equation for continuous chaos , 1976 .

[6]  Donald B. Johnson,et al.  Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.

[7]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[8]  Jürgen Kurths,et al.  How much information is contained in a recurrence plot , 2004 .

[9]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[10]  Kazuyuki Aihara,et al.  Reproduction of distance matrices and original time series from recurrence plots and their applications , 2008 .

[11]  I. Amit,et al.  Comprehensive mapping of long range interactions reveals folding principles of the human genome , 2011 .

[12]  Yoshito Hirata,et al.  Reconstruction of driving forces through recurrence plots , 2009 .

[13]  William Stafford Noble,et al.  A Three-Dimensional Model of the Yeast Genome , 2010, Nature.

[14]  Marc A. Martí-Renom,et al.  Bridging the Resolution Gap in Structural Modeling of 3D Genome Organization , 2011, PLoS Comput. Biol..

[15]  Mathieu Blanchette,et al.  Three-dimensional modeling of chromatin structure from interaction frequency data using Markov chain Monte Carlo sampling , 2011, BMC Bioinformatics.

[16]  Reza Kalhor,et al.  Genome architectures revealed by tethered chromosome conformation capture and population-based modeling , 2011, Nature Biotechnology.

[17]  Marc A Marti-Renom,et al.  Genome structure determination via 3C-based data integration by the Integrative Modeling Platform. , 2012, Methods.

[18]  Liang-Yu Fu,et al.  The sequencing bias relaxed characteristics of Hi-C derived data and implications for chromatin 3D modeling , 2013, Nucleic acids research.

[19]  Kim-Chuan Toh,et al.  3D Chromosome Modeling with Semi-Definite Programming and Hi-C Data , 2013, J. Comput. Biol..

[20]  A. Tanay,et al.  Single cell Hi-C reveals cell-to-cell variability in chromosome structure , 2013, Nature.

[21]  Dario Meluzzi,et al.  Recovering ensembles of chromatin conformations from contact probabilities , 2012, Nucleic acids research.

[22]  Ming Hu,et al.  Bayesian Inference of Spatial Organizations of Chromosomes , 2013, PLoS Comput. Biol..

[23]  A. Lesne,et al.  3D genome reconstruction from chromosomal contacts , 2014, Nature Methods.

[24]  J. Dekker,et al.  Predictive Polymer Modeling Reveals Coupled Fluctuations in Chromosome Conformation and Transcription , 2014, Cell.

[25]  William Stafford Noble,et al.  A statistical approach for inferring the 3D structure of the genome , 2014, Bioinform..

[26]  Neva C. Durand,et al.  A 3D Map of the Human Genome at Kilobase Resolution Reveals Principles of Chromatin Looping , 2014, Cell.

[27]  Yaniv Lubling,et al.  Single-cell Hi-C for genome-wide detection of chromatin interactions that occur simultaneously in a single cell , 2015, Nature Protocols.

[28]  Yannick G. Spill,et al.  Restraint‐based three‐dimensional modeling of genomes and genomic domains , 2015, FEBS letters.

[29]  Kazuyuki Aihara,et al.  Faithfulness of Recurrence Plots: A Mathematical Proof , 2015, Int. J. Bifurc. Chaos.

[30]  Philippe Collas,et al.  Manifold Based Optimization for Single-Cell 3D Genome Reconstruction , 2015, PLoS Comput. Biol..

[31]  Michael Small,et al.  Examining k-nearest neighbour networks: Superfamily phenomena and inversion. , 2016, Chaos.