Frustration and the Kinetic Repartitioning Mechanism of Substrate Inhibition in Enzyme Catalysis

Abstract

Substrate inhibition, whereby enzymatic activity decreases with excess substrate after reaching a maximum turnover rate, is among the most elusive phenomena in enzymatic catalysis. Here, based on a dynamic energy landscape model, we investigate the underlying mechanism by performing molecular simulations and frustration analysis for a model enzyme adenylate kinase (AdK), which catalyzes the phosphoryl transfer reaction ATP + AMP ⇋ ADP + ADP. Intriguingly, these reveal a kinetic repartitioning mechanism of substrate inhibition, whereby excess substrate AMP suppresses the population of an energetically frustrated, but kinetically activated, catalytic pathway going through a substrate (ATP)-product (ADP) cobound complex with steric incompatibility. Such a frustrated pathway plays a crucial role in facilitating the bottleneck product ADP release, and its suppression by excess substrate AMP leads to a slow down of product release and overall turnover. The simulation results directly demonstrate that substrate inhibition arises from the rate-limiting product-release step, instead of the steps for populating the catalytically competent complex as often suggested in previous works. Furthermore, there is a tight interplay between the enzyme conformational equilibrium and the extent of substrate inhibition. Mutations biasing to more closed conformations tend to enhance substrate inhibition. We also characterized the key features of single-molecule enzyme kinetics with substrate inhibition effect. We propose that the above molecular mechanism of substrate inhibition may be relevant to other multisubstrate enzymes in which product release is the bottleneck step.

Figure 1

(A) Three-dimensional structure of AdK at the closed state. The three domains are shown by different colors (red, LID; blue, NMP; gray, CORE). The ATP binding site and AMP binding site were labeled by red and blue circles. The binding states of the site with ATP, AMP, ADP, or empty are represented by T, M, D, or ⌀, respectively. Due to geometrical compatibility, AMP may also nonspecifically bind to the ATP binding site. (B) Schematic diagram showing the sterically frustrated catalytic pathway utilized by the multisubstrate enzyme to overcome the bottleneck product release step. Other parallel pathways with minor distributions have not been shown for clarify. (C) Two-dimensional free energy profile using the distances between the LID-CORE domains and between the NMP-CORE domains as collective coordinates for the wild-type AdK. (D) Turnover rates of the AdK as a function of AMP concentrations with the ATP concentrations being fixed at 300 μM (green), 600 (orange) and 1000 (blue). The solid lines are found by fitting using eq 2.

Figure 2

Dependence of the substrate inhibition on the pre-existing protein conformational equilibrium. (A, B) Two-dimensional free energy profiles for enzyme models with extremely open (A, P_close ≈ 0.01) and extremely closed (B, P_close ≈ 0.99) conformational equilibria. The conformational equilibria was tuned by changing the parameters in the dynamic energy landscape model. (C) Turnover rates as a function of AMP concentrations for the enzyme models with different P_close values. The solid lines are the fitting by eq 2. The P_close values were shown in the panel. (D–F) The enzymatic parameters k_cat, K_M, and K_I as a function of P_close values. The dash line corresponds to the parameters of the wild-type enzyme.

Figure 3

Kinetic repartitioning mechanism of substrate inhibition. (A) Mean first passage time (MFPT) for sampling the catalytically competent complex (including productive substrate binding and conformational closing steps) as a function of AMP concentrations for the ADK models with different P_close. The MFPT was normalized by the value at the AMP concentration of 200 μM. (B) MFPT of product release as a function of AMP concentrations for the ADK models with different P_close. (C) Probabilities of the frustrated pathway (blue), canonical pathway via empty state (black), and other pathways via nonfrustrated substrate–product cobound state (DM) as a function of AMP concentrations. The ATP concentration was fixed at 1000 μM in all the above simulations. In this work, chemical state “XY” represents that the LID domain site and NMP domain site are occupied by “X” and “Y”, respectively, with X = T, D, M, or ⌀ and Y = M, D, or ⌀. For example, the chemical state TD (DM) represents the chemical state in which the LID domain site and NMP domain site are occupied by ATP and ADP (ADP and AMP), respectively. (D) Schematic showing the substrate inhibition mechanism, whereby nonspecific binding of excess substrate S₂ to the S₁ site suppresses the population of the frustrated catalytic pathway and, therefore, the overall turnover rate. Other competitive pathways with increased probabilities at excess substrate were not shown here for clarity.

Figure 4

Localized frustration around the ligand binding sites of AdK. (A) Localized frustration pattern of the two product ADP binding sites at the chemical state DD. The protein is shown by cartoon representation. The contacts between the binding residues and the two product ADPs with minimal frustration and high frustration were shown by green lines and red lines, respectively. The two ligands were colored orange. (B, C) Localized frustration pattern of the two ligand binding sites at the chemical states TD (B) and MD (C).

Figure 5

Conformational distribution of the bottleneck product ADP binding site (NMP domain) sampled by short atomistic MD simulations along the reaction coordinates RMSD and contact energy for the chemical states DD (A), TD (B), and MD (C). Here the RMSD measures the root-mean-square deviation of the bottleneck product ADP binding site with respect to the corresponding structure at the native state. The total contact energies correspond to the summation of pairwise contact energies between all the residue pairs at the ADP binding site of the NMP domain. The pairwise contact energies were calculated following ref (36) based on the rosseta energy function. The total contact energies were shown with the rosseta energy unit (REU).

Figure 6

Effect of substrate inhibition on the single-molecule enzymatic kinetics for ATP concentrations of 1000 μM. (A) Distribution of the single-molecule turnover time at different AMP concentrations calculated based on the time interval of the full catalytic-cycle; (B) Distribution of the time interval for sampling the catalytically competent state; (C) Distribution of the time interval for the release of the rate-limiting product ADP.