Global Dynamics of a Protein on the Surface of Anisotropic Lipid Nanoparticles Derived from Relaxation-Based NMR Spectroscopy

Abstract

The global motions of ubiquitin, a model protein, on the surface of anisotropically tumbling 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (POPG):1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) bicelles are described. The shapes of POPG:DHPC bicelles prepared with high molar ratios q of POPG to DHPC can be approximated by prolate ellipsoids, with the ratio of ellipsoid dimensions and dimensions themselves increasing with higher values of q. Adaptation of the nuclear magnetic resonance (NMR) relaxation-based approach that we previously developed for interactions of ubiquitin with spherical POPG liposomes (Ceccon, A. J. Am. Chem. Soc. 2016, 138, 5789-5792) allowed us to quantitatively analyze the variation in lifetime line broadening of NMR signals (ΔR₂) measured for ubiquitin in the presence of q = 2 POPG:DHPC bicelles and the associated transverse spin relaxation rates (R_2,B) of bicelle-bound ubiquitin. Ubiquitin, transiently bound to POPG:DHPC bicelles, undergoes internal rotation about an axis orthogonal to the surface of the bicelle and perpendicular to the principal axis of its rotational diffusion tensor on the low microsecond time scale (∼3 μs), while the rotation axis itself wobbles in a cone on a submicrosecond time scale (≤ 500 ns).

Figure 1.

Model of global ubiquitin dynamics on the surface of POPG SUV and LUV liposomes, and a comparison of ¹⁵N-ΔR₂ profiles measured for ubiquitin in the presence of SUVs and POPG:DHPC bicelles. (A) Left panel shows a ribbon diagram of ubiquitin in the coordinate system of the inertia tensor (blue), with the position of the axis of internal rotation r (red) defined by the polar angles θ and φ. The right panel shows the structure of ubiquitin on the surface of the lipid bilayer in the frame of internal rotation (with the axis of rotation r orthogonal to the plane of the liposome surface). The coordinates of ubiquitin are taken from the X-ray structure (PDB 1UBQ). (B) Comparison of ubiquitin ¹⁵N-ΔR₂ profiles obtained in the presence of POPG:DHPC bicelles prepared with a POPG:DHPC molar ratio q = 2 (red circles) with those obtained in the presence of spherical POPG SUVs uniformly scaled by a factor of 0.3 (blue circles). A schematic representation of the ubiquitin secondary structure is shown on top of (B). Residues at the C-terminus (73–76) and in the flexible loops (8–11, 18, 36) and residues exhibiting residual chemical shift line broadening, R_ex (40, 48), are excluded from the plot. The data were recorded at 800 MHz and 25 °C on a 0.5 mM sample of ¹⁵N-labeled ubiquitin.

Figure 2.

Effect of lipid particle size on the variability of ¹⁵N-ΔR₂ profiles and determination of bicelle anisotropy by MALS. (A) Contour plot of the variability of theoretical ¹⁵N-ΔR₂ values (defined as the ratio of the maximal to minimal ΔR₂ values, ΔR_2,max/ΔR_2,min) as a function of the correlation time of global molecular motion (τ_c,eff, x-axis) and internal rotation (τ_r; y-axis). The values of ¹⁵N-ΔR₂ were calculated using the expression for the spectral density function J(ω) for spherical particles (isotropic diffusion) described in Ceccon et al. (B) ¹⁵N-ΔR₂ profiles obtained for ubiquitin in the presence of q = 2 (red circles) and q = 1 (blue circles) POPG:DHPC bicelles and POPG nanodiscs (green circles), the latter uniformly scaled by a factor of 0.4 (see the text for the rationale behind the use of an empirical scaling factor). The inset shows dynamic light scattering (DLS) profiles obtained for the three POPG lipid-based nanoparticles: normalized intensities (y-axis) versus hydrodynamic diameters d of equivalent spheres (x-axis; nm). The polydispersity index (PDI) in all DLS measurements is <0.1. Residues at the C-terminus (71–76) and in the flexible loops (8–11, 18, 36), as well as residues (40 and 48) showing residual chemical shift line broadening, R_ex were excluded from the plot. The data were recorded at 800 MHz and 25 °C on a 0.5 mM sample of ¹⁵N-labeled ubiquitin. (C) MALS Rayleigh intensity ratios obtained for q = 4 POPG:DHPC bicelles as a function of the scattering vector q = sin²(θ/2). Experimental data are shown with black open circles, while the best-fits to an ellipsoid of revolution and a sphere are shown as red and blue curves, respectively (see the text).

Figure 3.

Comparison of experimental and fitted ¹⁵N-R_2,B profiles of ubiquitin bound to q = 2 POPG:DHPC bicelles. (A) R_2,B profiles for ubiquitin bound to the surface of q = 2 POPG:DHPC bicelles. The experimental values are shown as red circles, while blue circles show the values obtained from the best-fit using (top panel) the expression for the spectral density in eqs 2 and 3 encompassing diffusion anisotropy and (bottom panel) the isotropic approximation (D_||/D_⊥ = 1). A schematic representation of the ubiquitin secondary structure is shown on top. (B) R_2,B values for ubiquitin bound to the surface of q = 2 POPG:DHPC bicelles plotted as a function of the angles α (top panel) and γ (bottom panel) using the same color code as in (A). Experimental values of four amide sites with the highest R_2,B rates are labeled with residue numbers and discussed in the text. The curves shown in green are calculated using the best-fit global dynamics parameters (see text) with angles γ and α fixed at 90°.

Figure 4.

Angular dependence of ¹⁵N-R_2,B values for ubiquitin bound to q = 2 of POPG:DHPC bicelles. (A) Color-coded surface plots of R_2,B values for ubiquitin bound to q = 2 POPG:DHPC bicelles as a function of the γ and α angles, calculated using the expression for the spectral density function in eqs 2 and 3 and the best-fit parameters of global dynamics (see the text). Experimental values are shown as black circles. (B) Ribbon diagram of ubiquitin bound to a bicelle nanoparticle oriented in the frame of the global rotational diffusion, with the principal axis of the diffusion tensor aligned along the z-axis (green; bottom to top) and the internal rotation axis r orthogonal to the bicelle surface (red; in the plane of the plot).