Hyperconjugation-mediated solvent effects in phosphoanhydride bonds

Abstract

Density functional theory and natural bond orbital analysis are used to explore the impact of solvent on hyperconjugation in methyl triphosphate, a model for "energy rich" phosphoanhydride bonds, such as found in ATP. As expected, dihedral rotation of a hydroxyl group vicinal to the phosphoanhydride bond reveals that the conformational dependence of the anomeric effect involves modulation of the orbital overlap between the donor and acceptor orbitals. However, a conformational independence was observed in the rotation of a solvent hydrogen bond. As one lone pair orbital rotates away from an optimal antiperiplanar orientation, the overall magnitude of the anomeric effect is compensated approximately by the other lone pair as it becomes more antiperiplanar. Furthermore, solvent modulation of the anomeric effect is not restricted to the antiperiplanar lone pair; hydrogen bonds involving gauche lone pairs also affect the anomeric interaction and the strength of the phosphoanhydride bond. Both gauche and anti solvent hydrogen bonds lengthen nonbridging O-P bonds, increasing the distance between donor and acceptor orbitals and decreasing orbital overlap, which leads to a reduction of the anomeric effect. Solvent effects are additive with greater reduction in the anomeric effect upon increasing water coordination. By controlling the coordination environment of substrates in an active site, kinases, phosphatases, and other enzymes important in metabolism and signaling may have the potential to modulate the stability of individual phosphoanhydride bonds through stereoelectronic effects.

Figure 1

Anomeric effect given by anti-periplanar alignment of n(O_γ) → σ*(O_β—P_γ). The orbitals are colored green and purple with arbitrary phase.

Figure 2

Orientation of lone pairs. a) Lewis structure of methyl phosphate triester. b) Corresponding Newman projection. The O_3β—P_γ—O_3γ—X dihedral (highlighted in red) was rotated from −60° to 60° to change the orientation of lone pairs with respect to the σ*(O_3β—P_γ) anti-bonding orbital. c) X represents either a proton (structure 1) or a hydrogen bond donated by water (structure 2).

Figure 3

Eight structures with different hydrogen bonding configurations were used in a detailed examination of the effects of hydrogen bonding on phosphodiester bonds. Structure 3 has no hydrogen bonding interactions and serves as a reference. Waters are placed at a O_3β—P_γ—O_γ•••OH₂ dihedral angle of 180° or 90° as depicted in red in the Newman projections above each column of structures. White = hydrogen, grey = carbon, red = oxygen, yellow = phosphorus.

Figure 4

a) Calculated E(2) hyperconjugative energies and O_3β—P_γ bond lengths for rotamers of structure 1. Changes are measured with reference to ∠O_3β—P_γ—O_3γ—H = 180°. b) Correlation between O_3β—P_γ bond length and σ*(O_3β—P_γ) orbital occupancy.

Figure 5

a) E(2) energy shows a strong angular dependence for rotation of the O_3β—P_γ—O_3γ—H dihedral angle. b) The orbital overlap, as mirrored in the numerator of equation 1, 2F_ij² and c) the energy gap for the hyperconjugative interaction with σ*(O_3β—P_γ) and lone pairs n1(O₃γ) (orange), n2(O_3γ) (blue) or σ(O—H) (red).

Figure 6

Orientation of a hydrogen bond from water relative the O_3β—P_γ bond has little impact on O_3β—P_γ bond length. a) Neither the O_3β—P_γ bond length or E(2) energy vary greatly as a function of O_3β—P_γ—O_3γ•••OH₂ dihedral angle. The maximal change in bond length is only 0.003 Å and in E(2) energy is only 2 kcal/mol. b) When one lone pair orbital rotates away from an optimal anti-periplanar orientation, the other improves. The E(2) energies are nearly symmetric, in spite of the fact that a water is interacting with lone pair 2 (orange), but not 1 (blue).

Figure 7

Images of the O_3γ lone pairs 1 and 2 from figure 6b at a) O_3β—P_γ—O_3γ•••OH₂ = 180° and b) O_3β—P_γ—O_3γ•••OH₂ = 90°. Water is always coordinated to lone pair 2 (colored orange in parts b and d). In a) water interacts with lone pair 2, which in this configuration, is anti-periplanar to O_3β—P_γ whereas in b) water interacts with lone pair 2 which is at a 90° angle to O_3β—P_γ. When lone pair 2 is at 90°, it contributes nothing to the overall E(2) energy of n(O_γ) → σ*(O_3β—P_γ). However, the E(2) energy of n(O_γ) → σ*(O_3β—P_γ) and the O_3β—P_γ bond length are similar in both orientations. Atoms are colored; white (hydrogen), grey (carbon), yellow (phosphorus) and red (oxygen). The orbital lobes of the lone pairs on O_3γ are colored red and green, depicting opposite polarities.

Figure 8

Waters coordinated at 180° (a – d) or 90° (e – f) from the O_3β—P_γ bond both decrease (a, e) O_3β—P_γ bond length and (b, f) hyperconjugation between γ-oxygen lone pairs and the σ*(O_3β—P_γ) anti-bonding orbital. Open triangles represent values of hyperconjugative interactions where there is no hydrogen bond. Closed triangles represent values where there is a hydrogen bond. (c, g) In both orientations, water reduces 2F_ij² relative to structure 3, water-free methyl triphosphate. (d, h) However only structures with waters at 180° show a pronounced change in orbital energy gap. This discrepancy accounts for the slightly larger depression in O_3β—P_γ bond length for structures with waters at 180°. Only orbitals in the anti-periplanar orientation contribute to E(2) energy and thus values for the other two orbitals on each oxygen were not plotted.

Figure 9

For structures 4 through 10, there is a strong correlation between Δ2F_ij² of the interaction n(O_γ) → (O_3β—P_γ) and non-bridging P_γ—O_γ bond length. Changes are measured relative to structure 3. Open diamonds represent P_γ—O_γ bond lengths where there is no hydrogen bond with O_γ. Closed diamonds represent P_γ—O_γ bond lengths where there is a hydrogen bond with O_γ. Inset: the schematic highlights (red arrow) the bond that is lengthened indirectly by any configuration of hydrogen bond to O_γ, thereby affecting the proximity and overlap of the O_γ, lone pair orbitals and the σ*(O_3β—P_γ) anti-bonding orbital.

Figure 10

Effect of hydrogen bond length, O_γ⋯H(OH) on O_3β—P_γ bond length for structure 8.