Comparative studies of disordered proteins with similar sequences: application to Aβ40 and Aβ42

Abstract

Quantitative comparisons of intrinsically disordered proteins (IDPs) with similar sequences, such as mutant forms of the same protein, may provide insights into IDP aggregation-a process that plays a role in several neurodegenerative disorders. Here we describe an approach for modeling IDPs with similar sequences that simplifies the comparison of the ensembles by utilizing a single library of structures. The relative population weights of the structures are estimated using a Bayesian formalism, which provides measures of uncertainty in the resulting ensembles. We applied this approach to the comparison of ensembles for Aβ40 and Aβ42. Bayesian hypothesis testing finds that although both Aβ species sample β-rich conformations in solution that may represent prefibrillar intermediates, the probability that Aβ42 samples these prefibrillar states is roughly an order of magnitude larger than the frequency in which Aβ40 samples such structures. Moreover, the structure of the soluble prefibrillar state in our ensembles is similar to the experimentally determined structure of Aβ that has been implicated as an intermediate in the aggregation pathway. Overall, our approach for comparative studies of IDPs with similar sequences provides a platform for future studies on the effect of mutations on the structure and function of disordered proteins.

Figure 1

A schematic illustrating the construction of coarse-grained models for IDP ensembles using BW or VBW.

Figure 2

(a) Ensembles for Aβ40 and Aβ42 could be constructed independently, using different structural libraries, but comparing the resulting ensembles requires the difficult task of identifying important features, a priori. (b) Because the sequences of Aβ40 and Aβ42 are so similar, we assumed that a single structural library was adequate for describing the thermally accessible states for both peptides. With this assumption, the task of comparing the two ensembles is simplified to comparing the relative population weights of the structures. The ensemble shown at the top of panel b is a backbone alignment of all structures in the Aβ42 structural library.

Figure 3

Agreement between experimental data (blue) and the data predicted from the Bayes ensemble (black) constructed for Aβ40. The error bars reflect a combination of experimental and prediction errors.

Figure 4

Agreement between experimental data (blue) and the data predicted from the Bayes ensemble (black) constructed for Aβ42. The error bars reflect a combination of experimental and prediction errors.

Figure 5

Relationship between errors in ³J_HNHα and the associated error in the ϕ-angle. Recall that the Karplus equation is $J\left(\varphi \right)=A{\cos }^2\left(\varphi -60\right)+B\cos \left(\varphi -60\right)+c$. The error in the J-coupling, denoted Δ, as a function of the error in the ϕ-angle, denoted δ, was estimated using $\Delta \left(\delta \right)=\underset{\varphi \in \left[-180,180\right]}{\max }\left|J\left(\varphi +\delta \right)-J\left(\varphi \right)\right|$, where $\left|J\left(\varphi +\delta \right)-J\left(\varphi \right)\right|$ is the given ³J_HNHα error. (Dotted line) Position associated with the average error between the calculated J-couplings and the measured values (and the corresponding error in the ϕ-angle) are shown.

Figure 6

(a) Structure s1 (top), and the corresponding posterior probability distributions for its weight in the Aβ40 and Aβ42 ensembles (bottom). (b) Structure s2 (top), and the corresponding posterior probability distributions for its weight in the Aβ40 and Aβ42 ensembles (bottom). (c) Structure s3 (top), and the corresponding posterior probability distributions for its weight in the Aβ40 and Aβ42 ensembles (bottom). (d) Structure s4 (top), and the corresponding posterior probability distributions for its weight in the Aβ40 and Aβ42 ensembles (bottom).

Figure 7

(a) Structure s1. (b) Structure of the experimentally determined β-hairpin conformer of Aβ (Model 1 of PDB:2OTK) (55). (c) Cα alignment of structure s1 and PDB:2OTK. The first 15 residues are not shown because these residues were disordered in the PDB:2OTKβ-hairpin conformer.