Computing the Rotational Diffusion of Biomolecules via Molecular Dynamics Simulation and Quaternion Orientations

Probing Methyl Group Dynamics in Proteins by NMR Cross-Correlated Dipolar Relaxation and Molecular Dynamics Simulations

Nuclear magnetic resonance (NMR) spin relaxation is the most informative approach to experimentally probe the internal dynamics of proteins on the picosecond to nanosecond time scale. At the same time, molecular dynamics (MD) simulations of biological macromolecules are steadily improving through better physical models, enhanced sampling methods, and increased computational power, and they provide exquisite information about flexibility and its role in protein stability and molecular interactions. Many examples have shown that MD is now adept in probing protein backbone motion, but improvements are still required toward a quantitative description of the dynamics of side chains, for example, probed by the dynamics of methyl groups. Thus far, the comparison of computation with experiment for side chain dynamics has primarily focused on the relaxation of ¹³C and ²H nuclei induced by autocorrelated variation of spin interactions. However, the cross-correlation of ¹³C-¹H dipolar interactions in methyl groups offers an attractive alternative. Here, we establish a computational framework to extract cross-correlation relaxation parameters of methyl groups in proteins from all-atom MD simulations. To demonstrate the utility of the approach, cross-correlation relaxation rates of ubiquitin are computed from MD simulations performed with the AMBER99SB*-ILDN and CHARMM36 force fields. Simulation results were found to agree well with those obtained by experiment. Moreover, the data obtained with the two force fields are highly consistent.

A novel non-linear neuron model based on multiplicative aggregation in quaternionic domain

The learning algorithm for a three-layered neural structure with novel non-linear quaternionic-valued multiplicative (QVM) neurons is proposed in this paper. The computing capability of non-linear aggregation in the cell body of biological neurons inspired the development of a non-linear neuron model. However, unlike linear neuron models, most non-linear neuron models are built on higher order aggregation, which is more mathematically complex and difficult to train. As a result, building non-linear neuron models with a simple structure is a difficult and time-consuming endeavor in the neurocomputing field. The concept of a QVM neuron model was influenced by the non-linear neuron model, which has a simple structure and the great computational ability. The suggested neuron’s linearity is determined by the weight and bias associated with each quaternionic-valued input. Non-commutative multiplication of all linearly connected quaternionic input-weight terms accommodates the non-linearity. To train three-layered networks with QVM neurons, the standard quaternionic-gradient-based backpropagation (QBP) algorithm is utilized. The computational and generalization capabilities of the QVM neuron are assessed through training and testing in the quaternionic domain utilizing benchmark problems, such as 3D and 4D chaotic time-series predictions, 3D geometrical transformations, and 3D face recognition. The training and testing outcomes are compared to conventional and root-power mean (RPM) neurons in quaternionic domain using training–testing MSEs, network topology (parameters), variance, and AIC as statistical measures. According to these findings, networks with QVM neurons have greater computational and generalization capabilities than networks with conventional and RPM neurons in quaternionic domain.

Rotational dynamics of proteins in nanochannels: role of solvent's local viscosity

Viscosity variation of solvent in local regions near a solid surface, be it a biological surface of a protein or an engineered surface of a nanoconfinement, is a direct consequence of intermolecular interactions between the solid body and the solvent. The current coarse-grained molecular dynamics study takes advantage of this phenomenon to investigate the anomaly in a solvated protein's rotational dynamics confined using a representative solid matrix. The concept of persistence time, the characteristic time of structural reordering in liquids, is used to compute the solvent's local viscosity. With an increase in the degree of confinement, the confining matrix significantly influences the solvent molecule's local viscosity present in the protein hydration layer through intermolecular interactions. This effect contributes to the enhanced drag force on protein motion, causing a reduction in the rotational diffusion coefficient. Simulation results suggest that the direct matrix-protein non-bonded interaction is responsible for the occasional jump and discontinuity in orientational motion when the protein is in very tight confinement.

Coarse-grained simulation of the translational and rotational diffusion of globular proteins by dissipative particle dynamics

With simplified interactions and degrees of freedom, coarse-grained (CG) simulations have been successfully applied to study the translational and rotational diffusion of proteins in solution. However, in order to reach larger lengths and longer timescales, many CG simulations employ an oversimplified model for proteins or an implicit-solvent model in which the hydrodynamic interactions are ignored, and thus, the real kinetics are more or less unfaithful. In this work, we develop a CG model based on the dissipative particle dynamics (DPD) that can be universally applied to different types of proteins. The proteins are modeled as a group of rigid DPD beads without conformational changes. The fluids (including solvent and ions) are also modeled as DPD beads. The electrostatic interactions between charged species are explicitly considered by including charge distributions on DPD particles. Moreover, a surface friction between the protein and fluid beads is applied to control the slip boundary condition. With this model, we investigate the self-diffusion of a single globular protein in bulk solution. The translational and rotational diffusion coefficients of the protein can be tuned by the surface frictional constant to fit the predictions of the Stokes-Einstein (SE) relation. We find that both translational and rotational diffusion coefficients that meet with the prediction of the SE relation based on experimental results of the hydrodynamic radius are reached at almost the same frictional constant for different types of proteins. Such scaling behavior indicates that the model can be applied to simulate the translational and rotational diffusion together for various types of proteins.

Environmentally Friendly Fluoroquinolone Derivatives with Lower Plasma Protein Binding Rate Designed Using 3D-QSAR, Molecular Docking and Molecular Dynamics Simulation

Comparative molecular similarity index analysis (CoMSIA) was used to establish a three-dimensional quantitative structure–activity relationship (3D-QSAR) model with structural parameters of quinolones as the independent variables and plasma protein binding rate (logf_b) as the dependent variable to predict the logf_b values of remaining quinolones in this study. In addition, the mono-substituted and bis-substituted reaction schemes that significantly influenced the plasma protein binding rate of quinolones were determined through an analysis of the 3D-QSAR contour maps. It was found that the replacement of small groups, hydrophobic groups, electronegative groups, or hydrogen bond acceptor groups at the substitution sites significantly reduce the logf_b values of quinolone derivatives. Furthermore, the mechanism of decrease in binding rate between trovafloxacin (TRO) derivatives and plasma protein was revealed qualitatively and quantitatively based on molecular docking and molecular dynamics simulation. After modification of the target molecule, 11 TRO derivatives with low plasma protein binding rates were screened (reduced by 0.50–24.18%). Compared with the target molecule, the molecular genotoxicity and photodegradability of the TRO derivatives was higher (genotoxicity increased by 4.89–21.36%, and photodegradability increased by 9.04–20.56%), and their bioconcentration was significantly lower (by 36.90–61.41%).

Trajectory-Based Simulation of EPR Spectra: Models of Rotational Motion for Spin Labels on Proteins

Direct time-domain simulation of continuous-wave (CW) electron paramagnetic resonance (EPR) spectra from molecular dynamics (MD) trajectories has become increasingly popular, especially for proteins labeled with nitroxide spin labels. Due to the time-consuming nature of simulating adequately long MD trajectories, two approximate methods have been developed to reduce the MD-trajectory length required for modeling EPR spectra: hindered Brownian diffusion (HBD) and hidden Markov models (HMMs). Here, we assess the accuracy of these two approximate methods relative to direct simulations from MD trajectories for three spin-labeled protein systems (a simple helical peptide, a soluble protein, and a membrane protein) and two nitroxide spin labels with differing mobilities (R1 and 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC)). We find that the HMMs generally outperform HBD. Although R1 dynamics partially resembles hindered Brownian diffusion, HMMs accommodate the multiple dynamic time scales for the transitions between rotameric states of R1 that cannot be captured accurately by a HBD model. The MD trajectories of the TOAC-labeled proteins show that its dynamics closely resembles slow multisite exchange between twist-boat and chair ring puckering states. This motion is modeled well by HMM but not by HBD. All MD-trajectory data processing, stochastic trajectory simulations, and CW EPR spectral simulations are implemented in EasySpin, a free software package for MATLAB.

The hydrodynamic motion of Nanodiscs

We present a fluorescence-based methodology for monitoring the rotational dynamics of Nanodiscs. Nanodiscs are nano-scale lipid bilayers surrounded by a helical membrane scaffold protein (MSP) that have found considerable use in studying the interactions between membrane proteins and their lipid bilayer environment. Using a long-lifetime Ruthenium label covalently attached to the Nanodiscs, we find that Nanodiscs of increasing diameter, made by varying the number of helical repeats in the MSP, display increasing rotational correlation times. We also model our system using both analytical equations that describe rotating spheroids and numerical calculations performed on atomic models of Nanodiscs. Using these methods, we observe a linear relationship between the experimentally determined rotational correlation times and those calculated from both analytical equations and numerical solutions. This work sets the stage for accurate, label-free quantification of protein-lipid interactions at the membrane surface.

Enhanced stability of manganese superoxide dismutase by amino acid replacement designed via molecular dynamics simulation

In order to improve manganese-SOD stability, three mutations were constructed via site-directed mutagenesis, and the root mean square fluctuation (RMSF) and root mean square deviation (RMSD) were used as stability assessment indexes. The amino acids of V140, E155 and E215 from wild-type mouse Mn-SOD was replaced to L140, W155 and W215, and a recombinant plasmid containing DNA segment coding wild-type and mutant Mn-SOD protein was transformed into Escherichia coli BL21 for expression. The highest enzyme activity of the mutations-MnSOD was 2050 U/mg. In addition, the recombinant protein, TM-MnSOD^{V140L, E155W, E215W} exhibited higher working temperature and improved stability compared with the wild-type Mn-SOD. Furthermore, CD spectrum analysis of the improved mutants and wild-type enzyme showed that there was no significant change in their secondary structures. This study not only expands the scope of the application of enzymes, but also helps us understand the relationship between protein structure and function.

Ab Initio Prediction of NMR Spin Relaxation Parameters from Molecular Dynamics Simulations

¹H-¹⁵N NMR spin relaxation and relaxation dispersion experiments can reveal the time scale and extent of protein motions across the ps-ms range, where the ps-ns dynamics revealed by fundamental quantities R₁, R₂, and heteronuclear NOE can be well-sampled by molecular dynamics simulations (MD). Although the principles of relaxation prediction from simulations are well-established, numerous NMR-MD comparisons have hitherto focused upon the aspect of order parameters S² due to common artifacts in the prediction of transient dynamics. We therefore summarize here all necessary components and highlight existing and proposed solutions, such as the inclusion of quantum mechanical zero-point vibrational corrections and separate MD convergence of global and local motions in coarse-grained and all-atom force fields, respectively. For the accuracy of the MD prediction to be tested, two model proteins GB3 and Ubiquitin are used to validate five atomistic force fields against published NMR data supplemented by the coarse-grained force field MARTINI+EN. In Amber and CHARMM-type force fields, quantitative agreement was achieved for structured elements with minimum adjustment of global parameters. Deviations from experiment occur in flexible loops and termini, indicating differences in both the extent and time scale of backbone motions. The lack of systematic patterns and water model dependence suggests that modeling of the local environment limits prediction accuracy. Nevertheless, qualitative accuracy in a 2 μs CHARMM36m Stam2 VHS domain simulation demonstrates the potential of MD-based interpretation in combination with NMR-measured dynamics, increasing the utility of spin relaxation in integrative structural biology.

Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

A synergistic analysis of methyl NMR relaxation data and MD simulations identifies ways to improve studies of protein dynamics.

Quantification of Membrane Protein-Detergent Complex Interactions

Although fundamentally significant in structural, chemical, and membrane biology, the interfacial protein-detergent complex (PDC) interactions have been modestly examined because of the complicated behavior of both detergents and membrane proteins in aqueous phase. Membrane proteins are prone to unproductive aggregation resulting from poor detergent solvation, but the participating forces in this phenomenon remain ambiguous. Here, we show that using rational membrane protein design, targeted chemical modification, and steady-state fluorescence polarization spectroscopy, the detergent desolvation of membrane proteins can be quantitatively evaluated. We demonstrate that depleting the detergent in the sample well produced a two-state transition of membrane proteins between a fully detergent-solvated state and a detergent-desolvated state, the nature of which depended on the interfacial PDC interactions. Using a panel of six membrane proteins of varying hydrophobic topography, structural fingerprint, and charge distribution on the solvent-accessible surface, we provide direct experimental evidence for the contributions of the electrostatic and hydrophobic interactions to the protein solvation properties. Moreover, all-atom molecular dynamics simulations report the major contribution of the hydrophobic forces exerted at the PDC interface. This semiquantitative approach might be extended in the future to include studies of the interfacial PDC interactions of other challenging membrane protein systems of unknown structure. This would have practical importance in protein extraction, solubilization, stabilization, and crystallization.