Molecular Structure Refinement Based on Residual Dipolar Couplings: A Comparison of the Molecular Rotational-Sampling Method with the Alignment-Tensor Approach.

In NMR experiments, residual dipolar couplings (RDCs) in a molecule can be measured by averaging the dipolar couplings (DCs) over the rotational motion of a molecule in an environment that induces a slight anisotropic orientation distribution of the molecule. Since the shape of the anisotropic distribution cannot be measured, it is standard practice to use a particular orientation distribution of the molecule with respect to the magnetic field, in the form of a so-called alignment tensor (AT), to calculate RDC-values for the molecule. Since the same alignment tensor is commonly used to calculate the different RDCs of a molecule, this approach rests on the assumption that the rotational motion of the molecule is decoupled from its internal motions and that the molecule is rigid. The validity of these two assumptions is investigated for a small, simple molecule, using a relatively rigid atomic interaction function or force field and a more flexible one. By simulating the molecule using an orientation-biasing force an anisotropic rotational distribution can be generated, for which RDCs can be obtained. Using these RDCs as target RDCs when applying one of the two approaches of structure refinement based on RDCs, it can be investigated how well the target RDCs are approximated in the RDC restraining and whether the corresponding nonuniform orientation distribution is reproduced. For the relatively rigid version of the molecule, the AT approach reproduces the target RDC-values, although the nonuniform orientation distribution of the angle θab,H between the vector r⃗ab connecting two atoms a and b in the molecule and the vector representing the direction of the magnetic field H⃗ as generated in the orientation-biasing simulation cannot be reproduced in the AT RDC-restraining simulation. For the relatively flexible version of the molecule, the AT approach fails to reproduce both the target RDC values and the nonuniform orientation distribution. For biomolecules with flexible parts, the application of the AT approach is thus not recommended. Instead, a method based on sampling of the rotational and internal degrees of freedom of the molecule should be applied in molecular structure determination or refinement based on measured RDCs.

A Method to Derive Structural Information on Molecules from Residual Dipolar Coupling NMR Data.

A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using rotational and molecule-internal configurational sampling instead of the common refinement procedure that is based on the approximation of the nonuniform rotational distribution of the molecule by a single alignment tensor representing the average nonuniformity of this distribution. Using rotational sampling, as is occurring in the experiment leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and thus the assumption that the overall rotation of the molecule is decoupled from its internal motions and that the molecule be rigid. Two simple molecules, two-united-atomic ethane and a cyclooctane molecule with eight side chains, containing 24 united atoms, serve as the so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility and force-field deficiencies on the outcome of structure refinement based on RDCs. For a molecule of a given size (number of atoms Nat), there must be a sufficiently large number NRDC of measured RDC values available to allow the restraining forces to bias the overall orientation distribution of the molecule. If the ratio NRDC/Nat gets too small, the RDC-restraining forces will either not be strong enough to change the overall rotational direction of the molecule such that the target RDC values are approximated well or will be so strong that they induce a local deformation of the molecule. In the latter case, the size or inertia of the molecule hinders a restraining-induced overall rotation and the internal structure of the molecule is not strong enough to avoid local deformation due to the restraining forces.

Exploring the Effect of Enhanced Sampling on Protein Stability Prediction.

Changes in protein stability due to side-chain mutations are evaluated by alchemical free-energy calculations based on classical molecular dynamics (MD) simulations in explicit solvent using the GROMOS force field. Three proteins of different complexity with a total number of 93 single-point mutations are analyzed, and the relative free-energy differences are discussed with respect to configurational sampling and (dis)agreement with experimental data. For the smallest protein studied, a 34-residue WW domain, the starting structure dependence of the alchemical free-energy changes, is discussed in detail. Deviations from previous simulations for the two other proteins are shown to result from insufficient sampling in the earlier studies. Hamiltonian replica exchange in combination with multiple starting structures and sufficient sampling time of more than 100 ns per intermediate alchemical state is required in some cases to reach convergence.

On the use of 3J-coupling NMR data to derive structural information on proteins.

Values of 3J-couplings as obtained from NMR experiments on proteins cannot easily be used to determine protein structure due to the difficulty of accounting for the high sensitivity of intermediate 3J-coupling values (4-8 Hz) to the averaging period that must cover the conformational variability of the torsional angle related to the 3J-coupling, and due to the difficulty of handling the multiple-valued character of the inverse Karplus relation between torsional angle and 3J-coupling. Both problems can be solved by using 3J-coupling time-averaging local-elevation restraining MD simulation. Application to the protein hen egg white lysozyme using 213 backbone and side-chain 3J-coupling restraints shows that a conformational ensemble compatible with the experimental data can be obtained using this technique, and that accounting for averaging and the ability of the algorithm to escape from local minima for the torsional angle induced by the Karplus relation, are essential for a comprehensive use of 3J-coupling data in protein structure determination.

An Analysis of the Association between Epilepsy-Related Genes and Vertigo in the Polish Population.

Considering the possibility of a common genetic background of vertigo and epilepsy, we genotyped an affected group of individuals with vertigo and an unaffected group, by studying 26 single-nucleotide polymorphisms (SNPs) in 14 genes which were previously reported to be of particular importance for epilepsy. Significant differences were found between the patients and the control group (χ2 = 38.3, df = 3, p = 1.6 × 10-7) for the frequencies of haplotypes consist ing of 2 SNPs located in chromosome 11 (rs1939012 and rs1783901 within genes MMP8 and SCN3B, respectively). The haplotype rs1939012:C-rs1783901:A, consisting of the minor-frequency alleles was found to be associated with a higher risk of vertigo (OR = 5.0143, 95% CI = 1.6991-14.7980, p = 0.0035). In contrast, the haplotype rs1939012:T-rs1783901:A showed a significant association with a decreased risk of the disease (OR = 0.0597, 95% CI = 0.0136-0.2620, p = 0.0002). Our results suggest that the SNPs rs1939012 and rs1783901 may play a potential role of gene regulation and/or epistasis in a complex etiology of vertigo.

Methodology of selecting the reference source for an active noise control system in a car.

At the end of the 20th century, a significant development in digital technologies of signal processing made it possible to apply active noise control methods in new domains. A proper selection of the reference signal source is a main problem in implementing such systems. This paper presents an estimation method based on an indicator of the coherent power level. It also presents a simple system of active noise control in a car, operating according to the proposed method of optimising the positioning of reference sources. This system makes it possible to considerably increase the comfort of work of drivers in various kinds of road transport without a great increase in cost. This is especially significant in the case of trucks and vans. Passive barriers are considerably more expensive in them, which results in a higher level of noise than in passenger cars.