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BioMed Research International
Volume 2015, Article ID 689745, 14 pages
http://dx.doi.org/10.1155/2015/689745
Research Article

Shaped Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the Early Drosophila Embryo

1Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetsky Pr. 28, 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 4 July 2014; Revised 10 September 2014; Accepted 10 September 2014

Academic Editor: Hongwei Wang

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.

Abstract

In recent years, with the development of automated microscopy technologies, the volume and complexity of image data on gene expression have increased tremendously. The only way to analyze quantitatively and comprehensively such biological data is by developing and applying new sophisticated mathematical approaches. Here, we present extensions of 2D singular spectrum analysis (2D-SSA) for application to 2D and 3D datasets of embryo images. These extensions, circular and shaped 2D-SSA, are applied to gene expression in the nuclear layer just under the surface of the Drosophila (fruit fly) embryo. We consider the commonly used cylindrical projection of the ellipsoidal Drosophila embryo. We demonstrate how circular and shaped versions of 2D-SSA help to decompose expression data into identifiable components (such as trend and noise), as well as separating signals from different genes. Detection and improvement of under- and overcorrection in multichannel imaging is addressed, as well as the extraction and analysis of 3D features in 3D gene expression patterns.