Protein Dynamics to Define and Refine Disordered Protein Ensembles

Abstract

Intrinsically disordered proteins and unfolded proteins have fluctuating conformational ensembles that are fundamental to their biological function and impact protein folding, stability, and misfolding. Despite the importance of protein dynamics and conformational sampling, time-dependent data types are not fully exploited when defining and refining disordered protein ensembles. Here we introduce a computational framework using an elastic network model and normal-mode displacements to generate a dynamic disordered ensemble consistent with NMR-derived dynamics parameters, including transverse R₂ relaxation rates and Lipari-Szabo order parameters (S² values). We illustrate our approach using the unfolded state of the drkN SH3 domain to show that the dynamical ensembles give better agreement than a static ensemble for a wide range of experimental validation data including NMR chemical shifts, J-couplings, nuclear Overhauser effects, paramagnetic relaxation enhancements, residual dipolar couplings, hydrodynamic radii, single-molecule fluorescence Förster resonance energy transfer, and small-angle X-ray scattering.

Figure 1.. The dynamical description of the unfolded state of the drkN SH3 domain using an anisotropic network model.

Three lowest frequency normal modes for a single structure out of the disordered ensemble where green arrows, blue arrows, and black arrows represent the direction and amplitudes of the three lowest frequency motional modes, super-imposed on a schematic representation of the protein backbone in the unfolded state.

Figure 2.. R2 and S2 profiles for the unfolded state of the drkN SH3 domain.

(a) ¹⁵N ${\text{R}}_2$ relaxation rates and (b) ${\text{S}}^2$ order parameters as a function of residue number.^, Units in (a) are in 1/sec.

Figure 3.. The change in RMSD error of the eight experimental data types (x-axis) for the R2 and S2-selected ensembles (red-bar) vs the R2- and S2-dynamic ensembles (blue-bar).

The panels (a-c) show the results for ${\text{R}}_2$ and panels (d-f) show the results for ${\text{S}}^2$ for the ENSEMBLE, RANDOM, and MIXED pool optimizations using X-EISD. There are negligible errors according to the Bayesian model for SAXS, ${\text{R}}_{\text{h}}$ and smFRET. RMSD units are different for each experimental data type and are found in Table 1.

Figure 4.. RMSD errors by optimizing the X-EISD score with a single experimental data type for R2-dynamic ensembles derived from (a) ENSEMBLE, (b) RANDOM, and (c) MIXED pools.

The values are averages over 1000 ensembles of 100 structures each, and the numbers in parenthesis are standard deviations. The last row refers to the unoptimized ${\text{R}}_2$-dynamic pool of structures. Units are different for each experimental data type and are found in Table 1.

Figure 5.. Radius of gyration distributions of the original (red) and R2-dynamic (blue) ensembles for the unfolded state of drkN SH3 domain.

Shown for the (a) ENSEMBLE, (b) RANDOM, and (c) MIXED pools.