The promoting vibration in human heart lactate dehydrogenase is a preferred vibrational channel

Abstract

We examine whether the rate-promoting vibration of lactate dehydrogenase is a preferred axis of thermal energy transfer. While it seems plausible that such a mechanistically important motion is also a favored direction of energy transfer, none of the previous studies of rate-promoting vibrations in enzymatic catalysis have addressed this question. It is equally likely that the promoting vibration, though catalytically important, has no different properties than any other axis in the protein. Resolution of this issue is important for two reasons: First, if energy is transferred along this axis in a preferred fashion, it shows that the protein is engineered in a way that transfers thermal energy into a motion that is coupled to the chemical step. Second, the discovery of a preferred direction of thermal transfer provides a potential route to experimental verification of the promoting vibration concept. Our computational experiments are specifically designed to mimic potential laser experiment with the deposition of thermal energy in an active-site chromophore with subsequent measurement of temperature at various points in the protein. Our results indicate that the promoting vibration is indeed a preferred channel of energy transfer. In addition, we study the vibrational structure of the protein via the dynamical structure factor to show preferred vibrational motion along the promoting vibration axis is an inherent property of the protein structure via thermal fluctuations.

Figure 1

Shown in the first panel are the different spherical shells containing members of the promoting vibration. The highlighted residues represent the different members of the promoting vibration. Drawn adjacent to the first panel are the temperatures of each the residues. Promoting vibration residues closer to the active site maintain higher temperatures throughout the course of the simulation.

Figure 2

The average temperatures over the 20 ps heating window are shown as spikes. The brown spikes correspond to residues that are both part of the promoting vibration and the kernel PCA residues, the red spikes correspond to the promoting vibration residues, the green spikes correspond to kernel PCA residues.

Figure 3

Bar graphs showing the temperatures of all the residues in each respective concentric 3 Å shell. The residues in red correspond to PV-Res, the residues in green correspond to kPCA-Res, and the residues in brown correspond to both PV-Res and kPCA-Res. Horizontal lines are drawn from the PV-Res temperatures for aid in visual comparison

Figure 4

The structure factor S(k, ω) for k = 0.2 Å⁻¹ along the PV axis (black line) and along an axis perpendicular to the promoting vibration. There is strong anisotropy. The sharpness of the peak at 125 cm⁻¹ means that there are stable fluctuations along the PV axis for that frequency.