Escapement mechanisms: Efficient free energy transduction by reciprocally-coupled gating

Abstract

Conversion of the free energy of NTP hydrolysis efficiently into mechanical work and/or information by transducing enzymes sustains living systems far from equilibrium, and so has been of interest for many decades. Detailed molecular mechanisms, however, remain puzzling and incomplete. We previously reported that catalysis of tryptophan activation by tryptophanyl-tRNA synthetase, TrpRS, requires relative domain motion to re-position the catalytic Mg²⁺ ion, noting the analogy between that conditional hydrolysis of ATP and the escapement mechanism of a mechanical clock. The escapement allows the time-keeping mechanism to advance discretely, one gear at a time, if and only if the pendulum swings, thereby converting energy from the weight driving the pendulum into rotation of the hands. Coupling of catalysis to domain motion, however, mimics only half of the escapement mechanism, suggesting that domain motion may also be reciprocally coupled to catalysis, completing the escapement metaphor. Computational studies of the free energy surface restraining the domain motion later confirmed that reciprocal coupling: the catalytic domain motion is thermodynamically unfavorable unless the PPi product is released from the active site. These two conditional phenomena—demonstrated together only for the TrpRS mechanism—function as reciprocally-coupled gates. As we and others have noted, such an escapement mechanism is essential to the efficient transduction of NTP hydrolysis free energy into other useful forms of mechanical or chemical work and/or information. Some implementation of both gating mechanisms—catalysis by domain motion and domain motion by catalysis—will thus likely be found in many other systems.

1 |. INTRODUCTION

Proteins are complicated machines. Despite the immense progress of the past half century—a rich and growing library of three-dimensional structures, understanding of many factors that stabilize them, rudimentary understanding of how they stabilize reaction transition states for many different chemical reactions, and the ability to re-design existing proteins and design new ones—protein science has only begun to crack open the mysteries of how they function. Foremost among the puzzling questions to which we have only preliminary answers, is how they exploit long-range intramolecular coupling to convert catalysis of NTP hydrolysis—a highly exergonic reaction—into directional and useful forms of work and information?

The work of Prigogine¹ provided a theoretical understanding of how living things sustain themselves far from equilibrium by trapping and transforming chemical free energy while exporting high entropy waste products. Jencks^2,3 and others^4–6 outlined various conceptual requirements for how utilization of ATP would drive vectorial processes, but failed to capture the mechanism(s) that fulfill those requirements. Such molecular details emerged slowly in the intervening years.

2 |. THE “BINDING CHANGE” MODEL

Broad outlines of a molecular model grew out of the recognition that NTPases exhibit at least three different conformational states, with differential binding affinity for NTP, hydrolysis products, or neither ligand. Boyer called that achievement the “binding change” model^7–9 and in the case of the F1 ATPase that work resulted in a share of the Nobel Prize in 1997. By a fortunate irony,¹⁰ a single crystal structure produced coordinates for all three states of the ATPase, establishing explicit support for the binding change model.

Because it can work in either direction, depending on the local chemical potentials of NTPs and their hydrolysis products, the binding change model also potentially describes free energy transformations by a broad range of enzymes—transducing NTPases—that convert NTP hydrolysis free energy into useful forms of chemical (synthetases) and biomechanical (motors) work^11,12 and/or information (GTPases).^13,14 This new understanding of mechanical and informational coupling of domain motion to NTP hydrolysis deepened perspectives on how biological processes appear to transcend the second law of thermodynamics.^15,16

The binding change model—three conformational states with decisively different ligand affinities for nucleoside triphosphates and their hydrolysis products—however, still does not answer the important mechanistic question: how is domain motion so seamlessly integrated with the catalytic acceleration of chemical changes in the NTP at the active site?

3 |. BEYOND THE BINDING CHANGE MODEL: COUPLING CATALYSIS TO DOMAIN MOTION

A deeper answer to this question requires identifying and quantifying detailed thermodynamic networks that link differential conformational stability to catalytic function. We review here work to date on this question for Bacillus stearothermophilus tryptophanyl-tRNA synthetase, TrpRS, for which the structural landscape (Figure 1) and key elements of the transduction mechanism have been identified and characterized.^17–19 That work furnishes a heuristic picture of where more explicit answers lie.

FIGURE 1.

Conformational transition states along the pathway for TrpRS activation of tryptophan. The plot shows the variation in energy along the most probable trajectory¹⁸ as estimated by the minimum action path program. X-axis values indicate the number of steps into which the path is divided (both energy and time are thus arbitrary; see Reference 18 for details). Two barriers are evident, a major one corresponding to the induced-fit closure of the anticodon-binding (brown) and connecting peptide 1 (CP1) (red) domains toward the active site (curved arrows for the cartoons of the TrpRS monomer). The second corresponds to the catalytic event, and is accompanied by an untwisting of the ABD and an opening of CP1. Prior to the induced-fit TS, the two phenylalanines of the D1 switch (red side chains, inset) are oriented such that the edge of one faces the center of the plane of the other. In the PreTS state, this orientation changes such that their ring planes are parallel. This orientation is preserved in the Products state. Red lines indicate edges of high likelihood Delaunay tetrahedra.^73,74 These intensify in number in the PreTS and again in the Product states

It seems likely that transition-state affinity in other transducing NTPases develops during domain rearrangement, as is true for TrpRS.¹⁷ Warshel describes as “Pre-organization”²⁰ the non-transient configuration complementary to the chemical transition state of a catalyzed reaction. TrpRS domain motion continuously re-configures the active site, taking it only transiently through a pre-organized alignment, in which the active-site metal ion can optimally compensate the dynamic charge distribution of the transition state for dissociative phosphoryl transfer (see figure 11 of Reference 17). The importance of such dynamic pre-organization was also anticipated by Kay.^21,22 Thus, it seems likely that the active-site pre-organization in all such enzymes is under sophisticated control, in order to ensure that active-site chemistry and domain configurations are efficiently coupled. That, in turn, requires substantial intramolecular communication via “networks” effecting long-range, coupled equilibria within the protein.

Stated in these terms, the question is wildly open-ended. However, we have shown how to tame it by focusing directed combinatorial mutagenesis on key side chains.^{17,19,23–28} Identification and mutagenesis of the TrpRS D1 switch²⁶ afforded an ensemble of 16 variant proteins whose wide-ranging steady-state and single turnover kinetic parameters could be confidently attributed either to main effects or to one or more higher-order interactions, most notably to the five-way energetic coupling of −5.5 kcal/mol between the four mutated D1 residues and the active-site Mg²⁺ ion.²⁵

4 |. THE D1 SWITCH

The D1 switch (Figure 1) is a tertiary packing motif whose seven nonpolar side chains interleave to bind the first two parallel β-strands to the intervening N-terminal α-helix of the TrpRS Rossmann fold domain. We called it a “switch” because these side chains exchange the nearest neighbors, mediating the shear created by relative motion of the anticodon-binding domain against the Rossmann fold. The D1 switch motif was identified using two, distinct, bioinformatic algorithms that made use of the crystallographic polymorphism that TrpRS exhibits when bound to different ligands related to the catalytic cycle.^29–33 TrpRS crystal structures assume three distinct conformers—the Open, Pre-transition state (PreTS), and Product states—because different substrates and substrate analogs bind to the Open state (either tryptophan or ATP, but not both), the PreTS state (both ATP and/or a tryptophan analog), and the Product state (tryptophanyl-5’-AMP and its stable analogs).

The distinction between the two breakdown products of ATP—the AMP and/or its derivatives and the phosphoryl product, PPi—is important. A similar distinction has long been noted in the field of muscle contraction, where the “Products” complex containing both ADP and inorganic phosphate³⁴ and the ADP complex occur at distinct, successive stages of the myosin cross-bridge cycle.³⁵ Accordingly, we will refer to complexes containing only the adenosine moiety as “Product” and those with both hydrolysis products as “Products.”

The D1 switch was identified initially from the intersection of sets of TrpRS residues at the interface between domains that move as rigid bodies. Packing differences between the successive structural states were identified using differential Delaunay tessellation²⁶ to locate Delaunay tetrahedra present in one but not the other conformer and which therefore differentiate them. Using the protein design program, Rosetta,³⁶ to stabilize the least stable TrpRS conformer (the Pre-transition or PreTS state) relative to the more stable Open and Products ground states on either side produced a second list of individual side chains whose environments were sensitive to conformational differences. The D1 switch was the largest cluster of residues in the intersection of the two lists.²⁶ Finally, a global search for recurring 3D packing motifs with short and equivalent intervals between participating residues later identified that same motif as one of the most widespread representative in the proteome.³⁷

In the TrpRS conformational cycle (Figure 1) the D1 switch mediates the shear limiting the relative domain motion of the anticodon-binding domain (ABD) and the connecting peptide-1 (CP1) insertion within the Rossmann fold domain. Combinatorial mutagenesis of the D1 switch identified a long-range coupling energy of −5.5 kcal/mol between the four mutated D1 residues and the active-site Mg²⁺ ion.²⁵ That coupling energy was the initial evidence that this packing motif functions to couple domain movement to catalysis^17,19,25 and specificity,^24,38 by imposing a barrier to the induced-fit stage of catalysis.^18,26 A more modest repacking accompanies the catalytic conformational change.^18,39

The manifold benefits of the ensemble of perturbed D1 switch variants did much to establish higher-order thermodynamic cycle analysis as the gold standard for mapping internal networks related to enzyme catalysis.^17,19 Not least among the benefits is that these variants are all structurally closely related and yet functionally distinguishable. Those two properties allowed us to relate mutant-induced changes quantitatively to ΔG values for both kinetic and computational rate parameters, establishing for the first time a coherent, quantitative mapping between structural perturbation, experimental kinetic rates, and computationally-derived parameters (see figures 4 and 7 of Reference 39).

The substantial coupling energy between the D1 switch and the metal implies that catalytic assist by the metal—increasing the transition-state stabilization by −5.5 kcal/mol, reflected in a ~10⁵-fold increase in k_cat—occurs if and only if the D1 switch residues and metal rearrange, which occurs if and only if the ABD and CP1 domains move, relative to one another.³⁸

5 |. ESCAPEMENT MECHANISMS REQUIRE RECIPROCALLY-COUPLED GATING

We previously invoked the escapement mechanism of a mechanical clock (Figure 2) as a metaphor for the mechanism that makes catalysis conditional to domain motion. Use of the term “escapement” in biology dates at least from the early 1990s in the context of molecular clocks⁴⁰ and early this century in the context of cricket ticking mechanisms.⁴¹ Branscomb and Russell were first to embrace fully the escapement metaphor at the molecular level.^15,16,42 As noted in,¹⁵ an essential feature of molecular escapement mechanisms is that they trap fluctuations by separating the driving force furnished by NTP hydrolysis into half reactions, which are “obligatorily interleaved,” as outlined first by Jencks.^2,43 That separation underlies all “ratchet” models, for example for molecular motors.^44–47 We elaborate further here on the molecular mechanisms underlying the phrase “obligatorily interleaved.”

FIGURE 2.

Schematic diagram of an escapement mechanism. This is the critical component of a mechanical clock. A torque, τ, is applied around the axis of the crown gear, providing the thermodynamic driving force, and represented in transducing NTPases by NTP hydrolysis, which becomes thermodynamically favorable only after both adenosine and phosphoryl products are released to water.⁵⁰ The Crown Gear (light green) represents the active site where the hydrolysis is catalyzed. The escapement itself consists of the two dark green blades (1) and (2) attached to the Verge (red post) that alternatively function to limit rotation of both the Foliot (transverse rod with yellow balls) and the crown gear such that the Verge rotates sufficiently to allow one gear to slip past the upper escapement blade at a time, representing here the Mg²⁺ ion. PPi release functions as the second blade, checking rotation of the Crown Gear until the Folio reverses direction. Together, the two blades of the escapement convert the rotary motion of the crown gear into periodic motion of the Verge and Foliot necessary to keep accurate time. The Folio itself represents the anticodon-binding domain, which must re-position in order to bind tRNA^Trp for acyl transfer after amino acid activation by ATP

The elegance of NTP hydrolysis arises from three, essentially unique properties of phosphodiester bond hydrolysis. Two were identified by Westheimer⁴⁸: (a) the reaction is, energetically, overwhelmingly favorable because water favors the products over the reactants by a factor of roughly a million⁴⁹ and (b) the reaction is inordinately slow in the absence of a catalyst because the triphosphate is kinetically metastable. We must add to these two properties the experimental demonstration that, although the equilibrium constant for hydrolysis in water is ~10⁶, it can be close to 1 inside an enzyme active site.⁵⁰ These three properties imply that: (a) NTP hydrolysis requires a catalyst, (b) irreversibility requires dissociation of both products, and (c) release of the phosphoryl product can re-configure the relative free energies of different conformational states.

The molecular basis of enzymatic escapement mechanisms, as anticipated by Jencks, thus must separate coupling of the acceleration of NTP hydrolysis to domain motion from coupling of domain motion to product release. Our mechanistic studies of tryptophan activation by ATP elucidated key details of how TrpRS separates the two coupling processes and makes them interdependent to achieve the interleaved control required of an escapement mechanism essential to free-energy transduction (Figure 3).

FIGURE 3.

Reciprocally-coupled gating during TrpRS catalysis of Trp activation by ATP. The 15 D1 switch variants are indicted by the bar code beneath the free energy histogram for ΔG_kcat, which also serves to illustrate the design matrix and includes wild type TrpRS, which served as the reference for the ΔΔG histograms. Semiquantitative conformational and ligand-binding free energies are indicated by dashed brown and green curves, and these vary quantitatively between different D1 variants. The transition-state complex forms transiently, as domains move (green arrow). Following transition state stabilization, the domain movement necessary for catalysis is gated by the release of the PPi product, which shifts the equilibrium for the catalytic domain motion from unfavorable in the presence to favorable in the absence of PPi (red arrows). Cartoons show the PreTS (green) and Product (purple) states of TrpRS, ± PPi

(a) Four residues that mediate the shear created by domain motion all repack coordinately with movement of the Mg²⁺ ion at the active site to a new position necessary to accelerate the ATP utilization. Computational determination of the minimum action path demonstrated that repacking of the three aromatic residues—F26, Y33, F37—in the D1 switch is rate limiting for the induced-fit phase of the catalytic cycle.¹⁸ Moreover, a modular thermodynamic cycle³⁸ in which we added either ABD or the CP1 domain back to the TrpRS Urzyme exhibited a Δ(ΔG) value similar (−5.0 kcal/mol) to that observed for the 5-way interaction between the four mutated D1 switch residues and the active-site Mg²⁺ ion.

That high-dimensional coupling²⁵ of the location of the active-site Mg²⁺ ion to the domain motion creates the first part of the escapement mechanism by ensuring that catalytic assist by Mg²⁺ ion requires domain motion. Crystallographic and thermodynamic studies of Williams^51,52 verified that this catalytic assist entails re-positioning of the Mg²⁺ ion from a catalytically inactive, to a catalytically active position in the active site.

(ii) A second aspect of the catalytic cycle comes into play as the result of the second conformational transition state along the reaction path between the PreTS and Products states. In order to validate the computed structure of that high-energy state, we carried out replica exchange/discrete molecular dynamics to obtain a temperature profile of the free energy surfaces of the PreTS and Products states and the transition state that lies between them.¹⁸ Simulations performed in the presence and absence of the pyrophosphate product revealed that the free energy change for the catalytic domain motion is favorable if and only if the PPi leaving group is absent from the active site, that is, only after the phosphoryl product is released to solution.

That paradoxical conditioning of the domain motion by the chemical catalysis—catalytic domain motion is favorable if and only if the ATP reaction is catalyzed—is reciprocal to the previous conditioning—TS stabilization is favorable if and only if the domains move. Thus, the former accelerates the chemistry if and only if the domains move. The latter, in turn, promotes domain motion if and only if the chemistry is catalyzed.

It is useful to define these phenomena in terms of gating, which implies using a conditional test to determine whether something happens. In biology, gating is often used to describe the function of receptors, like ion channels, that exist in open vs closed forms, depending on the presence or absence of a signal, which can be a membrane depolarization (voltage-gating⁵³) or the binding of a neurotransmitter (ligand-gating⁵⁴). The latter authors articulate the close relationship between gating and allosteric phenomena,⁵⁵ which in turn imply energetic coupling between distant parts of a protein. Although “gating” has not previously been applied to such systems, it should be apparent that, together, the two conditions considered here—catalysis gated by domain motion and domain motion gated by catalysis—assure that domain motion is tightly coupled to ATP utilization. They help transduce free energy as reciprocally-coupled gates.

6 |. PARADOXES IN NANOSCALE STATISTICAL THERMODYNAMICS

Structural biology and mechanistic enzymology of tryptophan activation by TrpRS,^18,25,39 identified two novel gating functions that coordinate domain motion with catalysis of NTP utilization and enable efficient conversion of its hydrolysis free energy. Ironically, those gating functions uncover a paradox: the active-site Mg²⁺ ion could not stabilize the transition state on a macroscopic scale, because the unfavorable conformational free energy change would prohibit configuring it within the active site without first releasing the PPi leaving group. Catalysis, prevented by an unfavorable conformational change, is nevertheless required to enable that conformational change. Such gating can arise only from nanoscale fluctuations. Such paradoxes have animated recent discussion of nanoscale statistical thermodynamics^47,56–62 centering on the distinction between “Brownian Ratchet” and “Powerstroke” models.⁶¹

6.1 |. Thermalization

Domain motion and NTP hydrolysis occur on radically different timescales. This was established first for myosin by Lymn and Taylor.⁶³ The pre-steady state rate of tryptophan activation by TrpRS is ~100 times faster than turnover in the absence of tRNA^Trp17 and 6 to 7 orders of magnitude slower than the transition-state lifetime. Consequently, the hydrolysis free energy is not realized immediately in any transducing NTPase. Rather, the reaction approaches equilibrium, or “thermalizes”⁶¹ much more slowly when bound to an NTPase than it does in solution, because motor proteins, GTPases, and synthetases bind one or both NTP cleavage products tightly, leading to the requirement for “release factors,” also referred to as “GEFs” in the case of GTPases. The first release factor to be identified, actin, releases the ADP product from myosin.⁶⁴ tRNA serves as the release factor for aminoacyl-tRNA synthetases, by accepting transfer of the amino acid with the release of AMP. Dynamic transition-state stabilization and release factor-dependence lengthen thermalization of NTP hydrolysis to the timescale of domain motion.

6.2 |. Overdamping facilitates near-equilibrium approximations

Astumian⁶⁵ introduced a key element of the discussion by noting that nanoscale behavior is dominated by the size of macromolecules, relative to the frictional forces they encounter as domains move. In general, for objects smaller than a few micrometers in solution—different domains of a conformationally-active protein— the inertial force (mass times acceleration) of such a small particle is negligible in comparison to the viscous force (velocity times coefficient of viscous drag). Thus, macromolecules in solution, even under the influence of an external force, are at every instant very close to mechanical equilibrium, because the viscous drag force is equal to, and opposes the net mechanical force. Such “overdamped systems”^59,65,66 therefore remain in mechanical equilibrium throughout their range of motion and on time scales longer than a few microseconds. Consequently, the near-equilibrium terms of the Onsager-Machlup theory⁶⁷ furnish an unexpectedly appropriate description even if the source driving their motion is far from equilibrium with the path in which the system moves,⁶⁵ and their fluxes are proportional to the forces that cause them.^18,39,56,68

6.3 |. Product release

Making product release rate-limiting lengthens both the length and time scales for thermalization of the ATP hydrolysis reaction, typically to nanometers and longer than microseconds, allowing motors to overcome randomizing effect of thermal fluctuations and enabling them to generate unidirectional motion.⁶¹ For these reasons, the power stroke model as presented in textbooks, is conceptually incomplete for all catalysis-driven motors biomolecular motors.^68,69 The missing element is a mechanism for gating the catalysis such that reaction with substrate is fast and reaction with product slow in one state of the mechanical cycle, and reaction with substrate slow and reaction with product fast in a different state of the mechanical cycle.^15,60,68,69

6.4 |. Gating

In their discussion of free energy transduction, Branscomb, et al.⁴² distinguish two processes—the driving, here, NTP hydrolysis, and the driven, here, the conformational change. They emphasize that using enzymes to create disequilibria requires operating “…in the following somewhat counterintuitive manner: (a) the driven process fully completes before the driving one is permitted to do so, (b) the state in which the driven process is fully complete is what triggers, or ‘gates’, the completion of the driving process, and (c) the state in which both processes are fully complete functions as the necessary precondition ‘trigger’ for the engine to return to its starting configuration.” Details in Figure 3 compose a quite precise molecular realization of that description.

Our results in some form are likely to be general. The myosin power stroke also appears to be triggered by phosphate release,^11,12 establishing a strict homology to the back-end gating—making domain motion contingent on product release—observed for TrpRS. Further, ATP cleavage to ADP and Pi presumptively differentiates the 90° Products state from the 45° position liberated by ATP from the rigor state actin-myosin complex. Functional homology of front- and back-end gating in TrpRS and myosin implies that in motor proteins, and potentially a wider range of biosynthetic and signaling NTPases, an as-yet unidentified homolog of the TrpRS front-end gating likely also makes transient catalysis depend on domain movement.

Although our initial use of the escapement metaphor²⁵ is rarely cited, Branscomb and Russell^15,16 recognized the pervasive requirement for escapement mechanisms to sustain living things far from equilibrium: “We are here arguing, however, that Brownian ratchet escapement mechanisms form the enabling heart of all molecular-level disequilibrium converting systems.”

6.4.1 |. Combinatorial mutagenesis: Using the unfolded states as a reference for assessing how ligand-dependent stability changes implement the escapement mechanism

Reciprocally-coupled gating illustrates the deep dependence of free energy transduction on differential conformational thermodynamics. A key question remains: do different conformational states lead to different relative stabilities, and if so, how do altered side chain packing interactions contribute to the differential stabilities? Answers to these questions can, in principle, be drawn from thermal melting profiles of combinatorial mutagenesis as performed for the D1 variant ensemble. The denatured state of a protein serves as a reference state analogous to the use of the vapor phase as a reference state for amino acid phase behavior.^70,71 As the distinct stable structures along the reaction coordinate have all been realized in X-ray crystal structures with different bound ligands, it is now possible to carry out thermal melting studies in high throughput mode using Thermofluor (differential scanning fluorimetry) in the presence of saturating concentrations of the ligands used for crystallization. Effects of the D1 mutations on each conformation should combine in a manner consistent with the quantitative effect of the mutational ensemble on the kinetic rate measurements.¹⁷

This objective depends, however, on the ability to draw thermodynamic inferences from melting curves. We present elsewhere²³ two distinct kinds of evidence for the thermodynamic significance of Thermofluor measurements. First, the melting profiles match in detail that obtained from a computational free energy thermal surface. Second, Thermofluor measurements are sufficiently precise to test the underlying linearity of their relationship to the mutated sites via the experimental design matrix from which the mutants were generated, and those linear models validate the use of an assumption advanced for perturbations on melting behavior by Calvin, et al.⁷²

7 |. CONCLUSIONS

I have reviewed 75 years of successive approaches to understanding enzymatic free energy transduction,^1–9 highlighting the missing molecular details that enable efficient storage and re-use of NTP hydrolysis free energy.^15,16 Recent structural biology, mechanistic enzymology, and computational studies reveal the molecular mechanisms that enable transduction by tryptophanyl-tRNA synthetase. Long-range coupling of Mg²⁺ catalytic activation of tryptophan activation by TrpRS to domain motion²⁵ acts as a front-end gating mechanism, coupling catalysis to domain motion by ensuring that catalysis of ATP utilization occurs if and only if domain motion occurs simultaneously. That front-end gating is reciprocally-coupled to a back-end gating: release of the phosphoryl fragment of the ATP hydrolysis products is necessary before the TrpRS catalytic domain motion can become thermodynamically favorable, making domain motion conditional on catalysis.¹⁸ The directionality essential to sustain far-from-equilibrium processes is effected by chemical gating—the affinities of successive conformational states for successive stages of the hydrolytic reaction are tightly orchestrated to be optimally interdependent. As both gating mechanisms are necessary to complete the originally proposed escapement metaphor,²⁵ it seems likely that reciprocally-coupled gating will eventually be demonstrated for most or all motor proteins and other free-energy transducing enzymes. In a practical sense, important goals for developing autonomous, chemically driven molecular machines are to better understand the allosteric mechanisms by which gating can be achieved,⁶⁹ re-invigorating the role of stability measurements in the context of combinatorial mutagenesis.