Enzyme millisecond conformational dynamics do not catalyze the chemical step

Abstract

The idea that enzymes catalyze reactions by dynamical coupling between the conformational motions and the chemical coordinates has recently attracted major experimental and theoretical interest. However, experimental studies have not directly established that the conformational motions transfer energy to the chemical coordinate, and simulating enzyme catalysis on the relevant timescales has been impractical. Here, we introduce a renormalization approach that transforms the energetics and dynamics of the enzyme to an equivalent low-dimensional system, and allows us to simulate the dynamical coupling on a ms timescale. The simulations establish, by means of several independent approaches, that the conformational dynamics is not remembered during the chemical step and does not contribute significantly to catalysis. Nevertheless, the precise nature of this coupling is a question of great importance.

Fig. 1.

The effective 2-D free energy surface for the ADK system. Here, I, II, and III denote the reactant state (RS) in the open conformation, the RS in the closed conformation, and the product state (PS) in the closed conformation respectively.

Fig. 2.

A long-timescale trajectory along the conformational coordinate, showing (A) the time dependence of and (B) the corresponding ACF for the conformational coordinate in the 2-D model.

Fig. 3.

The relationship between the first passage (fp) time, τ_fp, over the chemical barrier, and the height of the conformational barrier (for the case where Δg_chem^≠ = 5 kcal/mol). The calculations represent the average from several runs. The figure considers two correlations: The inverse fp time, (τ_fp)⁻¹, as a function of the conformational barrier, where it is shown that the crossing time of the chemical barrier is independent of the characteristic time of motion along the conformational coordinate as long as k_conf > k_chem (A), and τ_fp and τ_fp′ (which is the fp time when we start the counting from the moment the trajectory reaches the RS) (B). It can be seen that even when k_conf < k_chem, the time of crossing the chemical barrier is independent of the conformational landscape.

Fig. 4.

Exploring the possible effect of excess binding energy on the chemical step in the 2-D effective model. (A and B) The figure shows the following two situations: a hypothetical case where the trajectory starts from a high energy open state (I), rapidly moves to the closed RS (II), and finally crosses to the PS (III) (A), and a case where the simulations start at the closed RS (II) and move to the PS (III) (B). In both cases, the trajectory appears to be randomized in the closed reactant state.

Fig. 5.

Obtaining the first passage time for different trajectories in the CG model. The system starts at the closed structure (A), the partially open structure with a weak constraint (0.5 kcal mol⁻¹Å⁻²) with a minimum at the closed configuration (this pushes the system to the closed state) (B), and the partially open structure with a strong constraint (5 kcal mol⁻¹Å⁻²) (C). The chemical TS is reached when the energy gap changes sign. For simplicity, we describe the reaction by considering only the two first EVB states, and assuming a one-step mechanism. The resulting figures describe the time dependence of different trajectories starting with different initial conditions and demonstrate that having excess kinetic energy that drives the system toward the closed form does not lead to a shorter time for the chemical process.

Fig. 6.

The effect of introducing additional fast relaxation components to the conformational dynamics on τ_fp in the 2-D model. The notation for the different configurations is the same as that used in Fig. 1. The figure demonstrates that drastic qualitative changes in the features of the landscape along the conformational coordinate have almost no effect on the first passage time for the chemical barrier.