Quantitative characterization of intrinsic disorder in polyglutamine: insights from analysis based on polymer theories

Abstract

Intrinsically disordered proteins (IDPs) are unfolded under physiological conditions. Here we ask if archetypal IDPs in aqueous milieus are best described as swollen disordered coils in a good solvent or collapsed disordered globules in a poor solvent. To answer this question, we analyzed data from molecular simulations for a 20-residue polyglutamine peptide and concluded, in accord with experimental results, that water is a poor solvent for this system. The relevance of monomeric polyglutamine is twofold: It is an archetypal IDP sequence and its aggregation is associated with nine neurodegenerative diseases. The main advance in this work lies in our ability to make accurate assessments of solvent quality from analysis of simulations for a single, rather than multiple chain lengths. We achieved this through the proper design of simulations and analysis of order parameters that are used to describe conformational equilibria in polymer physics theories. Despite the preference for collapsed structures, we find that polyglutamine is disordered because a heterogeneous ensemble of conformations of equivalent compactness is populated at equilibrium. It is surprising that water is a poor solvent for polar polyglutamine and the question is: why? Our preliminary analysis suggests that intrabackbone interactions provide at least part of the driving force for the collapse of polyglutamine in water. We also show that dynamics for conversion between distinct conformations resemble structural relaxation in disordered, glassy systems, i.e., the energy landscape for monomeric polyglutamine is rugged. We end by discussing generalizations of our methods to quantitative studies of conformational equilibria of other low-complexity IDP sequences.

FIGURE 1

Scaling laws for the two reference models (see Eqs. 1 and 2). The fit for the EV limit is done only over the last five points. As can be seen, finite-size effects cause the data for shorter chain lengths to fall off this line. Including these points would significantly overestimate the scaling exponent. In the globular reference state, finite-size effects are restricted to much shorter chain lengths. The theoretical exponent of ∼0.33 is slightly underestimated.

FIGURE 2

Two-dimensional histograms of the normalized radius of gyration and asphericity (see Eq. 4) for Q₂₀ in water and the two reference models. The data are binned with a spacing of 0.05 Å on the R_g axis and 0.02 on the δ axis, respectively. For the purpose of clarity, the colors are slightly offset from the white background.

FIGURE 3

Contact maps for Q₂₀ in water (B), in the EV limit (A), and in the globular limit (C). Grayscale indicates the frequency of observing a given residue-residue contact throughout the simulation. Short-range contacts are excluded to enhance the signal/noise ratio. A contact is defined by any two atoms k and l from residues i and j having a distance ≤3 Å. The maps are by definition symmetric.

FIGURE 4

The scaling of average internal distances as a function of sequence separation (see Eq. 5). A theoretical good solvent scaling law is indicated by the dotted line. SE are indicated by error bars for the data in water and the globular reference state. Errors are negligible for the EV ensemble and hence not shown. The polypeptide caps are included in this analysis, which is why there are effectively 22 residues in the chain.

FIGURE 5

The angular correlation function (see Eq. 6) as a function of sequence separation. The polypeptide caps are excluded from this analysis. For details on errors see caption to Fig. 4.

FIGURE 6

The average density as a function of distance to the center of mass (see Eq. 7). For details on errors see caption to Fig. 4.

FIGURE 7

Ensemble averaged Kratky profiles (see Eq. 8) calculated for the three different models. For details on errors see caption to Fig. 4.

FIGURE 8

The left column shows site-site correlation functions for different atom pairs for Q₂₀ in water. The data are normalized by an ideal chain prior (see Appendix). Dotted lines indicate SE intervals. The right column shows analogous site-site correlation functions for the solutions of NMF and PPA in water normalized by an ideal gas prior. Data for three different concentrations are shown (1 m, solid curves; 2 m, dashed curves; and 4 m dash-dotted curves). The sensitivity of the results to amide concentration is small. SE are negligible for these simulations.

FIGURE 9

Checkerboard map of the average all-atom RMSD in angstroms of the structures observed in trajectory j (y axis) from the final structure of trajectory i (x axis). This map is by construction not symmetric.

FIGURE 10

(A) The time evolution of S(t), a normalized measure of 〈R_g〉 as a function of time, t. The plot also shows the fit to a single exponential function with S_o = 0.40 and τ = 5 ns. The norm of the residuals between the raw data and the exponential function is 0.01. (B) RMSD of the structures within a trajectory from their final structure (gray diamonds) is compared to that of the structures within a trajectory to the final structure of other trajectories (gray circles). SE for the former could not be obtained because there is only one value per trajectory and per time point. For the cross-term, the 59 values per trajectory and per time point were preaveraged and SE could be obtained as usual. Data for the average conformational relaxation within a trajectory (gray diamonds) are fit to a stretched exponential function of the form described in the text. This is shown as the solid curve in the plot. Deviations from the stretched exponential function are largest for the earliest time points, t < 5 ns, and for the last 10-ns interval. The former is explained by the rapid collapse over short timescales, whereas the latter is entirely due to our choice of the final snapshot of the trajectory as the reference snapshot for analyzing conformational relaxation.