Capturing Transition States for tRNA Hybrid-State Formation in the

Aug 1, 2016 - How the Ribosomal A-Site Finger Can Lead to tRNA Species-Dependent Dynamics. Kien Nguyen , Huan Yang , and Paul C. Whitford. The Journal...
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Capturing Transition States for tRNA Hybrid-State Formation in the Ribosome Kien Nguyen and Paul C. Whitford* Department of Physics, Northeastern University, Dana Research Center 123, 360 Huntington Avenue, Boston, Massachusetts 02115, United States S Supporting Information *

ABSTRACT: In order to quantitatively describe the energetics of biomolecular rearrangements, it is necessary to identify reaction coordinates that accurately capture the relevant transition events. Here, we perform simulations of A-site tRNA movement (∼20 Å) during hybrid-state formation in the ribosome and quantify the ability of interatomic distances to capture the transition state ensemble. Numerous coordinates are found to be accurate indicators of the transition state, allowing tRNA rearrangements to be described as diffusion across a one-dimensional free-energy surface. In addition to providing insights into the physicalchemical relationship between biomolecular structure and dynamics, these results can help enable single-molecule techniques to probe the free-energy landscape of the ribosome.

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INTRODUCTION Biological dynamics are often described in terms of diffusion on a free-energy surface1−3 where the rate of interconversion between conformational states is determined by the height of the intervening barrier. When applying this framework, one must know which reaction coordinates unambiguously identify the endpoint/intermediate states and transition state ensembles. In the context of protein folding and function, a wide range of experimental4,5 and theoretical6−13 studies have established techniques for analyzing biomolecular energetics. These approaches provide strategies for evaluating the quality of reaction coordinates14−20 and quantifying energetics from single-molecule data.21−24 In this study, we utilize this rich body of energy landscape principles in order to identify accurate reaction coordinates for describing tRNA hybrid-state formation in the ribosome. The ribosome is a massive molecular machine responsible for the translation of mRNA sequences into proteins.25−30 The bacterial 70S ribosome is composed of a large (50S) and a small (30S) subunit (Figure 1a). Together, the assembly contains three large RNA molecules and over 50 proteins. During the synthesis of a polypeptide chain, tRNA molecules deliver amino acids to the ribosome. There are three bindings sites (the A, P, and E sites) in the ribosome to which the tRNAs sequentially bind during peptide chain elongation. At the beginning of each cycle of elongation, an aminoacyl-tRNA (aa-tRNA) molecule binds the ribosomal A site (i.e., initial selection and accommodation). Following aa-tRNA accommodation, the nascent chain is transferred from the peptidyl-tRNA (in the P site) to the aa-tRNA (in the A site), resulting in extension of the chain by one amino acid. After peptide bond formation, the © XXXX American Chemical Society

A- and P-site tRNAs (along with the associated mRNA) translocate to the adjacent P and E sites in order to vacate the A site for the next incoming aa-tRNA. Translocation of tRNA and mRNA is described in terms of two general steps.25,29,31,32 In the first step, the tRNAs move relative to the large subunit from their classical A/A and P/P conformations into hybrid A/P and P/E conformations (Figure 1b,c). In this hybrid state, the acceptor stems of the A- and Psite tRNAs contact the P and E sites of the large subunit, while their anticodon stem loops (ASLs) remain bound to the A and P sites of the small subunit. During the second step of translocation, the mRNA and ASLs of the tRNAs move relative to the small subunit, allowing the tRNAs to adopt classical P/P and E/E conformations. While hybrid-state formation can occur spontaneously,33−36 mRNA-tRNA movement on the small subunit is facilitated by elongation factor G (EF-G).30 In this study, we use energy landscape principles and molecular simulations to quantitatively probe the dynamics of A/P hybrid-state formation, where the A-site tRNA moves between A/A (Figure 1b) and A/P (Figure 1c) conformations. Consistent with cryo-EM and kinetic modeling,37 singlemolecule (smFRET) experiments have provided evidence that the A-site tRNA undergoes reversible fluctuations between classical and hybrid conformations.38,39 While these studies have helped elucidate the overall sequence of tRNA rearrangements, it remains unclear how accurately interatomic distances can measure barrier crossing events. To address this question, Received: May 3, 2016 Revised: August 1, 2016

A

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analyzing the dynamics projected along each. Through this analysis, we identify numerous coordinates that may be used in experiments or simulations to more precisely characterize the energetics of A/P hybrid-state formation in the ribosome.

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METHODS To simulate A-site tRNA movement, we used an all-atom structure-based (SMOG) model42 of the entire 70S ribosome with bound mRNA and tRNAPhe molecules. In structure-based models, the lowest potential energy configuration of the system is predefined by a specific structure. Here, we used an atomic model of the ribosome with the tRNAs in A/A and P/E conformations43 to define the potential energy function. In the simulations with this energetic model, the A-site tRNA can spontaneously adopt classical A/A or hybrid A/P conformations (Figure 1d). Since the focus of the current investigation is to describe A-site tRNA movement, stabilizing interactions were defined such that the P-site tRNA remains in the P/E conformation throughout the simulation. Similarly, by defining the A/A-P/E configured ribosome as the global potential energy minimum, the 30S and 50S subunits maintain an intersubunit rotation of ∼6° (rotation angle defined elsewhere44). This overall energetic representation was used in order to mimic an ideal experiment in which there would be isolated movement of the A-site tRNA between classical and hybrid conformations. By studying this idealized system, one may establish a baseline understanding of how to describe Asite tRNA dynamics, which may be subsequently extended to account for more complex motions. As discussed below, we find that the analysis of reaction coordinates is robust to the precise details of tRNA-ribosome interactions, including different configurations of the 3′-CCA end of the A-site tRNA. Force Field. To construct a potential energy function, we first generated an all-atom structure-based model for an A/A-P/ E configured ribosome.43 As a technical note, prior to generating the structure-based model, the A/A-P/E configuration was energy minimized in explicit solvent; see the SI for details. In the current force field, the classical A/A conformation of the A-site tRNA is defined as the global potential energy minimum. Since tRNA binding to the ribosome is transient relative to the lifetime of the fully formed assembly, multiple variants of the model were considered in which tRNA-50S interactions were modified. Specifically, stabilizing interactions between the A-site tRNA and the 50S subunit were either removed (Model 1; see below) or reduced in strength (Models 2 and 3). We find that these variants of the model lead to reversible fluctuations of the A-site tRNA between endpoints (15−20 Å), consistent with observations from single-molecule experiments.38,39 In the structure-based force fields employed, each nonhydrogen atom is explicitly represented as a bead of unit mass. Backbone geometry is preserved through harmonic interactions, which maintain bond lengths, bond angles, and improper/planar dihedral angles. Flexible dihedral angles are described by cosine interaction terms. Nonbonded atom pairs that are in contact in the A/A-P/E configuration are given 6-12 interactions, where the minima correspond to the distances found in the A/A-P/E configuration. Contacts were defined according to the Shadow Contact Map algorithm,45 with a cutoff distance of 6 Å, shadowing radius of 1 Å, and residue sequence separations of 3 for proteins and 1 for RNA. All atom pairs not identified as being in contact in the A/A-P/E

Figure 1. Simulating tRNA hybrid-state formation. (a) Structure of the 70S ribosome with P/E (red) and A/A (yellow) tRNA molecules. The 23S and 5S rRNA are shown in white and the 50S proteins are in ice blue. The 16S rRNA and 30S proteins are in cyan and dark blue. (b, c) Close-up perspective of the A-site tRNA in A/A (b) and A/P conformations (c). Interatomic distances (Ri,j) between the tRNAs were used as reaction coordinates to describe A-site tRNA movement. Several representative coordinates R8,j are shown in panel b, each involving the P-tRNA residue at position 8 and A-tRNA residue j. (d) Time trace (one-third of the total simulated time) of R8,18 shows two distinct ensembles: A/A and A/P. (e) Same as in panel d, shown for a shorter time scale. The endpoint values of the coordinate (RA/A 8,18 and RA/P 8,18) are indicated by dashed lines. Transition paths/events as detected with R8,18 are highlighted in red. All structural representations were generated using VMD.71

we analyze simulations in which reversible A/A-to-A/P transitions occur (Figure 1d) and determine which interatomic distances (i.e., putative reaction coordinates) can accurately capture transition events and the associated transition state ensemble (TSE). There are numerous quantitative measures available for determining the quality of a reaction coordinate. When a poor choice of coordinate is used, the projected dynamics may exhibit subdiffusive behavior with artificial memory effects. In contrast, when an appropriate coordinate is used, the projected dynamics is expected to be diffusive.18 This diffusive character implies that when the system reaches the TSE there will be equal probabilities of reaching the product or reactant state. In other words, for a configuration x that is in the TSE, the conditional probability P(TP|x) of being on a transition path (TP) will reach a maximum value of 0.5.14,15 Further, if ρ = ρ(x) is an appropriate coordinate, then P(TP|ρ) will have a single peak of 0.5 that collapses the TSE onto a single value of ρ. Accordingly, P(TP|ρ) can serve as a measure for the quality of a reaction coordinate.40,41 To establish a framework for describing the energy landscape of A/P hybrid-state formation, we systematically evaluate reaction coordinates that may be monitored in single-molecule experiments. To this end, we perform molecular dynamics (MD) simulations of the entire 70S ribosome using a structurebased model42 and observe 138 spontaneous transitions between A/A and A/P tRNA conformations (Figure 1d). We then compare the performance of 1369 different coordinates by B

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Simulation Details. Molecular dynamics simulations were performed using the Gromacs (version 4.6.1) software package.50,51 Force field files for Gromacs were generated by the SMOG web server (smog-server.org).46 Reduced units were employed for all calculations, and a time step of 0.002 was used. Langevin dynamics protocols were applied to maintain a constant temperature of 0.5. The scale of structural fluctuations at this temperature is consistent with those obtained using an explicit-solvent model at 300 K52 and those derived from crystallographic B-factors.53 Two simulations were performed for each model, where model parameters remained fixed throughout each simulation. The trajectories with Model 1 included 1.2 × 109 time steps (138 barrier crossing events). Simulations with Model 2 were performed for an aggregate of 9.6 × 108 time steps (102 barrier crossing events). Simulations with Model 3 were performed for an aggregate of 9.6 × 108 time steps (88 barrier crossing events). Coordinates were saved every 600 time steps. According to the time scale correction factor reported by Kouza et al.,54 the total effective simulated time for each model is on the order of several milliseconds.

configuration interact through a repulsive term. The potential energy function is V=

∑

ϵr(r − ro)2 +

bonds

∑

+

∑

ϵθ (θ − θo)2

angles

ϵχ (χ − χo )2

impropers/planar

+

∑

∑

ϵbbF(ϕ) +

backbone dihedrals

ϵscF(ϕ)

side chain dihedrals

⎡⎛ ⎞12 ⎛ σij ⎞6 ⎤ σij ⎢ ⎜ ⎟ + ∑ ϵc⎢⎜ ⎟ − 2⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ contacts ⎣⎝ ij ⎠

⎛ σ ⎞12 ∑ ϵnc⎜⎜ nc ⎟⎟ ⎝ rij ⎠ noncontacts (1)

where F(ϕ) = [1 − cos(ϕ − ϕo)] +

1 [1 − cos(3(ϕ − ϕo))] 2

■

(2)

RESULTS AND DISCUSSION To evaluate which reaction coordinates can most accurately capture transition events associated with hybrid-state formation of the A-site tRNA, we analyzed simulations of the ribosome that include 138 reversible transitions between A/A and A/P tRNA conformations (Figure 1). The simulations were performed using an all-atom structure-based model of the full ribosome, where the global potential energy minimum of the Asite tRNA corresponds to the classical A/A conformation. This energetic description implicitly accounts for the effects of electrostatics and solvation in that the modeled stabilizing interactions describe the cumulative effect of all interactions that stabilize the A/A conformation. Since this model does not include nonspecific attractive interactions (i.e., interactions not found in the A/A conformation), the primary contributors to the simulated dynamics are steric effects and molecular flexibility. While in the current simulations the global potential energy minimum is defined a priori, steric and entropic contributions can lead to a more complex free-energy landscape. For example, simulations of mRNA-tRNA translocation44 have shown that structural effects can give rise to free-energy barriers, even in the absence of nonspecific energetic roughness. This is similar to studies of protein folding, where models that lack roughness also predict significant free-energy barriers.55 With regard to molecular flexibility, by defining a single conformation as the potential energy minimum, our model provides a description that is consistent with the notion of tRNA acting as a (nonlinear) spring,56 where strain energy57 is accumulated and released throughout the elongation process. As described below, we find that the contributions of sterics and flexibility give rise to approximately two-state dynamics for this transition (Figure 1d,e). Using the simulated trajectories, we assess the ability of 1369 different coordinates (Figure S1) to identify hybrid-state formation events. Each coordinate Ri,j is defined as the distance between the O3′ atoms in residue i of the P-tRNA and residue j of the A-tRNA (see Figure 1b and Figure S1). Since it is possible, in principle, to monitor these distances experimentally, this analysis provides a theoretical foundation that can help guide the development of new single-molecule measurements. Here, we use the following criteria to determine whether

and {ro}, {θo}, {χo}, {ϕo}, and {σi,j} were given the values found in the A/A-P/E configuration. Setting the energy scale ϵ = 1, the coefficients were assigned uniform values as follows: ϵr = 50ϵ/Å2, ϵθ = 40ϵ/rad2, ϵχ = 20ϵ/rad2, ϵnc = 0.1ϵ, and σnc = 2.5 Å. To set the dihedral weights, we first determined the number of dihedral angles (ND) that have a common middle bond. For example, in a protein backbone, there may be up to four dihedrals passing through the same C−Cα bond. The energy of each dihedral associated with a bond was then scaled by 1/ND. Consistent with previous implementations of these models,42,46 the dihedral and contact energies were distributed according to ϵbb = 2 for proteins (1 for RNA) ϵsc ∑ ϵc =2 ∑ ϵbb + ∑ ϵsc

∑ ϵc + ∑ ϵbb + ∑ ϵsc = N ϵ where N is the number of atoms. In this paper, we focus the discussion on the results obtained using a model (denoted by Model 1) in which all stabilizing contacts between the A-site tRNA acceptor-stem and the 50S subunit were removed. Since biochemical47 and structural48,49 studies have shown that C75 in the 3′-CCA end of A-site tRNA forms base pair with G2553 in the A loop of 23S rRNA, C75G2553 base-pairing interactions were introduced as harmonic restraints. This mimics the effect of the tRNA being tethered to a polypeptide chain that is extended into the nascent peptide tunnel. To test for robustness of the results, two additional models (Models 2 and 3) were considered. In these alternative models, variations were introduced in the interactions between the Asite tRNA acceptor-stem and the 50S subunit, and different base-pairing configurations of the 3′-CCA end were tested. See the SI for a detailed description of Models 2 and 3. Reversible fluctuations between A/A and A/P conformations were observed with all three models, and the coordinate analysis yielded consistent results. Given that the results were robust to the energetic details, the remaining discussion describes the results obtained with Model 1. C

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improves, artifacts from the use of suboptimal reaction coordinates are expected to become more pronounced. Capturing the Transition State Ensemble. Another aspect of a good reaction coordinate is that it can uniquely identify the transition state ensemble (TSE). To measure how precisely a given coordinate ρ captures the TSE, one may calculate P(TP|ρ), the conditional probability of being on a transition path (TP), as a function of ρ.14,15 Provided that ρ is an appropriate choice, then in the limit of overdamped dynamics P(TP|ρ) may be expressed as

a given interatomic distance is suitable for characterizing the dynamics: (1) the correct number of transition events is detected by the coordinate (i.e., no false positives); (2) the identified TSE represents configurations that are maximally reactive (i.e., most likely to be associated with a transition); and (3) the dynamics is diffusive along the coordinate. We also show that if these criteria are satisfied then the kinetics of barrier crossing can be described as diffusion on a onedimensional free-energy surface. Detecting Transition Events. One criterion for a good reaction coordinate is that the projected dynamics should minimize the number of detected transitions. As seen in the context of aa-tRNA accommodation,58 when a poor choice of coordinate is employed, fluctuations about a free-energy minimum can lead to the detection of false positives. To count the number of transition events, endpoint values for each A/P coordinate (RA/A i,j and Ri,j ) were first calculated using reference configurations for the A/A and A/P states (see the SI for technical details). Transition events/paths were then defined as and trajectory segments for which Ri,j(t) evolves from RA/A i,j A/A reaches RA/P i,j without recrossing Ri,j and vice versa (Figure 1e). Since the objective here is to identify reaction coordinates that have the potential to be monitored in single-molecule measurements, we only considered coordinates for which the separation between the A/A and A/P endpoints is at least 10 Å A/P (i.e., |RA/A i,j −Ri,j | ≥ 10 Å). That is, for a coordinate to be of immediate practical use, there should be an appreciable change in FRET signal associated with the rearrangement, which typically requires a change of ∼10 Å. Out of the 1369 coordinates considered, 872 satisfy this condition. For all further analysis, we evaluate the statistical properties of the dynamics as described by these 872 coordinates. Depending on the choice of coordinate, the number of identified transitions NT ranges from 138 to 364. The minimum number of events (NT = 138) was detected by 200 coordinates (listed in Table S1). Further, all 138 transition events were common to those 200 coordinates. The consistent detection of these transitions provides evidence that 138 is the correct number of simulated barrier-crossing events. Accordingly, apparent transitions that are not common to these 138 were defined as false positives. Similar to the analysis of coordinates for aa-tRNA accommodation,58 we find that the distance between U8 and U47 (R8,47), which is commonly used in single-molecule experiments,34,38 slightly overestimates the number of transitions (NT = 144). While this may raise some questions about the interpretation of earlier experiments, it is important to note that the inherent time averaging in FRET measurements can reduce the number of false positives. To address the extent to which time averaging influences the detection of transition events, we repeated the analysis using time-averaged coordinates R̅ i,j(t). That is, each distance Ri,j(t) was averaged over 2M sampled frames (M = 1, 2, ..., 10), and the number of transitions was evaluated for each time-averaging interval. For M ≥ 7, no false positives were detected with any coordinates (Figure S2). With regard to R8,47, we find that no false positives were detected when M = 1, which roughly corresponds to a time-averaging interval of 10−100 ns.54 This suggests that current single-molecule experiments are unlikely to report false positives due to the use of U8-U47 labeling, since the experimental signals are typically averaged over significantly longer time scales. However, as the time resolution of smFRET

P(TP|ρ) = 2ϕA (ρ)ϕB(ρ)

(3)

where ϕA(ρ) is the probability of reaching state A before state B. Similarly, ϕB(ρ) is the probability of reaching state B before state A, where ϕB(ρ) = 1 − ϕA(ρ). Accordingly, P(TP|ρ) will reach a maximum value of 0.5 at the TSE, where ϕA(ρ) = ϕB(ρ) = 0.5. In contrast, for a poor choice of coordinate, the projected dynamics may have memory effects (i.e., non-Markovian and subdiffusive dynamics), in which case P(TP|ρ) will reach values less than 0.5. To assess the extent to which interatomic distances can identify the TSE, we evaluated P(TP|Ri,j) for each coordinate. We find that the maximum value of P(TP|Ri,j), max{P(TP|Ri,j)}, ranges from 0.17 to 0.5 (Figure S3). For the 200 coordinates that minimize the number of transitions, this range is more narrowly distributed about larger values, with max{P(TP|Ri,j)} = 0.35−0.5 (see Figure S3 and Table S1). Out of these 200 coordinates, there are 36 for which max{P(TP|Ri,j)} = 0.5. Interestingly, coordinates with such high maxima only involve A-tRNA residues (j) at positions 17, 18, or 58. In contrast, there are more P-tRNA residues (i = 7−9, 16−21, and 45−62) associated with those same coordinates. This shows that measurements of dynamics will depend more strongly on the choice of A-tRNA residue than P-tRNA residue, which is intuitive, since this rearrangement is associated with A-site tRNA movement. To illustrate the dependence of P(TP|Ri,j) on the choice of coordinate, it is instructive to compare a few examples. Figure 2 shows P(TP|R8,j) for several distances involving residue 8 of the P-tRNA and different residues of the A-tRNA. We find that

Figure 2. Probability of being on a transition path P(TP|Ri,j) indicates whether a coordinate Ri,j can capture the transition state ensemble (TSE). For an accurate coordinate, P(TP|Ri,j) will reach a maximum value of 0.5 at the TSE. P(TP|R8,j) is shown for the representative coordinates depicted in Figure 1b. These probabilities illustrate that different coordinates identify the TSE with different degrees of accuracy. R8,18 is a good indicator of the TSE, where P(TP|R8,18) = 0.5 (black). In contrast, the coordinate commonly used in smFRET studies (R8,47) identifies the TSE less accurately, with max{P(TP| R8,47)} = 0.37 (orange). D

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The Journal of Physical Chemistry B R8,47 (the coordinate used in current smFRET experiments) is a less accurate indicator of when the A-site tRNA is on a transition path, as suggested by the lower value of max{P(TP| R8,47)} = 0.37. Note that while R8,47 does not provide precise information about the TSE, this coordinate correctly identifies the number of transitions (when accounting for the effect of time averaging, see above), making it a useful metric for discerning between the endpoints. In contrast, R8,18 is an example of an accurate indicator of the TSE, where max{P(TP| R8,18)} = 0.5 and NT = 138. For all further discussion, we use R8,18 as a representative high-performing coordinate, though 36 coordinates describe the dynamics equally well. For a complete list of coordinates with performance metrics, see Table S1. Together, these results suggest that single-molecule experiments can more precisely characterize transition events through the implementation of alternate labeling sites. The presented transition path analysis provides a comparison of the dynamics projected along coordinates that measure atomic-scale motions. This highly detailed description exceeds the spatial and temporal resolution of current single-molecule techniques. There are multiple factors that can contribute to experimental uncertainties, such as time averaging effects and the relatively large size of fluorescent dyes. In addition, anisotropic fluctuations of the dyes59 and photon-counting noise60,61 also impact the analysis of single-molecule data. However, as these effects become better understood, our results will provide strategies for experiments to more precisely measure ribosome energetics. Distinguishing between Diffusive and Subdiffusive Dynamics. When a trajectory is projected onto a good reaction coordinate, the dynamics should be diffusive around the TSE, whereas the dynamics along a poor coordinate may be subdiffusive. To probe the diffusive behavior of the projected dynamics, we calculated the mean squared displacement (MSD) along each coordinate as a function of lag time: ⟨ΔRi,j2 (τ)⟩. To specifically characterize the dynamics around the TSE, MSD analysis was performed by averaging over segments of the trajectory that start from values of Ri,j for which P(TP| Ri,j) is maximized. The function cτα was fit to each MSD curve, where the fit parameter α (i.e., diffusion exponent) indicates whether the projected dynamics is diffusive (α = 1), subdiffusive (α < 1), or superdiffusive (α > 1). When α = 1, the diffusion coefficient D is calculated according to D = c/2. We find that when the dynamics is projected onto an accurate coordinate (i.e., for which the number of transitions NT is minimized and max{P(TP|Ri,j)} ≈ 0.5), the MSD scales linearly with time (i.e., α ≈ 1.0), consistent with diffusive movements around the TSE (Figure 3, Figure S3, and Table S1). In contrast, for poorly performing coordinates (i.e., NT not minimized and max{P(TP|Ri,j)} < 0.3), the MSD increases slower than linearly with time (α ≈ 0.5−0.8), indicating subdiffusive dynamics. For the coordinate used in smFRET experiments (R8,47) we note that the projected motion is distinctly subdiffusive with α = 0.74 (Figure 3), which is consistent with the relatively low value of max{P(TP|R8,47)}. It is important to emphasize that a single metric alone is insufficient to assess the quality of a coordinate. That is, while there is an overall positive correlation between max{P(TP|Ri,j)} and α (Figure S3), there are coordinates that have relatively high values of max{P(TP|Ri,j)} and yet small values of α. Similarly, some coordinates do not minimize the number of transitions NT, yet they have relatively high values of max{P(TP|Ri,j)} and α. Here, by considering all three measures,

Figure 3. To characterize the diffusive behavior around the TSE, the mean squared displacement (MSD) as a function of lag time: ⟨ΔR2i,j(τ)⟩ was calculated for segments starting at the TSE. The function cτα was fit to each MSD curve. The fitted value for α indicates whether the projected dynamics is diffusive (α = 1) or subdiffusive (α < 1) in character. The dynamics along the accurate coordinate R8,18 appears diffusive (black), while the dynamics along R8,47 exhibits subdiffusive behavior, with α = 0.74 (orange).

we provide a more comprehensive approach to identifying the degrees of freedom that most accurately describe the underlying landscape. Kinetics of Barrier Crossing. The above analysis suggests that A/P hybrid-state formation may be appropriately described in terms of diffusion across a one-dimensional free-energy surface. To directly test this description, we compare the kinetics calculated from the free energy and diffusion with the kinetics obtained by counting transition events. If the dynamics along a coordinate ρ is accurately described as diffusion on the projected free-energy profile F(ρ), then the mean first-passage time ⟨tfp⟩ for a transition from the A/A to the A/P state may be calculated via the relation1,62,63 ⟨tfp⟩ =

∫ρ

ρA/P

A/A

ρ

dρ

∫∞

dρ ′

exp{[F(ρ) − F(ρ′)]/kBT } Dρ(ρ) (4)

where Dρ(ρ) is the coordinate- and position-dependent diffusion coefficient. For each high-performing coordinate (defined as one for which max{P(TP|Ri,j)} = 0.50, NT = 138, and α = 0.9−1.0; see Table S1), we calculated ⟨tfp⟩ from the free energy (e.g., F(R8,18) in Figure 4) and diffusion coefficient. When evaluating eq 4, we assume Dρ is a constant and set it to the value obtained for the TSE, since the value of the integrand at the TSE provides the largest contribution. When an appropriate choice of coordinate is employed, ⟨tfp⟩ will be consistent with the average passage time observed in the simulations: ⟨tfp:obs⟩. It is worth noting that similar selfconsistency tests have been employed previously to test reaction coordinates for other processes.64−66 We find that, for R8,18 (a representative high-performing coordinate) the ratio of these passage times ⟨tfp⟩/⟨tfp:obs⟩ is approximately 0.8, suggesting that the kinetics is well characterized by this coordinate. Similar ratios (0.8 ± 0.05) were obtained for all high-performing coordinates, indicating that they may also be used to describe diffusive barrier-crossing events. In accordance with the presence of a single dominant freeenergy barrier (Figure 4, black curve), the observed transitions are consistent with single-exponential kinetics. To show this, we fit the function A0exp(−t/tc) to the dwell time (i.e., first-passage time) distribution, as obtained using R8,18 as a reaction E

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shortest distance was less than 3 Å, as calculated using g_contacts.67 We find that ASF residues 897−899 and residues 54−57 in the T-loop of the tRNA form steric interactions in ∼75% of all sampled TSE configurations. This implies that excluded volume effects of the ASF and tRNA significantly contribute to the observed free-energy barrier (Figure 4, black curve), as suggested by previous explicitsolvent simulations of the ASF.68 The predicted steric barrier also qualitatively agrees with single-molecule and biochemical experiments showing that deletion of the ASF leads to increased rates of A/P hybrid-state formation69 and translocation.70 While there may be additional stabilizing interactions between the ASF and tRNA that favor the endpoints, the steric influence of the ASF alone can affect the observed dwell time of the A/A state.

Figure 4. Projected free-energy barriers can vary with the choice of coordinate. Consistent with higher values of P(TP|R8,18) relative to P(TP|R8,47) (cf. Figure 2), the barrier along R8,18 is larger than the one along R8,47. As discussed in the main text, the mean first-passage time ⟨tfp⟩ calculated from the free-energy profile and diffusion coefficient along R8,18 is consistent with the average passage time ⟨tfp:obs⟩ observed in the simulations. This demonstrates that the kinetics and free-energy barrier are consistently described by R8,18. In contrast, the coordinate used in experiments (R8,47) underestimates the barrier and does not recover the observed kinetics.

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CONCLUSIONS Using physical-chemical principles and molecular dynamics simulations, we have presented an analysis of potential reaction coordinates for characterizing the energy landscape of tRNA hybrid-state formation. We have shown that, despite the structural similarity of many interatomic distances, the projected dynamics can be highly dependent on the choice of coordinate. Most notably, if an appropriate coordinate is used, one may describe tRNA hybrid-state formation in terms of diffusive movements along a one-dimensional free-energy profile. These results provide a foundation upon which new experiments may be developed that more precisely quantify the energy landscape of the ribosome.

coordinate (Figure S4). There is excellent agreement between tc and ⟨tfp:obs⟩ (i.e., the average passage time obtained from the simulations), with tc/⟨tfp:obs⟩ = 0.97. The comparable values of ⟨tfp:obs⟩, ⟨tfp⟩, and tc further support the use of interatomic distances between the tRNA molecules to probe the kinetics of hybrid-state formation. Structural Characteristics of the TSE. A long-term objective of landscape analysis is to identify the energetic and structural content of the transition states associated with biomolecular dynamics. By identifying which coordinates can accurately capture transition events, we can now characterize the mechanistic aspect of this rearrangement. To illustrate the structural composition of the TSE, we calculated the average configuration of all sampled TSE frames (Figure 5), as

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b04476. Detailed description of methods and results (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 617-373-2952. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a National Science Foundation CAREER Award (Grant No. MCB-1350312). We are also grateful for the generous computing resources provided by the Northeastern University Discovery Cluster, as well as for technical support from the Information Technology Services (ITS) team at Northeastern University.

Figure 5. Average configuration of the TSE as calculated using a highperforming coordinate (R8,18). The A-site tRNA (yellow) closely interacts with the A-site finger (ASF, i.e., H38 of 23S rRNA; shown in gray). Residues 897−899 in the ASF and residues 54−57 in the tRNA T-loop form steric interactions (marked by a star) in ∼75% of the sampled TSE configurations. For reference, the yellow arrows in the middle panel indicate the relative positions of the A/A and A/P conformations.

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