Subnanometre enzyme mechanics probed by single-molecule force spectroscopy

Abstract

Enzymes are molecular machines that bind substrates specifically, provide an adequate chemical environment for catalysis and exchange products rapidly, to ensure fast turnover rates. Direct information about the energetics that drive conformational changes is difficult to obtain. We used subnanometre single-molecule force spectroscopy to study the energetic drive of substrate-dependent lid closing in the enzyme adenylate kinase. Here we show that in the presence of the bisubstrate inhibitor diadenosine pentaphosphate (AP5A), closing and opening of both lids is cooperative and tightly coupled to inhibitor binding. Surprisingly, binding of the substrates ADP and ATP exhibits a much smaller energetic drive towards the fully closed state. Instead, we observe a new dominant energetic minimum with both lids half closed. Our results, combining experiment and molecular dynamics simulations, give detailed mechanical insights into how an enzyme can cope with the seemingly contradictory requirements of rapid substrate exchange and tight closing, to ensure efficient catalysis.

Figure 1. Structure of AdK.

The three-dimensional structure of the open (a) and closed (b) conformation of AdK from A. aeolicus (PDB ID Code 2RH5 and 2RGX). The CORE domain is labelled in green, and ATP and AMP lid in red and blue, respectively. The closed conformation is shown in the presence of the bisubstrate inhibitor AP5A (orange). The yellow spheres indicate the position of the inserted cysteines between position 42 and 43, and 144 and 145. The distance between the cysteines in the open and closed conformation is shown above.

Figure 2. Single-molecule force experiments of AdK by optical tweezers.

(a) Optical trap assay (for details, see Methods). (b) Sample traces of the closing and opening fluctuations of AdK at different Mg-AP5A concentrations and force biases. The grey and black dashed lines indicate the position of the closed (contracted) and open (extended) state, respectively (see also Supplementary Fig. 2). (c) Closing rate as a function of force for different Mg-AP5A concentrations. Solid lines are extrapolations of the closing rates to zero force, which are indicated by the asterisks (for details, see Methods). (d) Opening rate as a function of force for different Mg-AP5A concentrations (colours as in c) (see also Supplementary Fig. 3). The solid line is a fit extrapolating the opening rate to zero force (asterisk). (e) Comparison of two binding and closing models for AdK and AP5A adapted from Okazaki and Takada. Binding and unbinding of the inhibitor is represented as the jump between a ligand-free and ligand-bound energy landscape. Exemplary routes from open ligand-free to closed ligand-bound form are shown for the conformational selection (blue) and induced-fit model (red). For the ligand-bound energy landscape, distances from open and closed state to the transition state from optical trap experiments are shown.

Figure 3. Nucleotide-induced conformational changes of AdK.

(a) Sample traces of AP5A-induced closing and opening in the single-molecule competition assay at 1 μM AP5A with varying concentrations of ATP at a force of 10.5 pN. (b) Decrease in apparent binding free energy of AP5A in the single-molecule competition assay for the nucleotides ADP (yellow), Mg-ADP (green) and Mg-ATP (blue). Solid lines are fits of the binding model described in Methods (equation (2)) resulting in the following dissociation constants: , and . (c) ATP-induced fraction of full closing as a function of force for different ATP concentrations from the AP5A competition assay. Solid lines are fits to equation (7) yielding a size of the conformational change of Δx=0.5 nm. The dashed line shows the force-dependent closing expected if complete ATP lid closure is assumed. (d) Fraction of full closing at zero force induced by nucleotides Mg-ADP (green) and Mg-ATP (blue) as a function of nucleotide concentration extracted from the AP5A competition experiments. Solid lines are fits to the data assuming a binding model (equation (12)) with an affinity of the nucleotides to open and closed state of AdK. The resulting dissociation constants are , and and . (e) ADP-dependent lid closing from AP5A competition experiments. The upper dashed line indicates the position of the fc AP5A-bound state and the lower three lines indicate the position of the ADP-dependent AP5A-unbound state.

Figure 4. Effect of the phosphate linker length between the adenosine moieties.

(a) Equilibrium traces of the closing and opening of AdK in the presence of AP5A (left panel), AP4A (middle panel) and AP6A (right panel) at a force of 8 pN for AP5A and AP4A, and 12 pN for AP6A. The dashed lines represent the position of the fc (grey) and open (black) state of AdK. (b) Distance between closed and open state as a function of force in the presence of the different inhibitors AP5A (red), AP4A (purple) and AP6A (green). (c–d) Closing rate of AdK as a function of force for different AP4A (c) or AP6A (d) concentrations. It is noteworthy that the dashed lines are not fits to the AP4A and AP6A data, but fits to the rates obtained at the corresponding AP5A concentrations for comparison. (e) Opening rate of AdK as a function of force for different AP4A (purple) and AP6A (green) concentrations. Solid lines are fits to the closing rates extrapolated to zero force (asterisks). For comparison, a fit to the rates obtained at the corresponding AP5A concentrations is shown as a red dashed line. (f) Calculated free energy along the opening of AdK bound to AP5A (red), AP4A (purple) and AP6A (green) obtained from free-energy simulations without load (dashed lines) and with a subsequently added bias corresponding to an external load of 15 pN (solid lines). The free-energy curves are projections of free-energy landscapes (Supplementary Fig. 11) obtained from 2D H-REMD-US simulations in which the arrangements of AMP lid and ATP lid were controlled independently. (g) Model of the coupling between the conformational fluctuations and the binding of inhibitors or nucleotides to AdK. In the presence of nucleotides, a pc state is stably populated under force; however, AdK is still able to close fully especially in the absence of force. The binding of AP4A and AP5A induce the fc conformation of AdK, whereas the binding of AP6A stabilizes a pc state.