Multifractal Analysis of Polyalanines Time Series

TL;DR

This study applies multifractal detrended fluctuation analysis to energy time series of polyalanines, revealing multifractal behavior influenced by residues and temperature, and providing insights into protein folding mechanisms.

Contribution

It introduces the use of MF-DFA to analyze the multifractal properties of polyalanine energy series from molecular dynamics simulations, highlighting their dependence on system parameters.

Findings

All series exhibit multifractal behavior.

Multifractal spectra depend on residues and temperature.

Nucleation during folding influences multifractality.

Abstract

Multifractal properties of the energy time series of short $\alpha$-helix structures, specifically from a polyalanine family, are investigated through the MF-DFA technique ({\it{multifractal detrended fluctuation analysis}}). Estimates for the generalized Hurst exponent $h(q)$ and its associated multifractal exponents $\tau(q)$ 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 on 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.