Efficient construction of disordered protein ensembles in a Bayesian framework with optimal selection of conformations

Abstract

Constructing an accurate model for the thermally accessible states of an Intrinsically Disordered Protein (IDP) is a fundamental problem in structural biology. This problem requires one to consider a large number of conformations in order to ensure that the model adequately represents the range of structures that the protein can adopt. Typically, one samples a wide range of structures in an attempt to obtain an ensemble that agrees with some pre-specified set of experimental data. However, models that contain more structures than the available experimental restraints are problematic as the large number of degrees of freedom in the ensemble leads to considerable uncertainty in the final model. We introduce a computationally efficient algorithm called Variational Bayesian Weighting with Structure Selection (VBWSS) for constructing a model for the ensemble of an IDP that contains a minimal number of conformations and, simultaneously, provides estimates for the uncertainty in properties calculated from the model. The algorithm is validated using reference ensembles and applied to construct an ensemble for the 140-residue IDP, monomeric α- synuclein.

Figure 1

(A) The error between the true and estimated weights for the 20 reference ensembles. The solid and dashed lines indicate VBWSS and BW, respectively. The ensembles are ordered by increasing entropy. (B) The correlation (R = 0.9) between σ_w⃗^B and Ω(w⃗^T, w⃗^B) obtained from VBWSS. The best fit, y = 1.54 x, is shown as a dashed line.

Figure 2

αS VBWSS algorithm. (A) Alignment of non-zero weighted structures. (B) Agreement of calculated and experimental Cα chemical shifts. (C) Agreement of calculated and experimental RDCs.

Figure 4

Aggregation propensity in the ensemble. Colors represent the weight of each of structure. The star denotes a structure, shown to the right, with a relatively high weight.