The description of protein internal motions aids selection of ligand binding poses by the INPHARMA method

Abstract

Protein internal motions influence observables of NMR experiments. The effect of internal motions occurring at the sub-nanosecond timescale can be described by NMR order parameters. Here, we report that the use of order parameters derived from Molecular Dynamics (MD) simulations of two holo-structures of Protein Kinase A increase the discrimination power of INPHARMA, an NMR based methodology that selects docked ligand orientations by maximizing the correlation of back-calculated to experimental data. By including internal motion in the back-calculation of the INPHARMA transfer, we obtain a more realistic description of the system, which better represents the experimental data. Furthermore, we propose a set of generic order parameters, derived from MD simulations of globular proteins, which can be used in the back-calculation of INPHARMA NOEs for any protein-ligand complex, thus by-passing the need of obtaining system-specific order parameters for new protein-ligand complexes.

Fig. 1

Plots for the parameters of linear fits of INPHARMA NOEs calculated for the PKA/L_A and PKA/L_B complexes with uniform order parameters S² < 1 versus reference INPHARMA NOEs calculated for the rigid case with S² = 1. Slopes (upper panel) and Pearson correlation coefficients (lower panel) of best fit lines are shown in dependence of complex size (x axis, τ_c = 1–1,000 ns) and order parameter S² (contour lines) for different mixing times (left to right) and for the full build-up consisting of combined data from all four mixing times. Contour lines at values [0.1;0.9] are shown color-coded (red to green to blue). All combinations of INPHARMA NOEs between the groups of protons of Fig. S2 have been calculated; data are normalized to diagonal peak intensities in a NOESY spectrum at 150 ms mixing time

Fig. 2

Linear regression of experimental INPHARMA-NOEs (I-NOE_exp) at mixing times 300, 450, 600, and 750 ms versus simulated data (I-NOE_calc) ignoring (left panel) and considering (central and right panels) internal motions. In the central panel, tailored order parameters, derived from MD-simulations for the PKA, L_A, L_B system, are used; in the right panel generic order parameters are used. INPHARMA cross-peak intensities are normalized to diagonal peak intensities of L_A in a NOESY spectrum at mixing time of 150 ms. Best-fit lines (y = ax, black) are plotted after performing a linear regression (left, R = 0.82, a = 0.33; centre, R = 0.86, a = 0.86, right, R = 0.81, a = 0.73)

Fig. 3

Effect of randomization of the order parameters set. The INPHARMA NOEs, which are back-calculated using different sets of (randomized) order parameters are linearly fit to the experimental data. The values of the slopes a of the respective best-fit line (y axis) is plotted against the Pearson correlation coefficient R of the fit (x axis). Each dot represents a set of order parameters. The color code is as follows: red, the tailored order parameters extracted from MD simulation; blue, the generic set of order parameters; green, the rigid case; black, sets of order parameters randomized by shuffling proton pairs and order parameters; dark gray, sets of order parameters drawn from a Gaussian distribution with mean 0.62 and SD 0.22 to resemble the order parameter dataset extracted from MD simulation; light gray, a set of order parameters drawn uniformly from [0;1]

Fig. 4

Comparison of the selectivity of INPHARMA, when including (solid symbols) or excluding (empty symbols) internal motions, for the PKA/L_A and PKA/L_B complexes represented by a test set of four binding poses per ligand (yielding 16 ligands combinations). The correct pair of ligands binding poses, as seen in the crystal structures of PKA/L_A and PKA/L_B (PDB IDs 3dne and 3dnd, respectively), is indicated as triangle; other, incorrect, solutions as squares. a Slope of best fit line a plotted against Pearson correlation coefficient R for rigid and motional models. Equivalent solutions with R > 0.70 for the rigid model are connected by black lines. b Combined quality factor of motional against rigid model; Pearson correlation coefficients R and slopes of best fit line a are combined according to the formula [m(1 − R)² + n(1 − a)²]⁻¹ with m = n = 1, and resulting values are normalized to the interval [0;1]