Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q≈15nm(-1). Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by < 1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.

Small- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Because the calculations fully rely on explicit solvent, no fitting parameters associated with the solvation layer or excluded solvent are required, and the calculations remain valid at wide angles. The complementarity of SWAXS and MD is illustrated using three biological examples, namely a periplasmic binding protein, aspartate carbamoyltransferase, and a nuclear exportin. The examples suggest that SWAXS-driven MD is capable of refining structures against SWAXS data without foreknowledge of possible reaction paths. In turn, the SWAXS data accelerates conformational transitions in MD simulations and reduces the force-field bias.

Free energy calculations for protein-ligand dissociation have been tested and validated for small ligands (50 atoms or less), but there has been a paucity of studies for larger, peptide-size ligands due to computational limitations. Previously we have studied the energetics of dissociation in a potassium channel-charybdotoxin complex by using umbrella sampling molecular-dynamics simulations, and established the need for carefully chosen coordinates and restraints to maintain the physiological ligand conformation. Here we address the ligand integrity problem further by constructing additional potential of mean forces for dissociation of charybdotoxin using restraints. We show that the large discrepancies in binding free energy arising from simulation artifacts can be avoided by using appropriate restraints on the ligand, which enables determination of the binding free energy within the chemical accuracy. We make several suggestions for optimal choices of harmonic potential parameters and restraints to be used in binding studies of large ligands.

Ion channel-toxin complexes are ideal systems for computational studies of protein-ligand interactions, because, in most cases, the channel axis provides a natural reaction coordinate for unbinding of a ligand and a wealth of physiological data is available to check the computational results. We use a recently determined structure of a potassium channel-charybdotoxin complex in molecular dynamics simulations to investigate the mechanism and energetics of unbinding. Pairs of residues on the channel protein and charybdotoxin that are involved in the binding are identified, and their behavior is traced during umbrella-sampling simulations as charybdotoxin is moved away from the binding site. The potential of mean force for the unbinding of charybdotoxin is constructed from the umbrella sampling simulations using the weighted histogram analysis method, and barriers observed are correlated with specific breaking of interactions and influx of water molecules into the binding site. Charybdotoxin is found to undergo conformational changes as a result of the reaction coordinate choice--a nontrivial decision for larger ligands--which we explore in detail, and for which we propose solutions. Agreement between the calculated and the experimental binding energies is obtained once the energetic consequences of these conformational changes are included in the calculations.

H-N 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 R, R, 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 S 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.

For hospitals' admission management, the ability to predict length of stay (LOS) as early as in the preadmission stage might be helpful to monitor the quality of inpatient care. This study is to develop artificial neural network (ANN) models to predict LOS for inpatients with one of the three primary diagnoses: coronary atherosclerosis (CAS), heart failure (HF), and acute myocardial infarction (AMI) in a cardiovascular unit in a Christian hospital in Taipei, Taiwan. A total of 2,377 cardiology patients discharged between October 1, 2010, and December 31, 2011, were analyzed. Using ANN or linear regression model was able to predict correctly for 88.07% to 89.95% CAS patients at the predischarge stage and for 88.31% to 91.53% at the preadmission stage. For AMI or HF patients, the accuracy ranged from 64.12% to 66.78% at the predischarge stage and 63.69% to 67.47% at the preadmission stage when a tolerance of 2 days was allowed.

Ion flow in many voltage-gated K؉ channels (VGK), including the (human ether-a-go-go-related gene) hERG channel, is regulated by reversible collapse of the selectivity filter. hERG channels, however, exhibit low sequence homology to other VGKs, particularly in the outer pore helix (S5) domain, and we hypothesize that this contributes to the unique activation and inactivation kinetics in hERG K ؉ channels that are so important for cardiac electrical activity. The S5 domain in hERG identified by NMR spectroscopy closely corresponded to the segment predicted by bioinformatics analysis of 676 members of the VGK superfamily. Mutations to approximately every third residue, from Phe 551 to Trp 563 , affected steady state activation, whereas mutations to approximately every third residue on an adjacent face and spanning the entire S5 segment perturbed inactivation, suggesting that the whole span of S5 experiences a rearrangement associated with inactivation. We refined a homology model of the hERG pore domain using constraints from the mutagenesis data with residues affecting inactivation pointing in toward S6. In this model the three residues with maximum impact on activation (W563A, F559A, and F551A) face out toward the voltage sensor. In addition, the residues that when mutated to alanine, or from alanine to valine, that did not express (Ala 561 , His 562 , Ala 565 , Trp 568 , and Ile 571 ), all point toward the pore helix and contribute to close hydrophobic packing in this region of the channel.

Rotational diffusion (D) is a fundamental property of biomolecules that contains information about molecular dimensions and solute-solvent interactions. While ab initio D prediction can be achieved by explicit all-atom molecular dynamics simulations, this is hindered by both computational expense and limitations in water models. We propose coarse-grained force fields as a complementary solution, and show that the MARTINI force field with elastic networks is sufficient to compute D in >10 proteins spanning 5-157 kDa. We also adopt a quaternion-based approach that computes D orientation directly from autocorrelations of best-fit rotations as used in, e.g., RMSD algorithms. Over 2 μs trajectories, isotropic MARTINI+EN tumbling replicates experimental values to within 10-20%, with convergence analyses suggesting a minimum sampling of >50 × τ to achieve sufficient precision. Transient fluctuations in anisotropic tumbling cause decreased precision in predictions of axisymmetric anisotropy and rhombicity, the latter of which cannot be precisely evaluated within 2000 × τ for GB3. Thus, we encourage reporting of axial decompositions D, D, D to ease comparability between experiment and simulation. Where protein disorder is absent, we observe close replication of MARTINI+EN D orientations versus CHARMM22*/TIP3p and experimental data. This work anticipates the ab initio prediction of NMR-relaxation by combining coarse-grained global motions with all-atom local motions.