Steric interactions lead to collective tilting motion in the ribosome during mRNA–tRNA translocation

Translocation of mRNA and tRNA through the ribosome is associated with large-scale rearrangements of the head domain in the 30S ribosomal subunit. To elucidate the relationship between 30S head dynamics and mRNA–tRNA displacement, we apply molecular dynamics simulations using an all-atom structure-based model. Here we provide a statistical analysis of 250 spontaneous transitions between the A/P–P/E and P/P–E/E ensembles. Consistent with structural studies, the ribosome samples a chimeric ap/P–pe/E intermediate, where the 30S head is rotated ∼18°. It then transiently populates a previously unreported intermediate ensemble, which is characterized by a ∼10° tilt of the head. To identify the origins of head tilting, we analyse 781 additional simulations in which specific steric features are perturbed. These calculations show that head tilting may be attributed to specific steric interactions between tRNA and the 30S subunit (PE loop and protein S13). Taken together, this study demonstrates how molecular structure can give rise to large-scale collective rearrangements.

SUPPLEMENTARY FIG. 2. Probability distribution as a function of the RMSD of EF-G relative to the post-bound conformation (RMSD EF-G ), calculated for the A/P-P/E, ap/P-pe/E, and P/P-E/E ensembles. The distribution for the ap/P-pe/E ensemble (red curve) is virtually identical to that of the P/P-E/E ensemble (black curve). This suggests that when the ribosome adopts the chimeric ap/P-pe/E configuration, EF-G is in a post-translocation-like conformation, where its domain IV is extended towards the A site of the 30S subunit. SUPPLEMENTARY FIG. 3. Probability distributions (a) P (R P-ASL , φ head ) and (b) P (R P-ASL , θ head ) calculated from unrestrained simulations. These data are the same as presented in Fig. 3a,b of the main text, but shown from the A/A-P/E ensemble. In the main text, where translocation on the 30S subunit was the focus, movement from the A/A-P/E to the A/P-P/E ensemble was considered as initial equilibration period and was not included in the analysis. To compare the unrestrained dynamics with targeted translocation events, we performed 100 TMD simulations. From these targeted simulations, the probability distributions (c) P (R P-ASL , φ head ) and (d) P (R P-ASL , θ head ) were also calculated, analogous to Panels a and b. These TMD results clearly show that even weak targeting forces can have a dramatic impact on the dynamics, relative to unrestrained simulations. Here, the presence of a TMD potential precludes spontaneous largescale fluctuations (e.g. large-scale rotation of the head), and prevents the formation of intermediate state ensembles.
SUPPLEMENTARY FIG. 4. Probability as a function of body rotation (φ body ) calculated for the A/P-P/E, ap/P-pe/E, and P/P-E/E ensembles. Peak values of φ body show that the average body rotation relaxes from ∼6 • to ∼2 • to ∼0 • during the transition between the A/P-P/E, ap/P-pe/E, and P/P-E/E ensembles. While the range of values for each ensemble may appear large, the distribution of values is consistent with the range of values observed in a 1.3 µs explicit-solvent simulation of an A/A-P/P ribosome [1].

SUPPLEMENTARY FIG. 5. (a)
To describe compaction between tRNA ASLs during translocation, we calculated the distance between the P atoms of A31 in the tRNAs: R A31 . As introduced earlier, R P-ASL represents the distance from the ASL of the P-tRNA to the E site of the 30S body. (b) P (R P-ASL , R A31 ) together withR A31 (R P-ASL ) (average compaction as a function of P-tRNA ASL position, shown by dashed line) reveal a large degree of ASL compaction in the ap/P-pe/E ensemble (R A31 ≈ 18-20Å). In contrast, in the A/A-P/E and P/P-E/E ensembles (i.e. the endpoints of the simulations) the average compaction is ∼30Å and ∼25Å. SUPPLEMENTARY FIG. 6. Rotation coordinates for the 30S head and 30S body. The same steps were followed to calculate the rotation coordinates for the 30S head and 30S body. The subscript "i" of the angle variables stands for either "head" or "body". Rotation angles are determined by comparing the reference vectors r and n of the model plane (blue) with the corresponding vectors r o and n o of the reference plane (black). Tilting occurs about the vector s = n o × n (red) according to the right-hand rule. The magnitude of tilt is θ i . The direction of tilt (i.e. the orientation of vector s) is described by χ i . Counterclockwise rotations along χ i and ψ i are defined as positive angles. 30S head/body rotation is defined as φ i = χ i + ψ i .  Supplementary Fig. 6. The reference vector r o (black) was defined such that it is parallel to the axis of the mRNA. Head tilt direction is described by χ head , which is the angle between the reference r o and the tilt axis vector s (red). Tilting about s (indicated by blue arrow) follows the right-hand rule (cf. Supplementary  Fig. 6).  Supplementary Fig. 6. The reference vector r o (black) was defined such that it aligns with the projection of h44 onto the n o −plane. The direction of body tilt is described by χ head , which is the angle between the reference r o and the tilt axis vector s (red). Tilting about vector s (indicated by blue arrow) follows the right-hand rule (cf. Supplementary Fig. 6).

SUPPLEMENTARY TABLE 1. Comparison of the simulated ap/P-pe/E ensemble with experimental data
Simulated ap/P-pe/E ens. Atomic coordinates of the T. Thermophilus 70S ribosome with three tRNA Phe molecules were taken from Jenner et al. [6] (PDB ID code 4V6F). This structure lacks protein L1 and elongation factor G (EF-G). Based on this structure, classical A/A-P/P and P/P-E/E configurations with the L1 protein and EF-G were prepared, as described in Ref. [7]. To alleviate any atomic conflicts, these two classical configurations were then refined by energy minimization in explicit solvent.
Energy minimization was performed with the Gromacs (v4.6.1) software package [8,9], using the AMBER99 forcefield [10] and SPC/E [11] water model. Each configuration was solvated in a triclinic box with a 10Å buffer on all sides. 100 mM of K + ions were added to the system. Cl − ions were then added such that the net charge of the system was neutral. Energy minimization was conducted in multiple stages, and each stage was carried out using the steepest descent algorithm: 1) Unrestrained energy minimization was run for 50,000 steps. This step alleviated unfavorable interactions within the ribosome and allowed solvent and ions to relax. 2) Energy minimization was performed using harmonic position restraints on backbone atoms with respect to the initial configuration. Harmonic restraints were applied with a force constant of 1 kJ mol −1Å−2 , and energy minimization was run for 20,000 steps. 3) Restrained energy minimization as described for step 2 was performed with an increased restraint force constant of 100 kJ mol −1Å−2 . During the restrained energy minimization stages 2 and 3, the solvent and ions were allowed to further relax without affecting the backbone structure of the initial configuration. Steps 1, 2, and 3 were repeated before performing final unrestrained energy minimization.

Preparation of the atomic structures used as initial configurations in the simulations
The A/A-P/E and ap/P-pe/E configurations with protein L1 and EF-G were prepared according to Whitford et al. [7]. In Ref. [7], the A/A-P/E and ap/P-pe/E configurations are referred to as TI pre and TI post . These configurations were also refined by energy minimization in explicit solvent, using the same protocol as described above.
The refined A/A-P/E structure was used as the initial configuration for the full translocation simulations (Figs. 2-4 of the main text). The refined ap/P-pe/E structure was used as the initial configuration for the simulations with the modified forcefields where sterics of the PE-loop and/or protein S13 were removed (Fig. 5 of the main text).

Structure-based (SMOG) model
To simulate translocation, we used an all-atom multi-basin structure-based (SMOG) model [12]. All heavy (non-hydrogen) atoms (154,723) are explicitly represented as spherical beads of unit mass. In a single-basin SMOG model, an experimentally-derived structure is defined as the potential energy minimum, and the functional form of the potential is given by: where N is the number of atoms. Contact interactions were described by the 6-12 potential, and contacts were assigned based on the Shadow Contact Map algorithm [13].

Construction of the Multi-basin SMOG model
Single-basin models based on the A/A-P/P and P/P-E/E configurations were generated using the smog-server webtool (http://smog-server.org) [14]. All stabilizing interactions that are found in the P/P-E/E model (which includes EF-G) were included. Additionally, intermolecular contacts between the ribosome and mRNA-tRNA formed in the A/A-P/P model were added as stabilizing interactions. The strength of the contacts between the ribosome and mRNA-tRNA were rescaled by 0.3, to account for transient nature of mRNA-tRNA binding, relative to the lifetime of the ribosome. This construction defines the A/P-P/P and P/P-E/E configurations as dominant minima on the potential energy surface, and allows mRNA-tRNA to move between binding sites.
Interface contacts between the 30S and 50S subunits, and between the 30S head and body were weakened, to account for the fact that intra-and intersubunit rotations continuously occur in solution. With respect to the 30S-50S interface, the center of the interface was defined as the geometric center of the atoms involved in intersubunit contacts. The strength of intersubunit contacts within a radius of 20Å from the center was then rescaled by a factor of 0.3. And the strength of intersubunit contacts outside the radius was rescaled by 0.1. Defining weaker contacts on the outside is consistent with biochemical probing data suggesting that intersubunit bridges at the periphery of the interface are more flexible than bridges that are closer to the center [15]. Finally, to account for head movements, the strength of the intrasubunit contacts between the head and body were rescaled by 0.3. Here, the head domain is defined as residues C930 to C1388 in the 16S rRNA and proteins S3, S7, S9, S10, S13, S14, and S19.
Since EF-G transiently associates with the ribosome during the elongation cycle, the strength of the contacts between EF-G and the ribosome was rescaled. In preliminary simulations, the scaling factor was given values of 0.1, 0.2, 0.3, . . . , or 1.0. For production simulations, a factor of 0.6 was used since it was found to be sufficiently strong that EF-G would not prematurely dissociate from the ribosome during translocation. Further, all stabilizing interactions between domain IV of EF-G and ribosome-mRNA-tRNA were removed, so that domain IV only sterically interacts with the assembly.
It is instructive to note that the relative stability of the A/A-P/P and P/P-E/E conformations is determined by the differences in the number of attractive tRNA interactions with the A, P and E sites, as well as the presence of EF-G. In this model, the stabilizing energy is directly proportional to the number of tRNA-ribosome contacts found in the A/A-P/P and P/P-E/E crystal structures.
Due to the presence of interactions between the E/E-tRNA and the L1 stalk, there are more tRNAribosome contacts when a tRNA is in the E/E conformation, than in the A/A conformation. This leads to a net difference of approximately 10 units of energy (reduced units) between the A/A-P/P and P/P-E/E conformations. This difference in stability is relatively small compared to the scale of fluctuation in the potential energy of each tRNA, which is approximately 20 units of energy. Thus, the character of the dynamics is largely determined by thermal fluctuations, which is consistent with the notion of the ribosome acting as a Brownian ratchet machine. The second factor that can affect the relative stability of the endpoints is the presence of EF-G. As shown in Supplementary   Fig. 2, EF-G adopts a post-translocation-like conformation in the ap/P-pe/E ensemble (as also seen in cryo-EM reconstructions and crystal structures [2][3][4][5]). Hence, EF-G can influcence the relative stability towards the P/P-E/E ensemble by preventing tRNA reverse movement.

Variations of the multi-basin SMOG model
The following variations to the multi-basin model were introduced, to test the relative role of protein S13 and the PE-loop (G1338-U1341) during translocation (data shown in To exclude steric interactions between S13/PE-loop and tRNA, the repulsive 1 r 12 non-contact terms in Eq. (1) were not included between S13 and A-tRNA (Model 2), between PE-loop and P-tRNA (Model 3), or between S13, PE-loop and tRNA (Model 4).

Targeted molecular dynamics (TMD) description: Harmonic implementation
All translocation data presented in the main text were obtained from unrestrained simulations.
To compare and contrast those spontaneous, unrestrained translocation events with restrained, targeted dynamics, we performed 100 TMD simulations of the transition from the A/A-P/E to the P/P-E/E configuration (see results in Supplementary Fig. 3). That is, in addition to the multi-basin structure-based model described above (referred to as Model 1), which provides an underlying energy landscape, TMD simulations include an additional time-dependent potential that biases the simulation towards the endpoint P/P-E/E configuration. Here, the TMD potential is of the harmonic where RMSD(t) is the weighted root-mean-square deviation, In the equation above, N is the number of atoms, r k (t) denotes the position of atom k at time t, and r k, target represents the target location of that atom. The values of w k were set such that w k = 1 if the distance between the initial and the final (target) position of the k-atom, R f-i k , is below the threshold R thr = 20Å, and w k = R thr Note that the force on individual atoms is proportional to the distance from the target. By introducing a threshold distance, above which the weights are reduced, we ensure that atoms undergoing larger rearrangements will not be subject to much larger forces. Finally, D(t) is a linear function in time, which descreases from RMSD initial (i.e. RMSD between the A/A-P/E and P/P-E/E configurations) to zero, over a prescribed time interval τ , and remains zero for the rest of the simulation. That is, D(t) is given by

TMD simulation details
Each TMD simulation was initiated at the A/A-P/E configuration, where the coordinates of the P/P-E/E configuration were used as the target. All atoms (154,723) were included in the RMSD calculation, and RMSD initial = 6.6Å. Reduced units were used for all calculations. Each simulation was performed for 3.5 × 10 5 time steps of size 0.002. The effective timescale of each simulation may be estimated as microseconds. See Ref. [16] and the supplementary material of Ref. [17] for detailed discussion on timescale estimates in SMOG models. The same reduced temperature of 0.5 was used as for the unrestrained simulations described in the main text. D(t) was linearly reduced in time according to Eq. (4) for 2.5 × 10 5 time steps. The energetic weight TMD of the TMD potential in Eq. (2) was set to 2000 (where = 1). Note that the value of TMD used here is only 10% of that in previous TMD simulations of tRNA hybrid state formation [18].

Details of the reaction coordinates
VMD scripts that calculate all rotation angles are available on the Whitford Research Group webpage.
Reaction coordinates for the tRNAs Three coordinates were defined to measure the movement of the P-and A-site tRNAs. R P-ASL and R A-ASL describe the movement of the ASLs of the P-and A-site tRNAs relative to the 30S body.
They are the distances of the tRNAs to their positions when in the E/E and P/P sites. Similarly, R A-ELB describes the movement of the elbow of the A-site tRNA relative to the 50S subunit, or the distance of the A-tRNA elbow to its location when in the P/P position.
To calculate the elbow coordinate R A-ELB for a given trajectory frame, the 23S of the simulated structure was aligned to the reference P/P-E/E structure. R A-ELB was then defined as the distance of the U60:P atom in the A-tRNA to its location in the reference P/P-E/E structure.
The ASL coordinates R P-ASL and R A-ASL were determined after 16S-body alignment of the simulated structure to the P/P-E/E structure. R P-ASL (or R A-ASL ) was then defined as the distance of the A36:P atom in the P-tRNA (or A-tRNA) to its location in the reference P/P-E/E structure.
The 23S and 16S-body alignments were performed using the core residues in the respective domains, as described elsewhere [1].

Reaction coordinates for the 30S head
To describe the motions of the 30S head, we first defined a reference plane that represents the classical orientation of the head (Supplementary Fig. 6). This plane is fixed by three atoms within the head of the classical A/A-P/P configuration, which are A977:P, C1298:O2P, and A1374:P. Us- reference vectors. Note that the three atoms mentioned above were chosen such that the resulting reference plane (fixed by n o ) is consistent with the plane defined for head rotation in Ref. [1].
To calculate rotation angles of the head for a given structure, we employ the following protocol, which is an extension of the method reported in Ref. [1]: 1. The core residues of the 16S body are used to align the structural model to the reference A/A-P/P structure.
2. The core residues of the 16S head are used to align the head of the A/A-P/P reference to the rotated head of the model structure. 5. Calculate rotation angle φ head : head rotation is defined as φ head = χ head + ψ head . As shown in Supplementary Fig. 6, χ head is the angle between r o and s, and ψ head is the angle between s and r. Counterclockwise rotations along χ head and ψ head are defined as positive angles.
6. Calculate tilt angles: the magnitude of head tilt is denoted by θ head which is simply the angle between n o and n. Tilting occurs about the axis vector s and follows the right-hand rule. The orientation of s, which is the direction of head tilt, is described by the angle χ head .
Note that the alignment performed in step 2) provides an average orientation of the head, or "idealized" coordinates, as described in Ref. [1]. Using the idealized coordinates of the aligned (i.e. rotated) reference head structure, we ensure that collective movement of the 30S head is measured, and not individual atomic fluctuations.
To define a reference direction corresponding to the tilt direction angle χ head = 0, the reference vector r o was rotated in the n o −plane by a constant angle α = −35 • (clockwise rotation as viewed from the top of the head) such that r o points towards the 30S A site and aligns with the axis of the mRNA between the A-and P-site codons (axis between the P atoms of U48 and U45 in the mRNA in the A/A-P/P structure). With these definitions, χ head = 0 corresponds to tilting around the mRNA axis, where the head moves away from the 30S-50S interface (see Supplementary Fig. 7 for a schematic illustration of head tilt direction).
In simulation, the model structure, for which rotation angles are calculated, corresponds to a given frame of the trajectory. We used the trjconv module of Gromacs to align each simulated frame to the reference (same reference as used in step 1), based on the 16S-body-core residues.
Next, the coordinates of the 30S head were idealized through 16S-head-core alignment (step 2).
Using the idealized coordinates of each frame, the vectors and angles were calculated for each frame with Gromacs modules and in-house scripts.
Previously in Ref. [1], head rotation was calculated by projecting the rotated reference vector r onto the reference n o -plane. Let this projection be r , then head rotation was defined as the angle between r o and r . That protocol can lead to false detection of rotation angles when tilting is present. Consider, for example, the case where only tilting occurs and no rotation is present.
Further, let this tilting be about an axis vector s that does not align with the reference r o (i.e. when χ head = 0). In such case, the projection r and the reference r o can form nonzero rotation angles, even in the absence of any rotation. In the tilt-only case, it is χ head = −ψ head , and according to our rotation definition here: φ head = χ head + ψ head = 0 (step 5). That is, using an Euler-angle based set of coordinates eliminates the ocurrance of artificial rotation angle values. As a point of comparison with other coordinate definitions, it is worth noting that when there is no tilting, φ head will yield identical values to the Euler-Rodrigues angle employed by Mohan, Donohue and Noller [19]. While the values of the two coordinates are quantitatively similar, we chose to use Euler angles directly as they allow for tilting to be separately described.

Reaction coordinates for the 30S body
The rotation coordinates for the 30S body: φ body , θ body , and χ body were defined and calculated following the same strategy as for the 30S head. For completeness we will provide all the details explicitly. In this study, with respect to the motions of the body, we observe a signal for body rotation ( Supplementary Fig. 4) during translocation, but not for body tilting (also known as "subunit rolling" in the context of the 80S ribosome [20]). That is, here, the average tilt angle of the body (θ body ) is only 1.4 • .
To calculate the body rotation angles, a plane that represents the classical orientation of the body was defined (Supplementary Fig. 6). This reference plane is fixed by three atoms within the body of the classical A/A-P/P structure. These atoms are C237:P, C811:P, and G1488:O6.
Using the same vector notation as for the head case above, vectors between atom pairs were set as To calculate rotation angles of the body for a given model structure, we employed the following protocol: rotated) reference body structure, we ensure that collective movement of the body domain is measured, and not individual atomic fluctuations.
As explained above for 30S head rotation, the rotation definition in step 5) ensures that tilt movements do not lead to false detection of rotations.
The reference vector r o was chosen, such that it points towards the head and aligns with the axis of h44. That is, χ body = 0 corresponds to tilting roughly around the h44 axis, where the beak of the 30S is displaced towards the 30S-50S interface (see Supplementary Fig. 8 for a schematic illustration of head tilt direction).
In simulation, the model structure, for which rotation angles are calculated, corresponds to a given frame of the trajectory. We used the trjconv module of Gromacs to align each simulated frame to the A/A-P/P reference, based on the 23S-core residues (step 1). Next, the coordinates of the 30S body were idealized through 16S-body-core alignment (step 2). Using the idealized coordinates of each frame, the vectors and angles were calculated for each frame.