Protein structure along the order-disorder continuum

Abstract

Thermal fluctuations cause proteins to adopt an ensemble of conformations wherein the relative stability of the different ensemble members is determined by the topography of the underlying energy landscape. "Folded" proteins have relatively homogeneous ensembles, while "unfolded" proteins have heterogeneous ensembles. Hence, the labels "folded" and "unfolded" represent attempts to provide a qualitative characterization of the extent of structural heterogeneity within the underlying ensemble. In this work, we introduce an information-theoretic order parameter to quantify this conformational heterogeneity. We demonstrate that this order parameter can be estimated in a straightforward manner from an ensemble and is applicable to both unfolded and folded proteins. In addition, a simple formula for approximating the order parameter directly from crystallographic B factors is presented. By applying these metrics to a large sample of proteins, we show that proteins span the full range of the order-disorder axis.

Figure 1

BW ensemble for K18 Tau. (A) The 300 conformations used to construct the ensemble, aligned via Cα atoms. (B) Residual dipolar couplings (RDCs) predicted from the ensemble using PALES(1) compared to those measured experimentally.

Figure 2

Protein conformational heterogeneity as determined using crystallographic B factors. (A) Plots of order parameters (blue) and minimal ensemble sizes (red) for a large sample of proteins calculated from crystallographic B factors. (B) Structure of human PIM-1 kinase (PDB code 2BZH), which had the smallest order parameter. (C) Structure of a peptide model of prion fibrils (PDB code 3FVA), which had the largest order parameter.

Figure 3

Protein conformational heterogeneity as obtained from MD simulations. (A) Plots of order parameters (blue) and minimal ensemble sizes (red) calculated for a sample of protein folds from simulations in the Dynameomics database. The sample corresponded to 88 of the top 100 most common structural folds in the database, for which we were able to obtain the data required to compute the order parameter. (B) NMR structure of oryzacystatin-I (PDB code 1EQK), which had the smallest order parameter. (C) Structure of the antifungal peptide EAFP2 (PDB code 1P9G), which had the largest order parameter.