Direct observation of ultrafast large-scale dynamics of an enzyme under turnover conditions

Large-Scale Conformational Dynamics of AK Measured with smFRET.

Molecules of E. coli AK were labeled with FRET dyes at positions 73 and 142, which correspond to the CORE and the LID domains, respectively (Fig. 1A and SI Methods). We selected these two sites to maximize the difference in FRET efficiency between the open and closed conformations of the protein. Freely diffusing AK molecules emitted bursts of photons as they passed through a focused laser beam, and the arrival times of individual photons were registered on two detectors, one for the donor and one for the acceptor. Initially, all photons belonging to one molecule passing through the focus were used to calculate a FRET efficiency value. Histograms were created from thousands of such values (each histogram involved ∼15,000 photon bursts), and showed a peak FRET efficiency value of 0.4 in the absence of substrates, which shifted to a peak value of 0.6 upon addition of saturating concentrations of ATP (1 mM in the presence of 1 mM AMP and 160 µM ADP; Fig. 1B). This large shift suggested that the protein indeed populates one of two states: mostly open in the absence of ATP and mostly closed in the presence of substrate.

At intermediate ATP concentrations, a broad peak appeared in the histogram, with a FRET efficiency value in between the above two (Fig. 1B, gray histogram). The appearance of a broad peak rather than two separate and narrower peaks suggested fast exchange between two conformations, open and closed, presenting low and high FRET efficiency values, respectively (17). A series of data sets was obtained at increasing concentrations of ATP and ADP and a fixed AMP concentration of 1 mM. For each ATP concentration, an ADP concentration was selected to maintain the system under equilibrium, as verified experimentally (Fig. S1 and Table S1). Fluorescence bursts with a high photon flux, emanating from molecules that diffused through the center of the laser focus, were selected for further analysis. Observation of individual fluorescence bursts of AK molecules revealed the occurrence of fast transitions between low and high FRET efficiency values (Fig. 2 A–C), with anticorrelated jumps in the donor and acceptor channels between two levels. The frequency of jumps increased significantly as the concentration of ATP was increased from 0.5 μM (with 3.7 μM ADP; Fig. 2A) to 1 mM (with 160 μM ADP; Fig. 2C). Simulations suggested a jump rate of ∼104 s⁻¹ (Fig. S2).

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Fig. 2.

Domain closure dynamics under turnover conditions. (A–C) smFRET trajectories measured at increasing substrate concentration (ATP + ADP; Table S1): 4.2 μM (A), 16.8 μM (B), and 1.16 mM (C), with AMP at a fixed concentration of 1 mM. Top in each part shows donor (blue) and acceptor (light green) signals binned in 20 µs bins, and the Bottom shows the calculated FRET efficiency (orange), and the state of the system at each time bin, as calculated by the Viterbi algorithm based on the H²MM analysis (dark blue). (D) Closing and opening rates (cherry and green circles, respectively) as a function of substrate concentration, obtained from H²MM analysis of a series of smFRET experiments. Error bars represent standard errors of the mean. Continuous lines are fits to the model described in the text, from which closing and opening rate constants for the unbound and bound states of the enzyme were extracted. (E) Free energy profiles for the unbound (purple) and bound (gold) enzyme, calculated from the fitted rates (with an assumed preexponential factor of 1 μs in the Kramers rate expression) (38), indicate that the open conformation is more stable than the closed conformation in the unbound state, with the situation inverted in the bound state. The transition state free energy is reduced in the bound state, leading to faster domain closure dynamics. The curvatures and shapes of the free energy profiles were selected for visualization purposes only.

Analysis of smFRET Trajectories Yields a Dynamic Model for Domain Closure.

To accurately obtain the rates of domain closure in AK as a function of substrate concentration, we turned to H²MM, an analysis algorithm developed recently in our laboratory (16). This analysis uses photon arrival times as input for an optimization process that obtains populations and kinetic rates. The model we used involved only two states, open and closed, and analysis results were validated using three different independent methods, described in detail in SI Text, Figs. S3–S6, and Table S2. Analysis with three states did not yield better results. The domain closing and opening rates obtained by H²MM are shown in Fig. 2D as a function of substrate concentration (ATP + ADP; Table S1), and the populations of the open state are shown in Fig. S7. The analysis showed that, in the absence of substrate, 85% of the population is in the open state, while in the presence of saturating concentrations of substrates only 20% is in the open state. Surprisingly, it was found that both closing and opening rates increased dramatically upon substrate binding. The trend of the rise of the closing rate was different from that of the opening rate. To account for this behavior, we developed a model, which involves two sets of rates, one for the substrate-bound protein and one for the unbound protein. The model can be represented by Scheme 1.

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Scheme 1.

Kinetic model for domain closure of bound and unbound enzyme molecules. The terms in the scheme are defined in the text.

In this scheme, E and E_C are the unbound enzyme in its open and closed conformations, and E^S and ECS are the bound enzyme in its open and closed conformations, respectively. K_d is the substrate dissociation constant, kC and kO are the domain closing and opening rates of the unbound enzyme, whereas kCS and kOS are the domain closing and opening rates for the bound enzyme. The closing process occurs from E and E^S that interchange by substrate binding, but the opening process occurs from states that do not interchange, because the closed enzyme cannot release the substrate. Expressions for the apparent rate constants for the closing and opening reactions were derived (Methods), and used to fit the experimental results (continuous lines in Fig. 2D).

From the fit we find that Kd=55±6 μM, which matches nicely literature values (15, 18). We also find that kC=(2.2±1)×103 s⁻¹ and kO=(5.2±1.5)×103 s⁻¹, while kCS=(66.0±0.2)×103 s⁻¹ and kOS=(22.4±0.1)×103 s⁻¹. Thus, in the bound state of the protein the closing and opening rates are ∼10 times higher than in the unbound states, and are likely the fastest rates measured for a large-scale conformational change. Further, these rates are two orders of magnitude higher than the turnover rate of the enzyme, which is just 399 ± 14 s⁻¹. This finding is in stark contrast to previous literature (14, 15), which suggested that the opening reaction is rate limiting for the enzymatic reaction of AK. It is possible that previous work failed to observe the fast closing and opening rates due to the small changes in FRET efficiency values between the two states (which depended on the labeling positions selected in each experiment), as well as the more limited amount of single-molecule data.

It is illuminating to convert the four rates into two free energy profiles (FEPs), one for the unbound protein and one for the bound protein (Fig. 2E) (19). The protein switches between these two FEPs when it binds its substrates. On the unbound FEP the open state is more stable than the closed state, but on the bound FEP the open state is destabilized, making it less stable than the closed state. In addition, the transition state free energy is lower on the bound FEP, making both closing and opening reactions significantly faster than for the unbound protein.

Manipulating Conformational Dynamics with Substrate Analogs and Point Mutations.

It has been debated whether the domain closure of AK involves independent or cooperative motions of the LID and NMPbind domains (20, 21). Lee et al. (20) used all-atom structure-based simulation to study AK conformational transitions using Lorentzian attractive interactions based on native structures. They identified a dominant transition state that involves the LID-closed−NMPbind-open state. However, Pelz et al. (21) used single-molecule optical tweezers to measure the substrate-dependent forces that drive AK into a closed conformation. By using a substrate analog that binds both sites simultaneously, they directly showed that closing and opening of both lids is cooperative.

To shed additional light on this issue, we studied the effect of ATP in the absence of AMP or ADP. It was found that even a high concentration of ATP (50 μM) led to only a minimal change of the FRET efficiency histogram (Fig. 3A), proving that substrate binding to both LID and NMPbind domains is required for domain closure, and ruling out independent conformational changes. We further tracked the dynamics of the LID domain in the absence of the chemical step, using the two-substrate mimicking inhibitor P¹,P⁵-Di(adenosine-5′)pentaphosphate (AP₅A; Fig. S8) (22). AP₅A induced concentration-dependent changes in the closing and opening rates (Fig. 3B) that were similar to those observed with ATP, though shifted to lower concentrations, suggesting that it is the binding of the substrates that switches the enzyme from one FEP to the other, irrespective of the chemical step. We also studied domain closure dynamics with AMP-PNP, a nonhydrolysable analog of ATP with a similar K_d (23), and found that even at a high concentration and in the presence of AMP, the equilibrium did not fully shift to the closed conformation as in the presence of ATP and AMP (Fig. 3C). This finding is intriguing, because the only difference between ATP and AMP-PNP is the replacement of the oxygen between the β and γ phosphates by an amine. It suggests that the conformation of the substrate is crucial for the induction of the transition between the bound and unbound FEPs.

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Fig. 3.

smFRET experiments shed light on mechanistic aspects of domain closure. (A) Substrate binding to both domains is required for domain closure. FRET efficiency histograms of AK in the absence of substrate (royal blue), with 50 μM ATP (red), with 50 μM ATP and 1 mM AMP (orange), and with 50 μM ATP, 1 mM AMP, and a suitable concentration of ADP to maintain equilibrium (dashed black line). (B) The two-substrate mimicking inhibitor, AP₅A, leads to a concentration dependence of the closing and opening rates (cherry and green, respectively) similar to ATP. (C) The nonhydrolyzable ATP analog, AMP-PNP, does not fully shift the equilibrium to the closed conformation even at a high concentration. At 50 μM AMP-PNP and 1 mM AMP (red), the FRET efficiency histogram is similar to the one without any substrate (royal blue), while at 1 mM AMP-PNP and 1 mM AMP (orange), the histogram has shifted only halfway to the position obtained with 1 mM ATP and 1 mM AMP and a suitable amount of ADP (dashed black line).

To shed further light on the relation between substrate binding and FEP switching, we turned to study AK variants in which protein residues involved in substrate binding (11) were mutated. We found that mutations that fully or partially prevented switching between the two FEPs [K13M (24), Fig. 4A; T15A (25), Fig. 4B; and R123M (26), Fig. 4C] also reduced the enzyme’s turnover rate significantly (Table 1). These findings suggest that FEP switching has an effect on enzymatic turnover, and that specific substrate interactions with residues involved in catalysis are responsible also for the change in dynamics. It should be noted, however, that mutation could also reduce the turnover rate without affecting FEP switching, as found with the mutant R88M (26) (Fig. S9 and Table 1).

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Fig. 4.

Point mutations affect the conformational dynamics of AK. The mutations K13M (A), T15A (B), and R123M (C) reduced the turnover rate to different degrees (Table 1), but fully or partially prevented switching from the unbound FEP to the bound FEP. Indeed, at saturating concentrations of the substrates (1 mM ATP and AMP together with 164 µM ADP for K13M and R123M; 10 mM ATP and 15 mM AMP together with 0.1 mM ADP for T15A), only a small population of the closed conformation was noted in FRET efficiency histograms (orange), compared with the wild-type enzyme (dashed black line). In green are FRET efficiency histograms of the apo mutant enzymes. Insets show the structure of AK with the mutated residues marked in color.