Diffusional channeling in the sulfate-activating complex: combined continuum modeling and coarse-grained brownian dynamics studies

Abstract

Enzymes required for sulfur metabolism have been suggested to gain efficiency by restricted diffusion (i.e., channeling) of an intermediate APS(2-) between active sites. This article describes modeling of the whole channeling process by numerical solution of the Smoluchowski diffusion equation, as well as by coarse-grained Brownian dynamics. The results suggest that electrostatics plays an essential role in the APS(2-) channeling. Furthermore, with coarse-grained Brownian dynamics, the substrate channeling process has been studied with reactions in multiple active sites. Our simulations provide a bridge for numerical modeling with Brownian dynamics to simulate the complicated reaction and diffusion and raise important questions relating to the electrostatically mediated substrate channeling in vitro, in situ, and in vivo.

FIGURE 1

Two active sites in the type III SAC dimer and boundary information. The values Ξ and Δ represent the SAC domain and whole spherical domain, respectively. The value Ω = Δ − Ξ represents the diffusion domain. The active site of ATP sulfurylase is in yellow and that of APS kinase is in red. The values Γ_b and Γ_r represent the reflective Neumann boundary, while the two active sites Γ_as and Γ_ap are reactive Robin boundaries.

FIGURE 2

The active sites of ATP sulfurylase and APS kinase in the SAC dimer: (a) ATP sulfurylase; and (b) APS kinase.

FIGURE 3

Dependence of channeling efficiency on the intermediate charge at 40 mM ionic strength.

FIGURE 4

The intermediate concentration distribution in the solvent around SAC. Blue indicates extremely low concentration; cyan represents the medium low concentration and red the high concentration.

FIGURE 5

The influx of APS^2– and APS⁰ in one active site of the APS kinase along the simulation time: (a) APS^2– and (b) APS⁰.

FIGURE 6

Eighty-one planes divide the channel into 80 sections through the active center of ATP sulfurylase to the active center of APS kinase. The average width of the channel is ∼26 Å (20).

FIGURE 7

A dwell histogram indicates the region of the channel where APS^2– ions preferentially reside. The channel is divided into 80 sections, and the average probability in each slice is counted during 78 independent CGBD simulations of 2 μs. The standard deviation is represented with the line.

FIGURE 8

The APS^2– distribution in the channel in one of CGBD simulations. The blue represents one monomer and the green the other monomer. The yellow represents where the center of APS^2– resides in 2 μs simulation. The cyan and white spheres represent Lys⁺ and Arg⁺, respectively.

FIGURE 9

The electrostatic potential on the surface of the SAC complex. The red and blue represent the negative and positive potentials larger than 1 kT/e, respectively.

FIGURE 10

The APS⁰ distribution in the channel in one of CGBD simulations. The blue represents one monomer and the green the other monomer. The yellow represents where the center of APS^2– resides in 2 μs simulation. The cyan and white spheres represent Lys⁺ and Arg⁺, respectively.

FIGURE 11

The APS^2– axial distribution during the channeling process simulated with the SMOL solver. In each section, only the APS^2– ions within 15 Å from the axis were counted. When t = 0, 10, 50, 500, and 3000 ns, there are 39,497, 72,695, 75,611, 77,031, and 77,178 APS^2– ions released from one ATP sulfurylase active site.

FIGURE 12

A dwell histogram indicates the region of the channel where the neutral ligands preferentially reside. The channel is divided into 80 sections, and the average probability in each slice is counted during 69 independent CGBD simulations of 2 μs. The standard deviation is represented with the line.