Accurate Prediction of Protein NMR Spin Relaxation by Means of Polarizable Force Fields. Application to Strongly Anisotropic Rotational Diffusion

Assessment of an Electrostatic Energy-Based Charge Model for Modeling the Electrostatic Interactions in Water Solvent

The protein force field based on the restrained electrostatic potential (RESP) charges has limitations in accurately describing hydrogen bonding interactions in proteins. To address this issue, we propose an alternative approach called the electrostatic energy-based charges (EEC) model, which shows improved performance in describing electrostatic interactions (EIs) of hydrogen bonds in proteins. In this study, we further investigate the performance of the EEC model in modeling EIs in water solvent. Our findings demonstrate that the fixed EEC model can effectively reproduce the quantum mechanics/molecular mechanics (QM/MM)-calculated EIs between a water molecule and various water solvent environments. However, to achieve the same level of computational accuracy, the electrostatic potential (ESP) charge model needs to fluctuate according to the electrostatic environment. Our analysis indicates that the requirement for charge adjustments depends on the specific mathematical and physical representation of EIs as a function of the environment for deriving charges. By comparing with widely used empirical water models calibrated to reproduce experimental properties, we confirm that the performance of the EEC model in reproducing QM/MM EIs is similar to that of general purpose TIP4P-like water models such as TIP4P-Ew and TIP4P/2005. When comparing the computed 10,000 distinct EI values within the range of -40 to 0 kcal/mol with the QM/MM results calculated at the MP2/aug-cc-pVQZ/TIP3P level, we noticed that the mean unsigned error (MUE) for the EEC model is merely 0.487 kcal/mol, which is remarkably similar to the MUE values of the TIP4P-Ew (0.63 kcal/mol) and TIP4P/2005 (0.579 kcal/mol) models. However, both the RESP method and the TIP3P model exhibit a tendency to overestimate the EIs, as evidenced by their higher MUE values of 1.761 and 1.293 kcal/mol, respectively. EEC-based molecular dynamics simulations have demonstrated that, when combined with appropriate van der Waals parameters, the EEC model can closely reproduce oxygen-oxygen radial distribution function and density of water, showing a remarkable similarity to the well-established TIP4P-like empirical water models. Our results demonstrate that the EEC model has the potential to build force fields with comparable accuracy to more sophisticated empirical TIP4P-like water models.

Cross-correlation effects in the solution NMR spectra of near-equivalent spin-1/2 pairs

The nuclear magnetic resonance (NMR) spectra of spin-1/2 pairs contain four peaks, with two inner peaks much stronger than the outer peaks in the near-equivalence regime. We have observed that the strong inner peaks have significantly different linewidths when measurements were performed on a 13C2-labelled triyne derivative. This linewidth difference may be attributed to strong cross-correlation effects. We develop the theory of cross-correlated relaxation in the case of near-equivalent homonuclear spin-1/2 pairs, in the case of a molecule exhibiting strongly anisotropic rotational diffusion. Good agreement is found with the experimental NMR lineshapes.

Removing Thermostat Distortions of Protein Dynamics in Constant-Temperature Molecular Dynamics Simulations

Molecular dynamics simulations are widely used to determine equilibrium and dynamic properties of proteins. Nearly all simulations, currently, are carried out at constant temperature, with a Langevin thermostat among the most widely used. Thermostats distort protein dynamics, but whether or how such distortions can be corrected has long been an open question. Here, we show that constant-temperature simulations with a Langevin thermostat dilate protein dynamics and present a correction scheme to remove the dynamic distortions. Specifically, ns-scale time constants for overall rotation are dilated significantly but sub-ns time constants for internal motions are dilated modestly, while all motional amplitudes are unaffected. The correction scheme involves contraction of the time constants, with the contraction factor a linear function of the time constant to be corrected. The corrected dynamics of eight proteins are validated by NMR data for rotational diffusion and for backbone amide and side-chain methyl relaxation. The present work demonstrates that even for complex systems like proteins with dynamics spanning multiple timescales, one can predict how thermostats distort protein dynamics and remove such distortions. The correction scheme will have wide applications, facilitating force-field parameterization and propelling simulations to be on par with NMR and other experimental techniques in determining dynamic properties of proteins.

Detecting anisotropic segmental dynamics in disordered proteins by cross-correlated spin relaxation

Among the numerous contributions of Geoffrey Bodenhausen to NMR spectroscopy, his developments in the field of spin-relaxation methodology and theory will definitely have a long lasting impact. Starting with his seminal contributions to the excitation of multiple-quantum coherences, he and his group thoroughly investigated the intricate relaxation properties of these "forbidden fruits" and developed experimental techniques to reveal the relevance of previously largely ignored cross-correlated relaxation (CCR) effects, as "the essential is invisible to the eyes". Here we consider CCR within the challenging context of intrinsically disordered proteins (IDPs) and emphasize its potential and relevance for the studies of structural dynamics of IDPs in the future years to come. Conventionally, dynamics of globularly folded proteins are modeled and understood as deviations from otherwise rigid structures tumbling in solution. However, with increasing protein flexibility, as observed for IDPs, this apparent dichotomy between structure and dynamics becomes blurred. Although complex dynamics and ensemble averaging might impair the extraction of mechanistic details even further, spin relaxation uniquely encodes a protein's structural memory. Due to significant methodological developments, such as high-dimensional non-uniform sampling techniques, spin relaxation in IDPs can now be monitored in unprecedented resolution. Not embedded within a rigid globular fold, conventional 15 N spin probes might not suffice to capture the inherently local nature of IDP dynamics. To better describe and understand possible segmental motions of IDPs, we propose an experimental approach to detect the signature of anisotropic segmental dynamics by quantifying cross-correlated spin relaxation of individual 15 N 1 H N and 13 C ' 13 C α spin pairs. By adapting Geoffrey Bodenhausen's symmetrical reconversion principle to obtain zero frequency spectral density values, we can define and demonstrate more sensitive means to characterize anisotropic dynamics in IDPs.

Recent advances in atomic molecular dynamics simulation of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play important roles in cellular functions. The inherent structural heterogeneity of IDPs makes the high-resolution experimental characterization of IDPs extremely difficult. Molecular dynamics (MD) simulation could provide the atomic-level description of the structural and dynamic properties of IDPs. This perspective reviews the recent progress in atomic MD simulation studies of IDPs, including the development of force fields and sampling methods, as well as applications in IDP-involved protein-protein interactions. The employment of large-scale simulations and advanced sampling techniques allows more accurate estimation of the thermodynamics and kinetics of IDP-mediated protein interactions, and the holistic landscape of the binding process of IDPs is emerging.

Examination of Interactions of Hexafluoro-2-propanol with Trp-Cage in Hexafluoro-2-propanol-Water by MD Simulations and Intermolecular Nuclear Overhauser Effects

All-atom molecular dynamic simulations of the peptide Trp-cage in 30% hexafluoro-2-propanol- water (V/V) at 278 K have been carried out with the goal of exploring peptide hydrogen-solvent fluorine nuclear spin cross relaxation. Force field parameters for HFIP reported by Fioroni et al. along with the fluorine parameters of the TFE5 model reported by this lab were used. Water was represented by the TIP5P-Ew model. Peptide modeling used the AMBER99SB-ILDN force field. Translational diffusion coefficients of solution components at 278 K were predicted to within 35% of experimental values using these parameter sets. The simulations indicate that the solvent mixture is not homogeneous, with HFIP molecules clustered into aggregates as large as 53 fluoroalcohol molecules. The solvent environment of surface atoms of Trp-cage fluctuates between being HFIP-rich and more water-rich about every 10 ns. In accord with previous studies by other groups, the average concentration of HFIP near the surface of the peptide is significantly enhanced over the concentration of HFIP in the bulk solvent. In the simulations, ∼7% of the initial contacts between HFIP molecules and Trp-cage develop into peptide-fluoroalcohol interactions that persist for times as long as 8 ns. Most of the available experimental nuclear spin cross-relaxation rates (Σ_HF) for hydrogens of the Trp-cage in 30% HFIP-water are reproduced from the MD trajectories to within uncertainties of the experimental data and the simulations. However, a few calculated Σ_HF values for hydrogens of the Trp-cage do not agree with experiment. These tend to be situations where long-lived peptide-HFIP interactions are predicted. The disagreements between observed and calculated Σ_HF in these instances signal defects in the modeling parameters and procedures that are presently unrecognized.