Modelling the interaction of several bisphosphonates with hydroxyapatite using the generalised AMBER force field

Abstract

The ability of the Generalised AMBER Force Field (GAFF) of Kollman and co-workers to model the structures of bisphosphonate ligands, C(R 1)(R 2)(PO 3 2−) 2, important compounds in the treatment of bone cancer, by molecular mechanics methods is evaluated. The structure of 50 bisphosphonates and nine bisphosphonate esters were predicted and compared to their crystal structures. Partial charges were assigned from a RHF/6-31G ∗ single point calculation at the geometry of the crystal structure. Additional parameters required for GAFF were determined using the methods of the force field’s developers. The structures were found to be well replicated with virtually all bond lengths reproduced to within 0.015 Å, or within 1.2 σ of the crystallographic mean. Bond angles were reproduced to within 1.9° (0.8 σ). The observed gauche or anti conformation of the molecules was reproduced, although in several instances gauche conformations observed in the solid state energy-minimised into anti conformations, and vice versa. The interaction of MDP (R 1 = R 2 = H), HEDP (R 1 = OH, R 2 = CH 3), APD (R 1 = OH, R 2 = (CH 2) 2NH 3 +), alendronate (R 1 = OH, R 2 = (CH 2) 3NH 3 +) and neridronate (R 1 = OH, R 2 = (CH 2) 5NH 3 +) with the (001), (010) and (100) faces of hydroxyapaptite was examined by energy-minimising 20 random orientations of each ligand 20 Å from the mineral (where there is no interaction), and then at about 8 Å from the surface whereupon the ligand relaxes onto the surface. The difference in energy between the two systems is the interaction energy. In all cases interaction with hydroxyapatite caused a decrease in energy. When modelled with a dielectric constant of 78 ε o, non-bonded interactions dominate; electrostatic interactions become important when the dielectric constant is <10 ε o. Irrespective of the value of the dielectric constant used, the structure of the ligands on the hydroxyapatite surface is very similar. On the (001) face, both phosphonate groups interact near a surface Ca 2+ ion. The magnitude of the exothermic interaction energy varies with molecular volume (MDP<HEDP<APD<alendronate) except for neridronate which interacts less effectively than alendronate because the long amino side chain folds in on itself and does not align with the surface of the mineral. The bisphosphonates adopt two conformations on the (010) face. In the first of these, found for MDP and 40% of the alendronate structures, both phosphonates interact with the surface and the side chain points away from the surface. Hence, the interaction energy is similar for both species. In the second conformation, adopted by the majority of ligands, one phosphonate and the Cα side chain interact with the surface. The interaction energy, the magnitude of which is very similar to that on the (001) face, increases with the molecular volume of the ligand, again with the exception of neridronate. Two conformations also occur on the (100) face. In the first conformation, only one of the phosphonate groups points towards the surface and the Cα side chain interacts with the surface; in the second conformation the Cα side chain interacts strongly with the surface and both phosphonate groups point away from the surface towards the solution. The first conformation, which is the more common, is energetically more favourable. Its magnitude is virtually insensitive to the nature of the side chain and is similar to the magnitude of the interaction energy on the other two faces. The magnitude of the second conformation increases with the size of the Cα side chain.