Direct Comparison of Experimental and Calculated NMR Scalar Coupling Constants for Force Field Validation and Adaptation

Kinetic isotope effects and how to describe them

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.

A Toolkit to Fit Nonbonded Parameters from and for Condensed Phase Simulations

The quality of atomistic simulations depends decisively on the accuracy of the underlying energy function (force field). Of particular importance for condensed-phase properties are nonbonded interactions, including the electrostatic and Lennard-Jones terms. Permanent atomic multipoles (MTPs) are an extension to common point-charge (PC) representations in atomistic simulations. MTPs are commonly determined from and fitted to an ab initio Electrostatic Potential (ESP), and Lennard-Jones (LJ) parameters are obtained from comparison of experimental and computed observables using molecular dynamics (MD) simulations. For this a set of thermodynamic observables such as density, heat of vaporization, and hydration free energy is chosen, to which the parametrization is fitted. The current work introduces a comprehensive computing environment (Fitting Wizard (FW)) for optimizing nonbonded interactions for atomistic force fields of different qualities. The FW supports fitting of standard PC-based force fields and more physically motivated multipolar (MTP) force fields. A broader study including 20 molecules ranging from N-methyl-acetamide and benzene to halogenated benzenes, phenols, anilines, and pyridines yields a root mean squared deviation for hydration free energies of 0.36 kcal/mol over a range of 8 kcal/mol. It is furthermore shown that PC-based force fields are not necessarily inferior compared to MTP parametrizations depending on the molecule considered.

Explicit Hydrogen-Bond Potentials and Their Application to NMR Scalar Couplings in Proteins

Hydrogen bonds (H bonds) are fundamental for the stability, structure, and dynamics of chemically and biologically relevant systems. One of the direct means to detect H bonds in proteins is NMR spectroscopy. As H bonds are dynamic in nature, atomistic simulations offer a meaningful way to characterize and analyze properties of hydrogen bonds, provided a sufficiently accurate interaction potential is available. Here, we use explicit H-bond potentials to investigate scalar coupling constants (h3)JNC' and characterize the conformational ensemble for increasingly accurate intermolecular potentials. By considering a range of proteins with different overall topology a general procedure to improve the hydrogen-bonding potential ("morphing potentials") based on experimental information is derived. The robustness of this approach is established through explicit simulations in full solvation and comparison with experimental results. The H-bond potentials used here lead to more directional H bonds than conventional electrostatic representations employed in molecular mechanics potentials. It is found that the optimized potentials lead to H-bond geometries in remarkable agreement with previous ab initio and knowledge-based approaches to H bonds in model systems and in proteins. This suggests that, by combining theory, computation, and experimental data, H-bonding potentials can be improved and are potentially useful to better study coupling, energy transfer, and allosteric communication in proteins.

On the role of nonbonded interactions in vibrational energy relaxation of cyanide in water

The vibrationally excited cyanide ion (CN(-)) in H2O or D2O relaxes back to the ground state within several tens of picoseconds. Pump-probe infrared spectroscopy has determined relaxation times of T1 = 28 ± 7 and 71 ± 3 ps in H2O and D2O, respectively. Atomistic simulations of this process using nonequilibrium molecular dynamics simulations allow determination of whether it is possible at all to describe such a process, what level of accuracy in the force fields is required, and whether the information can be used to understand the molecular mechanisms underlying vibrational relaxation. It is found that, by using the best electrostatic models investigated, absolute relaxation times can be described rather more qualitatively (T1(H2O) = 19 ps and T1(D2O) = 34 ps) whereas the relative change in going from water to deuterated water is more quantitatively captured (factor of 2 vs 2.5 from experiment). However, moderate adjustment of the van der Waals ranges by less than 20% (for NVT) and 7.5% (for NVE), respectively, leads to almost quantitative agreement with experiment. Analysis of the energy redistribution establishes that the major pathway for CN(-) relaxation in H2O or D2O proceeds through coupling to the water-bending plus libration mode.

Scrutinizing molecular mechanics force fields on the submicrosecond timescale with NMR data

Protein dynamics on the atomic level and on the microsecond timescale has recently become accessible from both computation and experiment. To validate molecular dynamics (MD) at the submicrosecond timescale against experiment we present microsecond MD simulations in 10 different force-field configurations for two globular proteins, ubiquitin and the gb3 domain of protein G, for which extensive NMR data is available. We find that the reproduction of the measured NMR data strongly depends on the chosen force field and electrostatics treatment. Generally, particle-mesh Ewald outperforms cut-off and reaction-field approaches. A comparison to measured J-couplings across hydrogen bonds suggests that there is room for improvement in the force-field description of hydrogen bonds in most modern force fields. Our results show that with current force fields, simulations beyond hundreds of nanoseconds run an increased risk of undergoing transitions to nonnative conformational states or will persist within states of high free energy for too long, thus skewing the obtained population frequencies. Only for the AMBER99sb force field have such transitions not been observed. Thus, our results have significance for the interpretation of data obtained with long MD simulations, for the selection of force fields for MD studies and for force-field development. We hope that this comprehensive benchmark based on NMR data applied to many popular MD force fields will serve as a useful resource to the MD community. Finally, we find that for gb3, the force-field AMBER99sb reaches comparable accuracy in back-calculated residual dipolar couplings and J-couplings across hydrogen bonds to ensembles obtained by refinement against NMR data.