Random covering of multiple one-dimensional domains with an application to DNA sequencing

SIAM Journal on Applied Mathematics

Volumn 68, Issue 3, 2007, Pages 890-905

  Wendl, Michael C ^a  

^a WASHINGTON UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Coverage; Probabilistic modeling; Sequence redundancy

Indexed keywords

APPLIED MATHEMATICS; CLASSICAL THEORY; CURRENT MODELING; DENSITY FUNCTIONS; DNA LIBRARIES; DNA SEQUENCING; DOMAIN CONFIGURATIONS; MICRO SCALES; MULTIPLE DOMAINS; ONE-DIMENSIONAL; PYROSEQUENCING; RANDOM COVERINGS; SMALL TARGETS;

DNA; GENES; ORGANIC ACIDS; TARGETS;

NUCLEIC ACIDS;

EID: 47149090170     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/06065979X     Document Type: Article

References (49)

1. S. ANDERSON, Shotgun DNA sequencing using cloned DNase I-generated fragments, Nucleic-Acids Research, 9 (1981), pp. 3015-3027.
2. F. E. ANGLY, B. FELTS, M. BREITBART, P. SALAMON, R. A. EDWARDS, C. CARLSON, A. M. CHAN. M. HAYNES, S. KELLEY, H. LIU, J. M. MAHAFFY, J. E. MUELLER. J. NULTON, R. OLSON. R. PARSONS, S. RAYHAWK, C. A. SUTTLE, AND F. ROHWER, The marine viromes of four oceanic regions, PLoS Biology, 4 (2006), article e368.
3. E. T. BELL, Exponential polynomials, Ann. of Math., 35 (1934), pp. 258-277.
4. R. W. BLAKESLEY. N. F. HANSEN, J. C. MULLIKIN, P. J. THOMAS. J. C. MCDOWELL. B. MASKERI. A. C. YOUNG, B. BENJAMIN, S. Y. BROOKS, B. I. COLEMAN. J. GUPTA, S. L. HO. E. M. KARUNS. Q. L. MADURO, S. STANTRIPOP. C. TSURGEON. J. L. VOGT, M. A. WALKER. C. A. MASIELLO, X. B. GUAN. G. G. BOUFFARD. AND E. D. GREEN, An intermediate grade of finished genomic sequence suitable for comparative analyses, Genome Research, 14 (2004), pp. 2235-2244.
5. R. G. BLAZEJ, P. KUMARESAN, AND R. A. MATHIES, Microfabricated bioprocessor for integrated nanoliter - scale Sanger DNA sequencing, Proc. Nat. Acad. Sci. USA, 103 (2006), pp. 72407245.
6. J. BOUCK. W. MILLER, J. H. GORRELL, D. MUZNY, AND R. A. GIBBS, Analysis of the quality and utility of random shotgun sequencing at low redundancies, Genome Research, 8 (1998), pp. 1074-1084.
7. M. CHAISSON. P. PEVZNER, AND H. TANG, Fragment assembly with short reads, Bioinformatics, 20 (2004), pp. 2067-2074.
8. S. L. CHISSOE. M. A. MARRA, L. HILLIER, R. BRINKMAN. R. K. WILSON, AND R. H. WATERSTON, Representation of cloned genomic sequences in two sequencing vectors: Correlation of DNA sequence, and subclone distribution, Nucleic Acids Research, 25 (1997), pp. 2960-2966.
9. L. COMTET, Advanced Combinatorics, Reidel Publishing, Dordrecht, The Netherlands, 1974.
10. A. I. CULLEY. A. S. LANG, AND C. A. SUTTLE, Metagenomic analysis of coastal RNA virus communities, Science, 312 (2006), pp. 1795-1798.
11. P. L. DEININGER, Random subcloning of sonicated DNA: Application to shotgun DNA sequence analysis, Analytical Biochemistry, 129 (1983), pp. 216-223.
12. T. G. DOAK, A. R. O. CAVALCANTI, N. A. STOVER, D. M. DUNN, R. WEISS, G. HERRICK, AND L. F. LANDWEBER, Sequencing the Oxytricha trifallax macronuclear genome: A pilot project, Trends in Genetics, 19 (2003). pp. 603-607.
13. C. DOMB, The problem of random intervals on a line. Proceedings of the Cambridge Philosophical Society, 43 (1947), pp. 329-341.
14. C. DOMB, On Hammersley's method for- one-dimensional covering problems, in Disorder in Physical Systems, G. R. Grimmett and D. J. A. Welsh, eds., Oxford University Press, Oxford, UK, 1990, pp. 33-53.
15. B. EWING. L. HILLIER. M. C. WENDL. AND P. GREEN, Base calling of automated sequencer traces using Phred. I. Accuracy assessment, Genome Research, 8 (1998), pp. 175-185.
16. W. FELLER, An Introduction to Probability Theory and Its Applications, 3rd ed., John Wiley & Sons, New York, 1968.
17. R. A. FISHER, On the similarity of the distributions found for the test of significance in harmonic analysis and in Stevens' problem in geometrical probability, Annals of Eugenics, 10 (1940), pp. 14-17.
18. L. FLATTO AND A. G. KONHEIM, The random division of an interval and the random covering of a circle, SIAM Rev., 4 (1962), pp. 211-222.
19. J. E. GALAGAN, S. E. CALVO, K. A. BORKOVICH, E. U. SELKER, N. D. READ, D. JAFFE, W. FITZHUGH, L. J. MA, S. SMIRNOV, S. PURCELL, B. REHMAN. T. ELKINS, R. ENGELS, S. WANG, C. B. NIELSEN, J. BUTLER, M. ENDRIZZI, D. QUI, P. IANAKIEV, D. BELL-PEDERSEN, M. A. NELSON, M. WERNER-WASHBURNE, C. P. SELITRENNIKOFF, J. A. KINSEY, E. L. BRAUN, A. ZELTER, U. SCHULTE, G. O. KOTHE, G. JEDD, W. MEWES. C. STABEN, E. MARCOTTE, D. GREENBERG, A. ROY, K. FOLEY, J. NAYLOR, N. STANGE-THOMANN, R. BARRETT, S. GNERRE, M. KAMAL, M. KAMVYSSELIS, E. MAUCELI, C. BIELKE, S. RUDD, D. FRISHMAN, S. KRYSTOFOVA. C. RASMUSSEN, R. L. METZENBERG, D. D. PERKINS, S. KROKEN, C. COGONI, G. MACINO, D. CATCHESIDE, W. LI, R. J. PRATT, S. A. OSMANI, C. P. C. DESOUZA, L. GLASS, M. J. ORBACH, J. A. BERGLUND. R. VOELKER, O. YARDEN, M. PLAMANN, S. SEILER. J. DUNLAP, A. RADFORD, R. ARAMAYO, D. O. NATVIG, L. A. ALEX, G. MANNHAUPT, D. J. EBBOLE, M. FREITAG, I. PAULSEN, M. S. SACHS, E. S. LANDER, C. NUSBAUM, AND H. BIRREN, The genome sequence of the filamentous fungus Neurospora crassa, Nature, 422 (2003), pp. 859-868.
20. S. R. GILL, M. POP. R. T. DEBOY, P. B. ECKBURG, P. J. TURNBAUGH, B. S. SAMUEL, J. I. GORDON, D. A. RELMAN, C. M. FRASER-LIGGETT, AND K. E. NELSON, Metagenomic analysis of the human distal gut microbiome, Science, 312 (2006), pp. 1355-1359.
21. P. GREEN, Against a whole-genome shotgun, Genome Research, 7 (1997), pp. 410-417.
22. P. G. HOEL, Introduction to Mathematical Statistics, John Wiley & Sons, New York, 1947.
23. J. HÜSLER, Random coverage of the circle and asymptotic distributions, J. Appl. Probab., 19 (1982), pp. 578-587.
24. INTERNATIONAL HUMAN GENOME MAPPING CONSORTIUM, A physical map of the human genome, Nature, 409 (2001), pp. 934-941.
25. INTERNATIONAL HUMAN GENOME SEQUENCING CONSORTIUM, Finishing the euchromatic sequence of the human genome, Nature, 431 (2004), pp. 931-945.
26. U.-J. KIM, H. SHIZUYA, P. J. DE JONG, B. BIRREN, AND M. I. SIMON, Stable propagation of cosmid sized human DNA inserts in an F-factor based vector, Nucleic Acids Research, 20 (1992), pp. 1083-1085.
27. J. KLING, The search for a sequencing thoroughbred, Nature Biotechnology, 23 (2005), pp. 1333-1335.
28. V. F. KOLCHIN, B. A. SEVASTYANOV, AND V. P. CHRISTYAKOV, Random Allocations, John Wiley & Sons, New York, 1978.
29. E. S. LANDER AND M. S. WATERMAN, Genomic mapping by fingerprinting random clones: A mathematical analysis, Genomics, 2 (1988), pp. 231-239.
30. H. G. MARTÍN, N. IVANOVA, V. KUNIN, F. WARNECKE, K. W. BARRY, A. C. MCHARDY, C. YEATES, S. HE, A. A. SALAMOV, E. SZETO, E. DALIN, N. H. PUTNAM, H. J. SHAPIRO, J. L. PANGILINAN, I. RIGOUTSOS, N. C. KYRPIDES, L. L. BLACKALL, K. D. MCMAHON, AND P. HUGENHOLTZ, Metagenomic analysis of two enhanced biological phosphorus removal EBPR sludge communities, Nature Biotechnology, 24 (2006), pp. 1263-1269.
31. J. MORIARTY, J. R. MARCHESI, AND A. METCALFE, Bounds on the distribution of the number of gaps when circles and lines are covered by fragments: Theory and practical application to genomic and metagenomic projects, BMC Bioinformatics, 8 (2007), article 70.
32. G. MYERS, Whole-genome DNA sequencing, Comput. Sci. Engrg., 1 (1999), pp. 33-43.
33. D. M. PRESCOTT, J. D. PRESCOTT, AND R. M. PRESCOTT, Coding properties of macronuclear DNA molecules in Sterkiella nova (Oxytricha nova), Protist, 153 (2002), pp. 71-77.
34. RAT GENOME SEQUENCING PROJECT CONSORTIUM, Genome sequence of the Brown Norway rat yields insights into mammalian evolution, Nature, 428 (2004), pp. 493-521.
35. J. C. ROACH, Random subcloning, Genome Research, 5 (1995), pp. 464-473.
36. D. B. RUSCH, A. L. HALPERN, G. SUTTON, K. B. HEIDELBERG, S. WILLIAMSON, S. YOOSEPH, D. WU, J. A. EISEN, J. M. HOFFMAN, K. REMINGTON, K. BEESON, B. TRAN, H. SMITH, H. BADEN-TILLSON, C. STEWART, J. THORPE, J. FREEMAN, C. ANDREWS-PFANNKOCH, J. E. VENTER, K. LI, S. KRAVITZ, J. F. HEIDELBERG, T. UTTERBACK, Y. H. ROGERS, L. I. FALCÓN, V. SOUZA, G. BONILLA-ROSSO, L. E. EGUIARTE, D. M. KARL, S. SATHYENDRANATH, T. PLATT, E. BERMINGHAM, V. GALLARDO, G. TAMAYO-CASTILLO, M. R. FERRARI, R. L. STRAUSBERG, K. NEALSON, R. FRIEDMAN, M. FRAZIER, AND J. C. VENTER, The Sorcerer II global ocean sampling expedition: Northwest Atlantic through eastern tropical Pacific, PLoS Biology, 5 (2007), article e77.
37. F. SANGER, S. NICKLEN, AND A. R. COULSON, DNA sequencing with chain-terminating inhibitors, Proc. Natl. Acad. Sci. USA, 74 (1977), pp. 5463-5467.
38. A. F. SIEGEL, Random arcs on the circle, J. Appl. Probab., 15 (1978), pp. 774-789.
39. A. F. SIEGEL, Asymptotic coverage distributions on the circle, Ann. Probab., 7 (1979), pp. 651-661.
40. H. SOLOMON, Geometric Probability, CBMS-NSF Regional Conf. Ser. in Appl. Math. 28, SIAM, Philadelphia, 1978.
41. W. L. STEVENS, Solution to a geometrical problem in probability, Ann. Eugenics, 9 (1939), pp. 315-320.
42. J. C. VENTER, M. D. ADAMS, E. W. MYERS, P. W. LI, R. J. MURAL, G. G. SUTTON, H. O. SMITH, M. YANDELL, C. A. EVANS, R. A. HOLT, J. D. GOCAYNE, P. AMANATIDES, R. M. BALLEW, D. H. HUSON, J. R. WORTMAN, Q. ZHANG, C. D. KODIRA, X. Q. H. ZHENG, L. CHEN, M. SKUPSKI, G. SUBRAMANIAN, P. D. THOMAS, J. H. ZHANG, G. L. G. MIKLOS, C. NELSON, S. BRODER, A. G. CLARK, C. NADEAU, V. A. MCKUSICK, N. ZINDER, A. J. LEVINE, R. J. ROBERTS, M. SIMON, C. SLAYMAN, M. HUNKAPILLER, R. BOLANOS, A. DELCHER, I. DEW, D. FASULO, M. FLANIGAN, L. FLOREA, A. HALPERN, S. HANNENHALLI, S. KRAVITZ, S. LEVY, C. MOBARRY, K. REINERT, K. REMINGTON, J. ABU-THREIDEH, E. BEASLEY, K. BIDDICK, V. BONAZZI, R. BRANDON, M. CARGILL, I. CHANDRAMOULISWARAN, R. CHARLAB, K. CHATURVEDI, Z. M. DENG, V. DI FRANCESCO, P. DUNN, K. EILBECK, C. EVANGELISTA, A. E. GABRIELIAN, W. GAN, W. M. GE, F. C. GONG, Z. P. GU, P. GUAN, T. J. HEIMAN, M. E. HIGGINS, R. R. JI, Z. X. KE, K. A. KETCHUM, Z. W. LAI, Y. D. LEI, Z. Y. LI, J. Y. LI, Y. LIANG, X. Y. LIN, F. LU, G. V. MERKULOV, N. MILSHINA, H. M. MOORE, A. K. NAIK, V. A. NARAYAN, B. NEELAM, D. NUSSKERN, D. B. RUSCH, S. SALZBERG, W. SHAO, B. X. SHUE, J. T. SUN, Z. Y. WANG, A. H. WANG, X. WANG, J. WANG, M. H. WEI, R. WIDES, C. L. XIAO, C. H. YAN, A. YAO, J. YE, M. ZHAN, W. Q. ZHANG, H. Y. ZHANG, Q. ZHAO, L. S. ZHENG, F. ZHONG, W. Y. ZHONG, S. P. C. ZHU, S. Y. ZHAO, D. GILBERT, S. BAUMHUETER, G. SPIER, C. CARTER, A. CRAVCHIK, T. WOODAGE, F. ALI, H. J. AN, A. AWE, D. BALDWIN, H. BADEN, M. BARNSTEAD, I. BARROW, K. BEESON, D. BUSAM, A. CARVER, A. CENTER, M. L. CHENG, L. CURRY, S. DANAHER, L. DAVENPORT, R. DESILETS, S. DIETZ, K. DODSON, L. DOUP, S. FERRIERA, N. GARG, A. GLUECKSMANN, B. HART, J. HAYNES, C. HAYNES, C. HEINER, S. HLADUN, D. HOSTIN, J. HOUCK, T. HOWLAND, C. IBEGWAM, J. JOHNSON, F. KALUSH, L. KLINE, S. KODURU, A. LOVE, F. MANN, D. MAY, S. MCCAWLEY, T. MCINTOSH, I. MCMULLEN, M. MOY, L. MOY, B. MURPHY, K. NELSON, C. PFANNKOCH, E. PRATTS, V. PURI, H. QURESHI, M. REARDON, R. RODRIGUEZ, Y. H. ROGERS, D. ROMBLAD, B. RUHFEL, R. SCOTT, C. SITTER, M. SMALLWOOD, E. STEWART, R. STRONG. E. SUH, R. THOMAS, N. N. TINT, S. TSE, C. VECH, G. WANG, J. WETTER, S. WILLIAMS, M. WILLIAMS, S. WINDSOR, E. WINN-DEEN, K. WOLFE, J. ZAVERI, K. ZAVERI, J. F. ABRIL, R. GUIGO, M. J. CAMPBELL, K. V. SJOLANDER. B. KARLAK, A. KEJARIWAL, H. Y. MI, B. LAZAREVA, T. HATTON, A. NARECHANIA, K. DIEMER, A. MURUGANUJAN, N. GUO, S. SATO, V. BAFNA, S. ISTRAIL, R. LIPPERT, R. SCHWARTZ, B. WALENZ, S. YOOSEPH, D. ALLEN, A. BASU, J. BAXENDALE, L. BLICK, M. CAMINHA, J. CARNES-STINE, P. CAULK, Y. H. CHIANG, M. COYNE. C. DAHLKE, A. D. MAYS, M. DOMBROSKI, M. DONNELLY, D. ELY, S. ESPARHAM, C. FOSLER, H. GIRE, S. GLANOWSKI, K. GLASSER, A. GLODEK, M. GOROKHOV, K. GRAHAM, B. GROPMAN, M. HARRIS, J. HEIL, S. HENDERSON, J. HOOVER, D. JENNINGS, C. JORDAN, J. JORDAN, J. KASHA, L. KAGAN, C. KRAFT, A. LEVITSKY, M. LEWIS. X. J. LIU, J. LOPEZ, D. MA, W. MAJOROS, J. MCD ANIEL, S. MURPHY, M. NEWMAN, T. NGUYEN, N. NGUYEN, M. NODELL, S. PAN, J. PECK, M. PETERSON, W. ROWE, R. SANDERS, J. SCOTT, M. SIMPSON, T. SMITH, A. SPRAGUE, T. STOCKWELL. R. TURNER, E. VENTER, M. WANG, M. Y. WEN, D. WU, M. WU, A. XIA, A. ZANDIEH, AND X. H. ZHU, The sequence of the human genome, Science, 291 (2001), pp. 1304-1351.
43. J. C. VENTER, K. REMINGTON, J. F. HEIDELBERG, A. L. HALPERN, D. RUSCH, J. A. EISEN, D. WU. I. PAULSEN, K. E. NELSON, W. NELSON. D. E. FOUTS, S. LEVY. A. H. KNAP, M. W. LOMAS. K. NEALSON, O. WHITE, J. PETERSON, J. HOFFMAN, R. PARSONS, H. BADEN-TILLSON, C. PFANNKOCH, Y. H. ROGERS, AND H. O. SMITH, Environmental genome shotgun sequencing of the Sargasso Sea, Science, 304 (2004), pp. 66-74.
44. M. C. WENDL, Occupancy modeling of coverage distribution for whole genome shotgun DNA sequencing, Bull. Math. Biol., 68 (2006), pp. 179-196.
45. M. C. WENDL AND W. B. BARBAZUK, Extension of Lander-Waterman theory for sequencing filtered DNA libraries, BMC Bioinformatics, 6 (2005), article 245.
46. M. C. WENDL AND R. H. WATERSTON, Generalized gap model for bacterial artificial chromosome clone fingerprint mapping and shotgun sequencing, Genome Research, 12 (2002), pp. 1943 1949.
47. C. A. WHITELAW, W. B. BARBAZUK, G. PERTEA, A. P. CHAN, F. CHEUNG, Y. LEE, L. ZHENG, S. VAN HEERINGEN, S. KARAMYCHEVA, J. L. BENNETZEN, P. SANMIGUEL, N. LAKEY, J. BEDELL, Y. YUAN, M. A. BUDIMAN, A. RESNICK, S. VAN AKEN, T. UTTERBACK, S. RIED- MULLER, M. WILLIAMS, T. FELDBLYUM, K. SCHUBERT, R. BEACHY, C. M. FRASER, AND J. QUACKENBUSH, Enrichment of gene-coding sequences in maize by genome filtration, Science, 302 (2003), pp. 2118-2120.
48. R. WILSON, R. AINSCOUGH, K. ANDERSON, C. BAYNES, M. BERKS, J. BURTON, M. CONNELL, J. BONFIELD, T. COPSEY, J. COOPER. A. COULSON, M. CRAXTON, S. DEAR, Z. DU, R. DURBIN, A. FAVELLO, A. FRASER, L. FULTON, A. GARDNER, P. GREEN, T. HAWKINS, L. HILLIER, M. JIER, L. JOHNSTON, M. JONES, J. KERSHAW, J. KIRSTEN, N. LAISSTER, P. LATREILLE, C. LLOYD, B. MORTIMORE, M. OCALLAGHAN, J. PARSONS, C. PERCY. L. RIFKEN, A. ROOPRA, D. SAUNDERS, R. SHOWNKEEN, M. SIMS, N. SMALDON, A. SMITH, M. SMITH, E. SONNHAMMER, R. STADEN, J. SULSTON, J. THIERRY-MIEG, K. THOMAS, M. VAUDIN, K. VAUGHAN, R. WATERSTON, A. WATSON, L. WEINSTOCK, J. WILKINSON-SPROAT, AND P. WOHLDMAN, 2.2 Mb of contiguous nucleotide sequence from chromosome III of C. elegans, Nature, 368 (1994), pp. 32-38.
49. J. YU, S. HU, J. WANG, G. K. S. WONG, S. LI, B. LIU, Y. DENG, L. DAI, Y. ZHOU, X. ZHANG, M. CAO, J. LIU, J. SUN, J. TANG, Y. CHEN, X. HUANG, W. LIN, C. YE, W. TONG, L. CONG, J. GENG, Y. HAN, L. LI, W. LI, G. HU, X. HUANG, W. LI, J. LI, Z. LIU, L. LI, J. LIU, Q. QI, J. LIU, L. LI, T. LI, X. WANG, H. LU, T. WU, M. ZHU, P. NI, H. HAN, W. DONG, X. REN, X. FENG, P. CUI, X. LI, H. WANG, X. XU, W. ZHAI, Z. XU, J. ZHANG, S. HE, J. ZHANG, J. XU, K. ZHANG, X. ZHENG, J. DONG, W. ZENG, L. TAO, J. YE, J. TAN, X. REN, X. CHEN, J. HE, D. LIU, W. TIAN, C. TIAN, H. XIA, Q. BAO, G. LI, H. GAO, T. CAO, J. WANG, W. ZHAO, P. LI, W. CHEN, X. WANG, Y. ZHANG, J. HU, J. WANG, S. LIU, J. YANG, G. ZHANG, Y. XIONG, Z. LI, L. MAO, C. ZHOU, Z. ZHU, R. CHEN, B. HAO, W. ZHENG, S. CHEN, W. GUO, G. LI, S. LIU, M. TAO, J. WANG, L. ZHU, L. YUAN, AND H. YANG, A draft sequence of the rice genome (Oryza sativa L. ssp. indica), Science, 296 (2002), pp. 79-92.