Quantum and all-atom molecular dynamics simulations of protonation and divalent ion binding to phosphatidylinositol 4,5-bisphosphate (PIP2)

Abstract

Molecular dynamics calculations have been used to determine the structure of phosphatidylinositol 4,5 bisphosphate (PIP2) at the quantum level and to quantify the propensity for PIP2 to bind two physiologically relevant divalent cations, Mg(2+) and Ca(2+). We performed a geometry optimization at the Hartree-Fock 6-31+G(d) level of theory in vacuum and with a polarized continuum dielectric to determine the conformation of the phospholipid headgroup in the presence of water and its partial charge distribution. The angle between the headgroup and the acyl chains is nearly perpendicular, suggesting that in the absence of other interactions the inositol ring would lie flat along the cytoplasmic surface of the plasma membrane. Next, we employed hybrid quantum mechanics/molecular mechanics (QM/MM) simulations to investigate the protonation state of PIP2 and its interactions with magnesium or calcium. We test the hypothesis suggested by prior experiments that binding of magnesium to PIP2 is mediated by a water molecule that is absent when calcium binds. These results may explain the selective ability of calcium to induce the formation of PIP2 clusters and phase separation from other lipids.

Figure 1

(A) The optimized geometry of PIP₂ highlighting several intramolecular hydrogen bonds. (B) The atom-naming scheme used in the text.

Figure 2

(A) The results of a relaxed potential energy scan of the phosphodiester dihedral angle joining the headgroup of PIP₂ to the glycerol moiety and the acyl chains. The dihedral angle is defined by the atoms labeled on the left of panel C. A value of 0 indicates that the plane defined by C1, O1, and P1 is aligned with the plane defined by O1, P1, and O11. (B) The angle between the ‘head’ and ‘tail’ of PIP₂ measured after a geometry relaxation at the values of the phosphodiester dihedral angle reported in panel (A). The head-tail angle corresponds to the angle between the planes on the right of panel (C).

Figure 3

(A) The average surface area of PIP₂ as calculated by squaring the maximum distance between oxygen atoms on two different phosphomonoester groups. The two histograms come from two separate QM/MM simulations with trajectories of 5 and 10 ps. (B) A comparison between the average surface area in simulations and Langmuir monolayer experiments of PIP₂ without a divalent ion present, with calcium, or magnesium. The error bars are the standard deviation of the area. (C) The same data as in panel (B) but the values for calcium and magnesium have been normalized by the experimental or simulation reported average surface area in the absence of divalent ions.

Figure 4

(A) Free energy contours for calcium binding between the two phosphomonoester groups or to only the 4-phosphate group. (B) A scatter plot of the thermodynamic sampling path of the trajectory with renderings shown on the right for specific points along the path.

Figure 5

The free energy of spreading the phos phomonoester groups of PIP₂ in the presence of calcium, magnesium, or potassium using classical US simulations. The insets show renderings from the simulations. Calcium (blue) binds tightly to the 4-phosphate group of PIP₂. Magnesium (red) binds loosely to the 4-phosphate group and is coordinated by water molecules (TIP3 oxygens within 4 Å of the magnesium are shown as small blue spheres). Potassium does not appear to tightly bind PIP₂ and is not shown. The shaded background represents the mean square difference between analyzing only the first half umbrella sampling trajectories and the full window.

Figure 6

The free energy of total deprotonation of the PIP₂ phosphomonoester groups using QM/MM US simulations. The insets show the initial configuration, with proton H51 bound to the 5-phosphate, an intermediate structure with proton H51 bound to the 4-phosphate, and the final configuration with proton H51 (blue) forming a hydronium ion and water molecules hydrogen bonding (black dashed line) with the PIP₂ phosphomonoester groups.

Figure 7

(A) The equilibrium distance to PIP₂ obtained for the divalent ions, calcium or magnesium, in separate classical MD simulations and (B) the transient binding behavior of several potassium ions in a water sphere with a single PIP₂ molecule. Renderings of snapshots from simulations are shown in the insets.

Figure 8

The free energy landscape for dissociating divalent ions from PIP₂.

Figure 9

The free energy landscape for dissociating a proton from the 5-phosphate group of PIP₂ in the presence of calcium or magnesium. The shaded background represents the mean square difference between analyzing only the first half umbrella sampling trajectories and the full window. In the insets, the proton to be dissociated is shown in black, magnesium in red, and calcium in blue.