Motions and Entropies in Proteins as Seen in NMR Relaxation Experiments and Molecular Dynamics Simulations

Accuracy and Reproducibility of Lipari-Szabo Order Parameters From Molecular Dynamics

The Lipari-Szabo generalized order parameter probes the picosecond to nanosecond time scale motions of a protein and is useful for rationalizing a multitude of biological processes such as protein recognition and ligand binding. Although these fast motions are an important and intrinsic property of proteins, it remains unclear what simulation conditions are most suitable to reproduce methyl symmetry axis side chain order parameter data (Saxis2) from molecular dynamics simulations. In this study, we show that, while Saxis2 tends to converge within tens of nanoseconds, it is essential to run 10 to 20 replicas starting from configurations close to the experimental structure to obtain the best agreement with experimental Saxis2 values. Additionally, in a comparison of force fields, AMBER ff14SB outperforms CHARMM36m in accurately capturing these fast time scale motions, and we suggest that the origin of this performance gap is likely attributed to differences in side chain torsional parametrization and not due to differences in the global protein conformations sampled by the force fields. This study provides insight into obtaining accurate and reproducible Saxis2 values from molecular simulations and underscores the necessity of using replica simulations to compute equilibrium properties.

Double Mutant of Chymotrypsin Inhibitor 2 Stabilized through Increased Conformational Entropy

The conformational heterogeneity of a folded protein can affect not only its function but also stability and folding. We recently discovered and characterized a stabilized double mutant (L49I/I57V) of the protein CI2 and showed that state-of-the-art prediction methods could not predict the increased stability relative to the wild-type protein. Here, we have examined whether changed native-state dynamics, and resulting entropy changes, can explain the stability changes in the double mutant protein, as well as the two single mutant forms. We have combined NMR relaxation measurements of the ps-ns dynamics of amide groups in the backbone and the methyl groups in the side chains with molecular dynamics simulations to quantify the native-state dynamics. The NMR experiments reveal that the mutations have different effects on the conformational flexibility of CI2: a reduction in conformational dynamics (and entropy estimated from this) of the native state of the L49I variant correlates with its decreased stability, while increased dynamics of the I57V and L49I/I57V variants correlates with their increased stability. These findings suggest that explicitly accounting for changes in native-state entropy might be needed to improve the predictions of the effect of mutations on protein stability.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Electron Paramagnetic Resonance Measurements of Four Nitroxide Probes in Supercooled Water Explained by Molecular Dynamics Simulations

Electron paramagnetic resonance (EPR) measurements of the rotational diffusion of small nitroxide probes have been demonstrated to be a powerful technique for experimentally investigating the properties of supercooled liquids, such as water. However, since only the rotational diffusion of the probe molecules is measured and EPR measurements are indirect, it is not clear what the relationship between the behavior of water and the probe molecule is. To address this, we have performed molecular dynamics simulations of four nitroxide probes in TIP4P-Ew and OPC water models to directly compare with EPR experiments and to determine the behavior of the water and the underlying microscopic coupling between the water and the probes. In all, 200 ns simulations were run for 23 temperatures between 253 and 283 K for all four probes with each water model for an aggregate of 36.8 μs of simulation time. Simulations for both water models systematically underestimated the rotational diffusion coefficients for both water and probes, though OPC simulations were generally in better agreement with the experiments than TIP4P-Ew simulations. Despite this, when the temperature dependence of the data was fit to a power law, fit parameters for TIP4P-Ew were generally in better agreement with the experiments than OPC. For probe molecules, the singular temperature was found to be T₀ = 226.5 ± 0.4 K from experiments, T₀ = 208 ± 2 K for OPC water, and T₀ = 215 ± 2 K for TIP4P-Ew water. While for water molecules, the singular temperature was found to be T₀ = 220.3 ± 0.2 K from experiments, T₀ = 208 ± 2 K for OPC water, and T₀ = 220 ± 1 K for TIP4P-Ew water. Systematic underestimation of the rotational diffusion coefficients was most pronounced at lower temperatures and was clearly observed in changes to the Arrhenius activation energy. Above the maximum density temperature of T_ρmax = 277 K, an activation energy of E_A ≈ 16.7 kJ/mol was observed for the probes from experiments, while OPC had E_A ≈ 15.2 kJ/mol and TIP4P-Ew had E_A ≈ 14.6 kJ/mol. Below the maximum density temperature, the activation energy jumped to E_A ≈ 32.5 kJ/mol for experiments but only E_A ≈ 23 kJ/mol for OPC and E_A ≈ 22 kJ/mol for TIP4P-Ew. In all cases, we saw good agreement between the behavior of the probe molecules and water. To understand why, we calculated the average number of hydrogen bonds between the probe molecules and water. From this, we were able to explain the rotational diffusion times for all of the probes. These results show that current molecular models are sufficient to capture physical phenomena observed with EPR and to help elucidate why the probes provide accurate insights into the behavior of supercooled water.

Rotational Dynamics of Proteins from Spin Relaxation Times and Molecular Dynamics Simulations

Conformational fluctuations and rotational tumbling of proteins can be experimentally accessed with nuclear spin relaxation experiments. However, interpretation of molecular dynamics from the experimental data is often complicated, especially for molecules with anisotropic shape. Here, we apply classical molecular dynamics simulations to interpret the conformational fluctuations and rotational tumbling of proteins with arbitrarily anisotropic shape. The direct calculation of spin relaxation times from simulation data did not reproduce the experimental data. This was successfully corrected by scaling the overall rotational diffusion coefficients around the protein inertia axes with a constant factor. The achieved good agreement with experiments allowed the interpretation of the internal and overall dynamics of proteins with significantly anisotropic shape. The overall rotational diffusion was found to be Brownian, having only a short subdiffusive region below 0.12 ns. The presented methodology can be applied to interpret rotational dynamics and conformation fluctuations of proteins with arbitrary anisotropic shape. However, a water model with more realistic dynamical properties is probably required for intrinsically disordered proteins.

Identification of novel inhibitors of the translationally controlled tumor protein (TCTP): insights from molecular dynamics

The translationally controlled tumor protein (TCTP) is a highly conserved multifunctional protein, preferentially expressed in mitotically active tissues and is a potential biomarker and a therapeutic target for lung cancers. An understanding of the biology of this molecule and model systems for the screening of drugs is still awaited. In the absence of complete crystal structure, NMR structures as templates were used for homology modeling and MD optimization of both Dictyostelium discoideum and human TCTPs, which was followed by pocket-site prediction, ligand screening and docking. Rescoring of TCTP-ligand complexes was done using MD and MM-PBSA approaches. D. discoideum TCTP was expressed under a constitutive promoter and the endogenous RNA in multicellular structures formed was localized by in situ hybridization. Based on the interactions and binding energy scores, two novel compounds were identified as the best potential inhibitors that could be further used for the development of drug candidates. Inhibition of cell proliferation was observed in the strain overexpressing Dictyostelium TCTP and in situ hybridization results show them to be localized in the prestalk (dying cell population) cells. D. discoideum and human TCTPs share similar dynamic behaviors; overexpression of Dictyostelium TCTP inhibits cell proliferation. D. discoideum could be used as a model system for understanding the biology of this molecule and also for drug screening.

Information flow and protein dynamics: the interplay between nuclear magnetic resonance spectroscopy and molecular dynamics simulations

Proteins participate in information pathways in cells, both as links in the chain of signals, and as the ultimate effectors. Upon ligand binding, proteins undergo conformation and motion changes, which can be sensed by the following link in the chain of information. Nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations represent powerful tools for examining the time-dependent function of biological molecules. The recent advances in NMR and the availability of faster computers have opened the door to more detailed analyses of structure, dynamics, and interactions. Here we briefly describe the recent applications that allow NMR spectroscopy and MD simulations to offer unique insight into the basic motions that underlie information transfer within and between cells.