To investigate the relationship of K-Ras to other available Ras structures, we compiled a crystallographic ensemble comprising 51 chains from the 47 unique Ras structures in the RCSB PDB [19], [20]. Principal component analysis (PCA) was used to characterize inter-conformer relationships. Despite the inclusion of ten new chains from six recently-solved structures, we obtained a similar distribution of conformers along the dominant principal components (PCs) as obtained in an earlier study [15]. This indicates the robustness of the distribution to the inclusion of new structures and the suitability of the method for describing new inter-conformer relationships. Two major clusters are again evident along PC1 corresponding to distinct GTP and GDP bound conformations (Fig 2), confirming the previous observation that different chemical molecules at the active sites are associated with different global Ras conformations [15]. Note that some GTP/GTP-analog-bound structures were not situated within the main GTP-cluster. These structures have a mutation at the P-loop or switch regions. For example, H-Ras G12V, H-Ras A59G, and H-Ras Y32C (PDB: 2Q21, 1LF0, and 2CL0 respectively) did not reside in the GTP-cluster. Interestingly, the wild-type K-Ras conformer also resides outside the main GTP and GDP clusters in close proximity to the crystal conformer of H-Ras A59G mutant. Both structures are indeed similar in terms of Cα RMSD (0.68 Å).

While the first principal component revealed distinct clusters of Ras conformations corresponding to different bound-nucleotides (Fig 2), the third principal component showed distinct clusters of Ras conformations corresponding to mutant states (Fig 2). Ras crystal conformers with mutations at critical residues 32, 59, 61, and 118, affecting GTP hydrolysis, emerged far from the wild-type H-Ras conformers along the third principal component. Two H-Ras mutant conformers, G12P and G60A were found to reside within the majority wild-type cluster. Interestingly, these mutations are non-oncogenic. For example H-Ras G12P is known to possess wild-type like intrinsic GTP hydrolysis and GDP dissociation functions [21]. In summary, the current principal component projections based on the Ras crystallographic ensemble are robust to the inclusion of new structures and facilitate the discrimination of key ligand- and sequence-based structural perturbations.

To further probe the conformational dynamics of the different Ras isoforms we performed multi-copy molecular dynamics simulations on the following systems: wild-type K-Ras, wild-type H-Ras, and H-Ras A59G. Although the starting wild-type K-Ras and the wild-type H-Ras structures are similar in overall conformation (Cα RMSD is 1.03 Å), the active site of wild-type K-Ras is more similar to that of H-Ras A59G (Cα RMSD is 1.16 Å) than wild-type H-Ras (Cα RMSD is 1.74 Å) (Fig S1).

Comparison of the wild-type K-Ras and H-Ras trajectories in the GTP-bound form revealed variations in their dynamic behaviors, consistent with previous MD simulations of homology-built K-Ras and wild-type H-Ras in the nucleotide-free state [15]. Interestingly, wild-type K-Ras is similar to H-Ras A59G in sampling a wider region of conformational space proximal to the H-Ras G12V variant crystal conformer (Fig 3). Previous MD simulations of H-Ras G12V also displayed enhanced sampling when compared to wild-type H-Ras [15]. In terms of RMSD, the MD conformers of wild-type K-Ras and H-Ras A59G appear to be more similar to each other than to the MD conformers of wild-type H-Ras (Fig S2). The same trend is apparent for the canonical switches. For example, across the three sets of MD trajectories of the wild-type H-Ras, switch 1 RMSD values are generally higher than those of switch 2 (Fig S3) whereas the opposite is true for K-Ras and H-Ras A59G. Comparing RMSF values from the respective GTP-bound simulations indicates that wild-type K-Ras and H-Ras A59G are indeed more dynamic than wild-type H-Ras (Fig 4). These differences are significant as indicated by paired student's t tests (P<0.01). Particularly noteworthy are residues at the crucial switch 1, switch 2, loop3, α3 helix, and loop 7 regions, all of which are more flexible in K-Ras and A59G than in wild-type H-Ras.

To identify regions undergoing correlated motions we analyzed dynamic cross-correlation maps for the three sets of trajectories. The correlated motion between loop 3 and α5 helix is absent in H-Ras A59G but present in the wild-type K- and H-Ras (Fig 5). This suggests that the substitution at position 59 in switch 2 affects the correlated motion of structural elements that are sequentially and spatially distant. The loop 3 and the C-terminal of α5 helix are parts of switch 3 [22] and correlated motion between loop 3 and α5 was reported in previous accelerated MD simulations of wild-type H-Ras [23]. On the other hand, wild-type H-Ras and H-Ras A59G exhibit a similar pattern of correlated motions between α2 and α3-loop 7 (Fig 5). The α3-loop 7 region has recently been reported to function as an allosteric site regulating switch 2 ordering [24].

Residue Q61 of switch 2 is essential for GTP hydrolysis with its side chain involved in orienting and activating a nucleophilic water molecule [25]. To monitor the conformation of Q61, we tracked the distances between the γ-phosphate and Q61 side chain atom NE2. Their distances are greater in wild-type K-Ras than in wild-type H-Ras, although not as large as in H-Ras A59G simulations (Fig 6). Such displacement of Q61 toward R68 and away from the catalytic site likely contributes to the much slower intrinsic GTP hydrolysis of H-Ras A59G when compared to wild-type H-Ras [26].

Y64 is more distant to the γ-phosphate in both wild-type K-Ras and H-Ras A59G than in wild-type H-Ras (Fig 6). In simulations of wild-type H-Ras, the side chain of Y64 was persistently oriented and positioned close to the γ-phosphate of GTP (distance between Y64 OH atom and γ-phosphate ranged from 9.0 to 13.9 Å, with an average value of 11.7 Å). In wild-type K-Ras, the distance varied between 9.2 and 25.7 Å, with an average value of 22.4 Å. In A59G, this distance ranged from 19.8 to 25.4 Å, and the average was 22.1 Å. GTP hydrolysis can only occur in conformations with the Y64 side chain being close to the γ-phosphate. Though the average distance of Y64 side chain and γ-phosphate in wild-type K-Ras is as long as in H-Ras A59G, wild-type K-Ras can also adopt conformations in which their Y64:OH and γ-phosphate distance is as short as that of wild-type H-Ras. Fig 7 depicts the change in the orientation of K-Ras Y64, the shortening of Y64:OH - γ-phosphate distance, and the motion of α2 helix toward the nucleotide-binding site.

The crystallographic structure of H-Ras A59G, on which the current simulations are based, was proposed to represent the conformation of wild-type H-Ras following β/γ-phosphate bond breakage but before γ-phosphate dissociation [26]. This mutant was also shown to have an impaired intrinsic GTP hydrolysis activity [26]. When we replaced the original GTP-analog with GDP and performed unbiased 20-ns MD simulation, we observed a spontaneous GTP-to-GDP transition. This spontaneous GTP-to-GDP transition complements our previous characterization of the spontaneous GDP-to-GTP transition observed in the H-Ras G12V variant [15]. The GTP-to-GDP transition has been previously analyzed in some studies [18], [27], [28] that employed biased calculations, such as targeted MD, which introduces external constraints to drive the transition. Different solvation conditions of explicit [18] or implicit solvent [27], were also used. Our study provided new insight on the GTP-to-GDP transition based on unbiased MD simulation in explicit solvent, which better mimics natural physiological conditions [29].

We note that only one of our three multi-copy simulations managed to reach the GDP-cluster of the Ras crystallographic ensemble within 20-ns. Comparing the residue-wise flexibility from this simulation to the other two sets, indicates that the GTP-to-GDP transition involves higher RMSF at the loop 2, loop 4, and α2 regions, as well as lower RMSF at the loop 3 region (Fig 8). Below we focus on this transitioning in order to obtain atomic descriptions of the conformational conversion process.

When the MD-derived conformers are projected onto the first two principal components (PC) obtained from analyzing the Ras crystallographic ensemble, the GDP-bound H-Ras A59G MD conformers sample the GDP cluster of crystallographic conformers (PC 1: 15 to 20, PC 2: −5 to 0) (Fig 9A). Over time, the H-Ras A59G MD conformers evolve to resemble the GDP-bound more than the GTP-bound H-Ras A59G crystal structure (Fig 9B). Although both the GTP-to-GDP or GDP-to-GTP conformational changes involve rearrangements of the canonical switch regions [26] and partial unfolding and re-folding of helix 2, in each case multiple pathways are possible [27]. In the simulation, in the first 4 ns switch 2 has slightly higher RMSD values than switch 1 (Fig 9C) but the relative RMSD of the switches remains stable until 11.2 ns. Following this, the switch 2 RMSD increases significantly before the switch 1 RMSD catches up surpassing the switch 2 RMSD at about 13.8 ns. After a decrease in RMSD (∼16–18ns), the switches evolve again as the N-terminal of α2 helix unwinds (Fig 10A, Video S1). The unwinding of the α2 helical turn (residues 66–69) was also reported in a previous biased MD study of GTP-to-GDP conformational transitions [18]. Interestingly, despite some differences in the sequence of events, these results are similar to those reported based on the computation of minimum energy paths (MEPs) [27].

The side chain of Y32 lies across the nucleotide binding pocket in GTP-bound conformations but is displaced away from the binding pocket in GDP-bound H-Ras A59G and wild-type H-Ras crystal structures [21], [26], [30]. After 11.5 ns of simulation, Y32 moves away from nucleotide and comes closer to Y64 from 14 ns onwards (Fig 10B). The role of Y32 was also highlighted in the Y32F mutant with dysfunctional GTP hydrolysis [31]. Preceding the unwinding of helix 2 in switch 2, the Q61 of switch 2 orientates away from the switch 1 (Fig 10C). However, no significant change was seen in the distance between G60 and nucleotide preceding the unwinding of α2 (Fig 10C) as reported in [18]. This is to be expected as we commenced simulation form the A59G crystal structure conformation in which its G60, a possible hinge [32], had already moved away from the nucleotide to occupy the space made available by the A59G substitution. Next, the Y71 and R68 of switch 2 form close contacts with E37 of switch 1, stabilizing the protein during the α2 unwinding. The unwinding of α2 re-orientates switch 2 and brings Y64 closer to E37 of switch 1 (Fig 10C).

The MD conformers at different time frames also indicated interesting differences in their torsional angles with respect to the GTP-analog-bound versus the GDP-bound H-Ras A59G crystal conformers (Fig S4). The torsional angle differences were emphasized by the residues of loop 2 and loop 4 form switch 1 and 2 regions respectively. These regions exhibit correlated motions (Fig S5) and enhanced flexibility (Fig 8B) highlighting their roles in binding nucleotide and facilitating the GTP-to-GDP transition.

Combining the current results with previous reports [15], [18], [23], [27] on the reaction paths for the transition between the active and inactive states of Ras, we arrive at the following conclusions. (i) Conformational changes accompanying GTP hydrolysis (GTP-to-GDP) and nucleotide exchange (GDP-to-GTP) involve common intermediates that are represented by the A59G structure; (ii) there is a barrier to reach this intermediate upon GTP hydrolysis, which is consistent with the 24.3 kcal/mol activation energy estimated by the minimum energy paths method for the GTP-to-GDP transition of wild-type H-Ras [27]; (iii) that an unbiased simulation of H-Ras A59G led to a transition from the GTP to the GDP state may suggest that this point mutation lowers the barrier between the intermediate and the GDP state; and (iv) once the large barrier between the GTP state and the H-Ras A59G-like intermediate is crossed, the remaining (multiple) barriers to the GDP-bound form can be crossed relatively easily. Finally, it is noteworthy that the PCA analysis enabled us to effectively cluster the diverse Ras crystal structures into two major clusters interspersed by intermediates that are predominantly populated by mutants. Some of these mutant structures are susceptible to nucleotide-associated transitions.

Oncogenic mutations may interfere with the intrinsic ability of Ras to hydrolyze GTP or lead to insensitivity to the action of GAPs. The loss or deregulation of intrinsic GTP hydrolysis seems to be sufficient for causing diseases [12], but GAP-insensitivity is still rescuable in some variants. For example, the H-Ras G12P and G12A variants are GAP-insensitive, but their intrinsic GTPase function and their ability to release GDP only modestly differ from those of wild-type [21], hence these mutants do not transform cells. The intrinsic GTP hydrolysis activity appears to be biologically sufficient to stop continuous downstream signaling [12], [33]. Therefore, structural changes that have the potential to affect the intrinsic GTPase function of Ras may also modulate its aberrant functions. Thus, the enhanced dynamics of K-Ras (and G59A H-ras) in functionally crucial regions may have an important implication for its normal and tumorigenic functions, which may partly explain the more frequent discovery of K-ras in cancer cells than any other Ras isoforms [34].

We speculate that the observed differences in dynamics may be related to the measured differences in the intrinsic GTPase activity of the three proteins. The intrinsic GTP hydrolysis rate of K-Ras (1.2×10⁻⁴ s⁻¹ [33]) is roughly half the rate of the wild-type H-Ras (2.7×10⁻⁴ s⁻¹ [24]) whereas that of H-Ras A59G (0.35×10⁻⁴ s⁻¹ [26]) about eight times smaller. This may suggest that in the absence of GAP, K-Ras and H-Ras A59G spend more time in the GTP-bound conformational state than the wild-type H-Ras. The enhanced dynamics of K-Ras and H-Ras A59G may make the GTP-bound state entropically favored. This is consistent with a previous MD simulation on H-Ras G12V which revealed that the continuously changing active site makes GTP hydrolysis difficult [35]; the resulting elevation in the population of GTP-bound conformations will then lead to increased signaling through this oncogenic variant. However, caution is required in interpreting the existing rate constants as the measured intrinsic GTP hydrolysis rate is dependent on the GTP concentration present in the assay [25]. We thus believe that the current data would be even more useful if used in conjunction with GTP hydrolysis rates measured under identical experimental conditions.

We have performed multiple unbiased MD simulation on wild-type K-Ras, H-Ras A59G and wild-type H-Ras. Results from these simulations support the observation that the active, GTP-bound wild-type K-Ras and H-Ras A59G variant are more dynamic than wild-type H-Ras. We observed spontaneous GTP-to-GDP transition during an unbiased MD simulation of H-Ras A59G. The approach of multivariate clustering of crystal structure conformations to reveal differences due to ligands and sequences highlights intermediate conformers, such as the H-Ras G12V [15] and A59G in this study, that facilitate faster sampling of large scale conformational transitions. We speculate that Ras variants which fall outside the major GTP- or GDP-clusters may be intrinsically more susceptible to transition than wild-type H-ras. Further systematic investigation of the structural and dynamic properties of Ras isoforms and mutants is likely to be informative for drug development, particularly drugs which selectively target distinct structural conformations associated with specific Ras isoforms or mutations. Structure based drug design efforts in this direction are currently underway.

The Bio3D package [36] was used to retrieve homologous structures to K-Ras (PDB: 2PMX) from the PDB, perform principal component analysis (PCA) and additional trajectory analysis as described in [15], [23]. Core positions were first obtained from analysis of the crystallographic ensemble. Iterated rounds of structural superposition were used to identify the most structurally invariant region of the Ras structure. This procedure, implemented in the Bio3D package, entailed excluding those residues with the largest positional differences, before each round of superposition, until only the invariant “core” residues remained [36], [37]. The structurally invariant core was used as the reference frame for structural alignment of both crystal and simulation structures. Next, the Cartesian coordinates of aligned Cα atoms were used to define the elements of a covariance matrix. The covariance matrix was then diagonalized to derive principal components with their associated variances. After PCA, Ras crystal structures and MD conformers were projected on the subspace defined by principal components with the largest variances.

Systems for molecular dynamics simulations were prepared from high-resolution crystal structures of wild-type K-Ras, wild-type H-Ras, and H-Ras A59G variant (PDB: 2PMX, 1QRA, and 1LF0 respectively). Each system was simulated with Mg²⁺GDP and Mg²⁺GTP. All simulations were performed with the AMBER 10 package [38]. The LEaP module was used for model construction, adding missing atoms to initial coordinates, and including parameters for guanine nucleotides [39] and Mg²⁺ ion. The protonation states for all titratable residues were determined using PDB2PQR [40]. The systems were neutralized using charge-neutralizing counter ions at pH 7, followed by explicit solvation with TIP3P water molecules with the buffering distance set to 10 Å. Energy minimization with decreasing constraints on the heavy atoms' positions, constant volume heating (to 300 K) was carried out for over 10 ps, followed by constant temperature (300 K) and constant pressure (1 atm) equilibration for additional 200 ps. The production simulation, using ff99SB force field [41], was conducted with time step of 2 fs, using the isobaric-isothermal ensemble at 300 K, 1 atm, and long-range non-bonded interactions with 10 Å atom-based cutoff. Electrostatic interactions were evaluated using the Particle-Mesh Ewald sum [42]. The SHAKE algorithm was used to constrain all covalent bonds involving hydrogen atoms. To enhance sampling and improve the statistical accuracy of the simulations, three independent MD simulations were performed on each system using different random initial velocities. Each simulation was performed for 20 ns resulting in 60 ns cumulative simulation time for each system.