Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for BioMed Research International, enter your email address in the box below.

BioMed Research International
Volume 2015, Article ID 986436, 18 pages
http://dx.doi.org/10.1155/2015/986436
Research Article

Shaped 3D Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the Early Zebrafish Embryo

Alex Shlemov,1 Nina Golyandina,1 David Holloway,2 and Alexander Spirov3,4

1Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetsky Pr. 28, St. Peterhof, St. Petersburg 198504, Russia
2Mathematics Department, British Columbia Institute of Technology, 3700 Willingdon Avenue, Burnaby, BC, Canada V5G 3H2
3Computer Science and CEWIT, SUNY Stony Brook, 1500 Stony Brook Road, Stony Brook, NY 11794, USA
4The Sechenov Institute of Evolutionary Physiology & Biochemistry, Torez Pr. 44, St. Petersburg 194223, Russia

Received 8 February 2015; Accepted 1 May 2015

Academic Editor: Shigehiko Kanaya

Copyright © 2015 Alex Shlemov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Gorfinkiel, S. Schamberg, and G. B. Blanchard, “Integrative approaches to morphogenesis: lessons from dorsal closure,” Genesis, vol. 49, no. 7, pp. 522–533, 2011. View at Publisher · View at Google Scholar · View at Scopus
  2. C. C. Fowlkes, C. L. L. Hendriks, S. V. E. Keränen et al., “A quantitative spatiotemporal atlas of gene expression in the Drosophila blastoderm,” Cell, vol. 133, no. 2, pp. 364–374, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. G. B. Blanchard, A. J. Kabla, N. L. Schultz et al., “Tissue tectonics: morphogenetic strain rates, cell shape change and intercalation,” Nature Methods, vol. 6, no. 6, pp. 458–464, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Castro-González, M. A. Luengo-Oroz, L. Duloquin et al., “A digital framework to build, visualize and analyze a gene expression atlas with cellular resolution in zebrafish early embryogenesis,” PLoS Computational Biology, vol. 10, no. 6, Article ID e1003670, 2014. View at Publisher · View at Google Scholar
  5. M. A. Luengo-Oroz, M. J. Ledesma-Carbayo, N. Peyriéras, and A. Santos, “Image analysis for understanding embryo development: a bridge from microscopy to biological insights,” Current Opinion in Genetics and Development, vol. 21, no. 5, pp. 630–637, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. W. Supatto, T. V. Truong, D. Débarre, and E. Beaurepaire, “Advances in multiphoton microscopy for imaging embryos,” Current Opinion in Genetics and Development, vol. 21, no. 5, pp. 538–548, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiological Reviews, vol. 90, no. 3, pp. 1103–1163, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. A. C. Oates, N. Gorfinkiel, M. González-Gaitán, and C.-P. Heisenberg, “Quantitative approaches in developmental biology,” Nature Reviews Genetics, vol. 10, no. 8, pp. 517–530, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Muzzey and A. van Oudenaarden, “Quantitative time-lapse fluorescence microscopy in single cells,” Annual Review of Cell and Developmental Biology, vol. 25, pp. 301–327, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. N. Olivier, M. A. Luengo-Oroz, L. Duloquin et al., “Cell lineage reconstruction of early zebrafish embryos using label-free nonlinear microscopy,” Science, vol. 329, no. 5994, pp. 967–971, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. T. V. Truong and W. Supatto, “Toward high-content/high-throughput imaging and analysis of embryonic morphogenesis,” Genesis, vol. 49, no. 7, pp. 555–569, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. E. Quesada-Hernández, L. Caneparo, S. Schneider et al., “Stereotypical cell division orientation controls neural rod midline formation in zebrafish,” Current Biology, vol. 20, no. 21, pp. 1966–1972, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. M. A. Luengo-Oroz, D. Pastor-Escuredo, C. Castro-Gonzalez et al., “3D + t morphological processing: applications to embryogenesis image analysis,” IEEE Transactions on Image Processing, vol. 21, no. 8, pp. 3518–3530, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. C. Castro-González, M. J. Ledesma-Carbayo, N. Peyriéras, and A. Santos, “Assembling models of embryo development: image analysis and the construction of digital atlases,” Birth Defects Research Part C: Embryo Today: Reviews, vol. 96, no. 2, pp. 109–120, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. M. A. Luengo-Oroz, J. L. Rubio-Guivernau, E. Faure et al., “Methodology for reconstructing early zebrafish development from in vivo multiphoton microscopy,” IEEE Transactions on Image Processing, vol. 21, no. 4, pp. 2335–2340, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. L. Rubio-guivernau, V. Gurchenkov, M. A. Luengo-oroz et al., “Wavelet-based image fusion in multi-view three-dimensional microscopy,” Bioinformatics, vol. 28, no. 2, pp. 238–245, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. F. Long, H. Peng, X. Liu, S. K. Kim, and E. Myers, “A 3D digital atlas of C. elegans and its application to single-cell analyses,” Nature Methods, vol. 6, no. 9, pp. 667–672, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. EPIC: Expression patterns in Caenorhabditis, http://epic.gs.washington.edu.
  19. Berkeley Drosophila transcription network project, http://bdtnp.lbl.gov/Fly-Net/.
  20. BioEmergences, http://bioemergences.iscpif.fr.
  21. W. J. Blake, M. Kærn, C. R. Cantor, and J. J. Collins, “Noise in eukaryotic gene expression,” Nature, vol. 422, no. 6932, pp. 633–637, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, “Stochastic gene expression in a single cell,” Science, vol. 297, no. 5584, pp. 1183–1186, 2002. View at Publisher · View at Google Scholar · View at Scopus
  23. J. M. Raser and E. K. O'Shea, “Noise in gene expression: origins, consequences, and control,” Science, vol. 309, no. 5743, pp. 2010–2013, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. J. E. Ladbury and S. T. Arold, “Noise in cellular signaling pathways: causes and effects,” Trends in Biochemical Sciences, vol. 37, no. 5, pp. 173–178, 2012. View at Publisher · View at Google Scholar · View at Scopus
  25. A. N. Boettiger and M. Levine, “Synchronous and stochastic patterns of gene activation in the Drosophila embryo,” Science, vol. 325, no. 5939, pp. 471–473, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. D. M. Holloway, F. J. Lopes, L. da Fontoura Costa et al., “Gene expression noise in spatial patterning: hunchback promoter structure affects noise amplitude and distribution in Drosophila segmentation,” PLoS Computational Biology, vol. 7, no. 2, Article ID e1001069, 18 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. D. M. Holloway and A. V. Spirov, “Mid-embryo patterning and precision in Drosophila segmentation: Krüppel dual regulation of hunchback,” PLOS ONE, vol. 10, no. 3, Article ID e0118450, 2015. View at Publisher · View at Google Scholar
  28. A. N. Boettiger, “Analytic approaches to stochastic gene expression in multicellular systems,” Biophysical Journal, vol. 105, no. 12, pp. 2629–2640, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. F. Jug, T. Pietzsch, S. Preibisch, and P. Tomancak, “Bioimage Informatics in the context of Drosophila research,” Methods, vol. 68, no. 1, pp. 60–73, 2014. View at Publisher · View at Google Scholar · View at Scopus
  30. E. Wait, M. Winter, C. Bjornsson et al., “Visualization and correction of automated segmentation, tracking and lineaging from 5-D stem cell image sequences,” BMC Bioinformatics, vol. 15, no. 1, p. 328, 2014. View at Publisher · View at Google Scholar
  31. A. Shlemov, N. Golyandina, D. Holloway, and A. Spirov, “Shaped singular spectrum analysis for quantifying gene expression, with application to the early Drosophila embryo,” BioMed Research International, vol. 2015, Article ID 689745, 14 pages, 2015. View at Publisher · View at Google Scholar
  32. D. S. Broomhead and G. P. King, “Extracting qualitative dynamics from experimental data,” Physica D. Nonlinear Phenomena, vol. 20, no. 2-3, pp. 217–236, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. N. Golyandina, V. Nekrutkin, and A. Zhigljavsky, Analysis of Time Series Structure: SSA and Related Techniques, vol. 90 of Monographs on Statistics and Applied Probability, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  34. N. Golyandina and A. Zhigljavsky, Singular Spectrum Analysis for Time Series, Springer Briefs in Statistics, Springer, Heidelberg, Germany, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  35. T. Alexandrov, N. Golyandina, and A. Spirov, “Singular spectrum analysis of gene expression profiles of early Drosophila embryo: Exponential-in-distance patterns,” Research Letters in Signal Processing, vol. 2008, Article ID 825758, 5 pages, 2008. View at Publisher · View at Google Scholar
  36. N. E. Golyandina, D. M. Holloway, F. J. Lopes, A. V. Spirov, E. N. Spirova, and K. D. Usevich, “Measuring gene expression noise in early Drosophila embryos: nucleus-tonucleus variability,” Procedia Computer Science, vol. 9, pp. 373–382, 2012. View at Google Scholar
  37. N. Golyandina, A. Korobeynikov, A. Shlemov, and K. Usevich, “Multivariate and 2D extensions of singular spectrum analysis with the Rssa package,” Journal of Statistical Software, http://arxiv.org/abs/1309.5050.
  38. J. P. Snyder, Map Projections: A Working Manual, Geological Survey Bulletin Series, US Geological Survey, 1987.
  39. A. Shlemov and N. Golyandina, “Shaped extensions of singular spectrum analysis,” in Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems, pp. 1813–1820, Groningen, The Netherlands, July 2014.
  40. J. P. Lewis, K. Anjyo, and F. Pighin, “Scattered data interpolation and approximation for computer graphics,” in ACM SIGGRAPH ASIA Courses (SA'10), pp. 27:1–27:69, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  41. S. Pion and M. Teillaud, “3D triangulations,” in CGAL User and Reference Manual, CGAL Editorial Board, 4.5th edition, 2014. View at Google Scholar
  42. B. Mourrain and V. Y. Pan, “Multivariate polynomials, duality, and structured matrices,” Journal of Complexity, vol. 16, no. 1, pp. 110–180, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  43. R. E. Park, “Estimation with heteroscedastic error terms,” Econometrica, vol. 34, no. 4, p. 888, 1966. View at Publisher · View at Google Scholar
  44. R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2014.
  45. H. Edelsbrunner and E. P. Mücke, “Three-dimensional alpha shapes,” ACM Transactions on Graphics, vol. 13, no. 1, pp. 43–72, 1994. View at Google Scholar
  46. C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, “The quickhull algorithm for convex hulls,” ACM Transactions on Mathematical Software, vol. 22, no. 4, pp. 469–483, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  47. T. Lafarge and B. Pateiro-Lopez, alphashape3d: Implementation of the 3D Alpha-Shape for the Reconstruction of 3D Sets from a Point Cloud, R package version 1.1, 2014.
  48. K. Habel, R. Grasman, A. Stahel, and D. C. Sterratt, Geometry: Mesh generation and surface tesselation, R package version 0.3-5, 2014.
  49. D. Kelley, oce: Analysis of Oceanographic Data, R package version 0.9-14, 2014.
  50. A. Korobeynikov, A. Shlemov, K. Usevich, and N. Golyandina, Rssa: A Collection of Methods for Singular Spectrum Analysis, R Package Version 0.11, 2014.
  51. A. Korobeynikov, “Computation- and space-efficient implementation of SSA,” Statistics and Its Interface, vol. 3, no. 3, pp. 357–368, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  52. A. V. Spirov, N. E. Golyandina, D. M. Holloway, T. Alexandrov, E. N. Spirova, and F. J. P. Lopes, “Measuring gene expression noise in early Drosophila embryos: the highly dynamic compartmentalized micro-environment of the blastoderm is one of the main sources of noise,” in Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics, vol. 7246 of Lecture Notes in Computer Science, pp. 177–188, Springer, Berlin, Germany, 2012. View at Publisher · View at Google Scholar
  53. T.-M. Chan, W. Longabaugh, H. Bolouri et al., “Developmental gene regulatory networks in the zebrafish embryo,” Biochimica et Biophysica Acta—Gene Regulatory Mechanisms, vol. 1789, no. 4, pp. 279–298, 2009. View at Publisher · View at Google Scholar · View at Scopus
  54. E. Poustelnikova, A. Pisarev, M. Blagov, M. Samsonova, and J. Reinitz, “A database for management of gene expression data in situ,” Bioinformatics, vol. 20, no. 14, pp. 2212–2221, 2004. View at Publisher · View at Google Scholar · View at Scopus
  55. Y. F. Wu, E. Myasnikova, and J. Reinitz, “Master equation simulation analysis of immunostained Bicoid morphogen gradient,” BMC Systems Biology, vol. 1, article 52, 2007. View at Publisher · View at Google Scholar · View at Scopus
  56. F. He, Y. Wen, J. Deng et al., “Probing intrinsic properties of a robust morphogen gradient in Drosophila,” Developmental Cell, vol. 15, no. 4, pp. 558–567, 2008. View at Publisher · View at Google Scholar · View at Scopus