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

The ability of the Generalised AMBER Force Field (GAFF) of Kollman and co-workers to model the structures of bisphosphonate ligands, C(R1)(R2)(PO32−)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 1.2σ of the crystallographic mean. Bond angles were reproduced to within 1.9° (0.8σ). 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 (R1 = R2 = H), HEDP (R1 = OH, R2 = CH3), APD (R1 = OH, R2 =  (CH2)2NH3+), alendronate (R1 = OH, R2 = (CH2)3NH3+) and neridronate (R1 = OH, R2 = (CH2)5NH3+) 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 78εo, non-bonded interactions dominate; electrostatic interactions become important when the dielectric constant is <10εo. 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 Ca2+ ion. The magnitude of the exothermic interaction energy varies with molecular volume (MDP