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Journal of Spectroscopy
Volume 2013 (2013), Article ID 372596, 7 pages
Research Article

Singular Value Decomposition and Ligand Binding Analysis

Department of Physics, IBILCE, São Paulo State University (UNESP), Rua Cristóvão Colombo 2265, Jardim Nazareth, 15054-000 São José do Rio Preto, SP, Brazil

Received 20 May 2013; Revised 26 August 2013; Accepted 28 August 2013

Academic Editor: Adam F. Lee

Copyright © 2013 André Luiz Galo and Márcio Francisco Colombo. 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.


Singular values decomposition (SVD) is one of the most important computations in linear algebra because of its vast application for data analysis. It is particularly useful for resolving problems involving least-squares minimization, the determination of matrix rank, and the solution of certain problems involving Euclidean norms. Such problems arise in the spectral analysis of ligand binding to macromolecule. Here, we present a spectral data analysis method using SVD (SVD analysis) and nonlinear fitting to determine the binding characteristics of intercalating drugs to DNA. This methodology reduces noise and identifies distinct spectral species similar to traditional principal component analysis as well as fitting nonlinear binding parameters. We applied SVD analysis to investigate the interaction of actinomycin D and daunomycin with native DNA. This methodology does not require prior knowledge of ligand molar extinction coefficients (free and bound), which potentially limits binding analysis. Data are acquired simply by reconstructing the experimental data and by adjusting the product of deconvoluted matrices and the matrix of model coefficients determined by the Scatchard and McGee and von Hippel equation.