Korak Kumar Ray,Colin D. Kinz-Thompson,Jingyi Fei,Bin Wang,Qiao Lin,Ruben L. Gonzalez
Entropic control of the free-energy landscape of an archetypal biomolecular machine
biomolecular machines,ribosomes,kinetics,energy landscapes,entropy
Significance Nearly all fundamental cellular processes are executed by large macromolecular complexes. Such “biomolecular machines” undergo essential, ligand-controlled structural rearrangements that enable function. Despite their importance, however, the mechanisms through which ligands drive and regulate these structural motions have been technically challenging to investigate and therefore remain unknown. Here, we overcome these challenges to demonstrate that the ligands of an archetypal biomolecular machine, the bacterial ribosome, control its structural rearrangements by modulating its conformational flexibility, thereby driving key steps in its reaction pathway. We propose that such ligand-mediated modulation of conformational flexibility is a general mechanism for controlling the structural rearrangements and biological functions of all biomolecular machines and serves as a fundamental principle for the design of synthetic molecular machines.
Entropic control of the free-energy landscape of an archetypal biomolecular machine

Nearly all fundamental cellular processes are executed by large macromolecular complexes. Such “biomolecular machines” undergo essential, ligand-controlled structural rearrangements that enable function. Despite their importance, however, the mechanisms through which ligands drive and regulate these structural motions have been technically challenging to investigate and therefore remain unknown. Here, we overcome these challenges to demonstrate that the ligands of an archetypal biomolecular machine, the bacterial ribosome, control its structural rearrangements by modulating its conformational flexibility, thereby driving key steps in its reaction pathway. We propose that such ligand-mediated modulation of conformational flexibility is a general mechanism for controlling the structural rearrangements and biological functions of all biomolecular machines and serves as a fundamental principle for the design of synthetic molecular machines.

The structural motions of biomolecules are essential components of their function (1–3). While the contributions that such structural dynamics make to the reaction pathways of a number of small enzymes have been well studied, their role in the mechanisms of large biomolecular complexes remains underexplored. Such biomolecular “machines” play essential roles in the cell, driving processes as fundamental as DNA replication, RNA transcription, messenger RNA (mRNA) splicing, and protein synthesis (4). A unique, defining feature of these machines is that they utilize nano-scale structural rearrangements to convert thermal and chemical energy into molecular-level mechanical work (5, 6). The dynamics of these rearrangements are modulated by the interactions of the biomolecular machines with a host of different ligands, including substrates, inhibitors, and co-factors, in order to drive and regulate their functions (7–11). Unfortunately, technical challenges to studying the structural dynamics of large biomolecular complexes have thus far precluded an understanding of the physical and structural bases through which ligands exploit them to direct the functions of biomolecular machines. Over the past twenty years, we have developed the capability to study the structural dynamics of an archetypal biomolecular machine, the bacterial ribosome, responsible for translating mRNAs into proteins. Specifically, we have established a reconstituted in vitro translation system composed of ribosomes and other translation components purified from Escherichia coli (12, 13). Using this system, we have developed numerous single-molecule fluorescence resonance energy transfer (smFRET) (14–17) signals that report on the conformational dynamics of the translating ribosome (10, 18–21). Notably, two of these signals report on a fundamental, compound conformational change of the ribosome that is integral to many of the mechanistic steps of translation (22) (Fig. 1 and SI Appendix, Fig. S1). Utilizing these and similar signals, we and others have shown that various ribosomal ligands can modulate the rate of this conformational change (10, 18, 23–30). In particular, transfer RNAs (tRNAs), the set of adaptor molecules that deliver amino acid substrates to the ribosome in the order specified by the nucleotide sequence of the mRNA, have been shown to modulate the dynamics of the ribosome. Remarkably, tRNAs differentially modulate ribosome dynamics in a way that depends on the identity, post-transcriptional modification status, and aminoacylation state of the tRNA (10, 18, 23, 25, 30). With this understanding, here we have used ribosomal complexes (RCs) that either lack or carry one of two classes of bound tRNAs as a model system. Combined with two novel technological advances (see below), this model system has provided us with a unique opportunity to investigate the physical and structural mechanisms through which the binding of different ligands (i.e., tRNAs) to a biomolecular machine (i.e., the bacterial ribosome) differentially modulate the conformational dynamics of the machine in order to direct its biological function (i.e., mRNA translation). A very powerful framework for understanding the contributions of ligand interactions to the conformational dynamics of biomolecules is provided by free-energy landscape theory (31, 32). Using this framework, we define two ensembles of RC conformations corresponding to the initial and final states of the conformational change described above. We refer to these as Global States 1 and 2 (GS1 and GS2) and represent them as occupying two distinct local minima (i.e., wells) on a free-energy landscape where each point on the landscape corresponds to the free energy of a set of distinct RC conformations along the reaction coordinate between these two states. Given the compound nature of conformational transitions between GS1 and GS2 (GS1→GS2 and GS2→GS1 transitions), these transitions encompass several large-scale structural rearrangements of the RC, including changes to i) the relative orientation between the small, 30S, and large, 50S, ribosomal subunits that make up the complete 70S ribosome; ii) the position of the tRNA between two binding sites on the ribosome; and iii) the location of a ribosomal structural element called the L1 stalk between two positions on the surface of the ribosome (22). On the free-energy landscape, GS1→GS2 and GS2→GS1 transitions are represented as excursions of the RC over a higher free-energy region of the landscape called the “transition state ensemble” (TSE) that acts as a free-energy barrier separating GS1 and GS2 (Fig. 1A). The height of this barrier (ΔG‡), which corresponds to the difference in free energy between GS1 or GS2 and the TSE, governs the rate of transition between GS1 and GS2. In the case of GS1→GS2 and GS2→GS1 transitions, smFRET (10, 18, 25, 26) and cryogenic electron microscopy (33–35) experiments have been used to measure the rate constants that directly yield ΔG‡ after analysis with an appropriate theoretical model, such as transition state theory (TST) (36). Of much more interest, but as yet unmeasured for these transitions or, to the best of our knowledge, for any comparable conformational transition in a biomolecular machine, are the energetic components of the ΔG‡, known as the activation enthalpy (ΔH‡) and activation entropy (ΔS‡). These parameters directly report on the physical and structural properties of the biomolecular machine that give rise to the barrier in the first place and, consequently, uniquely provide molecular insights into the mechanisms that ligands use to modulate the conformational dynamics of the machine (SI Appendix, Fig. S2). By analyzing how the rates of GS1→GS2 and GS2→GS1 transitions depend on temperature, we have resolved the free-energy barriers of the RCs described above into their component ΔH‡s and ΔS‡s. Our measurements show that, while binding of tRNAs to the RC contributes to the barrier by remodeling intermolecular interactions within the RC (i.e., enthalpically) as well as by altering the structural flexibility of the RC and/or disorder of the surrounding solvent shell (i.e., entropically), it is the entropic component that modulates the dynamics of the RC in a manner that is conducive to overall ribosomal function. This tRNA-dependent entropic control of ribosome dynamics is the strategy that the ribosome has evolved to enable rapid GS1→GS2 and GS2→GS1 transitions while maintaining a tight interaction with the tRNA in both states. Since these considerations apply not just to ribosomes but to all biomolecular machines, we hypothesize that such ligand-dependent entropic control is a generalized mechanism for regulating the functional dynamics of such machines.

In this study, we used two previously characterized smFRET signals, each of which reports on a different aspect of the ribosomal structural changes comprising GS1→GS2 and GS2→GS1 transitions (10, 18). The first follows the position of the L1 stalk from the ribosomal frame of reference (18) (smFRETL1), while the second reports on the relative distance between the L1 stalk and the ribosome-bound tRNA (10) (smFRETL1-tRNA) (Fig. 1B). The distance-dependent FRET efficiencies (EFRETs, defined as the fluorescence intensity of the FRET acceptor fluorophore normalized by the sum of the fluorescence intensities of the FRET donor and acceptor fluorophores) for these signals allowed us to follow the motions of the L1 stalk alone, and the combined motions of the L1 stalk and the tRNA, respectively, as the RCs transitioned between GS1 and GS2 (Fig. 1C). Employing a novel, high precision, temperature-controlled, microfluidic flowcell that we have previously developed for use in a single-molecule total internal reflection fluorescence (TIRF) microscope (37), we performed smFRET experiments using these signals at temperatures between 298 K and 310 K on a range of different RCs. These include RCs carrying a deacylated tRNA specific to phenylalanine (tRNAPhe) (RCPhe); carrying a deacylated tRNA specific to formylmethionine (tRNAfMet) (RCfMet); and lacking a tRNA altogether (RCvacant). tRNAPhe belongs to the “elongator” class of tRNAs (25), that are responsible for decoding the triplet-nucleotide codon sequence of the mRNA and consecutively adding the corresponding amino acids (in this case, phenylalanine) to the growing polypeptide chain during the elongation phase of translation. On the other hand, tRNAfMet belongs to the “initiator” class of tRNAs (25), that are responsible for decoding the mRNA start codon and directing the RC to assemble at the correct location on the mRNA during the initiation phase of translation. Thus, comparisons between the free-energy landscapes of these different RCs allow us to investigate the unique energetic contributions made by tRNAs to facilitate different stages of translation (SI Appendix, Fig. S1). To obtain the necessary information for those comparisons, we used TST to model the GS1→GS2 and GS2→GS1 transitions for each RC with temperature-dependent ΔG‡s (Fig. 1C and Methods) and subsequently calculated ΔH‡s and ΔS‡s from the temperature-independent and dependent components, respectively, of the ΔG‡s for each RC (36). At temperatures near 310 K and above, the GS1→GS2 and GS2→GS1 transitions became too fast to be accurately detected by the electron-multiplying charge-coupled device (EMCCD) camera on our TIRF microscope (Fig. 1C), leading to potential errors in our estimates for rate constants (37, 38). We therefore used a novel, time-resolution-enhancing, machine-learning algorithm that we call Bayesian Inference for the Analysis of Sub-temporal-resolution Data (BIASD) (previously described in ref. 39) to analyze the EFRET versus time trajectories recorded for each RC. Briefly, BIASD analyzes the distribution of EFRET values collected from an entire ensemble of RC molecules and infers the rate constants for the forward and reverse transitions (in this case, the GS1→GS2 and GS2→GS1 transitions, respectively) that yield the observed EFRET distribution. Because even transitions that are too fast to be detected by the EMCCD will lead to broadening of the EFRET distribution (Fig. 1D and SI Appendix, Fig. S3), BIASD enables us to accurately estimate rate constants for even the fastest dynamics that we observe in our smFRET experiments. Applying BIASD across the entire temperature range for each dataset directly yielded the underlying ΔH‡s and ΔS‡s that are responsible for the observed GS1→GS2 and GS2→GS1 dynamics for each RC and each smFRET signal (Methods).

One of the longstanding questions in the study of ribosome dynamics is whether, and to what extent, the motions of distal structural elements within the RC are coordinated. This is particularly the case for the motions of the two ribosomal subunits, the tRNA, and the L1 stalk, which altogether make up the compound conformational rearrangement at the heart of GS1→GS2 and GS2→GS1 transitions. Based on previous studies, we and others have hypothesized that these motions are allosterically coupled (18, 23, 26, 28, 29) and that the relative rotation of the ribosomal subunits, which requires remodeling of a large number of intersubunit interactions, must be the slowest and, therefore, rate-governing step for all of the other motions (26). Contrasting with this, other studies have been interpreted as providing evidence against such coupling (27). In our measurements here, we found that the energetics of the GS1⇌GS2 equilibrium for both RCPhe and RCfMet are independent of the smFRET signal used to measure them. Specifically, we found that the ΔH‡ and ΔS‡ for both the GS1→GS2 and GS2→GS1 transitions measured using either smFRETL1 or smFRETL1-tRNA, which follow different aspects of the structural rearrangements between GS1 and GS2, are within experimental uncertainty for both RCs (Fig. 2A and SI Appendix, Table S1). This observation provides the most direct and strongest evidence to date that the motions of the L1 stalk and the ribosome-bound tRNA within an RC are directly coupled and that the barriers which control the motions of these RC components must have the same underlying physical and structural basis and thus arise from the same rate-governing step. The large ΔH‡s that we observe for the GS1→GS2 and GS2→GS1 barriers in all three RCs, including RCvacant, which lacks a bound tRNA (Fig. 3A and SI Appendix, Table S1), suggest that this rate-governing step involves remodeling of a large number of intermolecular interactions. While our measurements do not directly report on intersubunit rotation, the large enthalpic penalties we observe here are consistent with those that would be expected from remodeling of the large number of intersubunit interactions associated with the relative rotation of the subunits during GS1→GS2 and GS2→GS1 transitions. Thus, our results provide strong evidence that regardless of whatever process it is that governs the rate of L1 stalk and tRNA motions during GS1→GS2 and GS2→GS1 transitions, it involves intersubunit rotation. Nonetheless, we also observe that the presence and identity of the ribosome-bound tRNA modulate the ΔH‡s and ΔS‡s of these barriers (Fig. 2A and SI Appendix, Table S1). This leads us to the conclusion that the rate-governing step of the GS1→GS2 and GS2→GS1 transitions cannot be solely explained by the remodeling of intersubunit interactions and must include remodeling of tRNA–ribosome interactions. Specifically, the TSE for these transitions must involve the disruption of the interactions between the tRNA and its binding site in GS1 and/or GS2 that precede or be concurrent with the disruption of the intersubunit interactions during intersubunit rotation. By necessitating this order of events, the architecture of the RC can couple the motion of the tRNAs with the internal rotational motion of the ribosome, which, in turn, also couples it to the motion of the L1 stalk (26), forming an allosteric network encompassing distal structural elements of the RC. The findings we report here not only reveal that the motions of distal structural elements of the RC are coupled, but by uniquely providing information on the features of the TSE that control these dynamics (i.e., the ΔH‡s and ΔS‡s), they lead us to a mechanism for how coupling is achieved. The allosteric network formed by the motions of these structural elements also readily explains how changes made to any one element (e.g., the tRNA) can modulate the structural dynamics of the RC as a whole—a strategy which, most likely, was evolved to regulate the dynamics of the ribosome in a manner that aids it function (see below).

Beyond the coupling of motions within RCs, a further outstanding question in the field is how the specific interactions that particular tRNAs make to the ribosome modulate the dynamics of RCs. To address this question, we next compared the relative effects that different tRNAs have on the free-energy barriers separating GS1 and GS2. Since the presence of ribosome-bound tRNA is the only difference between RCvacant and the other RCs, the relative changes in ΔH‡ measured using smFRETL1 (i.e., ΔΔH‡Phe = ΔH‡Phe – ΔH‡vacant, and, similarly, ΔΔH‡fMet = ΔH‡fMet – ΔH‡vacant) should reveal the enthalpic effects a ribosome-bound tRNA has on the GS1→GS2 and GS2→GS1 transitions. We found that ΔΔH‡Phe is positive for both the GS1→GS2 and GS2→GS1 transitions (27 kcal mol–1 and 25 kcal mol–1, respectively), demonstrating that significant tRNAPhe-specific interactions need to be remodeled for both of these transitions in RCPhe (Figs. 2B and 3B). The ΔΔH‡fMet values for both the GS1→GS2 and GS2→GS1 transitions, while still positive, are much lower (8 kcal mol–1 and 0.8 kcal mol–1, respectively), indicating that tRNAfMet-specific interactions with the ribosome are significantly weaker, at least at the sites that are remodeled during these transitions (Figs. 2B and 3C). Strikingly, the very small ΔΔH‡fMet value for the GS2→GS1 transition (an order of magnitude less than the other ΔΔH‡ values) suggests that there are no significant tRNAfMet–ribosome interactions in GS2 that are remodeled upon the transition to GS1 or that these interactions are almost completely compensated by favorable remodeling of intramolecular tRNAfMet–tRNAfMet interactions during the transition. Despite this, structural studies of RCs analogous to RCPhe and RCfMet show that, in GS2-like conformations, both tRNAPhe and tRNAfMet exist in very similar conformations (40–43). Indeed, analysis of the positions of the tRNA and the L1 stalk (which forms part of the tRNA binding site in GS2) in these structures demonstrates that in spite of slight positional differences, tRNAPhe and tRNAfMet both exist in close proximity to the L1 stalk in these conformations (SI Appendix, Fig. S4). These structural observations agree with the very similar, high EFRET values for GS2 that we observe in the smFRETL1-tRNA signal for RCPhe and RCfMet (0.81 and 0.80, respectively). Collectively, the small ΔΔH‡fMet value for the GS2→GS1 transition and relative positioning of L1 stalk and tRNAfMet in GS2-like conformations leads us to conclude that the motion of tRNAs within RCs occurs as a consequence of the architecture of the ribosome, regardless of any stabilizing interactions that may or may not be formed between ribosomal elements and the tRNA in either GS1 or GS2. We should note at this point that, while the enthalpic differences between the RCs that we observe may in part originate from the remodeling of solvent interactions at the tRNA-binding sites of the RCs, the significant dependence of these ΔΔH‡s on the identity of the bound tRNA strongly suggest that the major contributions to the enthalpic differences derive from the remodeling of intermolecular tRNA–RC and intramolecular tRNA–tRNA interactions. Regardless of the molecular origin of these effects, we hypothesize that RCs have evolved to harness such enthalpic differences as a way to allosterically modulate their conformational dynamics through perturbations from only a single type of molecular component—in this case, the tRNAs. Unique tRNAs might then have evolved to form different interactions at the tRNA–ribosome interface with the goal of allosterically modulating the functional dynamics of the entire ribosome.

All things kept equal, the enthalpic penalties described above should have increased the activation barriers and thus decreased the rate constants of the GS1→GS2 and GS2→GS1 transitions in tRNA-bound RCs relative to RCvacant. Instead, however, we found that these rate constants were similar to or larger in the tRNA-bound RCs than in RCvacant (Fig. 4). This was driven by the fact the ΔΔS‡ (defined similar to ΔΔH‡ above) for the GS1→GS2 and GS2→GS1 transitions were also positive. At the temperatures used in our measurements [and especially around 310 K, which is the optimal growth temperature for E. coli (44)], the ΔΔS‡Phes for the GS1→GS2 and GS2→GS1 transitions (91 cal K–1 mol–1 and 77 cal K–1 mol–1, respectively) more than compensate for the enthalpic penalties observed for RCPhe in comparison to RCvacant, leading to faster dynamics at the higher temperatures (around 310 K) (Figs. 2 B and 3B). The same is true for the ΔΔS‡fMet values for the GS1→GS2 and GS2→GS1 transitions (31 cal K–1 mol–1 and 4 cal K–1 mol–1, respectively), even if they are smaller in comparison to RCPhe (Figs. 2B and 3C). In fact, in the absence of any significant opposing enthalpic penalty, the small ΔΔS‡fMet for the GS2→GS1 transitions is enough to increase the corresponding rate constant by nearly three-fold over that of RCvacant over the entire range of temperature, making it the fastest transition we observe in our study (Fig. 4). Surprisingly, we find that the ΔΔS‡ values we measure are largely correlated with their corresponding ΔΔH‡ values. While the reason for this enthalpy–entropy compensation is not immediately obvious, we hypothesize that this is necessary to not overcompensate the tRNA-induced enthalpic penalties for these transitions. The GS1→GS2 and GS2→GS1 transitions are part of a large number of structural rearrangements that RCs must undergo during translation. All of these rearrangements need to occur within a very specific kinetic regime for translation to occur as rapidly as possible while maintaining the integrity of the process. Specifically, while slowing down GS1→GS2 and GS2→GS1 transitions as a result of uncompensated tRNA-induced enthalpic penalties could hinder translation and therefore be detrimental to cellular fitness, speeding up these transitions too much via compensatory entropic modulations might result in inaccurate tRNA or ribosome movements that could be deleterious to translation (e.g., slipping of the RC on the mRNA). The need to optimize this trade-off between speed and accuracy would explain the enthalpy–entropy compensation that we observe and highlight the evolutionary pressures that underly these energetic modulations of ribosome dynamics. Indeed, when we compare reports of the propensity of RCs carrying specific tRNAs to make errors during translation, we find that RCs carrying tRNAfMet are more error prone than RCs carrying elongator tRNAs (45). Similar to the case for the ΔΔH‡s above, the ΔΔS‡s that we observe may arise either from modulating the available conformational entropy of the RCs themselves or from a change in the ordering of water molecules, metal cations, and/or polyamines around the RCs. Indeed, the contributions from these sources of entropy are not mutually exclusive, and further studies are required to parse out the effects of conformational and solvent entropies to these free-energy barriers. Regardless of the relative contributions of either source, we note that it is these ligand-dependent entropic modulations, and not the corresponding enthalpic penalties, which drive the GS1→GS2 and GS2→GS1 transitions in a manner that allows protein synthesis to take place rapidly, but accurately.

Our measurements show that both tRNAPhe and tRNAfMet employ the strategy of entropic modulation to overcome specific tRNA-induced enthalpic penalties and drive the functional dynamics of their corresponding RCs. However, we see that the net effects of these modulations are markedly different for the respective RCs (Fig. 3). In RCPhe, the effect of the tRNAPhe-specific entropic modulations leads to a larger increase in the GS1→GS2 transition rate than the GS2→GS1 transition rate, biasing the GS1⇌GS2 equilibrium toward GS2. In contrast, tRNAfMet-specific entropic modulations in RCfMet lead to a more significant increase in the GS2→GS1 transition rate over the GS1→GS2 transition rate, which biases the GS1⇌GS2 equilibrium toward GS1. In the context of the specific steps of translation these tRNAs are involved in (i.e., elongation versus initiation, respectively) (SI Appendix, Fig. S1), it is clear that these entropic modulations bias the GS1⇌GS2 equilibrium toward the respective state responsible for productive, forward progression through the translation cycle (i.e., toward GS2 for elongation and toward GS1 for initiation). Interestingly, comparing the GS2-like structures of RCs analogous to RCPhe (40, 41) with that of an RC carrying a different elongator tRNA, tRNAMet (the elongator tRNA specific to methionine; RCMet) (46) shows that the L1 stalk–tRNA interface in both structures are more similar to each other than to the one present in RCfMet (SI Appendix, Figs. S4 and S5). Given the similarities between the structures of RCs carrying different elongator tRNAs, and, indeed, the similarities in the rates of GS1→GS2 and GS2→GS1 transitions in such RCs (25), we hypothesize that the tRNAPhe-induced entropic modulation of RC dynamics we observe generalizes to other elongator tRNAs and collectively serve to speed up elongation. Analogously, we hypothesize that the tRNAfMet-induced entropic modulation of RC dynamics we observe is used to speed up initiation instead. Taken together, our findings strongly suggest that tRNAs and ribosomes have coevolved to utilize a complex interplay of ligand-induced enthalpic and entropic modulation to control the conformational dynamics of the entire biomolecular complex in ways that facilitate the overall process of translation. We note that, while our experiments focus on the entropic and enthalpic effects of tRNA binding to RC dynamics, a multitude of protein translation factors, RNA accessory factors, and mRNA structural elements interact with the RC during translation. The binding of many of these factors has also been shown to modulate RC dynamics in a manner that facilitates the specific steps of translation that each is involved in refs. 18, 23, 24. While the entropic and enthalpic contributions to the free-energy barriers underlying the dynamics of such factor-bound RCs have not yet been characterized, our results readily point to a mechanism for the compensation of the enthalpic penalties of factor binding to these RC using similar entropic modulation strategies.

Our experimental results reveal the existence of tRNA-induced entropic modulation of RC dynamics and uncover their role in kinetically facilitating those dynamics. The unique data provided by our temperature-dependent, single-molecule experiments have allowed us to characterize the thermodynamics of the TSE governing RC dynamics in a manner that is inaccessible to structural studies or kinetics studies performed at a single temperature (36, 47). For example, the increased ΔS‡s for the GS1→GS2 and GS2→GS1 transitions in RCPhe and RCfMet suggest that the TSEs in these RCs are relatively more flexible or disordered relative to that in RCvacant (SI Appendix, Fig. S2C). We hypothesize that it is this increase in the structural flexibility of the TSEs that leads to the faster rates of GS1→GS2 and GS2→GS1 transitions in the tRNA-bound RCs. In terms of free energies, the increase in structural flexibility corresponds to an increase in the number of microstates that have sufficiently low free energy to enable transitions between GS1 and GS2, thereby leading to an expansion of the TSE. This expansion provides a greater number of possible paths across the free-energy barrier separating GS1 and GS2, consequently increasing the rates of transitions between the two states (Fig. 5). We contrast this entropically driven increase in transition rates with an enthalpically driven mechanism commonly encountered in small enzyme kinetics (36), where the formation of stabilizing interactions in the TSE lowers the free-energy barrier between two states. We note that there is no such net change in favorable interactions in the TSEs of the RCs that we studied. The stabilizing interactions we do encounter are net unfavorable for the transitions between GS1 and GS2 and therefore need to be compensated for using entropic modulations. These differences in the relative roles of enthalpic and entropic contributions between the dynamics commonly seen in small proteins and the dynamics we see in the ribosome suggest that our understanding of the physical principles controlling small enzyme dynamics need not be readily translated to the dynamics observed in these machines. Our results, thus, highlight the need for further theoretical and experimental investigations of the dynamics of the ribosome and similar biomolecular machines. tRNA-induced entropic modulation of RC dynamics appears to be a mechanistic strategy used to overcome the enthalpic penalties associated with tRNA binding to the ribosome while simultaneously optimizing the dynamics of the RC such that it can successfully navigate the speed/accuracy trade-off that is inherent to mechanical processes such as translation. Additionally, by evolving an architecture that enables the allosteric coupling of multiple distal structural elements, RCs can utilize perturbations in a single component (in this case, the tRNA) to modulate the dynamics of the entire biomolecular complex. Moreover, by utilizing perturbations from ligands like tRNAs, which are modular and can be readily replaced in different contexts, RCs can differentially bias the same set of dynamics for multiple purposes at different phases of translation. Indeed, the generality of the constraints that these ligand-induced entropic modulations have evolved to overcome leads us to hypothesize that similar modulations are very likely to also play a major role in the regulation of the functional dynamics of other multicomponent biomolecular machines. Given their size and complexity, the dynamics of all such machines are expected to be associated with significant remodeling of inter- and intra-molecular interactions, especially in the presence of ligands which need to be tightly bound and moved across distal sites in the complex. The work we present here shows that when constraints exist on the possible number of ways in which the enthalpy of a biomolecular machine can be modulated, then biomolecular machines can evolve coherent strategies to instead utilize entropy to drive and regulate their conformational dynamics, and thus, their functions.

The use of enthalpy–entropy compensation has been previously observed in a range of biomolecular systems, including the folding of proteins (48), the recognition of ligands (49), and the kinetics of enzyme reactions (50). In this work, we show that the function and regulation of biomolecular machines also rely on enthalpy–entropy compensation and provide a detailed characterization of this compensation in the operation of a paradigmatic biomolecular machine. Given the ubiquity and diversity of biological processes performed by such large biomolecular complexes, we predict that the mechanisms for utilization of ligand-dependent entropic control of free-energy landscapes that we describe here will be a key concept that furthers our understanding of the workings of natural biomolecular machines and form an important design principle for the development of synthetic, biomimetic molecular machines.

Fluorophore-labeled ribosomes and tRNAs were prepared following published protocols (12). Briefly, a single-cysteine (Cys), E. coli ribosomal protein uL1 variant, uL1T202C, and a single-Cys, E. coli ribosomal protein bL9 variant, bL9Q18C, were designed, overexpressed, purified, and labeled with maleimide-activated Cy5 or Cy3, respectively. Cy5-labeled uL1T202C and Cy3-labeled bL9Q18C were then reconstituted into large ribosomal subunits lacking both wild-type uL1 and bL9 that had been purified from a uL1-bL9, double-deletion, E. coli strain, using multiple sucrose density gradient ultracentrifugation steps, to generate Cy5–Cy3, dual-labeled large subunits. Similarly, Cy5-labeled uL1T202C was reconstituted into large ribosomal subunits lacking wild-type uL1 that had been purified from a uL1-deletion E. coli strain to generate Cy5-labeled large subunits. E. coli tRNAfMet and tRNAPhe were labeled with Cy3-maleimide or N-hydroxysuccinimidyl (NHS) ester-activated Cy3 at the naturally posttranscriptionally modified 4-thiouridine at nucleotide position 8 (s4U8) and 3-(3-amino-3-carboxypropyl)uridine at nucleotide position 47 (acp3U47), respectively, to generate (Cy3)tRNAfMet and (Cy3)tRNAPhe. Unlabeled components were purified following published protocols (12). Briefly, unlabeled small ribosomal subunits were purified using multiple sucrose density gradient ultracentrifugation steps. Unlabeled translation factors, specifically initiation factors 1, 2, and 3, and elongation factors Tu and G, were purified using affinity chromatography, followed by subsequent size exclusion chromatography and/or cation exchange chromatography, as previously described (12). tRNAfMet, (Cy3)tRNAfMet, tRNAPhe, and (Cy3)tRNAPhe were aminoacylated with the corresponding amino acids and aminoacyl tRNA synthetases, and Met-tRNAfMet and Met-(Cy3)tRNAfMet were formylated using formylmethionyl-tRNA formyltransferase, as previously described (12).

RCs containing tRNAs were enzymatically assembled in vitro in the manner which had been previously described for temperature-dependent smFRET measurements of RCPhe (37). Briefly, RCfMet were prepared by enzymatically initiating unlabeled small subunits and large subunits (Cy5-Cy3 dual-labeled for smFRETL1-tRNA or Cy5 labeled for smFRETL1) at a start codon on a 5′-biotinylated mRNA with fMet-tRNAfMet (for smFRETL1) or fMet-(Cy3)tRNAfMet (for smFRETL1-tRNA) and translation initiation factors 1, 2, and 3. RCPhe was prepared by enzymatically elongating RCfMet prepared as described above using unlabeled fMet-tRNAfMet and Cy5–Cy3 dual-labeled large subunits (for smFRETL1) or Cy5 labeled large subunits (for smFRETL1-tRNA), with Phe-tRNAPhe or Phe-(Cy3)tRNAPhe respectively, delivered by translation elongation factor Tu and subsequently translocated by translation elongation factor G. RCvacant were assembled nonenzymatically according to a previously described protocol (26). Briefly, this reaction was conducted in two steps: i) incubating unlabeled small subunits with 5′-biotinylated mRNA in RC assembly buffer [50 mM Tris-Cl (pH25°C = 7.5), 70 mM NH4Cl, 30 mM KCl (potassiumchloride), and 6 mM βME (2-mercaptoethanol)] containing 20 mM MgCl2, for 10 min at 37 °C and ii) adding Cy5-Cy3 dual-labeled large subunits to the above reaction and incubating the resulting sample at 37 °C for 20 min. All RCs were purified using sucrose density gradient ultracentrifugation.

The fabrication, assembly, calibration, and performance of the temperature-controlled microfluidic flowcells used here for smFRET imaging have been previously described (37, 51). Briefly, each flowcell consists of a set of five parallel microchannels that are sandwiched between a quartz microscope slide (G. Finkenbeiner) and a borosilicate glass coverslip (VWR). Prior to assembling the flowcell, the slide was passivated against nonspecific binding of biomolecules by derivatizing the cleaned and aminosilanized (Vectabond, Vector Labs) quartz surface with a mixture of NHS ester-activated polyethylene glycol (NHS-PEG) and dilute NHS-PEG-biotin. Likewise, prior to assembling the flowcell, the coverslip was microfabricated in order to integrate thermal control elements. These elements included thin-film resistive microheaters that were distributed evenly across the length of each microchannel for uniform heating as well as thin-film resistive temperature sensors that were located along the long side and off-center of each microchannel to accurately probe the temperature in real time. Flowcells were then assembled by placing ~1-mm-wide strips of double-sided tape on each side of each microchannel on the slide and affixing the coverslip on top of the double-sided tape-containing face of the slide such that the fabricated face of the coverslip is positioned inside of the resulting flowcell. Subsequently, the sides of the flowcell were sealed with epoxy. The temperature sensor in each microchannel was then calibrated by characterizing the linear relationship between resistance and temperature such that the microchannel temperature could be accurately and precisely determined by measuring the temperature sensor resistance. Further performance characterization of the resulting temperature-controlled microchannels demonstrated that closed-loop control of the on-chip heaters and temperature sensors could accurately maintain the setpoint temperature to a precision of ± 0.01 °C.

As previously described in Wang et al. (37), experiments were carried out in Tris Polymix Buffer [50 mM tris(hydroxymethyl)aminomethane acetate (Tris-OAc) (pH25 °C = 7.0), 100 mM KCl, 5 mM ammonium acetate (NH4OAc), 0.5 mM calcium acetate (Ca(OAc)2), 0.1 mM ethylenediaminetetraacetic acid (EDTA), 10 mM βME, 5 mM putrescine dihydrochloride, and 1 mM spermidine, free base] at 15 mM magnesium acetate (Mg(OAc)2) (12), supplemented with an oxygen-scavenging system (300 μg/mL glucose oxidase (Sigma), 40 μg/mL catalase (Sigma), and 1% β-D-glucose), and a triplet-state quencher cocktail [1 mM 1,3,5,7-cyclooctatetraene (Aldrich), and 1 mM p-nitrobenzyl alcohol (Fluka)] (12). The biotin-functionalized RCs were flown into the microscope flowcell and surface immobilized utilizing biotin–streptavidin–biotin interactions. All RCs containing a peptide attached to the tRNA (RCfMet and RCPhe) were incubated in 1 mM puromycin in Tris Polymix Buffer at room temperature for 5 min prior to imaging. This caused hydrolysis and release of the tRNA-bound nascent peptide, leading to the formation of RCs containing only a deacylated tRNA.

As previously described in Wang et al. (37) for the smFRETL1-tRNA signal, imaging was performed with a laboratory-built, wide-field, prism-based TIRF microscope. A 532-nm diode-pumped solid-state laser (CrystaLaser, Inc.) was used as an excitation source, and a 512 pixel × 512 pixel EMCCD camera (Cascade II 512, Photometerics, Inc.) was used as a detector. For smFRETL1-tRNA experiments, the excitation density was 32 W cm−2 (the excitation area is estimated to be 0.05 mm2), and the acquisition rate for the EMCCD was 20 frames s−1. For smFRETL1 experiments, the experimental setup was nearly identical to the one described above and previously (37). The major experimental differences were an excitation density of 22 W cm−1 and an EMCCD acquisition rate of 10 frames s−1. Experiments for all RCs were conducted at five temperatures, 25 °C, 28 °C, 31 °C, 34 °C, and 37 °C (or 298 K, 301 K, 304 K, 307 K, and 310 K). The temperature inside a designated microchannel for single-molecule measurements was maintained at the setpoint using closed-loop control of the on-chip heaters and temperature sensors to within an accuracy of ± 0.01 °C (37). Pairs of Cy3 and Cy5 fluorophores corresponding to individual RCs were colocalized by aligning the fields-of-view containing the fluorescence emissions of hundreds of individual Cy3 and Cy5 fluorophores using an iterative closest point algorithm (52) to find the best affine transform between the two views. The fluorescence intensities of the colocalized Cy3 and Cy5 fluorophores were subsequently fit to two-dimensional Gaussian point spread functions and extracted from the movies to generate raw Cy3 and Cy5 fluorescence intensity versus time trajectories (intensity trajectories), which were subsequently corrected using a 5.5% Cy3-to-Cy5 bleedthrough parameter. The corrected intensity trajectories were transformed into EFRET trajectories by calculating EFRET = ICy5 /(ICy3 + ICy5) at each time point, where ICy3 and ICy5 correspond to the intensity for the Cy3 and Cy5 fluorophore channels, respectively. Outlying EFRET datapoints arising from estimates of EFRET made in the absence of sufficient Cy3 or Cy5 fluorescence (where EFRET > 2.0 or where EFRET < −1.0, respectively) were removed. Only EFRET trajectories exhibiting the complete loss of Cy3 and/or Cy5 fluorescence in a single step, which likely occurs due photobleaching and/or photoblinking of the fluorophores and can be distinguished from decreased, but still nonzero levels of fluorescence caused by conformation-dependent changes in FRET were selected for analysis. The EFRET trajectories were truncated at the first timepoint prior to the timepoint at which either the Cy3 or Cy5 fluorophore photobleached. In EFRET trajectories where photoblinking events occurred, only a single section of each EFRET trajectory, corresponding to the time period before the first photoblinking event, between two photoblinking events, or between a photoblinking event and the photobleaching event, was selected for further analysis.

The selected EFRET versus time trajectories for each smFRET signal at every temperature point T (T = 298, 301, 304, 307, 310 K) for each RC were concatenated into a single one-dimensional EFRET data vector ({d(T)}) consisting of the signals from each individual RC molecule of that specific type at the given temperature. The resulting set of vectors ({d}, consisting of individual {d(T)}’s) for each RC was analyzed using a global BIASD (39) algorithm. In this analysis, the {d} for each RC and each smFRET signal was modeled using seven temperature-independent parameters: two EFRET means (∈GS1 or ∈GS2) corresponding to the conformations GS1 and GS2 for each specific RC, respectively, an EFRET noise parameter (σ) describing the noise in the EFRET signal in both conformational states, and four activation parameters (ΔH‡(GS1→GS2) and ΔS‡(GS1→GS2), and ΔH‡(GS2→GS1) and ΔS‡(GS2→GS1)) describing the free-energy barriers for the GS1→GS2 and GS2→GS1 transitions, respectively. The rates of interconversion between the two states, kGS1→GS2 and kGS2→GS1, that were observed in each {d(T)} were determined using the respective activation parameters according to TST (36) with the equation: where kB is the Boltzmann constant, h is the Planck constant, R is the gas constant, T is the absolute temperature at which the rate constant is observed, and κ is a correction factor which is set to 1 (36). This model was then used to explain the data {d} for each RC using Bayesian inference. Briefly, the log likelihood function used in this case was where ln P({d}|∈GS1, ∈GS2, σ, kGS1→GS2, kGS2→GS1) is the BIASD log-likelihood function as has been derived previously (39) and {T} is the set of experimental temperatures from 298 K to 310 K. The prior distributions used can be found in the SI Appendix, Table S3. The posterior probability distribution for each RC dataset, defined here as the product of the above likelihood and prior distributions (assuming the evidence is a constant, since only a single model is used) (53), was sampled using an affine-invariant Markov chain Monte Carlo (MCMC) method, emcee (54, 55). The sampling process was carried out in two steps. First, for each dataset, the MCMC method was initialized using 1,000 walkers and 3,000 steps. The final walker positions after 3,000 steps were then sorted by posterior probability. The worst 500 positions were then discarded, and the remaining positions were used to initialize 500 new walkers, thereby eliminating sampling artifacts caused by improper initialization. In the second steps, these 500 walkers were employed to sample a further 6,000 steps, the first 1,000 of which were discarded to burn the chains. Uncorrelated samples were chosen from the remaining steps based on the maximum parameter correlation time (~100 steps), and these uncorrelated samples were used to calculate the means and SDs of the marginalized posterior probability distributions for each RC dataset. The analysis of the RCPhe smFRETL1 data showed allowed us to specify mean EFRET states for GS1 and GS2 with a much greater precision than could be previously achieved (18, 26). The more precise posterior distributions for the mean EFRET states were leveraged to specify tighter priors for the remaining two RCs for the smFRETL1 signal (53).

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