MD simulation of protein-ligand interaction: formation and dissociation of an insulin-phenol complex

Abstract

Complexes of proteins with small ligands are of utmost importance in biochemistry, and therefore equilibria, formation, and decay have been investigated extensively by means of biochemical and biophysical methods. Theoretical studies of the molecular dynamics of such systems in solution are restricted to 10 ns, i.e., to fast processes. Only recently new theoretical methods have been developed not to observe the process in real time, but to explore its pathway(s) through the energy landscape. From the profiles of free energy, equilibrium and kinetic quantities can be determined using transition-state theory. This study is dedicated to the pharmacologically relevant insulin-phenol complex. The distance of the center of mass chosen as a reaction coordinate allows a reasonable description over most of the pathway. The analysis is facilitated by analytical expressions we recently derived for distance-type reaction coordinates. Only the sudden onset of rotations at the very release of the ligand cannot be parameterized by a distance. They obviously require a particular treatment. Like a preliminary study on a peptide, the present case emphasizes the contribution of internal friction inside a protein, which can be computed from simulation data. The calculated equilibrium constant and the friction-corrected rates agree well with experimental data.

FIGURE 1

R₆ hexamer with six phenol molecules (blue) as seen along the threefold symmetry axis running through the two chloride and two zinc ions (red). The upper three dimeric insulin molecules are shown in orange. The only side chains shown are those of the zinc-coordinating histidines B10.

FIGURE 2

In the side view on a space-filling model of the R₆ hexamer, one phenol is seen in its binding pocket made up of amino acids from two of the lower insulin dimers. The side chain of Ile A10 is hiding the lower third of the phenol.

FIGURE 3

The hydrophobic pocket between two adjacent dimers is essentially defined by the residues His B5 (red) of the first and Cys A6, Cys A11, and Leu B11 (green) of the second dimer. Apparently the phenol hydroxyl group donates a hydrogen to the carbonyl oxygen of Cys A6 and accepts one from the amide proton of Cys A11, whereas the ring contacts the imidazol ring of His B5.

FIGURE 4

Snapshots of the escape of phenol from the binding pocket as obtained from equilibrations at indicated intermediate values of the reaction coordinate. The perspective is different from that of the previous figures (see text). Backbone sections of relevant residues are colored for Leu B11 (dark green), His B5 (orange), Ser A9 (green), Ile A10 with side chain (cyan), Cys A11 (yellow), and Cys A6 (red). The nomenclature was simplified by omitting the number of the subunit.

FIGURE 5

Displacement of Cys A11 (RMS averaged over all atoms) and cumulative mean of the constraint force f_R at R = 1.68 nm. The displacement is indicative of (and probably partially responsible for) the force opposing the dissociation at this stage, which is already close to the activation barrier. The apparent relaxation of the force is accompanied with the residue's return to its x-ray position.

FIGURE 6

RMS displacement of Ser A9 against the reaction coordinate. The gray section represents the displacement of the C_α atom, the whole bar the average over all atoms. The residue transiently moves away from its x-ray position, the maximum displacement occurring at the transition state (R = 1.87 nm).

FIGURE 7

RMS displacement of Ile A10 against the reaction coordinate analogous to Fig. 6. It transiently moves away from its x-ray position with a maximum displacement at the transition state (R = 1.87 nm). This movement is exceptionally pronounced and clearly correlated with the opening phase of the binding pocket. The black line is the profile of free energy discussed in the thermodynamics section.

FIGURE 8

Eulerian angles (φθψ) describing the orientation of phenol relative to insulin. The z axis is the symmetry axis of the hexamer; z′ denotes the “long” axis of phenol.

FIGURE 9

Time behavior of the Eulerian angles (φθψ) at different stages of the process. Over most of the pathway, restricted fluctuations about one or two well-defined orientations are observed. Note that this particular pattern does not change at the passage over the activation barrier (close to R = 1.88 nm, top right), but only later after the dissociation of the ligand from the protein surface (R ≥ 2.03 nm).

FIGURE 10

The constraint force f_R at R = 1.63 nm (black). The white curve is a 4-ps average.

FIGURE 11

Accumulated mean of the constraint force for different values of the reaction coordinate R.

FIGURE 12

Profile of the mean constraint force, the bars marking the statistical errors. The flat thin line is the expected entropic force that remains when the interaction between phenol and insulin disappears.

FIGURE 13

The profile of the free energy, ΔF, computed as the integral over the mean constraint force. The transition state at R = 1.87 nm (maximum) separates the bound state of the insulin-phenol complex (deep left minimum) from the dissociated state (beginning decline for large R).