Ensemble refinement

Figure 9 Treating internal dynamics during the refinement process. Due to dynamics and the weighting of the NOE, the measured distance may appear much shorter than the average distance. This can be accounted for by using ensemble refinement techniques. In contrast to standard refinement, an average distance is calculated over an ensemble of C structures (ensemble refinement) or a trajectory (time-averaged refinement). The time-averaged distance is defined with an exponential window over the trajectory. T is the total length over the trajectory, t is the time, and x is a relaxation time characterizing the width of the exponential window.

Our results were in excellent agreement with d3mamic ensemble refinement of ubiquitin structures, showing that the native state of this protein must be considered a heterogeneous ensemble of conformations [38] which are sampled over a wide range of time scales [39]. 

Levin EJ, Kondrashov DA, Wesenberg GE, Phillips GN Jr (2007) Ensemble refinement of protein crystal structures validation and application. Structure 15 1040-1052... 

Other techniques combine MD simulations techniques with appropriate restrains to conform to the NMR data such as NOEs, order parameters, RDCs, or J-couphngs themselves. For instance, the dynamic ensemble refinement method [32] yields a set of conformations that conform to both the average structure and the fluctuations. Other approaches are applied by Clore and Schwieters [33,34]. 

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

Since NMR data may reflect the conformational averaging resulting from a substantial flexibility of DNA/RNA fragments, the parameters of the ensemble of structures obtained by MD refinement and experimental NMR restraints can display internal inconsistency. James and coworkers developed a method to determine the family of structural conform-ers and their populations based on NMR data [83]. This approach applies multiple-copy refinement with floating weights, which better reflects the conformational dynamics of nucleic acids. 

MR is an ensemble of techniques that aims to place and orientate an approximate molecular model in the unit cell of the crystal being studied. This will provide the starting phases needed to calculate the initial electron density map from which the protein model can be built, either manually by iterative use of reconstruction with molecular graphics packages (Jones et al., 1991) followed by refinement (Murshudov et al., 1997), or automatically if diffraction data up to 2.3 Angstroms or better are available (ARP/wARP (Perrakis et al., 2001), Solve/Resolve (Terwilliger, 2003)). 

The resulting ensemble reflects the ps-ns time-scale internal dynamics of the inhibitor (Figure 6) and is superior to that determined by "conventional" structure calculation methods aimed at refining each replica for best agreement with NOE data. Improvements are observed both in terms of conforming to ideal geometry and correspondence to observed Hoc CSs. Moreover, specific interactions are more restricted in the dynamical ensemble than in the conventional one,... 

Formulation of local Si,Al ordering in faujasite in terms of pathway I, 6R - SC - faujasite, represents an extension and refinement of our previous treatment in terms of ordered SC sub-units (4). As we have noted, pathway I for K p = 0 corresponds to formulation of faujasite from the SC arrangements of Figure 1. Actually the set of SC units specified by Kjjp = 0 is more exclusive than that specified previously (4) since there are minimum Al, A1 next nearest neighbor SC units which cannot be formed using only and p2 6R s. Moreover, consideration of 6R ensembles with Kjjp f 0 provides a straightforward approach to the study of deviations from complete local order. 

Table III) the theoretical results for 1.4 < R < 3.0 for an infinitely narrow distribution in but with a small value kMP = 0.25, to illustrate the effect of slight deviations from complete P order in the 6R ensemble. The ideal theory would include both sources of local disorder, which refinement is left to a future publication.

Figure 9. Refined structure of patellamide C - ensemble of 14 lowest energy structures...

In further refinements of the theory, this LDOS is decomposed into contributions with different types of symmetry it is also possible to incorporate the concept of ensembles, but the discussion of NMR data does not require these details. I also note the respective roles played by the surface Ef LDOS and the work function a high LDOS ensures the availabihty of many electrons for the initial metal-adsorbate interaction, whereas a low work function makes the charge tail extend further in space. Once the metal-adsorbate bond has been formed, the LDOS at any energy on sites in or close to the surface can be different from that of the clean surface, but sufficiently far inside the particle the perturbation will be neghgible (Hcinc-Friedel invariance). 

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