Prediction of charge-induced molecular alignment of biomolecules dissolved in dilute liquid-crystalline phases

Abstract

Alignment of macromolecules in nearly neutral aqueous lyotropic liquid-crystalline media such as bicelles, commonly used in macromolecular NMR studies, can be predicted accurately by a steric obstruction model (Zweckstetter and Bax, 2000). A simple extension of this model is described that results in improved predictions for both the alignment orientation and magnitude of protein and DNA solutes in charged nematic media, such as the widely used medium of filamentous phage Pf1. The extended model approximates the electrostatic interaction between a solute and an ordered phage particle as that between the solute's surface charges and the electric field of the phage. The model is evaluated for four different proteins and a DNA oligomer. Results indicate that alignment in charged nematic media is a function not only of the solute's shape, but also of its electric multipole moments of net charge, dipole, and quadrupole. The relative importance of these terms varies greatly from one macromolecule to another, and evaluation of the experimental data indicates that these terms scale differently with ionic strength. For several of the proteins, the calculated alignment is sensitive to the precise position of the charged groups on the protein surface. This suggests that NMR alignment measurements can potentially be used to probe protein electrostatics. Inclusion of electrostatic interactions in addition to steric effects makes the extended model applicable to all liquid crystals used in biological NMR to date.

FIGURE 1

Experimental ¹D_NH values at 0.20 M NaCl (solid line) and ¹D_NH values best-fitted to the 1.1 Å crystal structure of GB3 (PDB code: 1IGD) (dashed line). The dipolar coupling quality factor Q (Ottiger and Bax, 1999) is 10%.

FIGURE 2

Comparison of experimental ¹D_NH values with values predicted on the basis of the molecules' three-dimensional shapes (not taking into account electrostatic effects) for ubiquitin (A), DinI (B), GB3 (C), GB1 (D), and the Dickerson dodecamer (E). Experimental values were obtained at 0.20 M NaCl, pH 7, 25°C, using Pf1 bacteriophage as alignment medium. Experimental and predicted ¹D_NH values were rescaled to 17 mg/ml Pf1. High-resolution NMR (PDB codes for DinI, ubiquitin, and DNA: 1GHH, 1D3Z, and 1DUF, respectively) or crystal structures (for GB3: residues 6–61 of 1IGD; for GB1: 1PGA) were used for shape prediction. Straight lines correspond to y = x.

FIGURE 3

Comparison of experimental ¹D_NH values with values predicted on the basis of the molecules' three-dimensional shapes and charge distributions (taking into account electrostatic effects) for ubiquitin (A), DinI (B), GB3 (C), GB1 (D), and the Dickerson dodecamer (E). For other details, see legend to Fig. 2.

FIGURE 4

Correlation between experimental ¹D_NH values and charge/shape-predicted couplings. Results for five molecules with very different electrostatic properties are shown: (A), ubiquitin; (B), DinI; (C), GB3; (D), GB1; and (E), Dickerson dodecamer. In (F) the charge/shape prediction results for the ensemble of 3GB1 structures is shown. Dashed line indicates R_P values for the regularized average structure of the ensemble. Alignment magnitudes are presented in Fig. 7.

FIGURE 5

Distribution in magnitude, D_a(NH), rhombicity, D_r/D_a, dipolar coupling correlation, R_P, and orientation of charge/shape-predicted alignment tensors, resulting from small structural differences across the NMR ensemble of 20 DinI structures (PDB code: 1GHH) at 0.20 M NaCl, pH 7. The prediction quality is evaluated using Pearson's linear correlation factor, R_P. The deviation in orientation is expressed as a generalized angle, according to Sass et al. (1999).

FIGURE 6

Correlation between experimental ¹D_NH values and charge/shape-predicted couplings as a function of ionic strength for increasing complexity of the charge model used for biomolecules. In the simplified electrostatic model the charge distribution is reduced to only the monopole q (dashed lines), only the dipole μ (dotted lines), only the quadrupole Q (dash-dot-dash lines), or to a combination of all three multipole moments (solid lines). Results are shown for four proteins: (A), ubiquitin; (B), DinI; (C), GB3; (D) GB1.

FIGURE 7

Dependence of alignment magnitude on ionic strength for ubiquitin (A), DinI (B), GB3 (C), GB1 (D), and the Dickerson dodecamer (E). Filled symbols mark values obtained from experimental dipolar couplings by SVD. Error bars represent the influence of structural noise on SVD calculations (Zweckstetter and Bax, 2002). Solid gray lines represent the alignment magnitudes for the full electrostatic model without multipole scaling using the following structures: (A), 1D3Z; (B), 1GHH; (C), residue 6-61 of 1IGD; (D), 1PGA; and (E), 1DUF. Solid black lines correspond to the charge/shape predictions that were obtained with empirically optimized scaling factors for the monopole, dipole, and quadrupole moment (see text). Error estimates (dotted lines) are standard deviations obtained from the ensemble of NMR structures (A,B) and amount to roughly 30%. The alignment magnitude, G_Mag, is defined in Eq. 1. To facilitate comparison with the familiar D_a(NH) values, G_Mag values have been multiplied by

FIGURE 8

Correlation between experimental ¹D_NH values and charge/shape-predicted couplings (solid lines), or SVD best-fit couplings (dotted lines) as a function of ionic strength. The dashed lines indicate the correlations between experimental couplings at a certain ionic strength and those observed at low salt (∼0.02 M NaCl). Results for five molecules with very different electrostatic properties are shown: (A), ubiquitin; (B), DinI; (C), GB3; (D), GB1; and (E), Dickerson dodecamer. Note that for ubiquitin, at the low Pf1 concentrations used, the drop in R_P above 0.30 M NaCl is dominated by the reduced relative accuracy of dipolar couplings. Note that these results were obtained with empirically optimized scaling factors for the monopole, dipole, and quadrupole moment (see text).

FIGURE 9

(A) Magnitude of DNA dodecamer alignment relative to the total alignment magnitude, as a function of distance between the center of gravity of the dodecamer and the axis of the viral rod, calculated using shells of 5 Å thickness for various ionic strengths. The x axis indicates the distance from the center of a Pf1 rod to the inner surface of the 5 Å shell. Different NaCl concentrations are indicated in the following way: solid line, 0.01 M; dashed line, 0.1 M; and dotted line, 0.3 M. In gray, the shell distribution for the steric case is shown. (B) Electrostatic potentials of bacteriophage Pf1, using a cylinder radius of 3.35 nm and a surface charge density of −0.475 e/nm², calculated from the nonlinear Poisson-Boltzmann equation at 0.01 M (solid line), 0.1 M (dashed line), and 0.3 M (dotted line) NaCl.