Spatio-temporal hierarchy in the dynamics of a minimalist protein model

Abstract

A method for time series analysis of molecular dynamics simulation of a protein is presented. In this approach, wavelet analysis and principal component analysis are combined to decompose the spatiotemporal protein dynamics into contributions from a hierarchy of different time and space scales. Unlike the conventional Fourier-based approaches, the time-localized wavelet basis captures the vibrational energy transfers among the collective motions of proteins. As an illustrative vehicle, we have applied our method to a coarse-grained minimalist protein model. During the folding and unfolding transitions of the protein, vibrational energy transfers between the fast and slow time scales were observed among the large-amplitude collective coordinates while the other small-amplitude motions are regarded as thermal noise. Analysis employing a Gaussian-based measure revealed that the time scales of the energy redistribution in the subspace spanned by such large-amplitude collective coordinates are slow compared to the other small-amplitude coordinates. Future prospects of the method are discussed in detail.

What are proteins teaching us on fundamental strategies for molecular nanotechnology?

“…We have to be aware that the involved atoms and groups of atoms are quantum objects, and all parts of the macromolecule undergo thermal activation, exchange of impulses, and permanent fluctuations. Therefore, the difference in mobility between the different parts of the macromolecule is mainly a differentiation in the time scales of the concerned motions [87]. The dynamics of the protein and its response to impulses from outside or its interactions with external partners is determined by these different time scales, by the universally present mixture of frequent reversible relaxations into the equilibrium, and non-frequent environmental-dependent switching processes.…”

Using Wavelet Analysis To Assist in Identification of Significant Events in Molecular Dynamics Simulations

“…The resolution of the time-scale space provided by dyadic decomposition in DWT is not as fine as the space created by full decomposition in CWT . Different algorithms based on wavelet transform have previously been used to analyze MD trajectories. − DWT has been used as a noise reduction method for processing atomic coordinates or reaction coordinates like folding of wild-type and mutant lysozyme . Another example is folding trajectory of the protein Trp-cage in which the denoising property of the DWT has been used to improve the efficiency of calculating a PMF from MD simulations using umbrella sampling .…”

“…Wavelet transforms also have been used in conjunction with singular value decomposition (SVD) on MD trajectories of proteins to extract collective motions . Moreover, DWT has been used as a multiresolution technique to capture vibrational energy transfer of folding/unfolding systems . The CWT using the Morlet wavelet has been applied on the distance between Cα atoms derived from MD simulation trajectory of Activated Protein C (APC) in order to identify the conditions that lead to resonance …”

“…36 Moreover, DWT has been used as a multiresolution technique to capture vibrational energy transfer of folding/unfolding systems. 38 The CWT using the Morlet wavelet has been applied on the distance between Cα atoms derived from MD simulation trajectory of Activated Protein C (APC) in order to identify the conditions that lead to resonance. 39 Recently, Benson and Daggett successfully performed CWT in combination with a statistical significance test for analyzing large databases of protein MD simulations 40 (in the Dynameomics project database 41−44 ).…”