Conformational modes in biomolecules: Dynamics and approximate invariance

Abstract

Understanding the physical mechanisms behind the folding and conformational dynamics of biomolecules is one of the major unsolved challenges of soft matter theory. In this contribution, a theoretical framework for biomolecular dynamics is introduced, employing selected aspects of statistical mechanics, dimensionality reduction, the perturbation theory, and the theory of matrices. Biomolecular dynamics is represented by time-dependent orthogonal conformational modes, the dynamics of the modes is investigated, and invariant properties that persist are identified. As an example, the dynamics of a human prion protein is considered. The theory provides a rigorous background for assessing the stable dynamical properties of biomolecules, such as their coarse-grained structure, through a multiscale approach using short subnanosecond segments of molecular dynamics trajectories. Furthermore, the paper offers a theoretical platform for models of conformational changes in macromolecules, which may allow complementing molecular dynamics simulations.

Molecular Mechanisms in the Activation of Abscisic Acid Receptor PYR1

“…In the ECD method, an all-atom projected image of the protein is constructed in the dimensional space of essential collective coordinates such that the position of each atom is characterized by , where . The theory shows that such an image represents the degree of dynamic correlation (coupling) between the protein's atoms: points (images of atoms) that are located close to each other correspond to atoms whose motions are strongly correlated regardless of their proximity in secondary or tertiary structure of the protein, and more distant points correspond to a relatively independent motion [31], [33]. A suite of simple structural descriptors, such as the main chain flexibility and domains of correlated motion, have been derived within the ECD framework and successfully employed to analyze dynamics of proteins [32], [35], [47], [34].…”

“…A suite of simple structural descriptors, such as the main chain flexibility and domains of correlated motion, have been derived within the ECD framework and successfully employed to analyze dynamics of proteins [32], [35], [47], [34]. It has been both proven theoretically [33] and confirmed by comparing numerical predictions with NMR experiments representing microsecond time regimes [31], [34].…”

Understanding the dynamics of monomeric, dimeric, and tetrameric α‐synuclein structures in water

“…Based on an analysis of the GLEs it has been shown that distances between images of atoms, , represent the level of correlation of atoms i and j regardless of their proximity in the primary, secondary, or tertiary structure of the protein. It was also demonstrated that the distances d ij represent persistent correlation in a molecule allowing extrapolating the predictions beyond the fragments of MD trajectories employed for the analysis. The ECD method employs several descriptors based on the distances d ij .…”

“…They include the dynamic domains of correlated motions [44], the main-chain flexibility profiles of the protein [45], and the pair correlation maps for main-chain and side-chain atoms [50]. These descriptors are directly comparable with NMR structural data obtained on a longer time scale than required for the ECD analysis [44,45,[48][49][50].…”

“…Our aim is to monitor the evolution of new emerging secondary structures, particularly the formation b-sheet structures, and compare the stability of these structures, in several hypothetical aS constructs starting from their respective unfolded configurations. We also report our analysis of the resulting structures obtained via MD simulations using the novel essential collective dynamics (ECD) methodology [44][45][46][47][48][49][50][51][52][53].…”