19F NMR and DFT Analysis Reveal Structural and Electronic Transition State Features for RhoA‐Catalyzed GTP Hydrolysis

Abstract Molecular details for RhoA/GAP catalysis of the hydrolysis of GTP to GDP are poorly understood. We use 19F NMR chemical shifts in the MgF3 − transition state analogue (TSA) complex as a spectroscopic reporter to indicate electron distribution for the γ‐PO3 − oxygens in the corresponding TS, implying that oxygen coordinated to Mg has the greatest electron density. This was validated by QM calculations giving a picture of the electronic properties of the transition state (TS) for nucleophilic attack of water on the γ‐PO3 − group based on the structure of a RhoA/GAP‐GDP‐MgF3 − TSA complex. The TS model displays a network of 20 hydrogen bonds, including the GAP Arg85′ side chain, but neither phosphate torsional strain nor general base catalysis is evident. The nucleophilic water occupies a reactive location different from that in multiple ground state complexes, arising from reorientation of the Gln‐63 carboxamide by Arg85′ to preclude direct hydrogen bonding from water to the target γ‐PO3 − group.

9. Movie S1. Visualization of the characteristic imaginary vibrational mode of the TS model in which the water nucleophile attacks the γ-phosphoryl group of GTP. 10. Table S1. Structural data for 45 substrate, inhibitor, and tbp TSA complexes of small GTPases. 11. Table S2. Selected internal coordinate values for the computational TS model, the RhoA/GAP-GDP-MgF3 -X-ray crystal structure (1ow3) and the calculated active site model for the RhoA/RhoGAP-GDP-MgF3complex.
14. Figure S3. Inclusion of Asp59 in the model is important for the correct computation of transition state. 15. Figure S4. The final computed TS structure for the RhoA/GAP-GTP complex.
17. Figure S6. Cross-eyed stereo view showing H-bonded Michaelis complex structures for 4 Ras superfamily GTPases with GTP. 18. References F NMR investigation of a TSA complex. The RhoA/GAP complex was shown previously to be amenable to solution NMR, [3] and crystallization, [4] including two of the best-resolved trifluoromagnesate TSA complex structures of small G proteins (1ow3, 1.80 Å and 3msx, 1.65 Å). All NMR experiments used a D2O capillary as deuterium lock except experiments for isotope shift measurement, done in 100% D2O. 1D 19 F NMR spectra were recorded on a Bruker Avance 500 MHz spectrometer equipped with a 5 mm dual 1 H/ 19 F probe. Typically, 32k scans were acquired over a spectral width of 200 ppm with carrier frequency set to -140 ppm. In order to suppress the free MgF + resonance (-155 ppm) by saturation transfer, continuous-wave 19 F radiation for the 19 F NMR experiments of the RhoA/GAP-GDP-MgF3 -TSA complex was applied to the free fluoride resonance (-120 ppm) with a power level of 42 dB over a 1 s recycle delay. This completely removed signal overlap between the broad MgF + resonance and the F2 resonance. Samples of RhoA/GAP-GDP-MgF3 -TSA complex contained 1.0 mM RhoA (GDP 1:1 bound), 1.1 mM RhoGAP in 5 mM Tris buffer, pH 7.4, with 150 mM NaCl, 10 mM MgCl2, 10 mM NH4F, and 1 mM deferoxamine. In contrast to the RhoA/GAP-GDP-AlF4 -TSA complex, which showed one rotationally averaged signal, [3] the 19 F NMR resonances for the individual fluorines in the trifluoromagnesate complex were clearly resolved ( Figure 2). This illustrates the improved ability of the enzyme to restrict the rotation of the equatorial atoms when binding a tbp rather than an octahedral TSA mimic. [5] The 19 F resonances span ~30 ppm and were readily assigned on the basis of solvent-isotope induced shifts (SIIS) by comparing the chemical shift differences in 100 % H2O and 100 % D2O buffers ( Figure 2). SIIS values accurately reflect the distance of solvent-exchangeable hydrogens from the fluorine nuclei in metal fluoride complexes. [5][6] The most shielded fluorine (F1, -173.4 ppm; SIIS 0.8 ppm) binds to the catalytic Mg and accepts a single H-bond from the backbone NH of Thr37. The most deshielded fluorine (F3, -143.4 ppm; SIIS 1.6 ppm) accepts one H-bond each from Gln63 and the arginine finger (Arg85') side-chains. The third fluorine (F2, -154.3 ppm; SIIS 1.4 ppm) is H-bonded to the NH3 + group of Lys18 and the backbone NH of the invariant Switch II Gly residue (Gly62).
The 19 F spectra of the RhoA/GAP-GDP-MgF3 -TSA complex reveal a minor population of a second conformer ( Figure S2). No resolved second resonance is observed for F3, and the changes in chemical shift for F2 (0.7 ppm) and F3 (0.6 ppm) are too small for a change of the number of H-bonds in which they are involved. This conclusion is supported by the lack of any measureable changes in the SIIS values for these resonances between the major and minor forms. The direction of chemical shift changes is consistent with the H-bonding partners being slightly more distant from F2 and F3 in the minor form, but not changed sufficiently to alter the SIIS values measurably. A likely rationale is that a conformational change peripheral to the active site is causing the Switch II region (including G62 and Q63) not to pack quite as tightly to the MgF3moiety in the minor form. There is no clear evidence in the crystal structures for the source of this change, and its true identity requires further investigation.
Obtaining the TS model. Our model for the transition state (TS) of the γ-phosphate hydrolysis reaction was obtained using Kohn-Sham Density Functional Theory (KS-DFT). We used the M06-2X functional formulation of KS-DFT. [7] A cc-pVDZ basis set was used to represent single-particle wavefunctions for all atoms excepting atoms for which more care was given due to reaction importance. Many atoms were expected to have a higher negative charge density (for example, the oxygens along GTP) and therefore require diffuse functions. Additionally, all of the atoms directly involved in the bond formation/breaking also had a triple zeta basis set given that these atoms are more important. Thus, the nucleophilic water oxygen had aug-cc-pVTZ (oxygen requiring diffuse functions due to possible charge density buildup) and the hydrogens had cc-pVTZ (hydrogens never require diffuse functions). The oxygens of the phosphoryl group had aug-cc-pVTZ given their higher charge density, whereas the phosphorus had cc-pVTZ (since it is more positive charged and therefore less in need of diffuse functions). The 03 oxygen of GDP was given the aug-cc-pVTZ basis set for similar rationales. As the remaining oxygens of GDP are of secondary importance, these oxygens received aug-cc-pVDZ basis functions (which proved essential to get the highly sensitive NMR correct). All phosphorus and magnesium atoms used cc-pVTZ given that they have greater polarizability and should therefore have greater basis flexibility to reflect that polarizability. Fluorines utilized aug-cc-pVTZ in the magnesium trifluoride for the same rationale as oxygens in the phosphoryl group [8] . The active site (cluster) model ( Figure 3c) was constructed so as to maintain all key hydrogen bonding capable of stabilizing the transition state. The initial geometry about the γphosphorus atom was obtained by replacing the tbp magnesium by phosphorus and the three fluorines by oxygens in the high-resolution X-ray structure (1ow3). More specifically, we included atoms in residues 12-19, 36-38, and 59-63 (from RhoA) and 85' (from RhoAGAP). All amino acid hydrogen bonds stabilizing the attacking water, the γ-phosphoryl group, or leaving group were included. Waters bonded to the catalytic magnesium were also retained. Where opportune, we truncated amino acid residues with a methyl group in which the carbon was fixed at the crystallographic coordinates of the cognate atom in the X-ray crystal structure. Initially, the TS search utilized cc-pVDZ for all atoms and an integration grid consisting of 99 radial points and 590 solid-angle points in the Lebedev grid. Upon calculating an initial TS structure in this manner, we increased the quality of the calculation for greater accuracy and to eliminate spurious small imaginary frequencies. We added basis functions in the manner most conducive of better representing the polarizations of different atoms (see above). The final refined integration grid had 160 radial points, 974 solid angle points. The structure was considered optimized when the force on all nuclei fell below 1 μHartree/Bohr. The SCF was considered converged when the density matrix residual was less than 10 −6 . After decreasing the initial 1.91 Å Mg-F distance to a value of 1.71 Å for the three new P-O bonds, we optimized the geometry of the resulting active site model (181 atoms) to obtain the TS using standard algorithms, [9] as implemented in the Gaussian09 software package. [10] All "terminal methyl" carbons were fixed at their initial locations in 1ow3, which did not introduce any significant error into the calculation. This procedure gave a converged TS model with a harmonic vibrational value of 191i cm -1 corresponding to motion along the reaction coordinate (see movie S1). However, in freezing the Cartesian coordinates associated with the terminal methyl groups, there were a small number of non-relevant imaginary frequencies associated methyl group librations (31i cm -1 , 25i cm -1 , 18i cm -1 , 11i cm -1 , 9i cm -1 ). Coordinates for the TS model are available on request (RichardsN14@cardiff.ac.uk). By partitioning the total electron density into localized orbitals, cognisant of the approximations inherent to local orbital representation, analysis of the three equatorial P-O bonds in the computed TS identified them as each having 33% s character, 65% p character, and 2% d character. These three oxygens can generally be described as having sp 3 hybridisation, which suggests that the equatorial P-O bonds are close to simple sp 2 hybrids with virtually no p-d double-bond character. This was obtained using standard NBO analysis.
Obtaining the calculated active site model for the RhoA/GAP-GDP-MgF3complex. An active site model for the RhoA/GAP-GDP-MgF3complex was obtained from the atomic coordinates of the TS model except that the P and O atoms in the γ-phosphoryl group were replaced by Mg and F, respectively. The optimized structure was obtained using a similar computational protocol to that used for the TS model except that standard optimization algorithms were used to find the ground state structure. Given the electronegativity of fluorine, it was necessary to add diffuse functions in the form of an aug-cc-pVTZ basis on the fluorine atoms. [11] Coordinates for the RhoA/GAP-GDP-MgF3active site model are available on request (RichardsN14@cardiff.ac.uk).
NMR chemical shift calculations. NMR shielding tensors for 17 O and 19 F nuclei in the TS model and the calculated RhoA/GAP-GDP-MgF3complex active site model, respectively, were computed from the coupled-perturbed Hartree-Fock equation and gauge-invariant atomic orbitals derived from the DFT electron densities using standard algorithms implemented in the Gaussian09 software package. [10,12] The values of the shielding tensor for the fluorines are 327.4, 312.2, and 305.3 for F1, F2, and F3 respectively using aug-cc-pVTZ for the fluorines. When the basis is increased to aug-cc-pVQZ, the values become 325.6, 310.8, and 304.0 respectively, demonstrating that we are quite converged. The same relative ordering in most shielded nucleic exists for oxygens as well as fluorines. For O1, O2, and O3, the aug-cc-pVDZ shieldings are 168. 4, 150.4, and 147.2, mirroring the same trends as fluorines. When we increase the basis to aug-cc-pVTZ, the values are 154. 5, 135.0, and 130.8. We adapted the expression of our absolute shielding tensors into solvent-adjusted chemical shifts via a database of solvent fluorine NMR [14] using established methods of relating gasphase NMR shielding tensors to solution-phase chemical shifts. [15] We remain open-minded that statements of the most shielded atomic nucleus is not a 1-1 mathematical statement of the reaction mechanism, as a higher electron density before proton transfer is at best a kinetic statement, rather than a thermodynamic statement.
Dissociative/Associative Mechanism. Our model has a direct bearing on the question of associative versus dissociative nature of the transition states, which remains controversial, particularly in computational studies. There is little deviation from planarity of the γ-PO3moiety, the Arg85' finger of RhoGAP interacts with oxygen atoms on each phosphoryl group, and the O3β-Pγ-Ow3 angle (175 o ) is consistent with in-line attack. The geometry of our TS model addresses whether phosphoryl transfer in RhoA/GAP proceeds via an associative or a dissociative TS. [16] Early analyses of the TS for phosphoryl transfer focused on a boundary of 4.9 Å for the separation of the apical oxygen atoms in fully dissociative processes. [17] For our TS model this O--O distance is 4.26 Å and, by the above definition, is consistent with an associative contribution to the concerted TS, in line with other mechanistic proposals. [18] Intriguingly, the axial O--O distance for the 8 tbp MF3 TSA analogs (4.27 ± 0.13 Å) is well within error of the value for the computed TS model (Figure 3b). The relative P--O distances for the departing oxygen (2.19 Å) and incoming oxygen (2.03 Å) indicate that bond breaking is hardly more advanced than bond making for the hydrolysis of GTP (Scheme 1), suggestive of partial associative character within a compact, concerted ANDN transition state. Our TS model contrasts with the proposal of a fully dissociative DN + AN mechanism based on a previous computation built from a Ras TSA structure (1wq1) and a Ras-GTP structure lacking a GAP protein (1qra), [19] a discrepancy that highlights the problem of modeling phosphoryl transfer with an inadequate number of QM atoms. [20] It seems likely that the transition states for Cdc42, Rab, Rac, and Ras will possess all the key structural features observed here for RhoA.
Movie S1. Visualization of the characteristic imaginary vibrational mode of the TS model in which the water nucleophile attacks the γ-phosphoryl group of GTP. Images were created in GaussView V5.0 [21] and are looped for ease of viewing. The scalar amplitude of the atomic motions along the eigenvector associated with this vibrational mode is defined by a factor A, which is computed according to the following equation: where S is an integer value that ranges from 2 to 100. Hence, A ranges from 0.2-1.5 Å.    with key 20 hydrogen bonds (black dashes) to the computed hydrogens (white sticks). The two structures are overlaid by aligning 11 terminal methyl groups on the corresponding carbons in 1ow3 (rmsd 0.05 Å). The complete amino acids are shown for 1ow3; non-polar computed hydrogens are omitted for clarity.
The isolated water (dark gray) shown to be off-line with the P-O3 bond. It coordinates O3, Thr37(CO), and Gln63(NH); in 1n6l, the water also coordinates one of 2 conformations of the Gln63 side chain NH2. Variable conformations of Gln63 (Leu63 for 1z0j) side chains contrast with uniform orientations of side chains for Lys18, Thr19, Thr37, and Gly62.