Modeling Intrinsically Disordered Proteins with Bayesian Statistics

Abstract

The characterization of intrinsically disordered proteins is challenging because accurate models of these systems require a description of both their thermally accessible conformers and the associated relative stabilities or weights. These structures and weights are typically chosen such that calculated ensemble averages agree with some set of prespecified experimental measurements; however, the large number of degrees of freedom in these systems typically leads to multiple conformational ensembles that are degenerate with respect to any given set of experimental observables. In this work we demonstrate that estimates of the relative stabilities of conformers within an ensemble are often incorrect when one does not account for the underlying uncertainty in the estimates themselves. Therefore, we present a method for modeling the conformational properties of disordered proteins that estimates the uncertainty in the weights of each conformer. The Bayesian weighting (BW) formalism incorporates information from both experimental data and theoretical predictions to calculate a probability density over all possible ways of weighting the conformers in the ensemble. This probability density is then used to estimate the values of the weights. A unique and powerful feature of the approach is that it provides a built-in error measure that allows one to assess the accuracy of the ensemble. We validate the approach using reference ensembles constructed from the five-residue peptide met-enkephalin and then apply the BW method to construct an ensemble of the K18 isoform of the tau protein. Using this ensemble, we indentify a specific pattern of long-range contacts in K18 that correlates with the known aggregation properties of the sequence.

Constructing Structure Ensembles of Intrinsically Disordered Proteins from Chemical Shift Data

“…Ensemble modeling has been believed to be the most accurate way to describe the 3D structures of IDPs (Choy and Forman-Kay, 2001;Fisher et al, 2010;Fisher and Stultz, 2011). In general, a structure ensemble consists of two parts: a set of 3D structures and the corresponding weights that describe the likelihoods of individual conformations.…”

“…When experimental data (e.g., chemical shifts, nuclear Overhauser effect (NOE) distances, and residual dipolar couplings) are available, the 3D structures and their weights are often constructed to optimally match these experimental observations. In the literature, numerous approaches have been proposed to construct 3D structure ensembles of IDPs from experimental data ( Jensen et al, 2010;Nodet et al, 2009;Marsh and Forman-Kay, 2009;Ganguly and Chen, 2009;Fisher et al, 2010). These approaches can be roughly divided into two categories (Fisher and Stultz, 2011).…”

“…As discussed in Ganguly and Chen (2009), such ensemble construction approaches usually fail when there is an insufficient number of constraints available for supporting the restrained MD simulation. The second group of ensemble construction approaches (Choy and Forman-Kay, 2001;Nodet et al, 2009;Fisher et al, 2010;Chen et al, 2007) applies a different strategy. They first generate an initial structure pool (which is also called the predefined conformational library) using MD simulation, and then select a subset of these structures to represent conformational space.…”

“…One main challenge in the IDP ensemble construction task lies in addressing the degeneracy problem (Fisher et al, 2010;Terakawa and Takada, 2011): Due to the large degrees of freedom in this problem, there can exist multiple ensemble solutions to satisfy experimental data. This problem remains a challenge even after the initial conformational library has been defined.…”

“…This problem remains a challenge even after the initial conformational library has been defined. The degeneracy problem in IDP ensemble construction has been well discussed in Fisher et al (2010) and Fisher and Stultz (2011).…”