Protein collective motions coupled to ligand migration in myoglobin

Abstract

Ligand migration processes inside myoglobin and protein dynamics coupled to the migration were theoretically investigated with molecular dynamics simulations. Based on a linear response theory, we identified protein motions coupled to the transient migration of ligand, carbon monoxide (CO), through channels. The result indicates that the coupled protein motions involve collective motions extended over the entire protein correlated with local gating motions at the channels. Protein motions, coupled to opening of a channel from the distal pocket to a neighboring xenon site, were found to share the collective motion with experimentally observed protein motions coupled to a doming motion of the heme Fe atom upon photodissociation of the ligand. Analysis based on generalized Langevin dynamics elucidated slow and diffusive features of the protein response motions. Remarkably small transmission coefficients for rates of the CO migrations through myoglobin were found, suggesting that the CO migration dynamics are characterized as motions governed by the protein dynamics involving the collective motions, rather than as thermally activated transitions across energy barriers of well-structured channels.

Figure 1

A schematic view of Mb structure. The protein is composed of eight α-helices (A–H) represented by rods. Spheres located inside the protein indicate the distal pocket and Xe sites. A cofactor, i.e., heme, and histidine residues in the F helix covalently coordinating to the heme Fe atom (the proximal His) and in the E helix (the distal His), respectively, are also depicted.

Figure 2

(a) External forces acting on protein groups due to interaction with CO passing through channels. Arrows in yellow, orange, and green represent the external forces upon the migrations between DP and Xe4, Xe4 and Xe2, and Xe2 and Xe1, respectively. DP, Xe4, Xe2, and Xe1 are denoted by arrows in magenta. Three-dimensional free energy map of the CO migration pathway with grid spacing of 0.2 Å reported in Nishihara et al. (17) is also shown. Dots indicate the free energy. (b) Large components of protein conformational changes in response to the external forces shown in panel a. Color scheme for arrows is the same as that used in panel a.

Figure 3

Protein conformational change, δr_i, in response to the external forces coupled to the CO transition between DP and Xe4 (red dots) and root mean-square fluctuations calculated with a 10-ns MD trajectory (blue dots). The protein conformational changes coupled to the CO transitions between Xe4 and Xe2, and Xe2 and Xe1, are shown in Fig. S5.

Figure 4

Protein backbone structural change in response to the external forces coupled to the CO transitions between DP and Xe4. Backbone traces of the average structure of the unperturbed deoxy Mb and of displaced structures undergoing the protein conformational changes in response to the external force are depicted in tube representation colored in blue and orange, respectively. Arrows in red along with labels of the helices indicate directions of the large conformational changes. To see the protein response easily, the protein response is depicted to be three times as large as the one shown in Fig 3. The protein backbone structure changes coupled to the CO transitions between Xe4 and Xe2, and Xe2 and Xe1, are shown in Fig. S6.

Figure 5

Relative contributions of PC vectors (dots and dotted lines) up to 50 cm⁻¹ and accumulated relative contributions (solid line) to protein conformational changes in response to the external forces coupled to the CO transition between DP and Xe4. The relative contributions of PC vectors for the transitions between Xe4 and Xe2, and Xe2 and Xe1, are shown in Fig. S7.

Figure 6

Time evolution of normalized population of CO in DP. Dashed and solid lines indicate P_DP(t) observed in MD trajectories and a curve given by Eq. 4 fitted to the observed P_DP(t), respectively.