Overcoming the Bottleneck of the Enzymatic Cycle by Steric Frustration

The enormous catalytic power of natural enzymes relies on the ability to overcome the bottleneck event in the enzymatic cycle, yet the underlying physical mechanisms are not fully understood. Here, by performing molecular simulations of the whole enzymatic cycle for a model multisubstrate enzyme with a dynamic energy landscape model, we show that multisubstrate enzymes can utilize steric frustration to facilitate the rate-limiting product-release step. During the enzymatic cycles, the bottleneck product is actively squeezed out by the binding of a new substrate at the neighboring site through the population of a substrate-product cobound complex, in which the binding pockets are frustrated due to steric incompatibility. Such steric frustration thereby enables an active mechanism of product release driven by substrate-binding energy, facilitating the enzymatic cycle.

Figure 1

Schematic of the enzymatic cycle of a bisubstrate-biproduct reaction $S_1+S_2\rightleftharpoons P_1+P_2$, which catalyzes the transfer of a chemical group (dashed ellipse) from one substrate ($S_1$) to another ($S_2$), producing two products ($P_1$ and $P_2$). Because each binding site can be substrate bound, product bound, or empty, the substrate-product exchange maximally encounters nine chemical states, including two hybrid complexes with substrate and product cobound at the neighboring sites. In the hybrid complex $S_1{P}_2$ (red), the substrate $S_1$ and product $P_2$ are sterically incompatible due to the overlap of the two transferring groups, leading to steric frustration in the binding pockets.

Figure 2

Dynamic energy landscape model of enzyme catalysis. (a) Structures of AdK at open (inactive)—left—and closed (active)—right—conformations. (b) Structures of the bound ligands in the chemical states DD and TD. (c) Free energy landscape showing the conformational fluctuations of the two lids at apo state. The reaction coordinates ${\chi }_{\mathrm{LID}}$ and ${\chi }_{\mathrm{NMP}}$ take negative (positive) values in the open (closed) conformations [31]. (d) Schematic diagram showing the dynamic energy landscape model of the whole enzymatic-cycle of AdK, assuming a stepwise ligand exchange process. The transitions with dashed lines are prohibited without supplying ADP. The effects of substrate-product exchange on the energy landscapes were schematically shown for selected chemical states. (e) MD trajectory showing the conformational motions and ligand exchange for a representative enzymatic cycle at $[\mathrm{ATP}]=[\mathrm{AMP}]=150\mu \mathrm{M}$. The shaded region corresponds to the substrate-product exchange. (f) Relative probabilities of the canonical pathway (black) and hybrid pathway (blue) of the enzymatic cycle as a function of substrate concentration. The results of two subpathways via TD and DM are also shown.

Figure 3

Steric frustration facilitates the bottleneck step of enzymatic cycle. (a) Turnover rates versus substrate concentrations for the intact simulations (filled circles), control simulations with substrate-product coupling deleted in the TD state (open circles), and simulations with the hybrid pathway prohibited (squares). The error bars represent standard deviation of 20 independent simulations. (b) Rates of the key steps in the substrate-product exchange for the intact simulations (filled) and the control simulations (open).

Figure 4

Role of conformational plasticity on the substrate-product exchange. (a) Projection of the snapshots, at which the LID-domain ADP dissociates from the state DD (red dots), onto the free energy landscape constructed from all conformations. The substrate concentration is $150\mu \mathrm{M}$. Black circle: center of the HOHC state in Ref. [22]; red triangles: crystal structures of the open and closed states. (b) Distributions of SASA for the ADP-releasing snapshots (red), together with the distributions of the closed (blue) and open (black) conformations. (c) A representative snapshot of partly open conformation taken from all-atom simulations with DD state (left). ADPs are colored white. Crystal structures of open (middle) and closed (right) conformations are also shown.