An automatic, multiscale, and three-dimensional (3D) summary of local configurations of the dynamics of proteins can help to discover and describe the relationships between different parts of proteins across spatial scales, including the overall conformation and 3D configurations of side chains and domains. These discoveries can improve our understanding of the function and allosteric mechanism of proteins and could potentially provide an avenue to test and improve the molecular mechanics force fields at different spatial resolutions. Many of the current methods are unable to effectively summarize shapes of 3D local configurations across all spatial scales. Here, we propose frequent substructure clustering (FSC) to fill this gap. Frequent substructure clustering of the Cβ atoms of the GB3 protein identifies six clusters of co-occurring local configurations. The clusters that are localized at different regions contribute to the overall conformation, and form two anticorrelating groups. The results suggest that FSC could describe dynamical relationships between different parts of proteins by providing a 3D description of the frequently occurring local configurations at different spatial resolutions. FSC could augment the use of other methods, such as Markov state models, to study the function of subcellular processes and highlight the role of local configurations in biomolecular systems.

Molecular dynamics (MD) simulation distinctly describes motions of biomolecules at high resolution and can potentially be used to explain allosteric mechanism in subcellular processes. Statistical methods are necessary to realize this potential because MD simulations generate a large volume of data and because the analysis is never efficient, objective, or thorough without using appropriate statistical approaches. Tracing the flow of information within a biomolecule requires not only a description of an overall mechanism but also a multiscale statistical description from atomic interactions to the overall mechanism. The foundation of this multiscale description, in general, is a measure of correlation between motions of atoms or residues, as reflected by dynamic cross-correlation, Pearson correlation, or mutual information. However, these correlations can be inadequate because they assume wide sense stationarity, which means that the instantaneous average and correlation of a particular property are time-independent. Consequently, these measures of correlation cannot account for correlation between motions of different frequencies, since frequency implies oscillation and variation over time. Here, we characterize the nonstationarity in the form of pure oscillatory instantaneous variance in the signed dihedral angular accelerations (SDAA) along the main chain of alanine tripeptide in MD simulations by power spectrum, corrected squared envelope spectrum (CSES), and cross-CSES. This oscillation has a physical interpretation of an oscillatory diffusion. The fraction of this oscillation in all motions is as high as about 40% at some frequencies. This shows that oscillatory instantaneous variance exists in the SDAA and that significant correlation may not be accounted for in current correlation analysis. This oscillation is also found to transmit between dihedral angles. These results could have implications in the understanding of the dynamics of biomolecules.

Although molecular dynamics simulations have been shown to accurately refold some proteins, commonly used metrics to describe the refolding pathways created by simulation require the presence of a crystal structure for reference or clustering techniques. Furthermore, metrics which rely on combining multiple individual distances like RMSD make it difficult to distinguish the refolding of individual amino acids compared to their counterparts. To better resolve amino acid stabilization, we examined the dihedral stabilities of amino acids in a stable I91 module as well as in its perturbed state with the A strand separated from the I91 domain. In doing so we find we were able to resolve the time at which individual amino acids stabilized along the folding pathway thereby providing additional information about the potential refolding pathways of the perturbation. Furthermore, we found significant variation in the phi dihedral angle of proline residues which was more pronounced in the Charmm 22* force field than the Amber force fields. This suggests that examining dihedral stabilities may provide a useful tool for analyzing polypeptide chain refolding as well as for examining the effects of force fields on various proteins.

The permeation of small molecules through membranes can presently be observed in conventional (i.e., non-enhanced) molecular dynamics simulations. This contribution focuses on three important aspects of such calculations. (1) The advantages and disadvantages of calculating permeability by direct counting of transition events versus Bayesian analysis based on the inhomogeneous solubility diffusion model. (2) A new Python/Cþþ tool that speeds up a previous implementation of the Bayesian analysis by two orders of magnitude and allows permeabilities to be extracted in a matter of seconds from a previously generated trajectory. (3) Simulated and permeabilities of water, oxygen, and ethanol through various homogeneous bilayers. The results fall short of the experimental values, clearly demonstrating the requirement for accurate polarizable force fields. There have been numerous methodologies developed over the years to address the time scale problem associated with molecular dynamics (MD) simulations of complex biological systems. In recent years, Markov State Models (MSM's) have gained prominence in computing long-time dynamics from a pool of short MD simulations. However, the predicted dynamics is prone to errors since MSM attempts to model a non-Markovian jump process by a Markov chain. In this work, we propose a new approach, dynamically corrected kinetic Monte Carlo (DC-KMC), that propagates a complex system from state to state with arbitrary accuracy on both short and long-time scales, irrespective of the definition of the metastable state boundaries, and irrespective of the basis set on which the states are defined. This method builds on concepts introduced in accelerated MD approaches and multistate dynamical corrections to transition state theory. We demonstrate the robustness of our approach by reproducing the folding dynamics of villin headpiece and the conformational transitions of membrane associated Kras-4B protein. An automatic, multi-scale, and three-dimensional (3D) summary of local configurations of the dynamics of proteins can help to discover and describe the relationships between different parts of proteins across spatial scales, including the overall conformation and 3D configurations of side chains and domains. These discoveries can improve understanding of the function and allosteric mechanism of proteins. Current methods are unable to effectively summarize 3D shapes or dynamics of local configurations across multiple spatial scales. We propose Frequent Substructure Clustering (FSC) and Subconformational Hierarchical Hidden Markov Model (SHHMM) to fill this gap. FSC of the C b atoms of the GB3 protein identifies six clusters of co-occurring local configurations. The clusters localize at different regions, contribute to the overall conformation, and form two anti-correlating groups. The results suggest FSC could describe dynamical relationships between different parts of proteins through 3D descriptions of the frequently occurring local configurations at different spatial resolutions. SHHMM consi...

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