Multifractal analysis of polyalanines time series

Abstract

a b s t r a c tMultifractal properties of the energy time series of short α-helix structures, specifically from a polyalanine family, are investigated through the MF-DFA technique (multifractal detrended fluctuation analysis). Estimates for the generalized Hurst exponent h(q) and its associated multifractal exponents τ (q) are obtained for several series generated by numerical simulations of molecular dynamics in different systems from distinct initial conformations. All simulations were performed using the GROMOS force field, implemented in the program THOR. The main results have shown that all series exhibit multifractal behavior depending on the number of residues and temperature. Moreover, the multifractal spectra reveal important aspects of the time evolution of the system and suggest that the nucleation process of the secondary structures during the visits on the energy hyper-surface is an essential feature of the folding process.

Quantitative approach to multifractality induced by correlations and broad distribution of data

“…MFDFA is now commonly accepted technique in searching for multifractal properties of data in time series. MFDFA has been applied so far in diversified scientific problems like, e.g., seismology [58,59], cosmology [60], biology [61,62], meteorology [63], medicine [64,65], music [66,67], geophysics [68], and mainly finances [1,26,36,37,38,39,40,41,42,43]. This technique is reported to have an advantage over the other known approach based on wavelets [69].…”

On the multifractal effects generated by monofractal signals

“…The MF-DFA has been applied so far in diversified scientific problems, just to mention: seismology [38,39], cosmology [40], biology [41,42], meteorology [43], medicine [44], music [45,46], geophysics [47], and finances [48]- [54] far from being exhaustive here. Let us remind that the main ingredient of MF-DFA is the q-weighted fluctuation F q (τ ) of the time series signal around its local trend in a time window of size τ .…”

MFDFA: Efficient Multifractal Detrended Fluctuation Analysis in Python

“…[18]. MFDFA has found application in various fields, such as the analysis of heartbeat rate [19], arterial pressure [10], EEG sleep data [11,13], physiology [20], keystroke time series from Parkinson's disease patients [21], cosmic microwave radiation [22,23], seismic activity [24,25], sunspot activity [26], atmospheric scintillation [27], temperature variability [28], meteorology [29], precipitation levels [30], streamflow and sediment movement [7,[31][32][33][34][35][36], protein folding [37], finance and econophysics [38][39][40][41][42], electricity prices [43,44], power-grid frequency [45,46], epidemiology [47], music [48][49][50], ethology [51,52], multifractal harmonic signals [53], and microrheology [54].…”