Assessing and refining molecular dynamics simulations of proteins with nuclear magnetic resonance data

Abstract

The sophistication of the force fields, algorithms and hardware used for molecular dynamics (MD) simulations of proteins is continuously increasing. No matter how advanced the methodology, however, it is essential to evaluate the appropriateness of the structures sampled in a simulation by comparison with quantitative experimental data. Solution nuclear magnetic resonance (NMR) data are particularly useful for checking the quality of protein simulations, as they provide both structural and dynamic information on a variety of temporal and spatial scales. Here, various features and implications of using NMR data to validate and bias MD simulations are outlined, including an overview of the different types of NMR data that report directly on structural properties and of relevant simulation techniques. The focus throughout is on how to properly account for conformational averaging, particularly within the context of the assumptions inherent in the relationships that link NMR data to structural properties.

Keywords: Biomolecular simulation; Molecular dynamics; Nuclear magnetic resonance; Protein.

Fig. 1

The combined effect of conformational averaging and the non-linear and multiple-valued relationships linking NMR observables to structural properties. Upper row four different distributions of inter-nuclear distances r _ij and (dashed lines) the corresponding (red) linearly, (blue) r ⁻³ and (green) r ⁻⁶ averaged distances. All four distributions have the same r ⁻⁶ average (0.227 nm) upon which PREs and many NOEs depend, and are therefore indistinguishable at the level of the NMR observable. Lower row three different distributions of values of a dihedral angle ϕ and (rightmost graph) the Karplus relation for the ϕ angle of the protein backbone (Pardi et al. 1984). All three distributions give rise to the same average ³ J-value (5.45 Hz, red dashed line in rightmost graph) and thus are indistinguishable at the level of the NMR observable. (Rightmost graph, green dashed line) the four dihedral angle values that would be predicted from a ³ J-value of 5.45 Hz without allowing for conformational averaging

Fig. 2

The types of structural information obtained from the NMR observables introduced in Section 3: dashed lines short-range NOE-derived distances, curved arrow dihedral angle ϕ reported on by ³ J _HNCαHα-couplings and heavy line the orientation of the N–H bond vector relative to the molecular frame specified by an alignment tensor A attainable from RDCs. The protein atoms are coloured according to type: cyan carbon, blue nitrogen, red oxygen and white hydrogen

Fig. 3

The degree of protein conformational motion associated with the time-scales encompassed by the different types of NMR observables discussed here. Note that the scale on the time axis is logarithmic

Fig. 4

Examples of the types of potential functions used to restrain or bias MD simulations to fit experimental data. Upper row, left to right a harmonic potential ( is shown as f for clarity), a harmonic potential that becomes linear when , a "flat-bottomed" harmonic potential that does not penalise deviations of less than Δf from and a half-harmonic potential as used for NOE-derived distances. Lower row, left-hand side potentials from (black) the torsional term of a force field and (red) a harmonic ³ J-value restraint acting on a dihedral angle ϕ. Lower row, right-hand side two sets of local elevation end-point potentials from simulations biased to fit multiple types (shown in black, red, green and blue) of ³ J-values reporting on the same dihedral angle. Left a case in which even allowing for conformational averaging, it is not possible to find a set of dihedral angle values in keeping with all four ³ J-values, so that the local elevation potentials clash with one another and continue to build throughout the simulation. Right a case where after an initial build-up period in which the dihedral angle is biased towards values that on average satisfy the data, the potentials remain static for the remainder of the simulation (Allison and van Gunsteren 2009)