Comparison of Structure Determination Methods for Intrinsically Disordered Amyloid-β Peptides

Intrinsically disordered proteins (IDPs) represent a new frontier in structural biology since the primary characteristic of IDPs is that structures need to be characterized as diverse ensembles of conformational substates. We compare two general but very different ways of combining NMR spectroscopy with theoretical methods to derive structural ensembles for the disease IDPs amyloid-β 1–40 and amyloid-β 1–42, which are associated with Alzheimer’s Disease. We analyze the performance of de novo molecular dynamics and knowledge-based approaches for generating structural ensembles by assessing their ability to reproduce a range of NMR experimental observables. In addition to the comparison of computational methods, we also evaluate the relative value of different types of NMR data for refining or validating the IDP structural ensembles for these important disease peptides.

S 2 state of each residue is picked independently of other residues by TraDES. The RC and Pred-SS ensembles each contain 100,000 structures as recommended in [ 4 ].
Pred-SS-ENS ensemble. As an example of a knowledge-based approach we consider the ENSEMBLE software package, which selects from a large starting pool (basis set) of structures, typically generated by TraDES, a subset of 100 conformations that best conform to various NMR experimental data supplied to it (see Section 5 of the paper on calculation of experimental observables from structures). The Pred-SS-ENS, was selected by the ENSEMBLE program from a starting 'soup' consisting of the Pred-SS ensemble structures. We supplied H α , H N , C α , and C β chemical shifts, J-coupling constants, RDCs and NOEs for both Aβ40 and Aβ42. We used default values of the ENSEMBLE program input parameters and the default output of a 100structure ensemble. We ran each ENSEMBLE optimization for 48 hours on a Cray XE6 at National Energy Research Scientific Computing Center (NERSC), during which ~500 rounds of ENSEMBLE optimization steps were completed. We found that the resulting Pred-SS-ENS ensemble satisfied most of the experimental criteria besides RDCs according to the ENSEMBLE software. Based on our subsequent analysis, the default convergence criteria for RDCs appear to be too strict. J-coupling criteria were not satisfied for Aβ40, while Cα chemical shifts were not satisfied for Aβ42, however we selected those ensembles with the best fit to the NMR data overall, which we found to be sufficient for quantitative analysis.
MD ensemble. We created the fourth ensemble with de novo molecular dynamics simulations of Aβ40 and Aβ42 using the Amber ff99SB force field 5 and aqueous solvent represented by the TIP4P-Ew water model 6 , which we chose because previous studies support its clear superiority relative to other biomolecular simulation force fields 7 . We simulated each amyloid-β peptide in a cubic box containing 6,251 water molecules for Aβ42 and 6,136 water molecules for Aβ40, with three Na+ ions to neutralize the charge of the peptide. The sander module of AMBER 8 was used in conjunction with Multi-Reservoir Replica Exchange (MRRE) method 9 to generate ~2 µs of MD trajectories, from which we created a Boltzmann weighted ensemble of 72,632 -89,469 structures each for Aβ40 and Aβ42 respectively at the experimental temperature of 287 K.

MD-ENS ensemble.
After reaching the conclusion that no true cooperative secondary structure can be generated from the purely knowledge-based method that selects from a pool of random structures, we decided to construct a fifth ensemble that uses a knowledge-based S 3 approach combined with MD. For this ensemble (MD-ENS), we employed the same ENSEMBLE procedure described above for the Pred-SS-ENS ensemble except that we used the de novo MD ensemble as the starting pool of structures from which the experimentally optimized 100-structure ensemble was selected. NOE data was not included in our final MD ENSEMBLE refinement because a more structured ensemble could not satisfy the large number of distance restraints. We again had the same problem satisfying RDC convergence criteria, but otherwise the MD-ENS ensemble was optimized well to the NMR data after ~500 ENSEMBLE rounds.
We note that in this paper the MD-ENS ensemble consists of only 100 structures, and not 2,000 structures as in our previous study 10 ..

Details of using the ENSEMBLE software
For knowledge-based approach we used the ENSEMBLE software package to select a final ensemble of 100 structures from a starting pool of structures. The ENSEMBLE method formulates energy functions that score structures favorably when they agree with an experimental observable and unfavorably when they do not. To generate the Pred-SS-ENS and MD-ENS ensembles we performed two sets of ENSEMBLE optimization. The first used the Pred-SS ensemble as the starting 'soup' of structures while the second used our de novo MD ensemble. In our first attempt to select a final ensemble that agreed with experiment we supplied multiple atom type chemical shifts, J-coupling constants, RDCs, and NOE contacts that we could assign directly from the experimental data for both Aβ40 and Aβ42. For the NOEs, we did not have specific distance restraints for the contacts, so we set the distance to a maximum of 7.0 Å for each contact. We used default values of the ENSEMBLE program for the experimental observable target energies. As recommended by the Forman-Kay group, we set chemical shifts and NOE distances to converge first, before converging J-coupling constants or RDCs. We ran each ENSEMBLE optimization for 48 hours on a Cray XE6 at NERSC, during which ~500 rounds of ENSEMBLE optimization steps were completed.
After this first ENSEMBLE attempt we saw that while the both chemical shifts and NOE distance restraints converged for the Pred-SS-ENS ensemble, in the MD-ENS calculation the NOE distance restraints did not converge. For the MD-ENS optimization the NOE distance restraint energies were extremely high (~800 in the best ensemble, compared with the target energy of 49). This was probably due to the approximation of the NOE cross-peaks as simple S 4 distance restrains, the large number of NOE distance restraints being optimized (177 for Aβ42 and 340 for Aβ40), and the fact that the MD starting pool was more diverse than the Pred-SS pool. We then attempted a second MD-ENS ENSEMBLE run without the NOE distance restraints, and this time the chemical shifts did converge.
The second stage of the ENSEMBLE runs optimized against J-coupling constants and RDCs. This round was able to successfully converged the J-coupling constants to the default energy tolerance (except for the Aβ40 Pred-SS-ENS ensemble), but not the RDCs. Although the RDC energies had improved (from ~80 to 51 on energy units), their convergence had stagnated so as to not meet the ENSEMBLE convergence tolerance of >0.2 Hz, keeping a constant energy of ~51, even with additional computation time of ~5000 ENSEMBLE optimization rounds. In actuality, the RDCs were sufficiently converged to permit the analysis in sections 5 and 6 of the paper, suggesting that the default RDC tolerance was too tight. We therefore selected the final ensembles of 100 structures with the lowest energy according to the ENSEMBLE weighting function, in order to give the overall best performance against the chemical shift, J-coupling, RDC, and, for the Pred-SS-ENS ensemble, NOE data. We then used these final ensembles as the Pred-SS-ENS and MD-ENS ensembles in our subsequent analyses. Table S1. Aβ40 and Aβ42 predicted secondary structure. For Aβ40 and Aβ42 the predicted secondary structure and confidence in that prediction are presented 29 . This corresponds to a TraDES ensemble generated with extended dihedral angles for those residues predicted to have extended structure. The percent of the TraDES ensemble that has that residue extended corresponds to the confidence of the prediction, and the rest of the TraDES ensemble is generated with random coil structure.  Figure S1. Percentage of Aβ42 simulated ensemble in different types of secondary structure by residue for the RC ensemble. The red line represents helix, the blue line for anti-parallel sheet, and the black line for β-turns.
Figure S1. Ball and co-workers