ENCORE:Software for Quantitative Ensemble Comparison

There is increasing evidence that protein dynamics and conformational changes can play an important role in modulating biological function. As a result, experimental and computational methods are being developed, often synergistically, to study the dynamical heterogeneity of a protein or other macromolecules in solution. Thus, methods such as molecular dynamics simulations or ensemble refinement approaches have provided conformational ensembles that can be used to understand protein function and biophysics. These developments have in turn created a need for algorithms and software that can be used to compare structural ensembles in the same way as the root-mean-square-deviation is often used to compare static structures. Although a few such approaches have been proposed, these can be difficult to implement efficiently, hindering a broader applications and further developments. Here, we present an easily accessible software toolkit, called ENCORE, which can be used to compare conformational ensembles generated either from simulations alone or synergistically with experiments. ENCORE implements three previously described methods for ensemble comparison, that each can be used to quantify the similarity between conformational ensembles by estimating the overlap between the probability distributions that underlie them. We demonstrate the kinds of insights that can be obtained by providing examples of three typical use-cases: comparing ensembles generated with different molecular force fields, assessing convergence in molecular simulations, and calculating differences and similarities in structural ensembles refined with various sources of experimental data. We also demonstrate efficient computational scaling for typical analyses, and robustness against both the size and sampling of the ensembles. ENCORE is freely available and extendable, integrates with the established MDAnalysis software package, reads ensemble data in many common formats, and can work with large trajectory files

Structure and dynamics of a nanodisc by integrating NMR, SAXS and SANS experiments with molecular dynamics simulations.

Nanodiscs are membrane mimetics that consist of a protein belt surrounding a lipid bilayer, and are broadly used for characterization of membrane proteins. Here, we investigate the structure, dynamics and biophysical properties of two small nanodiscs, MSP1D1ΔH5 and ΔH4H5. We combine our SAXS and SANS experiments with molecular dynamics simulations and previously obtained NMR and EPR data to derive and validate a conformational ensemble that represents the structure and dynamics of the nanodisc. We find that it displays conformational heterogeneity with various elliptical shapes, and with substantial differences in lipid ordering in the centre and rim of the discs. Together, our results reconcile previous apparently conflicting observations about the shape of nanodiscs, and pave the way for future integrative studies of larger complex systems such as membrane proteins embedded in nanodiscs

Mg2+-dependent conformational equilibria in CorA and an integrated view on transport regulation

The CorA family of proteins regulates the homeostasis of divalent metal ions in many bacteria, archaea, and eukaryotic mitochondria, making it an important target in the investigation of the mechanisms of transport and its functional regulation. Although numerous structures of open and closed channels are now available for the CorA family, the mechanism of the transport regulation remains elusive. Here, we investigated the conformational distribution and associated dynamic behaviour of the pentameric Mg2+ channel CorA at room temperature using small-angle neutron scattering (SANS) in combination with molecular dynamics (MD) simulations and solid-state nuclear magnetic resonance spectroscopy (NMR). We find that neither the Mg2+-bound closed structure nor the Mg2+-free open forms are sufficient to explain the average conformation of CorA. Our data support the presence of conformational equilibria between multiple states, and we further find a variation in the behaviour of the backbone dynamics with and without Mg2+. We propose that CorA must be in a dynamic equilibrium between different non-conducting states, both symmetric and asymmetric, regardless of bound Mg2+ but that conducting states become more populated in Mg2+-free conditions. These properties are regulated by backbone dynamics and are key to understanding the functional regulation of CorA.Peer reviewe

Assessing the rate of convergence in molecular simulations.

<p>Using the CES score we used ENCORE to assess the rate of convergence in seven molecular dynamics simulations of (A) protein G and (B) ubiquitin. In each case, we compared simulations of increasing length to the full ensemble obtained after 10μs of simulation. Per definition, the similarities thus decrease to zero at 10μs, but the rate at which low-values are obtained indicates how quickly the simulations have reached a distribution of conformations that is similar to the full ensemble. For example, simulations of both proteins with Amber ff99SB-ILDN and ff99SB*-ILDN quickly drop to very low values, reflecting the fact that the ensembles obtained after a few microseconds are very similar to those obtained at the end of the simulation. In contrast, for example, simulations with OPLS continue to explore new regions of conformational space during the entire simulations.</p

Calculating uncertainties of similarity scores using a bootstrap procedure.

<p>The uncertainties were calculated for representative entries from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004415#pcbi.1004415.g002" target="_blank">Fig 2</a> as standard deviations over 100 bootstrapped subsamples of the ensembles.</p

Comparing molecular simulations using ENCORE.

<p>We used ENCORE to calculate the similarity between seven molecular dynamics simulations of (A, B) protein G and (C) ubiquitin. (A) The plots show the pairwise similarity between the seven ensembles computed using the three different ensemble comparison methods. (B) Using the similarities calculated by the CES method as an example, a tree-preserving embedding method was used to represent the ensembles in two-dimensions. In this plot, the distance between pairs of ensembles mimics (to the extent possible in two dimensions) the similarity between different ensembles. In agreement with the pairwise similarities, three pairs of ensembles (CHARMM22*/CHARMM27, ff99SB-ILDN/ff99SB*-ILDN, and ff03/ff03*) are located relatively close to one another, in line with the similar origins of each pair of force fields. (C) We performed similar calculations on seven ubiquitin simulations, again using the CES method as an example and projecting the similarities into two-dimensions. A similar organization is found for the different ensembles for both proteins, as is also evident from directly comparing the matrices of ensemble similarities. Note that in the projections, the axes have no direct physical meaning beyond their scale, which are determined so that the distance in the projections are close to the calculated <i>D</i>_JS. Note also that since these distances are invariant to rotations, translations and inversions of the projections, it is the relative positions in the two plots that should be compared.</p