Equipartition Principle for Internal Coordinate Molecular Dynamics

The <i>principle of equipartition of (kinetic) energy</i> for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has <i>kT</i>/2 of kinetic energy in a canonical ensemble. This principle is used in molecular dynamics simulations to initialize velocities, and to calculate statistical properties such as entropy. Internal coordinate molecular dynamics (ICMD) models differ from Cartesian models in that the overall kinetic energy depends on the generalized coordinates and includes cross-terms. Due to this coupled structure, no such equipartition principle holds for ICMD models. In this paper, we introduce noncanonical <i>modal coordinates</i> to recover some of the structural simplicity of Cartesian models and develop a new equipartition principle for ICMD models. We derive low-order recursive computational algorithms for transforming between the modal and physical coordinates. The equipartition principle in modal coordinates provides a rigorous method for initializing velocities in ICMD simulations, thus replacing the <i>ad hoc</i> methods used until now. It also sets the basis for calculating conformational entropy using internal coordinates

Structure Refinement of Protein Low Resolution Models Using the GNEIMO Constrained Dynamics Method

The challenge in protein structure prediction using homology modeling is the lack of reliable methods to refine the low resolution homology models. Unconstrained all-atom molecular dynamics (MD) does not serve well for structure refinement due to its limited conformational search. We have developed and tested the constrained MD method, based on the generalized Newton–Euler inverse mass operator (GNEIMO) algorithm for protein structure refinement. In this method, the high-frequency degrees of freedom are replaced with hard holonomic constraints and a protein is modeled as a collection of rigid body clusters connected by flexible torsional hinges. This allows larger integration time steps and enhances the conformational search space. In this work, we have demonstrated the use of torsional GNEIMO method without using any experimental data as constraints, for protein structure refinement starting from low-resolution decoy sets derived from homology methods. In the eight proteins with three decoys for each, we observed an improvement of ∼2 Å in the rmsd in coordinates to the known experimental structures of these proteins. The GNEIMO trajectories also showed enrichment in the population density of native-like conformations. In addition, we demonstrated structural refinement using a “freeze and thaw” clustering scheme with the GNEIMO framework as a viable tool for enhancing localized conformational search. We have derived a robust protocol based on the GNEIMO replica exchange method for protein structure refinement that can be readily extended to other proteins and possibly applicable for high throughput protein structure refinement

Estimation of Hydrogen-Exchange Protection Factors from MD Simulation Based on Amide Hydrogen Bonding Analysis

Hydrogen exchange (HX) studies have provided critical insight into our understanding of protein folding, structure, and dynamics. More recently, hydrogen exchange mass spectrometry (HX-MS) has become a widely applicable tool for HX studies. The interpretation of the wealth of data generated by HX-MS experiments as well as other HX methods would greatly benefit from the availability of exchange predictions derived from structures or models for comparison with experiment. Most reported computational HX modeling studies have employed solvent-accessible-surface-area based metrics in attempts to interpret HX data on the basis of structures or models. In this study, a computational HX-MS prediction method based on classification of the amide hydrogen bonding modes mimicking the local unfolding model is demonstrated. Analysis of the NH bonding configurations from molecular dynamics (MD) simulation snapshots is used to determine partitioning over bonded and nonbonded NH states and is directly mapped into a protection factor (PF) using a logistics growth function. Predicted PFs are then used for calculating deuteration values of peptides and compared with experimental data. Hydrogen exchange MS data for fatty acid synthase thioesterase (FAS-TE) collected for a range of pHs and temperatures was used for detailed evaluation of the approach. High correlation between prediction and experiment for observable fragment peptides is observed in the FAS-TE and additional benchmarking systems that included various apo/holo proteins for which literature data were available. In addition, it is shown that HX modeling can improve experimental resolution through decomposition of in-exchange curves into rate classes, which correlate with prediction from MD. Successful rate class decompositions provide further evidence that the presented approach captures the underlying physical processes correctly at the single residue level. This assessment is further strengthened in a comparison of residue resolved protection factor predictions for staphylococcal nuclease with NMR data, which was also used to compare prediction performance with other algorithms described in the literature. The demonstrated transferable and scalable MD based HX prediction approach adds significantly to the available tools for HX-MS data interpretation based on available structures and models

Estimation of Hydrogen-Exchange Protection Factors from MD Simulation Based on Amide Hydrogen Bonding Analysis

Hydrogen exchange (HX) studies have provided critical insight into our understanding of protein folding, structure, and dynamics. More recently, hydrogen exchange mass spectrometry (HX-MS) has become a widely applicable tool for HX studies. The interpretation of the wealth of data generated by HX-MS experiments as well as other HX methods would greatly benefit from the availability of exchange predictions derived from structures or models for comparison with experiment. Most reported computational HX modeling studies have employed solvent-accessible-surface-area based metrics in attempts to interpret HX data on the basis of structures or models. In this study, a computational HX-MS prediction method based on classification of the amide hydrogen bonding modes mimicking the local unfolding model is demonstrated. Analysis of the NH bonding configurations from molecular dynamics (MD) simulation snapshots is used to determine partitioning over bonded and nonbonded NH states and is directly mapped into a protection factor (PF) using a logistics growth function. Predicted PFs are then used for calculating deuteration values of peptides and compared with experimental data. Hydrogen exchange MS data for fatty acid synthase thioesterase (FAS-TE) collected for a range of pHs and temperatures was used for detailed evaluation of the approach. High correlation between prediction and experiment for observable fragment peptides is observed in the FAS-TE and additional benchmarking systems that included various apo/holo proteins for which literature data were available. In addition, it is shown that HX modeling can improve experimental resolution through decomposition of in-exchange curves into rate classes, which correlate with prediction from MD. Successful rate class decompositions provide further evidence that the presented approach captures the underlying physical processes correctly at the single residue level. This assessment is further strengthened in a comparison of residue resolved protection factor predictions for staphylococcal nuclease with NMR data, which was also used to compare prediction performance with other algorithms described in the literature. The demonstrated transferable and scalable MD based HX prediction approach adds significantly to the available tools for HX-MS data interpretation based on available structures and models