Physica A 389 (2010) 2682–2686 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Self-affine analysis of protein energy P.H. Figueirêdo a , M.A. Moret b,c,∗ , P.G. Pascutti d , E. Nogueira Jr. e , S. Coutinho f a Departamento de Física, Universidade Federal Rural de Pernambuco, CEP 52171-900, Recife, Pernambuco, Brazil b Programa de Modelagem Computacional - SENAI - Cimatec, 41650-010 Salvador, Bahia, Brazil c Departamento de Física, Universidade Estadual de Feira de Santana, CEP 44031-460, Feira de Santana, Bahia, Brazil d Instituto de Biofísica Carlos Chagas Filho, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil e Instituto de Física, Universidade Federal da Bahia, CEP 40210-340, Salvador, Bahia, Brazil f Departamento de Física, Universidade Federal de Pernambuco, CEP 50670-901, Recife, Pernambuco, Brazil article info Article history: Received 14 March 2009 Received in revised form 26 February 2010 Available online 23 March 2010 Keywords: Protein packing Self-affinity abstract We study the time series of the total energy of polypeptides and proteins. These time series were generated by molecular dynamics methods and analyzed by applying detrended fluctuation analysis to estimate the long-range power-law correlation, i.e. to measure scaling exponents α. Such exponents were calculated for all systems and their values follow environment conditions, i.e., they are temperature dependent and also, in a continuum medium approach, vary according to the dielectric constants (we simulated ǫ = 2 and ǫ = 80). The procedure was applied to investigate polyalanines, and other realistic models of proteins (Insect Defensin A and Hemoglobin). The present findings exhibit results that are consistent with previous ones obtained by other methodologies. © 2010 Elsevier B.V. All rights reserved. In recent years, there has been a growing evidence that many complex physical, economical, and biological systems manifest self-affinity characterized by long-range power-law correlations. In such a context, the detrended fluctuation analysis (DFA) was recently proposed [1] to analyze long-range power-law correlations in nonstationary systems. One advantage of the DFA method is that it allows the long-range power-law correlations in signals with embedded polynomial trends that can mask the true correlations in the fluctuations of a noise signal. The DFA method has been applied to analyze the DNA and its evolution [1,2], file editions in computer diskettes [3], economics [4,5], climate temperature behavior [6], phase transition [7], astrophysics sources [8,9] and cardiac dynamics [10,11], among others. The study of fractal characteristics of the proteins provides countless results. The fractal analysis uncovered self- similarity in many research fields such as cluster dimension of proteins [12], anomalous temperature dependence of the Raman spin–lattice relaxation rates [13], relation between the fractal dimension and the number of hydrogen bridges [14], multifractality in the energy hypersurface of the proteins [15], packing of small protein fragments [16], surface volume [17], degree of compactness of the proteins [18], measurement of the average packing density [19] as well as a hydrophobicity scale [20] among others. Furthermore, the fractal methods identify different states of the same system according to its different scaling behaviors, e.g., the fractal dimension is different for structures with (without) hydrogen bonds [14,15]. In this sense, the correct interpretation of the scaling results obtained by the fractal analysis is crucial to understand the intrinsic geometry (and sometimes dynamics) of the systems under study. In this paper the DFA method was applied to investigate self-affinity presented in protein molecular dynamics. The long- term time-series energy of peptides and proteins were studied by the using the THOR modelling program. The THOR program ∗ Corresponding author at: Departamento de Física, Universidade Estadual de Feira de Santana, CEP 44031-460, Feira de Santana, Bahia, Brazil. Tel.: +55 71 82272352. E-mail address: mamoret@gmail.com (M.A. Moret). 0378-4371/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2010.03.021